**1. The microreactors and microchannel**

Microreactor is more commonly known in the field of process intensification and microsystems technology that has attracted significant interest in several years. The channel of microreactor is known as microchannel due to the micro size, while under microreactor group, there are micro mixers which are designed for mixing purpose. Numerous plausible advantages of microreactors for the pharmaceutical and fine chemical industries have been realized, thanks to their excellent capability for mixing and for thermal exchanges which increase yields and selectivity of reactions [1–4].

Microreactors have two major advantages with respect to smaller physical size and the increase in numbers of units. Benefits from reduction of physical size became more apparent in chemical engineering aspects. The difference of physical properties between microreactors and conventional reactor such as temperature, concentration, density, or diffusional flux increase with decreasing of linear dimension [5, 6]. Consequently, the driving forces for heat transfer, mass transport increase when using the microreactors. Besides, a significant reduction in volume for microreactor as compared to conventional reactors lead to smaller hold up that increase process safety and improves selectivity due to shorter residence time [7, 8].

### **2. Fluidic and mixing environment**

The smooth and constant fluid motion represents the laminar flow, whereas the vortices and flow fluctuation are properties of turbulent flow. These two types of flow are determined by using Reynolds number. Reynolds number (Re) measured the relative importance of viscous force and inertial forces. The Re is defined as

$$\text{Re} = \frac{\rho \nu D\_{\text{h}}}{\mu} \tag{1}$$

*<sup>σ</sup>*<sup>2</sup> <sup>¼</sup> <sup>1</sup> *N*

*Computational Fluid Dynamics of Mixing Performance in Microchannel*

*IM* <sup>¼</sup> <sup>1</sup> � ffiffiffi

segregated system and a value of 1 for the homogeneously mixed case.

or the so-called mixing intensity can be deduced as

*DOI: http://dx.doi.org/10.5772/intechopen.89928*

**3. Simulation of mixing in microchannel**

overall mixing element as shown in **Figure 2**.

**3.1 Geometric and meshing**

with a design study.

**107**

where *c* denotes the mean value of the concentration field *c* and *N* as the sampling point inside the cross section. Then, a measure for the intensity of mixing

> *Is* <sup>p</sup> <sup>¼</sup> <sup>1</sup> � *<sup>σ</sup>*

Geometry is defined as the computational domain of the flow region where the governing equation of fluid flow, mass, and energy is applied with its boundary condition. The computational domain is different from physical domain as the physical domain is the real physical flow that might include the wall, etc. [19]. The geometry may result from measurement of the existing configuration or may come

In this work, the geometry is chosen, aspired by the actual geometry domain (physical domain) which is depicted in **Figure 1** of the standard slit interdigital micro mixer (SSIMM) mixing element. The mixing element of the micro mixer consists of the corrugated wall of microchannels and discharge slit. Simulation of the complete geometry of this mixing element required large number of degree of freedom to be solved. This can only be achieved by large computational resources. However, due to the limitation of the computational resource, simplification of the geometry is preferred and required. Thus, to simplify the computational work, only the middle part of the mixing element structure domain was taken to represent the

The middle part was chosen based on strategies of the macro model approach of computational fluid dynamics in [9] that partitioned the reactor domain prior to simulation. It was noticed that the mixing element of the SSIMM has trapezoidal shape with two bifurcations and parallel microchannel that served as flow guide to avoid maldistribution of the fluid stream. A fluid maldistribution would induce unequal residence time in different channels, with undesired consequences for the product distribution in the micromixer [9]. However, this is not considered in this study as only the middle part of the mixing element is taken as computational fluid domain. There are two inlets and an outlet assigned to this model geometry as in **Figure 2**. An additional geometry domain with a straight-line microchannel was built for the purpose of comparisons with the SSIMM mixing element. The geometry has the same dimension as the simplified corrugated microchannel domain. On the other hand, meshing is the process of generating mesh or grid cell overlaying the whole domain geometry. In CFD, the domain is required to be subdivided into a number of smaller, non-overlapping subdomains in order to solve the flow physics within the domain. COMSOL Multiphysics software chosen as the simulation platform in this work provides two option types of meshing that can be used by the user which are physics-controlled meshing and user-controlled meshing. Physicscontrolled meshing sequence will build the mesh for the domain which is adapted to

Since *Is* is normalized, the quantity *Is* reaches a value of 0 for a completely

*σ*max

<sup>X</sup>ð Þ *<sup>c</sup>* �*<sup>c</sup>*

<sup>2</sup> (5)

(6)

where *ρ* and *μ* are the fluid density (kg/m<sup>3</sup> ) and viscosity (kg/m s), respectively; *v* is the velocity of the fluid (m/s) and *Dh* is the hydraulic diameter of the channel (m). Due to specific microstructuring technology employed to build microreactor, the channels of the microreactor have rectangular or trapezoidal cross section [9]. Thus, the hydraulic diameter *Dh* has to be properly defined. The hydraulic diameter of rectangular shapes is defined as [10]:

$$D\_h = \frac{2wh}{(w+h)}\tag{2}$$

where *w* is the width and *h* is the height of the microchannel.

