**Multiphase Mass Transfer in Iron and Steel Refining Processes**

Lucas Teixeira Costa and Roberto Parreiras Tavares

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60800

#### **Abstract**

In the present chapter, a computational fluid dynamics (CFD) model for multiphase flow was developed, allowing the simulation of two different processes, the desulfurization of hot metal in a ladle mechanically agitated by an impeller (KR process) and the desulfuri‐ zation of steel in a gas-agitated ladle. The model gives important information to charac‐ terize the fluid flow conditions, to define the velocity profiles of the phases involved, and to predict the evolution of the sulfur content during the desulfurization treatments. An expression for the rate of transfer of sulfur from the metal to the slag was proposed. This expression can be used in processes where sulfur is transferred from the metal to the slag phase. The predictions of the variations of sulfur content of the metal phase with time were validated based on experimental data obtained in a Brazilian industrial plant for steel desulfurization. After the validation, the model was used to simulate the effects of several parameters and to optimize the processes. Based on these simulations, it was pos‐ sible to set up the best operational conditions to improve the productivity of sulfur re‐ moval in the primary and secondary metallurgy.

**Keywords:** Mass transfer, CFD, desulfurization, hot metal, steel

#### **1. Introduction**

With the growing demand for high quality steels, several processes for hot metal and steel refining were developed for various purposes, such as decarburization, removal of inclusions, narrowing the range of chemical composition, thermal homogenization, and production of steels with low levels of impurities.

The efficiency and the productivity of these processes depend largely on the kinetics of the chemical reactions. Since these processes are usually developed at high temperatures, the ratecontrolling step of the reactions involved is usually a mass transfer step.

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In iron and steel refining, mass transfer is always a multiphase phenomenon. Different situations occur, depending on the phases involved, as follows:


In the present chapter, the importance of multiphase mass transfer in hot metal and steel refining processes will be emphasized. The fundamentals of multiphase mass transfer will be addressed, including the different techniques that are usually adopted to evaluate the mass transfer coefficient and to analyze the effects of the variables that affect its value.

Finally, two case studies, analyzing multiphase mass transfer rate during the desulfurization of hot metal and steel, will be presented and discussed.

Steels with ultralow sulfur contents are used in the manufacture of pipes for transporting oil and construction of offshore platforms, which require high impact strength and resistance to lamellar crack formation by interaction with hydrogen and sulfide inclusions.

It is well known that the efficiencies of the desulfurization of liquid hot metal and steel depends on the setting of the kinetic and thermodynamic factors that must be adjusted simultaneously to provide theoretical and practical ways to enable the optimization of the process parameters. In these case studies, a computational fluid dynamics (CFD) model for multiphase flow was developed, allowing the simulation of two different processes, the desulfurization of hot metal in a ladle mechanically agitated by an impeller and the desulfurization of steel in a gas-agitated ladle. The model gives important information to characterize the fluid flow conditions, to define the velocity profiles, and to predict the evolution of the sulfur content during the desulfurization treatments.

The model was able to predict the sulfur contents of hot metal and steel as a function of time. The predictions of the model were validated based on experimental data obtained in an industrial plant for steel desulfurization. After the validation, the model was used to simulate the effects of several parameters and to optimize the processes.

### **2. Multiphase mass transfer**

The desulfurization of hot metal and steel is a reaction that occurs at the interface between liquid metal and liquid slag. Due to the high temperatures involved, the reaction rate is usually controlled by mass transfer between these two phases. To enhance the mass transfer rate, different methods of agitation are used. The most common are gas injection and mechanical agitation using an impeller.

The mass transfer rate of sulfur between metal and slag is usually determined by the following relationship [1]:

$$j\_S = kA \left(\mathbf{C}\_S^m - \mathbf{C}\_S^i\right) \tag{1}$$

where

In iron and steel refining, mass transfer is always a multiphase phenomenon. Different

**•** Liquid–liquid mass transfer, in the case of reactions involving liquid hot metal and steel and

**•** Liquid–solid mass transfer, when solid particles are injected into liquid hot metal and steel

In the present chapter, the importance of multiphase mass transfer in hot metal and steel refining processes will be emphasized. The fundamentals of multiphase mass transfer will be addressed, including the different techniques that are usually adopted to evaluate the mass

Finally, two case studies, analyzing multiphase mass transfer rate during the desulfurization

Steels with ultralow sulfur contents are used in the manufacture of pipes for transporting oil and construction of offshore platforms, which require high impact strength and resistance to

It is well known that the efficiencies of the desulfurization of liquid hot metal and steel depends on the setting of the kinetic and thermodynamic factors that must be adjusted simultaneously to provide theoretical and practical ways to enable the optimization of the process parameters. In these case studies, a computational fluid dynamics (CFD) model for multiphase flow was developed, allowing the simulation of two different processes, the desulfurization of hot metal in a ladle mechanically agitated by an impeller and the desulfurization of steel in a gas-agitated ladle. The model gives important information to characterize the fluid flow conditions, to define the velocity profiles, and to predict the evolution of the sulfur content during the

The model was able to predict the sulfur contents of hot metal and steel as a function of time. The predictions of the model were validated based on experimental data obtained in an industrial plant for steel desulfurization. After the validation, the model was used to simulate

The desulfurization of hot metal and steel is a reaction that occurs at the interface between liquid metal and liquid slag. Due to the high temperatures involved, the reaction rate is usually controlled by mass transfer between these two phases. To enhance the mass transfer rate, different methods of agitation are used. The most common are gas injection and mechanical

transfer coefficient and to analyze the effects of the variables that affect its value.

lamellar crack formation by interaction with hydrogen and sulfide inclusions.

**•** Liquid–gas mass transfer, when a gas is injected into or onto liquid hot metal and steel

situations occur, depending on the phases involved, as follows:

of hot metal and steel, will be presented and discussed.

the effects of several parameters and to optimize the processes.

slag

to promote refining reactions

150 Mass Transfer - Advancement in Process Modelling

desulfurization treatments.

**2. Multiphase mass transfer**

agitation using an impeller.

*j*S is the sulfur transfer rate between metal and slag (kg/s),

*k* is the sulfur mass transfer coefficient (m/s),

*A* is the interface area (m2 ),

*C*S m is the sulfur concentration in the metal phase (kg/m3 ), and

*C*S i is the sulfur concentration at the metal–slag interface (kg/m3 ).

To apply Equation (1) in the evaluation of the mass transfer rate, the sulfur mass transfer coefficient, the interface area, and the sulfur concentration at the metal–slag interface must be known. These parameters depend on the fluid flow patterns of both phases, on the geometry of the interface, and on the partition coefficient of sulfur between metal and slag. The sulfur concentration at the metal–slag interface is usually considered the equilibrium concentration since the chemical reaction at the interface is very fast at the temperatures at which these processes are developed. To estimate the equilibrium concentration, it is necessary to know the partition coefficient of sulfur between metal and slag. This partition coefficient is a thermodynamic variable that depends on the temperature and on the chemical composition of the slag and can be estimated using data available in the literature or using thermodynamic softwares (i.e., FactSage, Thermocalc, etc.).

The fluid flow patterns of the phases involved and the geometry of the metal–slag interface can be determined by simulations using computational fluid dynamics (CFD). Independent of the method of agitation, the procedure adopted to simulate the sulfur mass transfer during hot metal or steel refining followed the same sequence of steps:


in the liquid metal was then compared to some experimental results obtained in an industrial plant for validation purposes.

In the next section, two case studies of metal desulfurization are present and discussed.

### **3. Case studies**

In this section, simulations of steel desulfurization in a gas-stirred ladle and hot metal desulfurization in a mechanically agitated ladle (KR-process) are presented and discussed. The validation of the predictions of the models using industrial data is also included. Finally, the effects of process variables on the desulfurization rate are analyzed.

#### **3.1. Steel desulfurization in a gas-agitated ladle**

Steel desulfurization is usually developed in a gas-stirred ladle. Different configurations of the gas injection system are adopted and that can affect the efficiency of the process. In the present case, the configuration considered was used in a Brazilian steelmaking industry.

#### *3.1.1. CFD model*

The ladle considered is schematically shown in Figure 1. Its main characteristics are presented in Table 1.


**Table 1.** Main characteristics of the ladle.

Three phases were considered: liquid steel, liquid slag, and argon. The turbulent form of the conservation equations for mass, momentum, and turbulence quantities for each individual phase were solved using the commercial software Ansys-CFX. For turbulence, the standard *k*–*ε* model was used. One additional equation for sulfur mass conservation was included to simulate the transfer of sulfur between steel and slag. The transfer of sulfur to the gas phase was not considered.

**Figure 1.** Schematic view of the ladle used for steel desulfurization with locations of the porous plugs at the bottom of the ladle.

Steel and slag were considered Newtonian fluids with constant density and viscosity. Argon was assumed as an ideal gas. Isothermal condition was considered in all simulations.

The diameter of the gas bubbles was considered uniform. It was evaluated using the equation proposed for liquid steel and argon [2]:

$$d\_b = \left[\frac{3\sigma d\_0}{\rho \mathcal{g}} + \left(\frac{9\sigma^2 d\_0^2}{\rho^2 \mathcal{g}^2} + \frac{10\mathbf{Q}^2 d\_0}{\mathcal{g}}\right)^{\frac{1}{2}}\right]^{\frac{1}{3}}\tag{2}$$

where

in the liquid metal was then compared to some experimental results obtained in an industrial

In the next section, two case studies of metal desulfurization are present and discussed.

In this section, simulations of steel desulfurization in a gas-stirred ladle and hot metal desulfurization in a mechanically agitated ladle (KR-process) are presented and discussed. The validation of the predictions of the models using industrial data is also included. Finally, the

Steel desulfurization is usually developed in a gas-stirred ladle. Different configurations of the gas injection system are adopted and that can affect the efficiency of the process. In the present

The ladle considered is schematically shown in Figure 1. Its main characteristics are presented

**Parameter Value**

Height 3.3 m

Diameter at the bottom 2.32 m

Diameter at the top 2.50 m

Diameter of the plugs 0.076 m

Nominal capacity 80 tons

Three phases were considered: liquid steel, liquid slag, and argon. The turbulent form of the conservation equations for mass, momentum, and turbulence quantities for each individual phase were solved using the commercial software Ansys-CFX. For turbulence, the standard *k*–*ε* model was used. One additional equation for sulfur mass conservation was included to simulate the transfer of sulfur between steel and slag. The transfer of sulfur to the gas phase

Number of porous plugs 2

case, the configuration considered was used in a Brazilian steelmaking industry.

effects of process variables on the desulfurization rate are analyzed.

**3.1. Steel desulfurization in a gas-agitated ladle**

plant for validation purposes.

152 Mass Transfer - Advancement in Process Modelling

**3. Case studies**

*3.1.1. CFD model*

**Table 1.** Main characteristics of the ladle.

was not considered.

in Table 1.

