Freeze Drying and Modeling

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Drying Technology

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Foam-Mat Freeze Drying of Egg White—Mathematical Modeling Part II: Freeze Drying and Modeling Arun Muthukumarana; Cristina Rattib; Vijaya G. S. Raghavana a Department of Bioresource Engineering, Macdonald Campus of McGill University, Ste-Anne-deBellevue, Canada b Département des sols et de génie agroalimentaire, Université Laval, Sainte-Foy, Canada

To cite this Article Muthukumaran, Arun , Ratti, Cristina and Raghavan, Vijaya G. S.(2008) 'Foam-Mat Freeze Drying of

Egg White—Mathematical Modeling Part II: Freeze Drying and Modeling', Drying Technology, 26: 4, 513 — 518 To link to this Article: DOI: 10.1080/07373930801929615 URL: http://dx.doi.org/10.1080/07373930801929615

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Drying Technology, 26: 513–518, 2008 Copyright # 2008 Taylor & Francis Group, LLC ISSN: 0737-3937 print/1532-2300 online DOI: 10.1080/07373930801929615

Foam-Mat Freeze Drying of Egg White—Mathematical Modeling Part II: Freeze Drying and Modeling Arun Muthukumaran,1 Cristina Ratti,2 and Vijaya G. S. Raghavan1 1

Downloaded By: [Canadian Research Knowledge Network] At: 16:04 17 December 2010

Department of Bioresource Engineering, Macdonald Campus of McGill University, Ste-Anne-de-Bellevue, Canada 2 De´partement des sols et de ge´nie agroalimentaire, Universite´ Laval, Sainte-Foy, Canada

Foam-mat freeze drying is one of the promising methods of drying, which utilizes advantages of both freeze drying and foammat drying. Egg white with its excellent foaming properties makes a suitable candidate for foam-mat freeze drying. Experiments were conducted to study foam-mat freeze drying of egg white, in an effort to determine the suitability of this method. Xanthan gum (XG) at 0.125% concentration was used as stabilizer for foaming. The results showed that the addition of xanthan gum during foaming has a positive impact in reducing the total drying time and also produces excellent quality egg white powder. The addition of stabilizer also plays an important role in improving drying. Simple models were applied for determining drying time and diffusion coefficients during freeze drying. Keywords Egg white; Foam; Freeze drying; Mathematical modeling

INTRODUCTION Freeze Drying Freeze drying is a dehydration method, which can produce high quality of dried products. This method takes advantage of triple point of water. Triple point is a state in which substances coexist in different states such as solid, liquid, and vapor and remain in thermodynamic equilibrium. Water has triple point at 0.01C and 611.73 Pa. Below triple point of water the ice can be directly sublimated into water vapor. This method of moisture removal gives many advantages over conventional methods.[1] Freeze drying has several advantages over conventional drying methods, like absence of air during drying, which reduces the risk of oxidation, preservation of flavor and volatile components, absence of movement of solvent during drying, and excellent rehydration properties. But the cost of operation is high as the drying rate Correspondence: Arun Muthukumaran, Department of Bioresource Engineering, Macdonald Campus of McGill University, Ste-Anne-de-Bellevue, Canada H9X 2B6; E-mail: [email protected]

is usually low, especially during secondary drying stage. Application of vacuum during drying increases the drying cost. Hence, freeze drying has conventionally been used only for high-quality and high-value commercial products.[2–5] Foam-Mat Drying In foam-mat drying the product to be dried is converted into foam before drying. This gives an advantage of increasing the total surface area available for drying, thereby improving drying rate as well. Another advantage with this method is that the drying temperature can be lower than that of conventional drying methods and this helps to reduce the loss of flavor and volatile components. Foam-mat drying was studied by Rao et al.[6] in 1987 for dehydration of whole egg. In their work they compared freeze drying of whole eggs to foam-mat drying and concluded that foam-mat drying produces higher quality dried product. Foam-mat drying was also tried for drying of cowpea,[7] star fruit,[8] and mango.[9] Modeling Modeling can be classified into theoretical, empirical, and semitheoretical based on the approach used to develop the model. Theoretical models can be quite complex and require a powerful computer. If properly constructed, the theoretical models can be more powerful and predictions can be done with accurate results. Theoretical models can also be used to explain the phenomena, whereas the other two models cannot be used for this purpose.[10] Heat and mass transfer models have been widely used in many of the drying applications to determine drying parameters like drying time, heat transfer rate, mass transfer rate, and diffusion coefficient. Many models have been developed for drying and (some of them specifically for freeze drying) and are widely available in the literature.[11–17]

