Prediction of Transient Temperature Distribution During Freeze Drying of Yoghurt

A one dimensional heat and mass transfer analysis is employed to predict the temperature distribution in the dry layer of a frozen food sample in the form of a slab undergoing freeze drying. The method avoids the use of the effective diffusivity and the Knudsen diffusivity, both parameters dependent upon the stnrcture of the food product. The accu acy of the numerical solution is validated with published data as well as data of present study obtained for the freeze drying of yoghurt. The predicted surface temperature of the food sample is in good agreement with the experimental data. Energy supplied to product surface through conduction across evacuated head space was found to be significant. The model is useful for the analysis of freeze drying of a food product.     

Some Aspects of Freeze Drying of Dairy Biomaterials

ABSTRACT

Different theoretical and experimental aspects of freeze drying of dairy biomaterials are reported. The following dairy biomaterials were chosen for investigations: three kefir bacterial cultures and one bacterial concentrate of a dairy vaccine. Experiments were performed both at one-region conductive or radiative heating and at combined two-region conductive-radiative heating. Emphasis was put on quality interactions between physical and biological properties of the material to be dried and freeze drying process parameters. Qualitative estimations of the following properties of biomaterials: a) colour, b)suppleness to caking and c) suppleness to scraping born the hot surface in dependence with the process parameters were performed using four-step subjective scales. On the basis of this estimations a synthetic quality criterion SQC was defined whose numerical value reflects general product quality. The results of mathematical modelling, numerical solution of the model and comparison with experimental data indicated that the process was heat transfer controlled and that the main factors resulting in good product quality and high SQC are low temperature of the conductive heated surface and vacuum chamber pressure affecting sublimation temperature. The influence of the sample freezing parameters on the elimination of the foaming or puffing and on the product quality was observed and examined. Furthermore, preliminary measurements of the dauy biomaterials viability after freeze drying were presented.     

Kinetic and Quality Study of Mushroom Drying under Microwave and Vacuum

Abstract

The aim of this work is to model the drying kinetics of mushrooms under several operational conditions, to evaluate the effective diffusivity coefficient of moisture removing by a drying model and inverse calculus method in finite differences and to study the effect on the final quality of dehydrated mushrooms. Different ways of microwave vacuum drying were compared to freeze-drying. Results show that a decrement of the applied pressure produces a certain increase in the drying rate together with a lower moisture in the dehydrated product at the end. Temperature control inside the sample helps to ensure a better quality in the dehydrated product, than when controlled at the surface. Diffusivity coefficients show a correspondence with product temperature during drying. The microwave dried samples obtained with moderate power and temperature control of product shown an important degree of quality similar to that obtained by freeze-drying.     

Effective Moisture Diffusivity Estimation from Drying Data. A Comparison Between Various Methods of Analysis

ABSTRACT

Moisture diffusivity is the most crucial property in drying calculations. Literature data are scarce due to the variation of both experimental measurement techniques and methods of analysis. The effect of using different methods of analysis on the same experimental drying data is examined in this work. Detailed and simplified mathematical models, incorporating moisture diffusivity as model parameter, are applied. It is proved, that significant differences in the calculated values of moisture diffusivity result when different models are used, and probably these differences explain the variation in literature data. Thus, the adoption of a standardised methodology will be of great importance in moisture diffusivity evaluation.

The above findings resulted from the application of four alternative models on the drying data of three common food materials, potato, carrot and apple. A typical pilot plant scale dryer with controlled drying air conditions was used for the experiments. The moisture content dependence of the diffusion coefficient was proved significant at the last drying stage, while the temperature dependence followed the well known Arrhenius relation. The effects of considering external mass transfer and volume shrinkage during drying, were also investigated.     

DETERMINATION OF MOISTURE DIFFUSIVITY OF RED DELICIOUS APPLE TISSUES BY THERMOGRAVIMETRIC ANALYSIS

ABSTRACT

Moisture diffusivity is an important parameter needed in the analysis, design and optimization of drying processes for food and other materials. Published data on moisture diffusivities of food materials are scarce and, sometimes, inconsistent due to a lack of a precise and repeatable experimental technique. Most experimental data are limited to low and moderate drying temperature (<70°C), whereas in the food industry hot air of up to 100°C is usually used in the falling rate period to speed up the drying processes. In this study, the effective moisture diffusivities of Red Delicious apple tissues were determined from drying curves produced with a Perkin Elmer thermogravimetric analyzer, using the slope method. The experiments were conducted at lour temperatures 60, 80, 100 and 120°C. Two well defined falling rate periods were observed. The effective moisture diffusivity, for the four temperature levels ranged from 3.2 × 10^?7 to 7.9 × 10^?8 m²/s for the first falling rate period and 3.8 × 10^?8 to 4.7 × 10^?8 m²/s for the second falling rate period. The temperature dependence of the effective diffusivity can be described with an Arrhenius-type equation.     