*d*b is the diameter of the bubble (cm),

*d*o is the diameter of the porous plug (cm),

*Q* is the gas flow rate (cm3 /s),

*σ* is the interfacial tension between liquid steel and argon (dyn/cm), and

*ρ* is the density of liquid steel (g/cm3 ).

Nonslip conditions were assumed on all the solid walls of the ladle. At the porous plug, the gas flow rates were specified. Since the gas is injected at ambient temperature, the gas flow rates were adjusted considering the thermal expansion to the temperature of the domain. The top of the ladle was considered as an opening. The volumetric fractions of the three phases involved in the simulations were calculated in each of the control volumes of the domain. This enabled the evaluation of the contours of the phases and the interphase areas.

Grid-independent solutions were attained dividing the domain in approximately 1.5 × 106 volume elements. Figure 2 shows the mesh configuration adopted in the simulations.

**Figure 2.** Mesh configuration considered in the simulations. Vertical plane passing through the porous plugs.

Nonuniform mesh was adopted, with smaller volume elements in the plume region and in the metal–slag interface.

#### *3.1.2. Sulfur transfer model*

An additional equation for sulfur transfer between metal and slag was incorporated into the model:

$$\frac{d\mathbf{M}\_{\rm S}}{d\mathbf{t}} = -k\_{\rm S}A \left( \mathbf{C}\_{\rm S,stack} - \frac{\mathbf{C}\_{\rm S,slag}}{L\_{\rm S}} \right) \tag{3}$$

where

*M*S the mass of sulfur transferred in the volume element interface(kg),

*t* is time (s),

*k*S is the mass transfer coefficient for sulfur (m/s),

*C*S,steel is the sulfur concentration in the metal (kg/m3 )

*C*S,slag is the sulfur concentration in the slag (kg/m3 ),

*L*S is the partition coefficient for sulfur between slag and metal, and

*A* is the metal–slag interface area.

This equation was applied in every volume element where metal and slag coexisted. The metal–slag interface area and the volume of metal in each control volume were calculated by the Ansys-CFX software.

The partition coefficient was determined according to an equation proposed by Gaye et al. [3]. The mass transfer coefficient was estimated based on the correlation proposed by Incropera and DeWitt [4]:

$$\text{Sh} = 0.029 \text{Re}^{4/5} \text{Sc}^{1/3} \tag{4}$$

where

Sh is the Sherwood number,

Re is the Reynolds number, and

Sc is the Schmidt number.

In this equation, most of the parameters depend on the physical properties of the liquid metal and are constant. Considering this, Equation (4) can be rewritten in the following form:

$$k\_s = \mathbb{C}v\_i^{4/5} \tag{5}$$

where

(3)

**Figure 2.** Mesh configuration considered in the simulations. Vertical plane passing through the porous plugs.

metal–slag interface.

model:

where

*t* is time (s),

*3.1.2. Sulfur transfer model*

154 Mass Transfer - Advancement in Process Modelling

Nonuniform mesh was adopted, with smaller volume elements in the plume region and in the

An additional equation for sulfur transfer between metal and slag was incorporated into the

æ ö =- - ç ÷

,steel dt *S S S S*

*M*S the mass of sulfur transferred in the volume element interface(kg),

*L*S is the partition coefficient for sulfur between slag and metal, and

*k*S is the mass transfer coefficient for sulfur (m/s),

*C*S,steel is the sulfur concentration in the metal (kg/m3

*C*S,slag is the sulfur concentration in the slag (kg/m3

*A* is the metal–slag interface area.

*dM C k CA*

,slag

*S*

*L*

)

),

è ø

*C* is the constant and

*v*<sup>i</sup> is the velocity of the metal in the interfacial region with the slag. This velocity is calculated during the CFD simulation.

The value of constant C was determined using industrial data in which samples of liquid steel were taken from the ladle desulfurization.

#### *3.1.3. Validation of the model*

To validate the predictions of the model, data from three industrial treatments were obtained. The information collected in these treatments included the following:


#### *3.1.4. Results and discussion*


The conditions adopted in all the CFD simulations are presented in Table 2.

**Table 2.** Conditions considered in the CFD simulations of desulfurization in a gas-stirred ladle.

Figure 3 illustrates the velocity profile of liquid steel in a vertical plane passing through the porous plugs. This profile is similar to those presented by Patil et al. [5].

**Figure 3.** Velocity profile of liquid steel in a vertical plane passing through the porous plugs.

Figure 4 shows the regions of liquid steel, slag, and plume (argon) for the same vertical plane seen in Figure 3.

*3.1.4. Results and discussion*

156 Mass Transfer - Advancement in Process Modelling

The conditions adopted in all the CFD simulations are presented in Table 2.

**Table 2.** Conditions considered in the CFD simulations of desulfurization in a gas-stirred ladle.

porous plugs. This profile is similar to those presented by Patil et al. [5].

**Figure 3.** Velocity profile of liquid steel in a vertical plane passing through the porous plugs.

seen in Figure 3.

Figure 4 shows the regions of liquid steel, slag, and plume (argon) for the same vertical plane

Argon flow rate

**Parameter Value** Height of liquid steel 2.48 m Mass of liquid steel 80.84 tons Thickness of the slag layer 0.12 m Mass of liquid slag 1430 kg

Porous plug 1 13.2 Nm3

Porous plug 2 4.8 Nm3

Viscosity of liquid steel 6.5 x 10-3 Pa.s Viscosity of liquid slag 0.65 Pa.s

Figure 3 illustrates the velocity profile of liquid steel in a vertical plane passing through the

/h

/h

**Figure 4.** Regions of liquid steel, slag, and plume (argon) in a vertical plane passing through the nozzles.

For the conditions simulated, there is an "open eye" of liquid steel at the top of the ladle.

To estimate the value of constant C in Equation (5), samples of liquid steel were taken during a desulfurization treatment. The samples were taken at intervals of 5 minutes. Adjusting the simulation predictions to the experimental results, it was possible to determine the value of 1.45 × 10–3. The composition of the slag used in this treatment was as follows (in weight percent): CaO, 54%; MgO, 5%; SiO2, 19%; and Al2O3, 22%. The sulfur partition coefficient for this slag is 18.4 (according to the equation proposed by Gaye et al. [3]). With this value of constant *C*, it was possible to simulate the desulfurization process for other treatments. The results obtained for one of these treatments are illustrated in Figure 5. The experimental results are also included in the figure. In this case, the slag composition was as follows: CaO, 57%; MgO, 8%; SiO2, 10%; and Al2O3, 25%. The partition coefficient was 52.

The model predictions reproduce very well the experimental data. Based on these results, the model was validated, and the effects of different parameters were analyzed. The effects of argon flow rate, slag composition, and slag thickness are presented here. These results were compared to the predictions using the conditions specified in Table2 (reference case).

Figure 6 shows the effect of the total argon flow rate on the variation of the sulfur content in the liquid steel. Only the last 15 minutes of the simulations are presented. In the range tested, there is only a slight effect of the argon flow rate on the sulfur contents. A significant increase in the argon flow rate does not have an important impact on the desulfurization but increases the area of the "open eye" of liquid steel, which can have deleterious effects on the steel quality.

**Figure 5.** Comparison of the variations of sulfur content of the liquid steel as a function of time predicted by the model and determined in the experiment.

This effect of the argon flow rate can be explained in terms of the increase of velocities of the steel at the metal–slag interface, which increases the mass transfer coefficient, and in terms of faster homogenization of the sulfur content of the steel inside the ladle.

**Figure 6.** Effect of the total argon flow rate on the desulfurization process.

Figure 7 illustrates the effect of slag composition. Slag 1 is the one considered in Figure 5. Slag 2 has a partition coefficient of 52. An increase in the partition coefficient leads to a pronounced increase in the desulfurization rate. The time to reach a sulfur content of 35 ppm is 15 minutes for slag 2 and 24 minutes for slag 1. This could lead to a significant increase in productivity of the steel plant.

**Figure 7.** Effect of the slag partition coefficient on the desulfurization process.

This effect of the argon flow rate can be explained in terms of the increase of velocities of the steel at the metal–slag interface, which increases the mass transfer coefficient, and in terms of

**Figure 5.** Comparison of the variations of sulfur content of the liquid steel as a function of time predicted by the model

Figure 7 illustrates the effect of slag composition. Slag 1 is the one considered in Figure 5. Slag 2 has a partition coefficient of 52. An increase in the partition coefficient leads to a pronounced increase in the desulfurization rate. The time to reach a sulfur content of 35 ppm is 15 minutes for slag 2 and 24 minutes for slag 1. This could lead to a significant increase in productivity of

faster homogenization of the sulfur content of the steel inside the ladle.

**Figure 6.** Effect of the total argon flow rate on the desulfurization process.

the steel plant.

and determined in the experiment.

158 Mass Transfer - Advancement in Process Modelling

Finally, the effect of the thickness of the slag layer is presented in Figure 8.

**Figure 8.** Variation of the sulfur content for different thicknesses of the slag layer.

As shown, an increase in the slag thickness has a positive effect on the desulfurization rate. With more slag, the sulfur concentration in the slag phase is smaller, and this leads to an increase in the driving force for sulfur transfer from steel to slag. Another benefit of a thicker slag layer is the reduction of the area of the "open eye."

#### **3.2. Hot metal desulfurization in a mechanically agitated ladle**

The KR process is largely used to promote hot metal desulfurization. In the process, an impeller is used to stir the liquid metal and to enhance the contact between metal and slag. Among the several variables that affect the desulfurization rate, the penetration in the liquid metal and position along the radius and the rotation speed of the impeller were chosen to be investigated. The geometries of the ladle and of the impeller were specified according to the design currently being used in a Brazilian industry. The simulations followed the same steps described for the analysis of steel desulfurization in gas-stirred ladle.

#### *3.2.1. CFD model*

The geometries of the ladle and of the impeller are schematically shown in Figure 9. Their main dimensions are given in Table 3.

**Figure 9.** Schematic view of the ladle and of the impeller.

The CFD model is similar to that for steel desulfurization described previously. Since there is no gas injection in the KR process, the conservation equations were solved only for the hot metal and for the slag. A free surface model was implemented to identify the interfaces between the phases. The commercial software Ansys-CFX was used in all the simulations.

Hot metal and slag were assumed as Newtonian fluids with constant density and viscosity. These two phases were in thermal equilibrium.

For boundary conditions, nonslip conditions were considered on all the solid walls, including the surface of the impeller. The rotation speed of the impeller was specified.