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OBJECTIVE Both freeze drying and foaming methods could be combined to achieve faster freeze drying, by utilizing increased surface (mass transfer) area made available by foaming. But this hypothesis should be tested to prove its validity. Hence, the main objective of this work is to determine the suitability of foam-mat freeze drying for egg white and to estimate the drying time. Simple heat and mass transfer models were also applied to determine drying time and drying rate during foam-mat freeze drying.


MATERIALS AND METHODS Experimental Procedure Foam Preparation Commercially available liquid egg white (Simply Egg White# by Burnbrae Farms) was used for the experiment. Egg white was kept under refrigeration (5C) until the next step of the experiment (not more than 48 h). If the temperature of the egg white is lower than the ambient conditions it can adversely affect the foam formation; hence, before the experiment the egg white was removed from the refrigerator and kept outside to let the temperature come into equilibrium with the ambient conditions. A graduated glass beaker was used as a container to make the egg white foam. One hundred milliliters of egg white was added to the glass beaker. Xanthan gum (XG; MP Biomedicals, Inc., Illkirch, France) at 0.125% concentration was used as a stabilizer. A 250-W kitchen blender (Black & Decker, Black & Decker Co., Towson, MD, USA) with various speed adjustments was used for making foam. The XG of 0.125% concentration was added gradually during the whipping for the stability of egg white foam. The total whipping time was 5 min. Egg white without stabilizer was used as control to compare the effect of XG on foam-mat freeze drying. Freezing Twenty five grams of foam was placed in a glass beaker (Fisherbrand PLAIN 12 550D) of 25 75 mm dimension. Before freezing the sample at 40C, thermocouples were placed in the middle of the sample to measure the center temperature during freeze drying. Freezing was done in a medical freezer (Sanyo MDF-234, Moriguchi, Osaka, Japan). The sample was allowed to freeze completely for 24 h. Drying The frozen egg white sample was dried in a Unitop 400 L (Virtis, Gardiner, NY) freeze dryer. The temperature of the heating plate was reduced to 40C before placing the sample inside. The frozen samples were then placed inside the drying chamber of the freeze dryer and the thermocouples were connected to a digital data logger (21X Micrologger, Cambell Scientific Inc., Edmonton, AB, Canada) for

automated temperature measurement during drying. After the samples were placed inside the drying chamber the vacuum pump was turned on to reduce the total pressure. Once the pressure inside the drying chamber was reduced, the heating system (1C=min) was turned on to increase the heating plate temperature to 20C. The drying was done at 2, 4, 6, 8 . . . and 24-h durations. For each time, the same procedure mentioned above was followed. Five replications were done for each experimental condition. After the drying process was completed, the vacuum inside the drying chamber was released slowly and then the samples were transferred to desiccators for attaining equilibrium. The final mass of the foammat freeze-dried sample was measured by using an electronic balance (Mettler Toledo Balance, PB 1502, 0.01 g, IM Langacher, Switzerland). Egg white without stabilizer and foaming (25 g) were freeze-dried to compare their drying rate and drying time to that with stabilizer and foaming. Determination of Moisture Content The dried mass of the sample was determined in a vacuum oven in order to calculate the moisture content. The final sample was placed inside the oven and was dried at 50C to attain bone-dry mass. P2O5 was used as a desiccator inside the vacuum oven. Initial moisture content of the egg white was also determined using vacuum oven. Moisture contents on wet basis and dry basis were determined for all the replicated freeze-dried samples.[10] Moisture ratio (MR) was calculated by Eq. (1) to determine the water loss during freeze drying.[10] Moisture Ratio ðMRÞ ¼

X X0

ð1Þ

Drying rate is and important parameter that helps us to understand the drying characteristics of a material. It is a moisture loss over a period of time and is calculated by using the drying rate equation.[10] Freeze-Drying Models Karel[13] made the following assumptions describing his model for freeze-drying:

when

1. The maximum permissible surface temperature (Ts) is reached instantaneously. 2. The surface temperature is maintained constantly by adjusting external heat output. 3. Sublimation occurs parallel to the surface at the interface. 4. At the interface the concentration water vapor and the ice are in equilibrium. 5. Solid layer is semi-infinite. 6. Binary mixture of water vapor and inert gas pass through dried layer.