DYNAMIC PRESSURE RISE IN THE DRYING CHAMBER AS A REMOTE SENSING METHOD FOR MONITORING THE TEMPERATURE OF THE PRODUCT DURING THE PRIMARY DRYING STAGE OF FREEZE DRYING

Abstract

A novel dynamic pressure rise method is developed as a remote sensing procedure for determining at different times during the primary drying stage of the freeze drying process (i) the temperature of the moving interface between the dried and frozen layers of the product, (ii) temperature close to the upper surface of the dried layer of the product, (iii) the temperature of the bottom surface of the frozen layer of the product, and (iv) the temperature profile of the frozen layer of the product. Furthermore, by knowing the temperature of the heating plate and determining the value of the temperature of the moving interface from the dynamic pressure rise method, the value of the position of the moving interface could be determined by an expression presented in this work     

A Simulation Study on Convection and Microwave Drying of Different Food Products

Abstract

It is now well recognized that matching the external drying condition with the drying kinetics of a material can lead to substantial savings of energy and in the case of heat-sensitive products, even to higher quality product. In this work, the effect of convection and microwave heat input and other product parameters on the batch drying characteristics of model materials, potato and carrot slabs, whose thermo-physical data are readily available in the literature, was modeled using a one dimensional liquid diffusion model. The influence of various thermo-physical properties of the product in drying of heat-sensitive materials was quantitatively assessed. Heat of wetting, temperature and moisture dependent effective diffusivity and thermal conductivity are considered in this model. The effect of moisture diffusivity on drying using convection and a microwave field is simulated in view of the interest in predicting the drying performance by simplified method. Conditions under which the drying rate is controlled by the external drying conditions and the internal thermo-physical properties of the product are computed and discussed.     

A SIMPLIFIED MODEL FOR DETERMINATION OF MOISTURE DIFFUSIVITY OF DATE FROM EXPERIMENTAL DRYING CURVES

ABSTRACT

Experimental drying curves for Tunisia Deglet Nour dates were obtained in a laboratory dryer under different drying conditions The air temperature was varied from 30 to 69^°C, relative humidity from 11.6 to 47.1 % and air velocity from 0.9 to 2.7 m/s. A numerical method to obtain a solution of a diffusion equation in which the diffusivity depends upon temperature and moisture content has been proposed to investigate the moisture movement in a date by assuming the sample to be a homogenous infinite cylinder. To rind the fitting moisture and temperature dependent diffusivity, the calculated drying curves are compared with the observed drying curves and an empirical equation for the moisture diffusivity of the date has presented as a function of temperature and moisture. It has been shown that the moisture distribution in the date during drying can be obtained by using the empirical equation presented.     

Experimental Estimation of Effective Transport Coefficients in Freeze Drying for Simulaton and Optimization Purposes

ABSTRACT

In this work a quasi-steady-state analysis is used to describe the evolution of the sublimation front temperature in freeze-drying of a food model (aqueous solution of Tylose. 3%). From the water loss data obtained in a freeze-drying experiment, in which the upper dried surface temperature and that of the frozen zone of the food model are conmlled to a cenain heating sttategy, several values of the transport coefficients in the dried layer are calculated under different operational conditions (i.e. chamber pressure and average product temperature). These values are correlated by non linear regression and expressions for the effective thermal conductivity and water vapour diffusivity in the dried layer of the material are     

On the investigation into the kinetics of the ultrasound-assisted atmospheric freeze drying of eggplant

Atmospheric freeze drying is a highly attractive process for the dehydration of thermosensitive products, like food, due to the fact that water is removed at low temperature by sublimation. Unfortunately, drying times can be very long because of the internal resistance of the product to vapor diffusion: power ultrasound can be an effective means of accelerating the process, thus reducing the operating cost. The aim of this study was to assess the effect of air temperature and velocity, ultrasound power and sample size on the drying kinetics of eggplant (Solanum melongena L.) samples and, afterward, to analyze in silico an industrial process. Experiments were performed under various conditions regarding air temperature (?5, ?7.5, ?10°C), velocity (2 and 5?m?s^?1), power ultrasound (0, 10.3, 20.5?kW?m^?3, 21.9?kHz), and sample size. Drying rate was measured experimentally. The air velocity showed no relevant effects on the drying kinetics, and the effect of air temperature was slight when compared to the marked reduction in the drying time obtained when ultrasound was applied. The uniformly retreating interface model was modified to account for the cubic shape of the samples and used to establish the kinetic parameters, in particular to evaluate water diffusivity in the dried product, searching for the best fit between measured and calculated moisture content. The model was finally used to optimize the process in silico, considering an industrial unit as test case. In this case, it appeared that power ultrasound can increase the productivity of a tunnel dryer up to four or five times, and it allows the operational and fixed costs of the plant to be reduced significantly.     