The equation for sulfur transfer between the hot metal and the slag is similar to that used for desulfurization. The partition coefficient was also calculated using the same method shown


**Table 3.** Dimensions of the ladle and of the impeller.

The geometries of the ladle and of the impeller were specified according to the design currently being used in a Brazilian industry. The simulations followed the same steps described for the

The geometries of the ladle and of the impeller are schematically shown in Figure 9. Their main

The CFD model is similar to that for steel desulfurization described previously. Since there is no gas injection in the KR process, the conservation equations were solved only for the hot metal and for the slag. A free surface model was implemented to identify the interfaces between

Hot metal and slag were assumed as Newtonian fluids with constant density and viscosity.

For boundary conditions, nonslip conditions were considered on all the solid walls, including

The equation for sulfur transfer between the hot metal and the slag is similar to that used for desulfurization. The partition coefficient was also calculated using the same method shown

the phases. The commercial software Ansys-CFX was used in all the simulations.

the surface of the impeller. The rotation speed of the impeller was specified.

analysis of steel desulfurization in gas-stirred ladle.

*3.2.1. CFD model*

dimensions are given in Table 3.

160 Mass Transfer - Advancement in Process Modelling

**Figure 9.** Schematic view of the ladle and of the impeller.

These two phases were in thermal equilibrium.

by Gaye et al. [3]. The mass transfer coefficient was estimated according to Equation (5), with a value of 1.45 × 10–3 for C.

Grid-independent solutions were attained dividing the domain in approximately 1.2 × 106 volume elements. Figure 10 shows the mesh configuration adopted in the simulations.

**Figure 10.** Mesh configuration considered in the simulations. Vertical plane passing the center of the ladle.

Nonuniform mesh was adopted, with smaller volume elements near the walls and in the metal–slag region.

#### *3.2.2. Results and discussion*

The conditions adopted in the CFD simulations are presented in Table 4.


**Table 4.** Conditions considered in the CFD simulations of desulfurization of hot metal in the KR process.

The impeller was located at the center of the ladle. The rotation speed was 40 rpm. The distance between the bottoms of the impeller and of the ladle was 2.5 m. These conditions are assumed as a reference to analyze the effects of some process variables.

**Figure 11.** Velocity profiles of liquid hot metal in a vertical plane passing through the center of the ladle and in a hori‐ zontal plane passing through the impeller.

Figure 11 illustrates the velocity profile of liquid hot metal in a vertical plane passing through the center of the ladle and in a horizontal plane passing through the impeller. This profile is similar to those presented by Shao et al. [6]. There is an upward flow underneath the impeller. The rotation of the impeller also induces a rotation flow of hot metal. This rotation affects the pressure field and leads to a reduction of the level of hot metal in the center and an increase near the wall of the ladle, as seen in Figure 12, which shows the regions of liquid hot metal and slag for a vertical plane passing through the center of the ladle. This variation in the level of the hot metal significantly increases the interface area between metal and slag and increases the desulfurization rate.

*3.2.2. Results and discussion*

162 Mass Transfer - Advancement in Process Modelling

zontal plane passing through the impeller.

The conditions adopted in the CFD simulations are presented in Table 4.

**Parameter Value**

Height of hot metal 4.20 m Mass of hot metal 315 tons

Thickness of the slag layer 0.12 m Mass of liquid slag 3500 kg Viscosity of hot metal 6.5 x 10-3 Pa.s Viscosity of liquid slag 0.65 Pa.s

**Table 4.** Conditions considered in the CFD simulations of desulfurization of hot metal in the KR process.

as a reference to analyze the effects of some process variables.

The impeller was located at the center of the ladle. The rotation speed was 40 rpm. The distance between the bottoms of the impeller and of the ladle was 2.5 m. These conditions are assumed

**Figure 11.** Velocity profiles of liquid hot metal in a vertical plane passing through the center of the ladle and in a hori‐

**Figure 12.** Regions of liquid hot metal and slag in a vertical plane passing through the center of the ladle.

Figure 13 shows the results of the simulation of the desulfurization of the hot metal for the reference conditions. The reduction of sulfur content is much faster than that observed with steel. The main reason for that is the higher initial sulfur content of the hot metal, which gives a more significant driving for sulfur transfer to the slag. As seen, a 5-minute treatment is sufficient to reduce the sulfur content from 300 to approximately 50 ppm. This result is consistent with data available in the literature [7–9].

Using the mathematical model, the effects of some process variables were investigated. Figure 14 shows the effect of positioning the impeller with its axis of rotation 40 cm off center. Compared to the impeller located at the center of the ladle, there is a slight reduction in the desulfurization rate. Although it was not considered in the model, locating the impeller off center might also increase refractory wear due to higher velocities near the wall of the ladle.

**Figure 13.** Variation of the sulfur content in the hot metal during the desulfurization. Reference conditions.

**Figure 14.** Effect of the location of the impeller on the variation of sulfur content of the hot metal.

The effect of the immersion depth of the impeller is presented in Figure 15. In this case, the immersion depth was increased in 40 cm (the distance between the bottoms of the impeller and of the ladle was reduced to 2.1 m). Increasing the immersion depth reduces the velocities in the region close to the interface between the hot metal and the slag. This leads to a decrease in the sulfur mass transfer coefficient and has a negative effect on the desulfurization rate.

Figure 16 illustrates the effect of an increase of 10 rpm in the rotation speed of the impeller (from 40 to 50 rpm). Among the variables analyzed, the rotation speed presented the most significant effect. With a rotation speed of 50 rpm, the velocities near the metal–slag interface increase and so does the mass transfer coefficient. Together with a faster homogenization of

**Figure 15.** Variation of sulfur content of the hot metal for two immersion depths of the impeller.

the sulfur of the hot metal, the consequence is a faster desulfurization. Considering a final content of sulfur of 50 ppm, it is observed that an increase in the rotation speed to 50 rpm can lead to approximately a 1-minute reduction in the treatment time, with possible increase of productivity.

**Figure 16.** Effect of the rotation speed of the impeller on the variation of sulfur content of the hot metal.

**Figure 14.** Effect of the location of the impeller on the variation of sulfur content of the hot metal.

**Figure 13.** Variation of the sulfur content in the hot metal during the desulfurization. Reference conditions.

164 Mass Transfer - Advancement in Process Modelling

The effect of the immersion depth of the impeller is presented in Figure 15. In this case, the immersion depth was increased in 40 cm (the distance between the bottoms of the impeller and of the ladle was reduced to 2.1 m). Increasing the immersion depth reduces the velocities in the region close to the interface between the hot metal and the slag. This leads to a decrease in the sulfur mass transfer coefficient and has a negative effect on the desulfurization rate.

Figure 16 illustrates the effect of an increase of 10 rpm in the rotation speed of the impeller (from 40 to 50 rpm). Among the variables analyzed, the rotation speed presented the most significant effect. With a rotation speed of 50 rpm, the velocities near the metal–slag interface increase and so does the mass transfer coefficient. Together with a faster homogenization of

Based on factor analysis, an equation to predict the sulfur content after a treatment of five minutes was determined:

$$S\_{pmu} = 300.13 - 87.45d\_g - 4.47r\_s + 9d\_{off} + 1.45d\_gr\_s \tag{6}$$

where

*S*ppm is the sulfur content after 5 minutes of treatment in the KR process (ppm),

*d*B is the distance between the bottoms of the impeller and of the ladle (m),

*r*S is the rotation speed of the impeller (rpm), and

*d*off is the off-center distance of the axis of the impeller (m).

### **4. Conclusions**

Mass transfer plays a significant role in the kinetics of steelmaking processes. In these proc‐ esses, mass transfer is usually a multiphase phenomenon, and its rate is affected by the flow conditions of the phases involved.

In the production of high-quality steels, especially those with very low sulfur content, desulfurization must be implemented. The desulfurization of hot metal and liquid are both commonly used. In most processes, desulfurization is promoted by transferring sulfur from the metal to a refining slag.

In the present chapter, the desulfurization of steel in a gas-stirred ladle and of hot metal in the KR process was studied by mathematical modeling. The model developed involved the simulation of the flow field of the different phases involved, coupled with a mass conservation equation for sulfur, which included an expression for the rate of transfer of sulfur from the metal to the slag. The commercial software Ansys-CFX was used to solve the turbulent form of the Navier–Stokes equations for multiphase flows. The predictions of the model were validated using industrial data of steel desulfurization.

For the desulfurization of steel in a gas-stirred ladle, it was shown that increasing the sulfur partition coefficient and the thickness of the slag layer at the top of the ladle have both positive effects on the desulfurization rate. The gas flow rate, in the range tested, presented a minor effect, but very high gas flow rates lead to an increase in the "open eye" area of liquid steel at the top of the ladle, which can have deleterious effects on the steel quality.

For the desulfurization of hot metal in the KR process, the effects of variables related to the impeller position and rotation speed were investigated. The predictions of the model indicated that, in the ranges tested, the rotation of the impeller has the most significant effect. Increasing the penetration depth of the impeller and locating its axis of rotation off center in the ladle have slight negative effects on the desulfurization rate.

### **Acknowledgements**

The financial support of FAPEMIG in the form of a research grant to R. P. Tavares (Process No. TEC-PPM-00118-13) is gratefully acknowledged. The authors also acknowledge the financial support of CAPES/PROEX to the graduate program. The scholarship from CNPq to the first author is also gratefully acknowledged.

### **Author details**

where

**4. Conclusions**

conditions of the phases involved.

166 Mass Transfer - Advancement in Process Modelling

the metal to a refining slag.

**Acknowledgements**

*S*ppm is the sulfur content after 5 minutes of treatment in the KR process (ppm),

Mass transfer plays a significant role in the kinetics of steelmaking processes. In these proc‐ esses, mass transfer is usually a multiphase phenomenon, and its rate is affected by the flow

In the production of high-quality steels, especially those with very low sulfur content, desulfurization must be implemented. The desulfurization of hot metal and liquid are both commonly used. In most processes, desulfurization is promoted by transferring sulfur from

In the present chapter, the desulfurization of steel in a gas-stirred ladle and of hot metal in the KR process was studied by mathematical modeling. The model developed involved the simulation of the flow field of the different phases involved, coupled with a mass conservation equation for sulfur, which included an expression for the rate of transfer of sulfur from the metal to the slag. The commercial software Ansys-CFX was used to solve the turbulent form of the Navier–Stokes equations for multiphase flows. The predictions of the model were

For the desulfurization of steel in a gas-stirred ladle, it was shown that increasing the sulfur partition coefficient and the thickness of the slag layer at the top of the ladle have both positive effects on the desulfurization rate. The gas flow rate, in the range tested, presented a minor effect, but very high gas flow rates lead to an increase in the "open eye" area of liquid steel at

For the desulfurization of hot metal in the KR process, the effects of variables related to the impeller position and rotation speed were investigated. The predictions of the model indicated that, in the ranges tested, the rotation of the impeller has the most significant effect. Increasing the penetration depth of the impeller and locating its axis of rotation off center in the ladle

The financial support of FAPEMIG in the form of a research grant to R. P. Tavares (Process No. TEC-PPM-00118-13) is gratefully acknowledged. The authors also acknowledge the

the top of the ladle, which can have deleterious effects on the steel quality.