FOAM-MAT DRYING OF EGG WHITE: PART II


7. In the dried layer, the solid and the enclosed gas are in thermal equilibrium. 8. Partial pressure variation inside the drying chamber is negligible. 9. There is no heat loss or accumulation; all the heat input is used for sublimation of water. 10. The frozen region is homogenous with uniform thermal conductivity, specific heat, and density. 11. The frozen layer has negligible amount of dissolved gases. 12. Only primary drying stage was considered for the model development. Heat and mass transfer are assumed to take place in opposite directions during freeze drying to simplify the model development. In this scenario, heat can be supplied by conduction alone or in combination with radiation. Convection heat transfer is often neglected as it has very little effect on freeze drying due to vacuum inside the drying chamber. The ice front is assumed to recede uniformly on both sides toward the middle layer during drying. The sample has slab geometry and only half thickness (t) is used for calculations. Karel’s[13] model can be expressed as: t¼

L2 qms ðX0 Xf Þ 8kd ðTs T0 Þ

ð2Þ

In this model, most parameters such as product thickness (L), product density (q), moisture content, and temperatures are available from experimental data. On the other hand, thermal conductivity of the dry layer (kd) is difficult to measure at low values. In our case, thermal conductivity was determined by fitting the model to experimental data. The average thermal conductivity value was used for drying time predictions. Moisture content X (kg moisture=kg dry matter) was plotted against time t (h) to prepare drying curves. Dimensionless water content expressed in an exponential form was used for fitting the experimental data: X Xe ¼ eKt X0 Xe

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On the other hand, Fick’s second law of diffusion (Eq. (5)) was also used for determining the diffusion coefficient during drying: Deff t X ¼ Ae 4L2 ð5Þ X0

RESULTS AND DISCUSSIONS Figure 1 shows the decrease in moisture content as a function of time for foams made with and without 0.125% xanthan gum. The moisture reduction was rapid during the initial stage of drying up to 6 h and then the moisture reduction slowed down and attained almost constant for the 20- to 24-h period. From the graph it is also observed that the time taken for drying of egg white foam with XG and without XG from the initial moisture content of about 88% WB (733.33% DB) to final moisture content of 7.74% WB (8.34% DB) and 8.47% WB (9.25% DB) was found to be 24 h. For comparison, egg white without foaming having the same foam volume was freeze dried and the results are shown in Fig. 2. It is obvious from the drying curve that the moisture reduction was lower due to higher initial mass of the sample and it took nearly 15 h to remove 50% of ice as compared to only 6 h with foamed sample. Egg white without foaming having the same initial mass of egg white foam was also freeze dried and the results are also shown in Fig. 2. The drying trend was almost similar to that of egg white foam. The drying rate curve for the egg white foam with 0.125% XG and without XG is shown in Fig. 3. The drying

ð3Þ

For most of the drying and moisture content calculations Eq. (3) is simplified, as equilibrium moisture content has negligible effect. Simplified Eq. (4) is used for calculating drying constant. X ¼ eKt X0

ð4Þ

where K is the drying constant. The drying constant is important in understanding the drying behavior of the product. It decreases during drying as the amount of free water decreases over time and is similar to that of diffusion coefficient.

FIG. 1. Foam-mat freeze drying of egg white with 0.125% xanthan gum and egg white without xanthan gum; 24-h drying.

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FIG. 2. Comparison of freeze drying of egg white and egg white foam (all with 0.125% xanthan gum).

rate of egg white foam with 0.125% XG and without XG was found to be 1.59 and 1.19 g=h, respectively, during the initial stage of drying. The drying rate during final stage of drying was found to be 0.35 and 0.32 g=h for egg white foam with 0.125% XG and egg white foam without XG, respectively. The drying rate of both egg white foam with 0.125% XG and without XG was higher during the initial stage of drying because of the increased surface area due to foaming, which helped in faster removal of moisture from the sample. Obviously, the heat transfer must also be higher during the initial stage, due to foamed surface with higher moisture content. The drying rate was lower at the end of drying due to reduced moisture content of the egg white sample. Also as expected the drying rate of XG treated sample was higher than that of the sample without XG due to the stabilized foamed surface during drying. The drying rate vs. moisture content of the egg white foam with 0.125% XG and without XG (Fig. 3) showed that the drying was mostly in the falling rate period. The free water available in the sample moves toward the surface during drying and is removed at the surface. The falling rate period continues as long as the free water is present in the sample.