Effect of Dielectric Material on Microwave Freeze Drying of Skim Milk

Abstract:

A simultaneous heat and mass transfer model of the dielectric material–assisted microwave freeze drying was derived in this study considering the vapor sublimation-desublimation in the frozen region. The mathematical model was solved numerically by using the finite-difference technique with two moving boundaries. Silicon carbide (SiC) was selected as the dielectric material, and the skim milk was used as the representative solid material in the aqueous solution to be freeze-dried. The results show that the dielectric material can significantly enhance the microwave freeze drying process. The drying time is greatly reduced compared to cases without the aid of the dielectric material. Profiles of the temperature, ice saturation, vapor concentration, and pressure during freeze drying were presented. Mechanisms of the heat and mass transfer inside the material sphere were analyzed. For an initially unsaturated frozen sample of 16 mm in diameter with a 4-mm-diameter dielectric material core, the drying time is 288.2 min, much shorter than 380.1 min of ordinary microwave freeze drying and 455.0 min of conventional vacuum freeze drying, respectively, under typical operating conditions.     

Determination of Moisture Diffusivity by Thermo-Gravimetric Analysis under Non-Isothermal Condition

Abstract:

In drying of solids, the diffusion model based on Fick's second law is usually applied to interpret the moisture migration within the solid. Then the temperature dependence of the moisture diffusivity, generally described by an Arrhenius-type equation, is obtained through the drying kinetics. In this article, a nonisothermal (linearly increasing temperature) procedure was used to determine the moisture diffusivity as a function of temperature with the complex optimization method, and the result was accessed by comparison with a classical isothermal procedure. All the experiments were conducted in a thermogravimetric analyzer (TGA) for accurately recording the mass loss from the sample and easily programming the heating profile.     

Effect of Processing Conditions on Drying Kinetics and Particle Microstructure of Carrot

The drying of carrot particles (6 mm × 6 mm × 12 mm) was studied in a tunnel dryer; a vacuum-freeze dryer, either with or without infrared radiation; a pulsed fluidized-bed dryer assisted by microwave radiation; and combinations of these methods. The effect of two freezing rates (quick freezing in liquid nitrogen and slow freezing in a household freezer) was also studied.

The drying kinetics for these drying methods were determined and modeled, and the dried products were subjected to texture (hardness), color, and rehydration analysis, as well as 2D and 3D image analysis of pictures from scanning electron microscope.

The combination of freeze drying with other dehydration techniques reduces the drying time by 6–70%, although, in general, the structural damage increases with respect to freeze drying alone. The hybrid drying systems did not show significant differences in drying times either for quick- or slow-frozen samples. The combination of freeze drying followed by conventional drying reduces the drying time between 23 and 40% on average.

The Page empirical model represents adequately the entire drying process for combined methods, with specific parameters for each drying zone. The values of effective diffusivity calculated with the simplified constant diffusivity model agree with those reported in the literature.     

Effective Diffusivity and Evaporative Cooling in Convective Drying of Food Material

This article presents mathematical models to simulate coupled heat and mass transfer during convective drying of food materials using three different effective diffusivities: shrinkage dependent, temperature dependent, and the average of those two. Engineering simulation software COMSOL Multiphysics was utilized to simulate the model in 2D and 3D. The simulation results were compared with experimental data. It is found that the temperature-dependent effective diffusivity model predicts the moisture content more accurately at the initial stage of the drying, whereas the shrinkage-dependent effective diffusivity model is better for the final stage of the drying. The model with shrinkage-dependent effective diffusivity shows evaporative cooling phenomena at the initial stage of drying. This phenomenon was investigated and explained. Three-dimensional temperature and moisture profiles show that even when the surface is dry, the inside of the sample may still contain a large amount of moisture. Therefore, the drying process should be dealt with carefully; otherwise, microbial spoilage may start from the center of the dried food. A parametric investigation was conducted after validation of the model.     