*d*B is the distance between the bottoms of the impeller and of the ladle (m),

*r*S is the rotation speed of the impeller (rpm), and

*d*off is the off-center distance of the axis of the impeller (m).

validated using industrial data of steel desulfurization.

have slight negative effects on the desulfurization rate.

Lucas Teixeira Costa and Roberto Parreiras Tavares\*

\*Address all correspondence to: rtavares@demet.ufmg.br

Federal University of Minas Gerais, Brazil

### **References**


## **Disintegration Kinetics of Microbial Cells**

Marek Solecki and Monika Solecka

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60797

#### **Abstract**

Results of the disintegration of yeast *Saccharomyces cerevisiae* in the bead mill with a multi disk impeller are presented. The degree of disintegration was specified on the basis of absorbency measurements at the wavelength 260 nm. The process was investigated by two integrated methods. The experimental values of maximum absorbency *A*m2 appeared to be smaller than theoretical ones *A*m1, which resulted from searching for the highest values of correlation coefficient between variables *t* and ln[*A*m1 / (*A*m1 *– A*)]. A significant increase of the process rate constant was observed when the slurry concen‐ tration increased in the range from 0.05 to 0.20 g d.m./cm3 . This phenomenon was explained by an additional mechanism of cell destruction, which was induced by fragments of ground walls. The rate constant changed during the process due to a change of inner process conditions, and not directly as a result of a changing number of microbial cells. Modeling of the process in which the first-order differential equation is used to describe the kinetics is correct, with the process rate constant being a function of parameters that describe inner conditions changing during the process.

**Keywords:** Random transformation of dispersed matter, disintegration of microor‐ ganisms, bead mill, kinetics of the process

#### **1. Introduction**

Chemical compounds contained in microorganisms provide the opportunity, often the only one, to satisfy a whole range of human needs. Commercial importance was gained by, among others, intracellular enzymes used to shape and preserve functional properties of foodstuffs, conducting clinical analyses, antibiotic conversion, or therapy applied during cancer diseases [1]. The genetic modification of microorganisms allows for a further increase in the range of

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

intracellular compounds' utilization. Such a possibility should lead to obtaining valuable components from microorganisms generally considered safe for people on an industrial scale [2].

The separation of compounds contained in microorganisms generally requires the destruction of cell walls and cytoplasmic membranes. The process is conducted in high pressure homog‐ enizers and bead mills on a semitechnical and technical scale. The device type depends on the type of destroyed microorganisms. Homogenizers are recommended for the disintegration of some bacteria and yeasts, while mills are for yeasts, fungi, and algae [3]. High-energy con‐ sumption of the process carried out by mechanical methods is the cause to seek more eco‐ nomical technical means of its implementation. The use of chemical, biological, and other physical methods at the present stage of technology development is not economically justified. It is expected that the use of mechanical methods, combined with others, for the disintegration of more resistant microorganisms in future will be beneficial [3].

The research carried out on the process improvement realized in bead mills is difficult to a large number of phenomena occurring in circulating mill filling and their specificity. During the disintegration of microorganisms, there occurs disruption of cell walls and membranes, releasing and dissolving intracellular compounds; organelle disruption; milling fragments of cell walls, cytoplasmic membranes, and other cellular fragments; interaction between the released compounds and microorganisms; and unprotected organelles and their mutual interaction. While conducting the process, rheological properties change, both of a suspension and its continuous phase. Mutual relativity of occurrence times of separate events during disintegration can have very small (cell disruption—dissolving intracellular compounds) or very large values (cell disruption—cell autolysis). The process course is affected by a very large number of parameters: instrumental (e.g., mill design and size, filling ball diameter, filling degree, materials used, and surface condition), raw material (e.g., conditions for microorgan‐ isms growth, their size and morphological form), and process (e.g., mixer rotation speed, duration of the process, temperature, microorganisms' suspension flow rate under conditions of continuous operation, and initial concentration of microorganisms' cells). So far, there are several models leading to the mathematical description of the disintegration of microorgan‐ isms in bead mills by a first-order linear differential equation [1–10]. A dependency of the release rate of enzymes on their distribution in a cell has been shown [11]. Taking into account the consequences of events: disruption of the cells - release of intracellular compounds, led Melendres et al. [12] to a nonlinear description of the overall process assuming the linear course of component processes. Some researchers showed a dependency of the process rate constant on the initial microorganism concentration. Marffy and Kula [4] presented the results of the disintegration of brewer's yeasts *Saccharomyces carlsbergensis* in a horizontal mill with a multiple disc mixer with a working chamber volume of 600 cm3 and indicated an almost twofold increase in the process rate constant at an increase in the suspended matter concen‐ tration described as the final amount of released protein from about 10 to 60 mg/cm3 . This effect was confirmed by Heim and Solecki [5] for the process carried out in a bead mill at a large concentration of *Saccharomyces cerevisiae* yeast suspension (0.14–0.20 g d.m./cm3 ) and high rotational speeds of the mixer (2500–3500 rpm). On the other hand, the analysis of the presented by Currie et al. [6] values of rate constants dependent on the size of bed balls for the increased concentrations of *S. cerevisiae* yeast suspension in the range of 0.3 to 0.75 g yeasts/cm3 indicates a continuous decrease in the obtained disintegration results. A rate constant decrease in a horizontal mill with a steel mixer at an increase in concentration from 0.15 to 0.30 kg yeasts/m3 was demonstrated by Limon-Lason et al. [7]. The same tendency was demonstrated by the same authors in a horizontal mill with a polyurethane mixer with an increase in concentration from 0.15 to 0.75 kg yeasts/m3 . A dependency of the disintegration of microor‐ ganisms that results in changes in their concentration is explained by the authors by a change in rheological properties of the suspension [4, 7] or an additional mechanism to destroy microorganisms [5]. Of course, some researchers show in their publications that there is no effect of microorganism concentration on the process course [2, 8].

For researching, describing, and managing processes of random transformation of the dispersed matter in a limited space, the theory basics were developed [13–15]. They include the assumed possibility of shaping and transforming material set elements during mass exchange between dispersed types of volume differing in properties. It was assumed that these processes can occur as a result of physical, chemical, and biological factors in specified limited volumes, and their separate types are generated randomly in the space of material medium. For the assumed paradigm, there is a possibility to build phenomenological and mathematical process models. The basic description of matter formation assumes the form of a system of differential equations. Modeling methodology enables taking into account many phenomena and mechanisms appropriate for the investigated processes in the conducted analyses. The kinetics of matter formation description allows to recognize the effect of many factors and to develop the model of a given process at the desired level of complexity. Application areas of the theory, with its great potential, include numerous domains, such as medicine, biology, agriculture, environmental protection, and industry. The theory of random transformation of the distributed matter was already used for the description of the disintegration of microor‐ ganisms, inter alia, for the description of the effect of yeast cell size on the process course [13, 14]. The aim of this study is to apply the theory of a random transformation of the distributed matter in order to explain the dependency of the process rate constant on the initial microor‐ ganism concentration.

#### **2. Theory**

intracellular compounds' utilization. Such a possibility should lead to obtaining valuable components from microorganisms generally considered safe for people on an industrial scale [2]. The separation of compounds contained in microorganisms generally requires the destruction of cell walls and cytoplasmic membranes. The process is conducted in high pressure homog‐ enizers and bead mills on a semitechnical and technical scale. The device type depends on the type of destroyed microorganisms. Homogenizers are recommended for the disintegration of some bacteria and yeasts, while mills are for yeasts, fungi, and algae [3]. High-energy con‐ sumption of the process carried out by mechanical methods is the cause to seek more eco‐ nomical technical means of its implementation. The use of chemical, biological, and other physical methods at the present stage of technology development is not economically justified. It is expected that the use of mechanical methods, combined with others, for the disintegration

The research carried out on the process improvement realized in bead mills is difficult to a large number of phenomena occurring in circulating mill filling and their specificity. During the disintegration of microorganisms, there occurs disruption of cell walls and membranes, releasing and dissolving intracellular compounds; organelle disruption; milling fragments of cell walls, cytoplasmic membranes, and other cellular fragments; interaction between the released compounds and microorganisms; and unprotected organelles and their mutual interaction. While conducting the process, rheological properties change, both of a suspension and its continuous phase. Mutual relativity of occurrence times of separate events during disintegration can have very small (cell disruption—dissolving intracellular compounds) or very large values (cell disruption—cell autolysis). The process course is affected by a very large number of parameters: instrumental (e.g., mill design and size, filling ball diameter, filling degree, materials used, and surface condition), raw material (e.g., conditions for microorgan‐ isms growth, their size and morphological form), and process (e.g., mixer rotation speed, duration of the process, temperature, microorganisms' suspension flow rate under conditions of continuous operation, and initial concentration of microorganisms' cells). So far, there are several models leading to the mathematical description of the disintegration of microorgan‐ isms in bead mills by a first-order linear differential equation [1–10]. A dependency of the release rate of enzymes on their distribution in a cell has been shown [11]. Taking into account the consequences of events: disruption of the cells - release of intracellular compounds, led Melendres et al. [12] to a nonlinear description of the overall process assuming the linear course of component processes. Some researchers showed a dependency of the process rate constant on the initial microorganism concentration. Marffy and Kula [4] presented the results of the disintegration of brewer's yeasts *Saccharomyces carlsbergensis* in a horizontal mill with a

of more resistant microorganisms in future will be beneficial [3].