FIG. 3. Comparison of drying rate vs. moisture content for foam-mat freeze drying of egg white foam with 0.125% XG and egg white foam without XG; 24-h drying.

The diffusion coefficients were obtained from the Eq. (5) by plotting the moisture content data ln (moisture ratio) vs. drying time for egg white foam with 0.125% xanthan gum and egg white foam without xanthan gum as shown in Figs. 4 and 5. Egg white foam with 0.125% xanthan gum had three diffusion coefficients (2.677 108, 5.962 108, and 1.247 107 m2=s) with an average diffusion coefficient of 7.036 108 m2=s. The R2 values were 0.9367, 0.9943, and 0.9641, respectively (Fig. 4). The increase in the diffusion coefficient as the drying progresses can be attributed to the foaming of egg white. As the drying continues, the development of porous structure reduces the resistance to mass transfer. But egg white foam without xanthan gum had only two diffusion coefficients (2.413 108, 3.781 108 m2=s) with an average coefficient of 3.097 108 m2=s and the R2 values were 0.976 and 0.991, respectively (Fig. 5). Higher diffusion rate during freeze drying allows better mass transfer and it is clear from Fig. 4 that egg white foam stabilized with XG had better mass transfer than foam sample without XG during drying. The results obtained from freeze drying of foam with 0.125% xanthan gum were fitted with Karel’s model (Eq. (2)). The thermal conductivity (kd) was obtained (0.0781 kW=mK) as described earlier. Foam density (q) was measured during foam making and was found to be 226.47 kg=m3. Latent heat of sublimation (2840 kJ=kg) was taken from the literature.[3,12] The same model was used for predicting the drying time and the result is shown in Fig. 6. The model was fairly accurate in predicting the foam freeze drying time of egg white foam. The model does not account for the radiation heat transfer and that could affect the prediction of the model. The thickness of the sample also can play a role in determining the accuracy of the sample as the temperature of the frozen layer depends on it.

FIG. 4. Moisture diffusion for foam-mat freeze drying of egg white foam with 0.125% XG; 24-h drying.

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more accurate for determining mass transfer rate and diffusion coefficient. The drying rate and moisture diffusion were higher with XG-treated than without XG-treated egg white foam. An increase in diffusion coefficient was found during freeze drying, which could be attributed to foaming; however, further studies are required to clarify specific mechanism involved in this scenario.


FIG. 5. Moisture diffusion for foam-mat freeze drying of egg white without XG; 24-h drying.

NOMENCLATURE D Diffusion coefficient or diffusivity (m2s1) k Thermal conductivity (W=mK) L Height or thickness (m) m Mass (kg) ms Latent heat of sublimation (kJ=kg) T Temperature (C) t Time (s) V Volume (kg=m3) X Amount of moisture (%) Greek Letters q Density (kg=m3)

FIG. 6. Drying time predictions for foam-mat freeze drying of egg white with 0.125% xanthan gum; 24-h drying.

The diffusion models developed for mass transfer based on Fick’s second law of diffusion were more accurate than heat transfer model. R2 values obtained from the graph are also indicative of the conclusion. In the case of egg white foam with XG, there were three distinct drying stages, whereas egg white foam without XG had only two distinct drying stages (Figs. 4 and 5). In the case of heat transfer model, number of parameters, like radiation heat transfer, variable ice front movement, and constant heat transfer rate throughout drying, could have affected the prediction. Some of the unrealistic assumptions like instantaneous reach of maximum surface temperature could greatly affect the performance of the model. CONCLUSIONS The use of Karel’s heat transfer model was appropriate and fairly accurate in predicting the drying time. But the thermal conductivity was determined from the experimental data and not determined separately. Determining the thermal conductivity of egg white foam could help a better understanding of the phenomena as well as the prediction of drying time. The diffusion models were

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