**3. Results**

#### **3.1 Pre-treatment**

At 1440 min for all the experiments, the water activity of osmodehydrated samples and sucrose solutions had non-significant differences (*p* > 0.05), which imply an equilibrium state of mass transfer [17]. The initial water activity of apples decreased from 0.983 � 0.004 to values between 0.914 and 0.958 (**Table 1**). The lowest water activity value was reached with the most concentrated osmotic solution, implying that increased sucrose concentration favors mass transfer [17, 37]. This behavior can be observed with the mass transfer parameters in which water loss values of 0.492 to 0.635 g/g were found with 40–60°Brix concentrations, respectively. In the case of solute gain, values of 0.130–0.203 g/g were reached using 40–60°Brix concentrations, respectively. Likewise, water loss was more significant than solute gain in all experiments, similar to found by others investigations during osmodehydration of foods with sucrose [37–39].

Osmodehydrated samples shrank in all the experiments (*p* < 0.05). The volume reduction of the osmodehydrated samples in the equilibrium state was 53–56%.The shrinkage of the samples increased (*p* < 0.05) with increasing concentration of the osmotic agent (**Table 1**), some authors associate this behavior with increased water


*a OD, osmodehydrated samples (40 °C and 1440 min) with 40, 50 y 60 °Brix sucrose solutions, data expressed as mean standard deviation of three independent experiments <sup>b</sup>*

*water activity at 25.02 0.40 <sup>c</sup>*

*L, characteristic length.*

#### **Table 1.**

*Estimated diffusion coefficients during convective drying of fresh and osmodehydrated apple cubes in sucrose solution.*

loss, which reduce the volume of the sample [27]. Souraki et al. [40] found a 75–80% volume reduction of osmodehydrated apple slabs with sucrose solutions of 30–50°Brix at different temperatures (30–50°C). In addition, the authors observed a significative (*p* < 0.05) volume reduction due to the increase of temperature and concentration of osmotic agent.

### **3.2 Drying**

**Figure 1** shows the free moisture fraction curves of convective drying (at 50°C and a constant air velocity of 3.5 m/s) of fresh and osmodehydrated (OD) apple cubes with sucrose solutions. The drying time for all the drying experiments was different (*p* < 0.05). The convective drying process had a longer duration for the fresh samples (26,400 s), followed by the osmodehydrated samples with the 40°Brix (12,900 s), 50° Brix (8400 min) and 60°Brix (7500 min) sucrose solutions. The pre-treated samples had a lower (*p* < 0.05) initial moisture content compared with the fresh sample (**Table 1**). However, after the drying process, the osmodehydrated samples showed a higher (*p* < 0.05) moisture content than the untreated dried samples. This behavior is accentuated with pre-treatments with higher concentration of the osmotic solution. Due to that, the increasing of osmotic solutions concentration increases the solutes impregnation [13, 41]. Some authors have reported that the solutes present on the outer part of the product form a crust that decreases the water transfer rate [42]. Assis et al. [25] osmodehydrated apple cubes in sucrose and sorbitol solutions (60° Brix, considering an osmotic solution to product ratio of 4, 1, 60°C, 50 rpm agitation for 8 h) and reached *aw* = 0.851–0.949. Untreated apple cubes took 21,600 s to dry, and osmodehydrated ones reduced from 20 to 22% drying time using sucrose and 30–39% using sorbitol. Sethi and Kaur [38] observed the same behavior during drying fresh and osmodehydrated pineapple, concluding that convective drying time with hot air decreases with increasing solids gain during osmotic dehydration.

The dimensionless volume (*V*/*V*0) and average perimeter were determined at different free moisture fraction (**Figures 2** and **3**, respectively), to investigate the morphometric characteristics of the cubes during the drying process. According to **Figure 2**, regardless of the experiment conditions, all samples subjected to convective drying shrank from free moisture fractions of 0.9. However, untreated dry samples

*Modeling of Drying Kinetics of Fresh and Osmodehydrated Apples during Convective Drying DOI: http://dx.doi.org/10.5772/intechopen.105162*

#### **Figure 1.**

*Experimental drying profiles and fitting numerical of drying models during convective drying of (a) fresh and osmodehydrated apple with (b) 40°brix (c) 50°brix and (d) 60°brix sucrose solutions.*

(fresh) shrank more (71% compared to the initial volume) than treated dry samples (10–45% compared to initial volume). Osmodehydrated samples increased their *V*/*V*<sup>0</sup> reduction during the drying process at lower concentrations of the osmotic agent, mainly because they had a lower water loss and solute gain during the osmodehydration process. However, according to **Figure 3** and **Table 1**, the shrinkage of the dried samples previously treated by osmodehydration increased at high concentrations of the osmotic agent.