On the other hand, mixing is a physical process with a goal of achieving a uniform distribution of different components in a mixture, usually within a short period of time [7]. Conventionally, at a macroscale level, the decrease in the mixing path and increase in the contact surface are achieved by a turbulent flow. The segregation of the fluid into small domain occurred by the help of vortices and flow fluctuation [11].

The fluid entity is constantly subdivided into thinner layers by an induced circular motion of fluid compartments, the so-called eddies, and subsequent breaking into fragments. In a laminar regime, a similar breaking of fluid compartments cannot occur due to the high viscous forces. Instead, the fluid entity has to be continuously split and recombined, forming regularly sized fluid embodiments [7].

Due to small dimension of microreactor, the fluid in microreactor is considered as microfluidic. The mixing in microfluidic is achieved and improvised by the decrease of mixing path and increase of surface area. The designed microreactor that highlights reduction of mixing path increases the effect of diffusion and advection on the mixing [11].

On top of that, mixing characterization is important to show how mixing performances in certain mixing process are described. Mixing performance of microreactor can be measured by evaluating the mixing quality as be done numerously in literatures [12–16]. A common definition of the mixing quality is based on Danckwerts' intensity of segregation [17] and is defined by

$$I\_s = \frac{\sigma^2}{\sigma\_{\text{max}}^2} \tag{3}$$

where *σ*<sup>2</sup> max is the maximum possible variance (which is 0.5 for symmetrical boundary condition) and *σ*<sup>2</sup> is defined by

$$
\sigma^2 = \frac{1}{|V|} \int\_V \left( \varepsilon - \overline{\varepsilon} \right)^2 dV \tag{4}
$$

and also can be written as

*Computational Fluid Dynamics of Mixing Performance in Microchannel DOI: http://dx.doi.org/10.5772/intechopen.89928*

$$
\sigma^2 = \frac{1}{N} \sum \left( c - \overline{c} \right)^2 \tag{5}
$$

where *c* denotes the mean value of the concentration field *c* and *N* as the sampling point inside the cross section. Then, a measure for the intensity of mixing or the so-called mixing intensity can be deduced as

$$I\_M = 1 - \sqrt{I\_t} = 1 - \frac{\sigma}{\sigma\_{\text{max}}} \tag{6}$$

Since *Is* is normalized, the quantity *Is* reaches a value of 0 for a completely segregated system and a value of 1 for the homogeneously mixed case.

## **3. Simulation of mixing in microchannel**

#### **3.1 Geometric and meshing**

**2. Fluidic and mixing environment**

*Computational Fluid Dynamics Simulations*

where *ρ* and *μ* are the fluid density (kg/m<sup>3</sup>

of rectangular shapes is defined as [10]:

fluctuation [11].

where *σ*<sup>2</sup>

**106**

advection on the mixing [11].

boundary condition) and *σ*<sup>2</sup> is defined by

and also can be written as

The smooth and constant fluid motion represents the laminar flow, whereas the vortices and flow fluctuation are properties of turbulent flow. These two types of flow are determined by using Reynolds number. Reynolds number (Re) measured the relative importance of viscous force and inertial forces. The Re is defined as

> Re <sup>¼</sup> *ρνD*<sup>h</sup> *μ*

*v* is the velocity of the fluid (m/s) and *Dh* is the hydraulic diameter of the channel (m). Due to specific microstructuring technology employed to build microreactor, the channels of the microreactor have rectangular or trapezoidal cross section [9]. Thus, the hydraulic diameter *Dh* has to be properly defined. The hydraulic diameter

*Dh* <sup>¼</sup> <sup>2</sup>*wh*

On the other hand, mixing is a physical process with a goal of achieving a uniform distribution of different components in a mixture, usually within a short period of time [7]. Conventionally, at a macroscale level, the decrease in the mixing path and increase in the contact surface are achieved by a turbulent flow. The segregation of the fluid into small domain occurred by the help of vortices and flow

The fluid entity is constantly subdivided into thinner layers by an induced circular motion of fluid compartments, the so-called eddies, and subsequent breaking into fragments. In a laminar regime, a similar breaking of fluid compartments cannot occur due to the high viscous forces. Instead, the fluid entity has to be continuously split and recombined, forming regularly sized fluid embodiments [7]. Due to small dimension of microreactor, the fluid in microreactor is considered

as microfluidic. The mixing in microfluidic is achieved and improvised by the decrease of mixing path and increase of surface area. The designed microreactor that highlights reduction of mixing path increases the effect of diffusion and

formances in certain mixing process are described. Mixing performance of

*<sup>σ</sup>*<sup>2</sup> <sup>¼</sup> <sup>1</sup> ∣*V*∣ ð *V* ð Þ *c* �*c* 2

Danckwerts' intensity of segregation [17] and is defined by

On top of that, mixing characterization is important to show how mixing per-

microreactor can be measured by evaluating the mixing quality as be done numerously in literatures [12–16]. A common definition of the mixing quality is based on

> *Is* <sup>¼</sup> *<sup>σ</sup>*<sup>2</sup> *σ*2 max

max is the maximum possible variance (which is 0.5 for symmetrical

where *w* is the width and *h* is the height of the microchannel.