170 Mass Transfer - Advancement in Process Modelling

multiple disc mixer with a working chamber volume of 600 cm3

twofold increase in the process rate constant at an increase in the suspended matter concen‐

was confirmed by Heim and Solecki [5] for the process carried out in a bead mill at a large

rotational speeds of the mixer (2500–3500 rpm). On the other hand, the analysis of the presented by Currie et al. [6] values of rate constants dependent on the size of bed balls for the increased

a continuous decrease in the obtained disintegration results. A rate constant decrease in a

tration described as the final amount of released protein from about 10 to 60 mg/cm3

concentration of *Saccharomyces cerevisiae* yeast suspension (0.14–0.20 g d.m./cm3

concentrations of *S. cerevisiae* yeast suspension in the range of 0.3 to 0.75 g yeasts/cm3

and indicated an almost

. This effect

) and high

indicates

A bead mill is a tank filled with beads set in circulating motion by a rotating impeller. Microorganisms dispersed in liquid are broken as a result of the filling elements' impact on them. The type of mechanism to destroy cells results from the system of combined normal and tangential loading. Its three basic forms can be distinguished as caused by crushing, grinding, and rolling by means of balls. Generally, cell destruction mechanisms do not occur in a pure form in the circulating chamber filling. The process of the disintegration of microorganisms, a very complex one as it was presented in the introduction, is a random transformation of matter. In order to enable the specification and analysis of phenomena occurring during its course, the following phenomenological model of the disintegration of microorganisms in the circulating mill filling was developed [13–15]. The suspension of microorganisms constituting a set of material objects *N* occupies space in a mill *V*. In volume *Vαti*, being its part, volumes of transformation *Vγji* are generated. It was assumed that the *i*th cell from the set *N* is destroyed after a relative transfer from volume *Vα*, where conditions are safe for it, to the *j*th volume *Vγji*. The transfer from volume *Vαji* to volume *Vγji* takes place through a boundary surface *Fγα→* . The mathematical description result of the phenomenological model is a first-order differential equation (Eq. 1) [15], in which the rate constant is determined by Eq. (2).

$$dN\_d = \frac{F\_{\mu \alpha \to}}{V\_a} \mu \left(N\_0 - N\_d\right) dt\tag{1}$$

$$k = \frac{F\_{\mu\alpha\rightarrow}}{V\_{\alpha}}u\tag{2}$$

The increase in the process rate of the disintegration of microorganisms in suspensions with high concentrations presumably is caused by the occurrence of the additional mechanism to destroy cells [5]. As a result of high concentration, microorganisms affect each other. By blocking cells between colliding balls with high kinetic energy, they cause an increase in volume *Vγji*. Thus, greater values of the process rate constant for large concentrations and high impeller rotational speeds may result.

If the above hypothesis is true, then during the process with a reduction in the number of live cells, volume *Vγji* should decrease, and consequently rate constant *k* as well. Its value describing the process for suspensions with large concentration, after obtaining a sufficiently large degree of disintegration, should be the same as in the case of suspensions with small concentration.

#### **3. Bead mill**

The process of disintegration was investigated in a horizontal bead mill with a multidisk impeller. The capacity of the working chamber 80 mm i.d. was 1 dm3 . Circular, full disks of the impeller of diameter 66 mm were placed every 30 mm. All parts of the mill were made from acid-resistant steel. The inside of the mill was filled in 80% with balls of diameter ranging from 0.8 to 1.0 mm made from leadless glass of density 2500 kg/m3 .

The shaft of the multidisk impeller was coupled with a d.c. motor. A voltage control system enabled smooth change of the impeller speed in the range from 0 to 3600 rpm. The cooling jacket of the mill was connected to a Fisherbrand FBC 735 thermostat (Fisher Scientific GmbH). The temperature of 50% water solution of ethylene glycol cooling the mill was 4°C at the inlet to the tank jacket. The slurry temperature was about 4°C.

### **4. Biological material**

Investigations were made using the suspension of commercially available baker's yeast *S. cerevisiae* produced in the Silesian Yeast Factory "Polmos" at Wołczyn. Biological material from a single fermentation was transported to a laboratory after cooling for 36 h, which completed the technological process. All experiments were carried out within 14 days. Yeast cubes of 100 g were stored at a temperature of 4°C. The continuous phase of microbial slurry was a 0.1% aqueous solution of β-mercaptoethanol containing 0.01 M EDTA and 0.001 M PMSF. A pH of 7 was ensured by a phosphate buffer (NaH2PO4, Na2HPO4).

### **5. Range of investigation**

after a relative transfer from volume *Vα*, where conditions are safe for it, to the *j*th volume *Vγji*. The transfer from volume *Vαji* to volume *Vγji* takes place through a boundary surface *Fγα→* . The mathematical description result of the phenomenological model is a first-order differential

*d d* ( ) <sup>0</sup>

® = - (1)

® = (2)

.

. Circular, full disks of

*dN u N N dt V* ga

> *F k u V* ga

a

The increase in the process rate of the disintegration of microorganisms in suspensions with high concentrations presumably is caused by the occurrence of the additional mechanism to destroy cells [5]. As a result of high concentration, microorganisms affect each other. By blocking cells between colliding balls with high kinetic energy, they cause an increase in volume *Vγji*. Thus, greater values of the process rate constant for large concentrations and high

If the above hypothesis is true, then during the process with a reduction in the number of live cells, volume *Vγji* should decrease, and consequently rate constant *k* as well. Its value describing the process for suspensions with large concentration, after obtaining a sufficiently large degree of disintegration, should be the same as in the case of suspensions with small concentration.

The process of disintegration was investigated in a horizontal bead mill with a multidisk

the impeller of diameter 66 mm were placed every 30 mm. All parts of the mill were made from acid-resistant steel. The inside of the mill was filled in 80% with balls of diameter ranging

The shaft of the multidisk impeller was coupled with a d.c. motor. A voltage control system enabled smooth change of the impeller speed in the range from 0 to 3600 rpm. The cooling jacket of the mill was connected to a Fisherbrand FBC 735 thermostat (Fisher Scientific GmbH). The temperature of 50% water solution of ethylene glycol cooling the mill was 4°C at the inlet

Investigations were made using the suspension of commercially available baker's yeast *S. cerevisiae* produced in the Silesian Yeast Factory "Polmos" at Wołczyn. Biological material from

impeller. The capacity of the working chamber 80 mm i.d. was 1 dm3

from 0.8 to 1.0 mm made from leadless glass of density 2500 kg/m3

to the tank jacket. The slurry temperature was about 4°C.

equation (Eq. 1) [15], in which the rate constant is determined by Eq. (2).

impeller rotational speeds may result.

172 Mass Transfer - Advancement in Process Modelling

**3. Bead mill**

**4. Biological material**

*F*

a

Experiments were carried out batchwise (constant feed) at the rotational speed of the impeller ranging from 1000 to 3500 rpm. Thirteen experimental series were made for a suspension prepared from living yeast cells at concentrations ranging from 0.05 to 0.20 g d.m./cm3 . The series consists of two experiments carried out at the same parameters. In the experiments, a slurry was used for which the mean concentration value determined for five measurements did not differ from an assumed value by more than 5%.


**Table 1.** Parameters of a slurry made from living and previously disintegrated cells.

Three experimental series were carried out for a mixture of slurries characterized by total biomass concentration of about 0.17 g d.m./cm3 and living cell concentration of about 0.06 g d.m./cm3 . The parameters of the slurry mixture and its components as well as the impeller speed during the process are given in Table 1. The slurry mixture was prepared by combining slurry 1 and slurry 2 in proper proportions. Microorganisms in slurry 2 were subjected to disintegration in the bead mill until reaching 99.5% disintegration degree. Rotational speed of the impeller during the disintegration of microbial cells in slurry 2 corresponded to the impeller speed used during the disintegration of yeast contained in the slurry mixture.

### **6. Methodology**

Changes in the slurry state were analyzed on the basis of spectrophotometric measurements of light absorbency in the supernatant at the wavelength 260 nm. Near this value, there are maximum spectra of spectral nucleic acids. The measurements were carried out using a Lambda 11 spectrophotometer (Perkin Elmer GmbH). The supernatant was obtained after 20 min centrifugation of slurry samples at the temperature 4°C with a centrifugal force of 34,000*g*. A 3K30 ultracentrifuge (B. Braun Biotech International GmbH) was used. The degree of microorganism disintegration after time *t* of the process duration (Eq. 3) was calculated from the ratio of relative absorbency *A*, determined for a sample to the maximum relative absorb‐ ency *A*m, which was observed at total yeast cell disintegration. A reference liquid was the supernatant obtained from the slurry prior to the process.

$$X = \frac{A}{A\_{\rm m}} = \frac{A^{\cdot} \cdot r - A\_{0}^{\cdot} \cdot r\_{0}}{A\_{\rm m}^{\cdot} \cdot r\_{\rm m} - A\_{0}^{\cdot} \cdot r\_{0}} \tag{3}$$

Depending on the cell disintegration degree, the slurry samples were diluted 0, 100, 200, or 400 times so that the measured absorbency did not exceed boundary values. Because of difficulties in using two parameters when describing the process kinetics, it was decided to convert the absorbency obtained at a given concentration into pure nucleic acids RNA released from the cell inside. Mean values for nucleotides used by Benthin et al. [16] were applied in the calculations. When solving the problem presented in this study, this simplifying assump‐ tion had no negative effects; however, the determined quantities of RNA could not be treated as precise values because of pollution of the supernatant with other intracellular components. In order to estimate the supernatant pollution, *A*/*A*250 and *A*/*A*280 ratios were studied. They were determined on the basis of the measurement of absorbencies *A*, *A*250, and *A*280 identified for each sample in all experiments at the wavelengths 260, 250, and 280 nm, respectively. The effect of process conditions, and first of all the applied inhibitors of serine proteases and metalopro‐ teases, was investigated by carrying out electrophoresis on 8% polyacryloamide gel SDS taken during slurry sample disintegration. The investigations were made for extreme concentrations of microorganisms at the impeller speed 2500 rpm.

The disintegration was investigated at different stages of the process, carrying out two experiments for fixed combinations of variable parameters. During the first experiment, 10 samples were taken in the time interval determined by the disintegration degree ranging from 0% to about 90%. On the basis of these data, a maximum amount of RNA possible to release, determined by the symbol *Cm*1, was obtained. At this amount, the correlation coefficient between variables *t* and ln[*Cm*1/(*C*m1 – *C*)] was the highest. From the process description obtained in this way, using the regression line passing through 0 (Eq. 4), the process time in which disintegration degrees ranged from 98.0% to 99.5% was calculated. These were boun‐ dary values of the time interval in which 9 slurry samples were taken during the second experiment. Having the measured absorbency values and disintegration degrees calculated on the basis of *k*1, a maximum amount of RNA *Cm*<sup>2</sup> was calculated for a given concentration, which would be observed after the disruption of yeast cell walls. Along with the data from the first experiment, this value was used to prepare again the process description by the regression line which passed through 0 (Eq. 5).

$$\ln \frac{\mathbb{C}\_{m1}}{\mathbb{C}\_{m1} - \mathbb{C}} = k\_1 \cdot t \tag{4}$$

#### Disintegration Kinetics of Microbial Cells http://dx.doi.org/10.5772/60797 175

$$\ln \frac{\mathcal{C}\_{\text{m2}}}{\mathcal{C}\_{\text{m2}} - \mathcal{C}} = k\_2 \cdot t \tag{5}$$

The first part of the methodology, involving a maximum amount of the intracellular compo‐ nent determined as a result of the tendency to reach the best description of the process by the first-order differential equation, was used by Currie et al. [6]. It was also employed to describe part of the experiments with yeast *S. cerevisiae* disintegration in the vertical bead mill. Accord‐ ing to the researchers, such necessity followed from the fact that it was impossible to obtain a satisfactory description of the process on the basis of a maximum amount of protein possible to release *R*m, determined for microorganisms disintegrated in a high-pressure homogenizer. The authors quote that in five cases, they had to reject the data referring to the released protein *R* defined by the ratio *R*/*R*<sup>m</sup> above 0.6, so that the first-order description was possible. In the subsequent six cases, such a description was not possible at all. A similar methodology was used by Limon-Lason et al. [7], who revealed the lack of any possibility to describe correctly the process carried out in the bead mill of volume 5 dm3 basing on the amount of protein *R*<sup>m</sup> specified in the mill of volume 0.6 dm3 . On the other hand, van Gaver et al. [8] in all investigated cases used only the values of *R*m determined as a result of tending to achieve agreement between the experimental data and the assumed first-order process description. This decision was probably caused by much worse results obtained for experimentally determined maxi‐ mum quantities of protein *R*m. According to the authors, the experimental value of *R*<sup>m</sup> was obtained after 10 cycles of slurry transition through the mill. In most publications, the maxi‐ mum amount of measured intracellular components was determined experimentally.