All the dry samples showed a shape change (**Figure 3**) known as the "corner effect", consisting of an accentuated shrinkage at mid-length and a less pronounced at the edges. This behavior was similar to those obtained for pumpkin cylinder or chayote slices [27, 43]. In addition, the fresh dried samples showed higher deformation than the dried osmodehydrated samples (**Figure 3**). Osmotic dehydration can reduce or prevent the collapse of the structure of osmodehydrated samples due to solute incorporation [13]. In addition, a moderate rate of solute transfer is important to avoid deformation of

**Figure 2.**

*Experimental data (dots) and simulated results (line) of volumetric shrinkage of slabs in relation to dimensionless moisture on dry basis. (a) fresh, and osmodehydrated apple with (b) 40°brix (c) 50°brix and (d) 60°brix sucrose solutions.*

osmodehydrated products before the convective drying process, as in the case of osmodehydrated sample at 60°Brix. This rate can be controlled by decreasing the osmotic agent's concentration, modifying the viscosity of the osmotic agent (adding pectins), or adjusting the process temperature [17]. Another alternative is to increase the impregnated solutes using vacuum impregnation, high hydrostatic pressures, among other nonthermal methods that allow modifying the rate of solute transfer [17, 44, 45].

The evolution of the dimensionless volume of the samples subjected to convective drying as a function of the free moisture fraction was described with the model *V*/ *<sup>V</sup>*<sup>0</sup> <sup>=</sup> *<sup>m</sup>* + (*<sup>1</sup><sup>m</sup>*) *<sup>Ψ</sup><sup>n</sup>* . The fit allowed to adequately describe the experimental data with a correlation coefficient of R2 > 0.870. The parameter *m* represents the fraction in which the studied response changes during drying. Low values of the parameter *m* indicate that the shrinkage of the sample during the process was fast. According to **Table 2**, *m* increased with the osmotic solution concentration in the case of the

*Modeling of Drying Kinetics of Fresh and Osmodehydrated Apples during Convective Drying DOI: http://dx.doi.org/10.5772/intechopen.105162*


#### **Figure 3.**

*Morphometric variations of fresh and osmodehydrated apple cubes processed by convective. Average perimeter corresponding to five samples.*


#### **Table 2.**

*Fit parameters of dimensionless volume model.*

osmodehydrated samples, and this implied that the presence of solutes reduced shrinkage during the drying process [4].

#### **3.3 Mathematical modeling of drying curves**

**Table 3** shows the kinetic parameters obtained for all the proposed models and their corresponding statistical values (R<sup>2</sup> and RMSE). Newton's model adequately described the experimental data for drying kinetics of the fresh sample (R2 = 0.997) and osmotic agent concentrations below 50°Brix (R2 > 0.965). However, Newton's model did not adequately describe (R2 = 0.775) the kinetics of the samples pre-treated with 60°Brix; this is because the model does not allow to describe kinetics with high mass transfer rates [46]. The Henderson and Pabis, Page, and Weibull models had a good fit (R2 > 0.90). In general, the model that best described the experimental data was the Page model with R2 > 0.948. Parameter *k*1, *k*<sup>2</sup> and *k*<sup>3</sup> correlate the ability of the drying process to exclude moisture from the food and moisture diffusivity [46]. **Table 3** shows that the parameter values of *k*<sup>1</sup> and *k*<sup>2</sup> increase with samples pretreated in solutions with higher solids content; this implies that the increase in drying


*k1, k2 and k3 are rate constant in 1/s for Newton, Henderson and Pabis and Page model, respectively; k4, scale parameter in s; a and b are empirical parameters (dimensionless) of Henderson and Pabis model; c is shape-parameter of Weibull model; and Deff is effective water diffusion (m2 /s).*

#### **Table 3.**

*Fit parameters of models applied to drying curves of fresh and osmodehydrated apple cubes.*

rate is favored by pre-treatment. This same behavior occurred with the diffusivity values, a tendency with increasing of concentration of osmotic agent for each of these parameters.

The diffusive model of convective drying solution allowed predicting the water distribution of fresh and osmodehydrated apple cubes with sucrose solutions. The

*Modeling of Drying Kinetics of Fresh and Osmodehydrated Apples during Convective Drying DOI: http://dx.doi.org/10.5772/intechopen.105162*

water diffusion coefficients of fresh cubes considering a constant volume were 14.1 <sup>10</sup><sup>10</sup> <sup>m</sup><sup>2</sup> /s and for the pre-treated samples were found between 6.37– 11.5 <sup>10</sup><sup>10</sup> <sup>m</sup><sup>2</sup> /s (**Table 3**). However, according to the evolution of the dimensionless volume (**Figure 3**) there is shrinkage of product during the process, which explains why the correlation coefficients (R<sup>2</sup> > 0.648) were not good. Also, R<sup>2</sup> decreased with increasing samples shrinkage. It is clear that considering the evolution of the dimensionless volume of the product in the estimation of the diffusion improves the model's fit (R<sup>2</sup> > 0.917). The diffusion equation considers the product's dimensions, so that shrinkage during the process affects the estimation of diffusion coefficients [4, 47, 48]. The *Deff* values of the drying process were 6.77 <sup>10</sup><sup>10</sup> <sup>m</sup><sup>2</sup> /s and between 3.77–7.03 <sup>10</sup><sup>10</sup> <sup>m</sup><sup>2</sup> /s for fresh and osmodehydrated samples, respectively. Similar to the values obtained for the drying process for yam flour, chayote slabs, apple, tomatoes, cucumbers or apricot [43, 46, 48–50]. In addition, *Deff* values without consider real dimensions caused overestimation of 108.27, 68.97, 75.16 and 63.58%.