Optimal Control of the Secondary Drying Stage of Freeze Drying of Solutions in Vials Using Variational Calculus

Abstract:

The problem of operating freeze drying of pharmaceutical products in vials loaded on trays of freeze dryer to obtain a desired final bound water content in minimum time is formulated as an optimal control problem. Two different types of freeze dryer designs were considered. In the type I freeze dryer design, upper and lower plate temperatures were controlled together, while in the type II freeze dryer design, upper and lower plate temperatures were controlled independently. The heat input to the material being dried and the drying chamber pressure were considered as control variables. Only the scorch temperature was considered as a constraint on the system state variables during the secondary drying stage, because all the free water content (frozen water) is removed from the solid matrix during the primary drying stage of freeze drying. Necessary conditions of optimality for the secondary drying stage of freeze drying process in vials were derived and presented by using rigorous multidimensional unsteady-state mathematical models. The theoretical approach presented in this work was applied in the freeze drying of skim milk. Significant reductions in drying times of the secondary drying stage of the freeze drying process in vials were observed and more uniform bound water and temperature distributions in the material being dried were obtained compared to the conventional operational policies.     

Dehydration of Garlic Slices by Combined Microwave-Vacuum and Air Drying

Abstract

Combination of microwave-vacuum drying and air drying was investigated as a potential mean for drying garlic slices. The sample was dried by microwave-vacuum until the moisture content reached 10% (wet basis), and then by conventional hot-air drying at the temperature of 45°C to final moisture content less than 5% (wet basis). Pungency, color, texture, and rehydration ratio of garlic slices dried by this method were evaluated and compared with those dried by freeze drying and conventional hot-air drying. The comparison showed that the quality of garlic slices dried by the current method was close to that of freeze dried garlic slices and much better than that of conventional hot-air dried ones. The lab microwave-vacuum dryer which the materials to be dried could be rotated in the cavity was developed by the authors.     

The Effect of Path Diffusion on The Effective Moisture Diffuslvlty in Carrot Slabs

ABSTRACT

In order to evaluate the effect of path diffusion on the average moisture diffusivity in carrot. drying curves for different shaves (slices and cylinders) and temperatures of 50, 60 and 70°C were ohtained takine into consideration the use of an average leneth of carrot sample (slice thickness or the cylinder radio). The. results showed significant differences betuecn radial and axial average diffusivities. Significant differences were also observed between core and annular diffusivity. The experimenta1 drying curves did not show enough evidence on the effect of drying temperature on the average moisture diffusivity.     

A STUDY OF TEMPERATURE AND SAMPLE DIMENSION IN THE DRYING OF POTATOES

Abstract

It is common knowledge that sample size and drying temperature are two of the most important factors affecting the drying rate and quality of food. However, what is less commonly known are how these two factors interact relative to each other and their effects on the drying behaviour of potato. These effects were evaluated under controlled drying conditions using a thermogravimetric analyser. The least-squares method was used to fit a model to the experimental data and the response variables (slope of the first drying stage, transition moisture content and slope of the second drying stage) were determined systematically. Central composite design was applied for response surface modelling of the factors and regression methodology was used to analyse the results. The results showed that both temperature and sample dimension have significant (P=0.01) effect on drying behaviour of potato. Sample dimension significantly affected the transition moisture content, whilst both temperature and sample dimension significantly affected the slopes of the first and second stage of drying.     

MICROWAVE FREEZE DRYING CHARACTERISTICS OF BEEF

ABSTRACT

Microwave freeze drying characteristics of unsaturated raw beef were studied experimentally for various levels of electric field strength, vacuum pressure, sample thickness and initial saturation. The results show that drying time is proportional to initial saturation and inversely proportional to the electric field strength and sample thickness. The effect of vacuum pressure on drying time is negligible. Some advantages of microwave freeze-drying over conventional freeze drying with radiant heating are pointed out     

Temperature Changes during Microwave-Vacuum Drying of Sliced Carrots

Abstract

The temperature changes during microwave-vacuum drying of sliced carrots were investigated. Sliced samples were dried to 7–10% moisture content (wet basis) at a wide range of microwave power and vacuum pressure levels. The experiments showed that for sample thickness less than 8 mm, the core temperature of the sample was the same as its surface temperature, with uniform temperature distribution within the sample. However, for sample thickness more than 8 mm, temperature gradient developed along the thickness of the sample. The experiments also showed that, with the decrease of moisture content X _w (dry basis), for samples with thickness ≤ 8 mm, the drying process of sliced carrots experienced three distinct periods: a warming-up period (X _w  = 7.68) without removal of moisture when the product temperature increased linearly with drying time until it reached the corresponding saturation temperature of water in the food at the vacuum pressure; a constant temperature period (2 ≤ X _w  < 7.68) in which most of moisture evaporated and flowed out of the sample efficiently with little resistance; and a heating-up period (X _w  < 2) in which the drying rate decreased and sample temperature increased rapidly. The mathematical models for predicting sliced sample temperature were also developed based on the energy conservation and regression of the experimental date.