#### **7. Results and discussion**

Lambda 11 spectrophotometer (Perkin Elmer GmbH). The supernatant was obtained after 20 min centrifugation of slurry samples at the temperature 4°C with a centrifugal force of 34,000*g*. A 3K30 ultracentrifuge (B. Braun Biotech International GmbH) was used. The degree of microorganism disintegration after time *t* of the process duration (Eq. 3) was calculated from the ratio of relative absorbency *A*, determined for a sample to the maximum relative absorb‐ ency *A*m, which was observed at total yeast cell disintegration. A reference liquid was the

' '

*<sup>A</sup> Ar A r <sup>X</sup> A A r Ar*

' ' m mm 00

Depending on the cell disintegration degree, the slurry samples were diluted 0, 100, 200, or 400 times so that the measured absorbency did not exceed boundary values. Because of difficulties in using two parameters when describing the process kinetics, it was decided to convert the absorbency obtained at a given concentration into pure nucleic acids RNA released from the cell inside. Mean values for nucleotides used by Benthin et al. [16] were applied in the calculations. When solving the problem presented in this study, this simplifying assump‐ tion had no negative effects; however, the determined quantities of RNA could not be treated as precise values because of pollution of the supernatant with other intracellular components. In order to estimate the supernatant pollution, *A*/*A*250 and *A*/*A*280 ratios were studied. They were determined on the basis of the measurement of absorbencies *A*, *A*250, and *A*280 identified for each sample in all experiments at the wavelengths 260, 250, and 280 nm, respectively. The effect of process conditions, and first of all the applied inhibitors of serine proteases and metalopro‐ teases, was investigated by carrying out electrophoresis on 8% polyacryloamide gel SDS taken during slurry sample disintegration. The investigations were made for extreme concentrations

The disintegration was investigated at different stages of the process, carrying out two experiments for fixed combinations of variable parameters. During the first experiment, 10 samples were taken in the time interval determined by the disintegration degree ranging from 0% to about 90%. On the basis of these data, a maximum amount of RNA possible to release, determined by the symbol *Cm*1, was obtained. At this amount, the correlation coefficient between variables *t* and ln[*Cm*1/(*C*m1 – *C*)] was the highest. From the process description obtained in this way, using the regression line passing through 0 (Eq. 4), the process time in which disintegration degrees ranged from 98.0% to 99.5% was calculated. These were boun‐ dary values of the time interval in which 9 slurry samples were taken during the second experiment. Having the measured absorbency values and disintegration degrees calculated on the basis of *k*1, a maximum amount of RNA *Cm*<sup>2</sup> was calculated for a given concentration, which would be observed after the disruption of yeast cell walls. Along with the data from the first experiment, this value was used to prepare again the process description by the regression

m1

m1 ln *<sup>C</sup> k t*

1

*C C* = × - (4)

0 0

×- × = = ×- × (3)

supernatant obtained from the slurry prior to the process.

174 Mass Transfer - Advancement in Process Modelling

of microorganisms at the impeller speed 2500 rpm.

line which passed through 0 (Eq. 5).

Results of the disintegration experiments performed in order to characterize biological material and the confirmation of its stability are given in Table 2. Strength properties of yeast cells derived from given fermentation were determined by means of parameters characteristic of the course of the disintegration process conducted for the extreme values of changed process parameters (*S* and *n*) in the assumed wider research plan [5, 9, 17]. Experimental series from the first to the fourth one were carried out at the beginning of the investigations, while those from the thirteenth to sixteenth at the end. In the two first columns, the values of variable parameters are quoted. In the subsequent columns, results obtained for the first (based on the value of *Cm1*) and second methods (based on the value of *Cm2*) are presented. The maximum concentrations of nucleic acids determined for 100% microorganism destruction, correlation coefficient, process rate constant, and its standard deviations are given in subsequent columns. On the basis of these results, it can be concluded that during storage, there were no changes in yeast cell sustainability to mechanical destruction in the bead mill significant for the investigations and changes that could distort the results of measurements.

Results of the investigations of process kinetics obtained by the first method revealed that the first-order differential equation, according to the present theory, described very well the


**Table 2.** Characteristics of biological material.

process run. The correlation coefficients for most of the experiments exceeded 0.9960. Only in two cases for slurry concentration 0.20 g d.m./cm3 and impeller velocities 1000 rpm they were slightly lower (Table 2). Experimental results along with regression lines obtained for different slurry concentrations are shown in Fig. 1. On the basis of these results, it can be concluded that the process rate increases with an increase of the initial yeast slurry concentration. Rate constants for the highest slurry concentrations determined at the impeller speed 2500 and 3500 rpm are higher by over 60% than those obtained for the lowest concentrations. In the process performed at the impeller speed equal to 1000 rpm, the differences between the values of constant *k*<sup>1</sup> obtained for slurries at concentrations 0.05 and 0.20 g d.m./cm3 are much smaller (about 40%) (Table 2). Standard deviations of the process rate constants for method 1 given in Table 3 are in the interval from 0.46% to 2.55%. In general, for higher slurry concentrations, higher values of the standard deviation were obtained. In the case of changes in the rotational speed of the impeller, the results are opposite.

**Figure 1.** Microbial cell disintegration at different slurry concentrations (method 1, *n* = 2500 rpm).


**Table 3.** Characteristics of experimental results.

process run. The correlation coefficients for most of the experiments exceeded 0.9960. Only in two cases for slurry concentration 0.20 g d.m./cm3 and impeller velocities 1000 rpm they were slightly lower (Table 2). Experimental results along with regression lines obtained for different slurry concentrations are shown in Fig. 1. On the basis of these results, it can be concluded that the process rate increases with an increase of the initial yeast slurry concentration. Rate constants for the highest slurry concentrations determined at the impeller speed 2500 and 3500 rpm are higher by over 60% than those obtained for the lowest concentrations. In the process performed at the impeller speed equal to 1000 rpm, the differences between the values of constant *k*<sup>1</sup> obtained for slurries at concentrations 0.05 and 0.20 g d.m./cm3 are much smaller (about 40%) (Table 2). Standard deviations of the process rate constants for method 1 given in Table 3 are in the interval from 0.46% to 2.55%. In general, for higher slurry concentrations, higher values of the standard deviation were obtained. In the case of changes in the rotational

0.9983 0.9984 0.9937 0.9971 0.9997 0.9996 0.9907 0.9962

*S n Cm1 R1 k1·10<sup>3</sup> Cm1 R2 k2·10<sup>3</sup>* **g d.m./cm3 rpm mg/cm3 --- 1/s mg/cm3 --- 1/s**

> 1.307 6.024 1.817 9.632 1.348 6.986 2.149 10.429

2.317 2.434 8.725 8.745 2.263 2.252 7.935 8.106 0.9955 0.9961 0.9764 0.9836 0.9962 0.9993 0.9898 0.9854

1.698 7.156 2.438 13.420 1.656 6.488 2.320 13.413

speed of the impeller, the results are opposite.

**Series**

0.0513 0.0491 0.1991 0.1991 0.0485 0.0485 0.1957 0.1957

176 Mass Transfer - Advancement in Process Modelling

**Table 2.** Characteristics of biological material.

2.631 2.626 9.352 9.622 2.450 2.173 8.071 8.651

**Figure 1.** Microbial cell disintegration at different slurry concentrations (method 1, *n* = 2500 rpm).

Results of electrophoretic research carried out for the largest suspension concentration demonstrated clear separation of macroparticles, confirming the maximum limit of cutting proteins by enzymes released from highly specialized organelles. An increase of the disinte‐ gration effect with an increasing slurry concentration is not caused by an intensified superna‐ tant pollution. Such a result was also confirmed by constant relations between absorbances being measured. Examples of the results obtained for experimental runs made for extreme parameters are shown in Table 4.


**Table 4.** Characteristics of the supernatant pollution degree.

**Figure 2.** The effect of yeast slurry concentration on process rate constant at rotational speed of the impeller *n* = 2500 rpm (method 2, bottom and upper limits are marked for 95% of the confidence interval).

Changes of rate constants obtained by the second method, which take place at an increasing initial yeast cell concentration (Fig. 2, Table 2), are close to the ones obtained using method 1. Significant differences between values *k*<sup>1</sup> and *k*2 were found. The process rate constants obtained by method 2 are from 7% to 39% higher than those obtained by method 1. An exception are the values obtained for slurry concentration 0.0485 g d.m./cm3 at the impeller speed 3500 rpm (Table 1). The correlation coefficients obtained when describing the process by Eq. (5) are lower than *R*<sup>1</sup> (Table 2) and are in the range from 0.9764 to 0.9993. Much less advantageous are also standard deviations of the process rate constant (Table 3).

**Figure 3.** Changes of disintegration degree on the second stage of the process (*S* = 0.05 g d.m./cm3 , *n* = 1000 rpm).

Higher values of constant *k*2 are due to the fact that values *Cm*2 are lower than *Cm*1. They are compared in Table 3. The amount of nucleic acids *Cm*2 for the slurry with disintegration degree *X*=100% was determined based on the result of an experiment planned and carried out on the basis of the rate constant *k*1. Therefore, values *Cm*1 and *Cm*2 should not differ very much and should reveal a typical statistical dispersion in relation to the real value. As it is not so, it was checked if the points used to determine *Cm*<sup>2</sup> were better described by the rate constant *k*1 or *k*2. Since the values of rate constant *k*<sup>2</sup> are higher than *k*1, then in time interval *∆t* (time of process investigation in the second experiment), differences of the disintegration degree *∆X*<sup>2</sup> are smaller than *∆X*1 (Fig. 3). For *k*1 and *k*<sup>2</sup> in time, which determines slurry sampling, the disin‐ tegration degrees *X*1 and *X*2 were specified. On this basis and taking into account the measured values of absorbency *A*, *A*250, and *A*280, such values that would occur at 100% microorganism disintegration were identified. Only for three experiments, rate constant *k*1 describes better absorbencies *A*, *A*250, and *A*280. In one experiment, the values of *A* are better described by rate constant *k*1 and the values of *A*250 and *A*280 by rate constant *k*2. In all other experiments, the values of standard deviation are lower than when rate constant *k*<sup>2</sup> is used to determine the value of relevant absorbencies, which occur when the total content of microbial cells is released. As differences between *∆X*2 and *∆X*1 were insignificant as compared to measuring errors of absorbency for the disintegration degree close to 100% [18], this result was assumed sufficient to claim that the rate constant *k*<sup>2</sup> described better the process tested in the second experiment. It follows that the values of *Cm*<sup>2</sup> should be closer to the real values at *X* = 100%. The correlation coefficient for linear regression between variables *Cm*1 and *S* was 0.9873, and between *Cm*2 and *S*, it was 0.9949 (Fig. 4).