(1)

(3)

*dV* (4)

) and viscosity (kg/m s), respectively;

ð Þ *<sup>w</sup>* <sup>þ</sup> *<sup>h</sup>* (2)

Geometry is defined as the computational domain of the flow region where the governing equation of fluid flow, mass, and energy is applied with its boundary condition. The computational domain is different from physical domain as the physical domain is the real physical flow that might include the wall, etc. [19]. The geometry may result from measurement of the existing configuration or may come with a design study.

In this work, the geometry is chosen, aspired by the actual geometry domain (physical domain) which is depicted in **Figure 1** of the standard slit interdigital micro mixer (SSIMM) mixing element. The mixing element of the micro mixer consists of the corrugated wall of microchannels and discharge slit. Simulation of the complete geometry of this mixing element required large number of degree of freedom to be solved. This can only be achieved by large computational resources. However, due to the limitation of the computational resource, simplification of the geometry is preferred and required. Thus, to simplify the computational work, only the middle part of the mixing element structure domain was taken to represent the overall mixing element as shown in **Figure 2**.

The middle part was chosen based on strategies of the macro model approach of computational fluid dynamics in [9] that partitioned the reactor domain prior to simulation. It was noticed that the mixing element of the SSIMM has trapezoidal shape with two bifurcations and parallel microchannel that served as flow guide to avoid maldistribution of the fluid stream. A fluid maldistribution would induce unequal residence time in different channels, with undesired consequences for the product distribution in the micromixer [9]. However, this is not considered in this study as only the middle part of the mixing element is taken as computational fluid domain.

There are two inlets and an outlet assigned to this model geometry as in **Figure 2**. An additional geometry domain with a straight-line microchannel was built for the purpose of comparisons with the SSIMM mixing element. The geometry has the same dimension as the simplified corrugated microchannel domain. On the other hand, meshing is the process of generating mesh or grid cell overlaying the whole domain geometry. In CFD, the domain is required to be subdivided into a number of smaller, non-overlapping subdomains in order to solve the flow physics within the domain. COMSOL Multiphysics software chosen as the simulation platform in this work provides two option types of meshing that can be used by the user which are physics-controlled meshing and user-controlled meshing. Physicscontrolled meshing sequence will build the mesh for the domain which is adapted to

this simulation work. The Navier-Stokes equation for incompressible flow is given

*Computational Fluid Dynamics of Mixing Performance in Microchannel*

þ *ρ*ð Þ *v* •∇ *v* ¼∇• �*pI* þ *μ* ∇*v* þ ð Þ ∇*v*

dynamic viscosity (SI unit: Pa.s); and *T* is the absolute temperature (SI: K).

*∂c ∂t*

where *v* is velocity vector (SI unit: m/s); *p* is the pressure (SI unit: Pa); *ρ* is the

The density and the viscosity data are those of water (*<sup>ρ</sup>* = 1 � <sup>10</sup><sup>3</sup> kg/m<sup>3</sup> and

The driving force for the fluid to flow through the mixing slot to the outlet is the applied inlet velocity boundary conditions on the inputs while the pressure boundary condition is assumed to be equal to zero. Meanwhile, the chamber wall is assumed to have a nonslip boundary condition. Mixing is obtained by diffusion of various species in the fluid. The species are diluted in the water, thus having material properties like water. The transfer equation is then taken as the convection-diffusion equation with a reaction term as shown below [20]:

); *F* is the volume force vector (SI unit: N/m<sup>3</sup>

*<sup>T</sup>* h i � � <sup>þ</sup> *<sup>F</sup>*

þ *ν* •∇*c* ¼∇•ð Þþ *D*∇*c R* (8)

(7)

); *μ* is the

as [20]:

**Figure 3.**

**Figure 4.**

**109**

*The meshing for corrugated microchannel.*

*The meshing for straight microchannel.*

*ρ ∂v ∂t*

*DOI: http://dx.doi.org/10.5772/intechopen.89928*

density (SI unit: kg/m<sup>3</sup>

<sup>μ</sup> = 1 � <sup>10</sup>�<sup>3</sup> Pa s).

*ρ*∇• *v* ¼ 0

the physics setting of the model, while the user-controlled meshing builds the mesh based on the user input of size, element type, etc. [19, 20]. **Figures 3** and **4** are the meshed geometry domains with different types of the mesh element can be seen. The mesh element of corrugated microchannel has a high number at the shape of the corrugated section, while the straight microchannel has a high number at the entrance of the discharge slit.