**Figure 4.** The effect of changes in the slurry concentration on determined values of *Cm*.

**Figure 2.** The effect of yeast slurry concentration on process rate constant at rotational speed of the impeller *n* = 2500

Changes of rate constants obtained by the second method, which take place at an increasing initial yeast cell concentration (Fig. 2, Table 2), are close to the ones obtained using method 1. Significant differences between values *k*<sup>1</sup> and *k*2 were found. The process rate constants obtained by method 2 are from 7% to 39% higher than those obtained by method 1. An

speed 3500 rpm (Table 1). The correlation coefficients obtained when describing the process by Eq. (5) are lower than *R*<sup>1</sup> (Table 2) and are in the range from 0.9764 to 0.9993. Much less

at the impeller

, *n* = 1000 rpm).

rpm (method 2, bottom and upper limits are marked for 95% of the confidence interval).

178 Mass Transfer - Advancement in Process Modelling

exception are the values obtained for slurry concentration 0.0485 g d.m./cm3

advantageous are also standard deviations of the process rate constant (Table 3).

**Figure 3.** Changes of disintegration degree on the second stage of the process (*S* = 0.05 g d.m./cm3

Higher values of constant *k*2 are due to the fact that values *Cm*2 are lower than *Cm*1. They are compared in Table 3. The amount of nucleic acids *Cm*2 for the slurry with disintegration degree If in two separate time periods the process run can be described more precisely using different values of rate constant, then it may be assumed that the disintegration rate constant changes during the process. Fig. 5 shows experimental changes in the disintegration degree described on the basis of *C*m2. The blue line denotes changes that result from the process description by Eq. (6) (Δ*t* = 0).

**Figure 5.** Changes of disintegration degree in the process carried out at slurry concentration 0.20 g d.m./cm3 and impel‐ ler speed 2500 rpm.

$$X\_2 = 1 - e^{-k\_2 \left(t + \Delta t\right)} \tag{6}$$

In first part of the process (from 0 to 120 s), the experimental points are located below the theoretical line, while in the second one, the results obtained are consistent. The position of the experimental points can be hardly taken as random. Real changes of the disintegration degree are close to the changes marked by the green line. Fig. 5 contains the process model obtained for the suspension concentration of 0.5 g d.m./cm3 (red line). In this case, the de‐ pendency presented in Eq. (5) described the process course very well (Fig. 1).

During the cell disintegration in a suspension with concentration of 0.20 g d.m./cm3 , the process initially (up to 20 s) proceeds at a considerably slower pace than the model disintegration (blue line) determined at this concentration and at even slower pace than the process determined for 0.05 g d.m./cm3 . This can result from very large cell density at their largest concentration. The analysis of changes in the distance between geometrical centers of yeasts followed by an increase in their concentration was presented [5, 17]. In these considerations, the assumption of distributing cells in a close-packed hexagonal network was adopted because such a distribution provides the largest distances between microorganisms. The determined distan‐ ces at such a distribution are boundary distances, the most favorable for minimizing interac‐ tions between microorganisms. Any other distribution of cells, including the actual one, causes a further increase in the intensity of their interaction. In accordance with the stated depend‐ encies, at concentration of 0.20 g d.m./cm3 , the interaction between neighboring microorgan‐ isms is very large. The cell size distribution for yeasts used for the research in this work (Fig. 6) was very similar to the size distribution of microorganisms used in earlier works [5, 9, 13, 14, 17]. The comparison of results obtained in tests by means of laser particle size analyzers, with results obtained as a result of the computer analysis of microscopic images is included in the published work [19]. A cell before being disrupted is compressed between balls. Its dimensions in a plane perpendicular to the compression axis increase. This is a consequence of neighboring microorganisms being driven out from the danger zone when, e.g., two balls approach them. The result of this visible in Fig. 5 is the reduction in the cell disruption rate at the initial stage of the process. The described mechanism does not cause changes in the transformation volume *Vγji* nor volume unavailable to a live *i*th cell *Vβji*. In the developed theory basics [15], in order to simplify the initial considerations, independence of transformation events was assumed. In the case described above, the disruption of one cell increases the chance of saving the neighboring cell. The result of such impact will be deviations of the process course from linearity. Changes in the process rate constant at the time of its duration are shown in Fig. 5.

**Figure 6.** The yeast particle size distribution in the suspension.

<sup>2</sup> ( )

**Figure 5.** Changes of disintegration degree in the process carried out at slurry concentration 0.20 g d.m./cm3

In first part of the process (from 0 to 120 s), the experimental points are located below the theoretical line, while in the second one, the results obtained are consistent. The position of the experimental points can be hardly taken as random. Real changes of the disintegration degree are close to the changes marked by the green line. Fig. 5 contains the process model

initially (up to 20 s) proceeds at a considerably slower pace than the model disintegration (blue line) determined at this concentration and at even slower pace than the process determined

The analysis of changes in the distance between geometrical centers of yeasts followed by an increase in their concentration was presented [5, 17]. In these considerations, the assumption of distributing cells in a close-packed hexagonal network was adopted because such a distribution provides the largest distances between microorganisms. The determined distan‐ ces at such a distribution are boundary distances, the most favorable for minimizing interac‐ tions between microorganisms. Any other distribution of cells, including the actual one, causes a further increase in the intensity of their interaction. In accordance with the stated depend‐

isms is very large. The cell size distribution for yeasts used for the research in this work (Fig. 6) was very similar to the size distribution of microorganisms used in earlier works [5, 9, 13, 14, 17]. The comparison of results obtained in tests by means of laser particle size analyzers, with results obtained as a result of the computer analysis of microscopic images is included in the published work [19]. A cell before being disrupted is compressed between balls. Its

. This can result from very large cell density at their largest concentration.

obtained for the suspension concentration of 0.5 g d.m./cm3

for 0.05 g d.m./cm3

ler speed 2500 rpm.

180 Mass Transfer - Advancement in Process Modelling

encies, at concentration of 0.20 g d.m./cm3

pendency presented in Eq. (5) described the process course very well (Fig. 1).

During the cell disintegration in a suspension with concentration of 0.20 g d.m./cm3

<sup>2</sup> <sup>1</sup> *kt t X e*- +D = - (6)

, the interaction between neighboring microorgan‐

(red line). In this case, the de‐

, the process

and impel‐

In the suspension with a concentration of 0.20 g d.m./cm3 , the rate of microorganism disruption and release of intracellular compounds increases significantly from about 20 to 120 s of the process duration (Fig. 5). Is it greater than the cell disintegration rate in a suspension with concentration of 0.05 g d.m./cm3 and also greater than the process course rate determined from Eq. (5) for the disintegration of microorganisms in the suspension with concentration of 0.20 g d.m./cm3 . Such an effect can result from an increase in the transformation volume *Vγji* and volume *Vβji* unavailable to the live *i*th cell. Hypothetically, it is the result of blocking a cell in the danger zone by neighboring unthreatened microorganisms [5].

At the final stage of disintegration, the course of the process of the yeast cells disintegration carried out in the suspension with concentration of 0.20 g d.m./cm3 is not in accordance with the course obtained for the suspension with concentration of 0.05 g d.m./cm3 . At the end of the process being carried out for the higher biomass concentration, there is a significant reduction in the number of viable cells. The rate constant is much higher than specified for the disinte‐ gration of the yeast cells at a concentration of 0.05 g d.m./cm3 .

Fig. 6 shows the graphic analysis of the process course for the cell disintegration in a mixture of slurries (Table 1, Series 11) analogical to the one presented above. In this case, due to less intensive interactions between neighboring yeast cells, there was probably no pushing out of cells fromthedanger zonebycompressedmicroorganisms.Theobtainedvaluesofrate constant (Table5)arelargeoveralltheinvestigatedtimeframe.Theyaremuchgreaterthanthoseobtained with a suspension concentration of 0.05 g d.m./cm3 (Fig. 7, red line). The values of the rate constant are similar to those obtained for the concentration of 0.17 g d.m./ cm3 (Fig. 2).

**Figure 7.** Changes of disintegration degree in the process carried out at biomass concentration 0.17 g d.m./cm3 , living cell concentration 0.05 g d.m./cm3 , and impeller speed 2500 rpm (Series 11, Table 1).

Such a process run, which is more or less distinct in all experiments performed, provides the evidence that the additional cell destruction mechanism is a result of the action of comminuted cell wall fragments, and not of the living microorganisms. The deviation of experimental points similar to the ones presented above was obtained by Melendres et al. [10], who investigated the process of disintegration on the basis of living cells specified using a hemocytometer. The results obtained by the researchers were a basis to develop a first-order mathematical model of the process based on the analogy to the theory of gas kinetics. Using their own data, Middelberg et al. [18] proved better agreement of the disintegration degree determined on the basis of the absorbency measurement (*λ* = 260 nm) and the number of living cells than that obtained from released proteins and living cells. According to Limon-Lason et al. [7], the process of disintegration is related to two phenomena: cell wall disruption and protein release. The latter phenomenon is much slower than the first one. According to the results obtained by Middelberg et al. [18], the difference between cell wall disruption rate and the rate of nucleic acid release is negligible.

Fig. 8 shows a graphical interpretation of disintegration kinetics described by Eq. (5). The regression line is not in agreement with experimental points. The real process run is not linear. Constant *k*<sup>a</sup> at the onset of the process (*t* → 0) is lower than the constant determined for time *t* = 200 s, and this in turn is smaller than constant *km* determined for time 1200 s. Changes in

Fig. 6 shows the graphic analysis of the process course for the cell disintegration in a mixture of slurries (Table 1, Series 11) analogical to the one presented above. In this case, due to less intensive interactions between neighboring yeast cells, there was probably no pushing out of cells fromthedanger zonebycompressedmicroorganisms.Theobtainedvaluesofrate constant (Table5)arelargeoveralltheinvestigatedtimeframe.Theyaremuchgreaterthanthoseobtained with a suspension concentration of 0.05 g d.m./cm3 (Fig. 7, red line). The values of the rate

(Fig. 2).

, living

constant are similar to those obtained for the concentration of 0.17 g d.m./ cm3

**Figure 7.** Changes of disintegration degree in the process carried out at biomass concentration 0.17 g d.m./cm3

, and impeller speed 2500 rpm (Series 11, Table 1).

Such a process run, which is more or less distinct in all experiments performed, provides the evidence that the additional cell destruction mechanism is a result of the action of comminuted cell wall fragments, and not of the living microorganisms. The deviation of experimental points similar to the ones presented above was obtained by Melendres et al. [10], who investigated the process of disintegration on the basis of living cells specified using a hemocytometer. The results obtained by the researchers were a basis to develop a first-order mathematical model of the process based on the analogy to the theory of gas kinetics. Using their own data, Middelberg et al. [18] proved better agreement of the disintegration degree determined on the basis of the absorbency measurement (*λ* = 260 nm) and the number of living cells than that obtained from released proteins and living cells. According to Limon-Lason et al. [7], the process of disintegration is related to two phenomena: cell wall disruption and protein release. The latter phenomenon is much slower than the first one. According to the results obtained by Middelberg et al. [18], the difference between cell wall disruption rate and the rate of nucleic

Fig. 8 shows a graphical interpretation of disintegration kinetics described by Eq. (5). The regression line is not in agreement with experimental points. The real process run is not linear. Constant *k*<sup>a</sup> at the onset of the process (*t* → 0) is lower than the constant determined for time *t* = 200 s, and this in turn is smaller than constant *km* determined for time 1200 s. Changes in

cell concentration 0.05 g d.m./cm3

182 Mass Transfer - Advancement in Process Modelling

acid release is negligible.

**Figure 8.** Yeast disintegration kinetics in the slurry at concentration 0.05 g d.m./cm3 and impeller speed 1000 rpm.

the rate constant during the microorganism disintegration can be explained by an increase of the concentration of very fine fragments of cell walls. Irrespective of the initial slurry concen‐ tration, the rate constant at the beginning of the process *k*a is always the same at lower concentrations. This is confirmed by the position of first experimental points obtained after starting the process. The mean value of *k*a for slurries made exclusively from living cells of yeast disintegrated at the impeller speed 2500 rpm is 0.005146, and its standard deviation is 6.21%. For high concentrations of microbial slurry, the process rate increases significantly as a result of formation of numerous fine fragments of cell walls. The further run of the process is affected by their concentration, which depends on the rate of microgrinding and the amount of material being ground.

**Figure 9.** Yeast disintegration kinetics in the slurry mixture (biomass concentration 0.17 g/cm3 , living cell concentration 0.05 g/cm3 , *n* = 2500 rpm).


**Table 5.** Results of microorganism disintegration in the slurry mixture.

In the case of the disintegration of microorganisms contained in the slurry mixture (experi‐ mental series 10, 11, and 12), much higher values of *k*1 and *k*2 (Table 5) were obtained than in the case of ordinary slurries with a comparable concentration of living cells. The change of conditions that define the increase of constant *k* during the process is determined not only by the presence of cell wall fragments but also by an increasing level of their comminution. Nonlinearity of the process kinetics (Fig. 9) is the evidence that the boundary value of con‐ centration of small cell fragments has not been reached yet. The rate constant after starting the process is higher by 25% than constant *k*a obtained for slurries made exclusively from living microorganisms. The correlation coefficients smaller than in other cases result from insignifi‐ cant changes of absorbency during the process as compared to the initial absorbency.

### **8. Conclusions**

At low concentrations of the suspension, cell disruption in the mill filling is an independent event. The process course is described very well by a linear first-order differential equation. During the disintegration of the microorganisms, disruption of the cells, release of intracellular compounds, and grinding of the fragments of broken walls take place.

An increase in the yeast suspension concentration in the range of 0.05 to 0.20 g d.m./cm3 causes a significant reduction in distances between geometrical centers of neighboring cells and significant intensification of interactions between them.

At very high concentrations of the suspension, at the initial stage, that is, from the disintegra‐ tion level 0% to 5%, the process course reveals deviations from linearity. An event consisting of cell disruption can affect the fate of neighboring cells. A cell being deformed as a result of compression pushes out cells adjacent to it from the danger zone. Thus, transformation events of objects from set *N* are not independent events. This effect does not cause an increase of the transformation volume and volume unavailable to the live *i*th cell. It seems that this phenom‐ enon causes a significant decrease of the rate of cell disruption and release of intracellular compounds.

At high concentrations of the suspension, the process course reveals deviations from linearity. The cell disruption and the intracellular compound release rate are greater than the rate determined from the linear model for smallest concentration. At high initial concentration of microbes, reducing the number of cells during the disintegration does not reduce the rate constant of the process. Increasing the transformation volume and the volume inaccessible to the *i*th cell is to increase the rate of disintegration. It appears that increasing the amount of the intracellular compounds released or increasing the grinding degree of cell walls increases the volume of the transformation, and the volume is inaccessible to the *i*th cell.

At very high concentrations of the suspension, at the initial stage, that is, from the disintegra‐ tion level 0% to 5%, the disintegration rate is influenced by both mentioned phenomena. In the case of the maximum concentration, the second mechanism, causing a significant reduction of the disintegration rate in comparison to the rate determined from the linear model, pre‐ dominates.

### **Nomenclature**

**Series**

10 11 12

**8. Conclusions**

compounds.

1000 2500 3500

184 Mass Transfer - Advancement in Process Modelling

2.803 2.950 2.742

**Table 5.** Results of microorganism disintegration in the slurry mixture.

0.9942 0.9970 0.9835

*n Cm1 R1 k1·10<sup>3</sup> Cm2 R2 k2·10<sup>3</sup>* **rpm mg/cm3 --- 1/s mg/cm3 --- 1/s**

> 2.647 2.621 2.511

0.9912 0.9936 0.9682

3.203 10.375 19.964

2.651 8.078 13.049

In the case of the disintegration of microorganisms contained in the slurry mixture (experi‐ mental series 10, 11, and 12), much higher values of *k*1 and *k*2 (Table 5) were obtained than in the case of ordinary slurries with a comparable concentration of living cells. The change of conditions that define the increase of constant *k* during the process is determined not only by the presence of cell wall fragments but also by an increasing level of their comminution. Nonlinearity of the process kinetics (Fig. 9) is the evidence that the boundary value of con‐ centration of small cell fragments has not been reached yet. The rate constant after starting the process is higher by 25% than constant *k*a obtained for slurries made exclusively from living microorganisms. The correlation coefficients smaller than in other cases result from insignifi‐

cant changes of absorbency during the process as compared to the initial absorbency.

compounds, and grinding of the fragments of broken walls take place.

significant intensification of interactions between them.

At low concentrations of the suspension, cell disruption in the mill filling is an independent event. The process course is described very well by a linear first-order differential equation. During the disintegration of the microorganisms, disruption of the cells, release of intracellular

An increase in the yeast suspension concentration in the range of 0.05 to 0.20 g d.m./cm3 causes a significant reduction in distances between geometrical centers of neighboring cells and

At very high concentrations of the suspension, at the initial stage, that is, from the disintegra‐ tion level 0% to 5%, the process course reveals deviations from linearity. An event consisting of cell disruption can affect the fate of neighboring cells. A cell being deformed as a result of compression pushes out cells adjacent to it from the danger zone. Thus, transformation events of objects from set *N* are not independent events. This effect does not cause an increase of the transformation volume and volume unavailable to the live *i*th cell. It seems that this phenom‐ enon causes a significant decrease of the rate of cell disruption and release of intracellular

At high concentrations of the suspension, the process course reveals deviations from linearity. The cell disruption and the intracellular compound release rate are greater than the rate determined from the linear model for smallest concentration. At high initial concentration of microbes, reducing the number of cells during the disintegration does not reduce the rate


### **Author details**

Marek Solecki1\* and Monika Solecka2

\*Address all correspondence to: marek.solecki@p.lodz.pl

1 Department of Process Equipment, Lodz University of Technology, Lodz, Poland

2 Institute of Fermentation Technology and Microbiology, Lodz University of Technology, Lodz, Poland

### **References**


[11] Hetherington PJ, Follows M, Dunnill P, Lilly MD. Mint: release of protein from bak‐ er's yeast (*Saccharomyces cerevisiae*) by disruption in an industrial homogeniser. Trans. Inst. Chem. Eng. 1971; 49: 142–148.

**Author details**

Lodz, Poland

**References**

York, 1979; 2.

14: 725–736.

745–774.

1998; Brighton: IchemE; 1998.

Marek Solecki1\* and Monika Solecka2

186 Mass Transfer - Advancement in Process Modelling

\*Address all correspondence to: marek.solecki@p.lodz.pl

1 Department of Process Equipment, Lodz University of Technology, Lodz, Poland

2 Institute of Fermentation Technology and Microbiology, Lodz University of Technology,

[1] Lilly MD. Mint: Applied Biochemistry and Bioengineering, Academic Press, New

[2] Garrido F, Banerjee UC, Chisti Y, Moo-Young M. Mint: Disruption of a recombinant

[3] Chisti Y, Moo-Young M. Mint: Disruption of microbial cells for intercellular prod‐

[4] Marffy F, Kula MR. Mint: Enzyme yields from cells of brewer's yeast disrupted by treatment in a horizontal disintegrator. Biotechnol. Bioeng. 1974; 16: 623–634.

[5] Heim A, Solecki M. Mint: Disintegration of microorganisms in bead mill with a mul‐

[6] Currie JA, Dunnill P, Lilly MD. Mint: release of protein from bakers' yeast (*Saccharo‐ myces cerevisiae*) by disruption in an industrial agitator mill. Biotechnol. Bioeng. 1972;

[7] Limon-Lason J, Hoare M, Orsborn CB, Doyle DJ, Dunnill P. Mint: Reactor properties of a high-speed bead mill for microbial cell rupture. Biotechnol. Bioeng. 1979; 21:

[8] van Gaver D, Huyghebaert A. Mint: Optimization of yeast cell disruption with a

[9] Heim A, Solecki M. Disintegration of microorganisms in a circulating bed of balls. In: Proceedings of the 3rd World Congress on Particle Technology (WCPT 3); 6–9 July

[10] Melendres AV, Honda H, Shiragami N, Unno H. Mint: A kinetic analysis of cell dis‐

newly designed bead mill. Enzyme Microb. Technol. 1990; 13: 665–671.

yeast for the release of β-galactosidase. Bioseparation. 1994; 4: 319–328.

ucts. Enzyme Microb. Technol. 1986; 8: 194–204.

ti-disc impeller. Powder Technol., 1999; 105: 390–396.

ruption by bead mill. Bioseparation. 1991; 2: 231–236.


### **Chapter 9**
