Fundamentals of Drying

Transcription

1 Drying Technologies for Foods: Fundamentals & Applications Pp 1-22 Editors, Prabhat K. Nema,Barjinder Pal Kaur,Arun S. Mujumdar,2015 New India Publishing Agency, New Delhi , India CHAPTER 1 Fundamentals of Drying Barjinder Pal Kaur 1, Vijay Singh Sharanagat 1 and Prabhat K. Nema 1 Abstract Food products can have moisture content as high as 90% which needs to be lowered to acceptable limits to prevent microbial growth and deteriorative reactions. Drying is one of the most common and cost effective techniques for removal of excess moisture from the food by application of heat. In addition to its role of extending the product shelf life and providing stability, drying also helps to produce variety of products from agricultural, horticultural and industrial products. But to obtain the desired quality product, adequate drying is essential which depends on type of dryer and drying technique employed which further requires proper understanding of drying process. Despite being important unit operation in food processing industry, appropriate scientific knowledge of the drying process is still limited. So, the fundamental principles and associated terminologies with drying has been discussed in detail in this chapter to have thorough understanding of the drying process. In addition, different models and calculation procedures for drying of different types of commodities has also been reviewed. 1 Introduction Drying is one of the oldest and most important preservation techniques which involves reduction of moisture content of the food to the level where microbial growth is inhibited and rate of deteriorative chemical reactions is minimized. It is a thermophysical and physicochemical operation in which excess moisture is removed; hence the water activity of the food is reduced. Besides increasing the shelf life of food product, drying has various other advantages such as it makes material handling easier by reducing the bulk weight and hence reduces packaging and transport cost, makes product available during the off season, Department of Food Engineering, National Institute of Food Technology Entrepreneurship and Management, Kundli , Sonepat, Haryana, India

2 2 Drying Technologies for Foods provides better physical and nutritional properties. It also permits early harvest of the crop and therefore minimizes losses due to shattering (Pendre et al., 2012). However, drying has certain disadvantages such as damage to the structure of the food, change in the appearance and difficult to regain the original properties on rehydration (Smith, 2011). Structure of the food material, characteristics of the air used, mechanism of moisture migration, types of drying method and dryer used are some of the parameters which determines the characteristics of the dried food (Prajapati et al., 2011). Inadequate drying not only deteriorates quality of the food but also lowers profit from trading of such products. So, selection of proper dryer and drying technique are of utmost importance to achieve commercially feasible desired quality product. Further, performance of dryer depends on different characteristics of air, product and equipment. Dryer and drying process selection for a specific operation is a complex process and various factors have to be considered while making the selection. However, the overall selection and design of a drying system is based on the desired quality of the product and process economics. As drying affects the product quality in a decisive manner, hence, it must be an essential part of dryer calculation and specification, especially for food products (Jangam & Mujumdar, 2010). So, one must have a thorough understanding of principle and basics of drying both for proper designing and selection of appropriate drying system. Fundamental principles of drying and associated terminologies viz., moisture content, psychrometric properties, water activity of food are described in this chapter for thorough understanding of detailed drying aspects and applications discussed in subsequent chapters in this book. 2 Principle of Drying Drying process is governed by principle of heat and mass transfer. The moist food is heated to an appropriate temperature either by conduction or convection using external drying medium usually hot air or steam or by radiations. The moisture gets vaporized and diffuses into the environment. The removal of moisture from the food involves two basic phenomenons: a) Vaporization of moisture from the surface of the material b) Movement of moisture from the interior of the food to its surface as a result of diffusion, cell contraction and vapor pressure gradient. Drying processes can be classified into three categories depending on the mode of heat transfer and water vapor removal.

3 Fundamentals of Drying 3 a) Contact drying or convective drying: Material is in direct contact with the drying air and moisture from the material directly evaporates to the surrounding air. Over 85% of the industrial dryers are of convective type. b) Vacuum drying: Material is dried under vacuum at much lower temperatures compared to contact drying. Heat is added indirectly either by conduction or by radiation. c) Freeze drying: In this method of drying, water is removed by process of sublimation. Suitable temperature and pressure conditions are maintained in the dryer to ensure sublimation to occur. 3 Basic Terminologies 3.1 Moisture content Moisture content of food plays an important role in maintaining the desirable quality of the product. Information of moisture content is important to decide whether the food is suitable for safe storage or for any other processing activity. Moisture content is defined as amount of water for present in the food material and is usually expressed in percent. It is defined in two ways as discussed below: a) Moisture Content on wet basis (X wb ): It is expressed as ratio of the weight of water present in food to the total weight of the food product. (%) = 100 (1) (%) = (2) where, W w = Weight of water in food product W d = Weight of dry matter of food product W p = Total weight of food product b) Moisture Content on dry basis (X wb ): It is expressed as ratio of the weight of water present in the food product to the weight of dry matter.

4 4 Drying Technologies for Foods (%) = 100 (3) The moisture content calculated on dry basis is always greater than the moisture content on wet basis. Normally the engineering calculations are done based on moisture content on dry basis. c) Relationship between X wb and X db Eq. 3 can also be written as = = = (4) 1 (5) 1 (6) As indicated in Fig. 1, water in product is present in three distinct forms as described below: 1. Unbound water: The moisture in food which exerts vapor pressure equal to that of saturated vapor pressure of pure water at the same temperature. 2. Bound water: The moisture content which exerts vapor pressure less than that of a pure water at the same temperature due to retention in small pores and solutions in cell walls. Fig. 1: Relationship between moisture content and relative humidity

5 Fundamentals of Drying 5 3. Free water: The moisture content in excess of equilibrium moisture content is called free water. This moisture content can be removed easily by drying under given conditions of temperature and humidity. Free water includes both unbound water and some of bound water which is part of larger capillaries. It has water activity equal to unity. 3.2 Psychrometry Moist air which is a mixture of dry air and water vapor is used as a medium in various unit operations such as cooling, heating, mixing and transport processes. The thermodynamic properties of moist air are called psychrometric properties. The subject which deals with the study of these properties of dry air-water vapor mixture is known as psychrometry. The knowledge of properties of moist air is important for designing of systems such as dryers, air conditioning units and cooling towers. Psychometric properties of moist air are defined and discussed below: Dry bulb temperature (T db ) The temperature of air determined using thermometer is known as dry bulb temperature Wet bulb temperature (T wb ) It is the temperature measured by thermometer with its bulb wrapped in a wet cloth. Difference between wet bulb and dry bulb temperature is called wet bulb depression. The wet bulb temperature is always lower than the dry bulb temperature. But at 100% relative humidity both wet and dry bulb temperatures are equal and wet bulb depression is zero. Wet bulb temperature is indirect measurement of dryness of air Dew point temperature (T dp ) The maximum temperature at which air becomes completely saturated with the available moisture during cooling at constant pressure and humidity ratio is called dew point temperature. Further cooling below dew point temperature leads to condensation of moisture present in air and it lowers the humidity ratio Absolute humidity (H) Absolute humidity also called specific humidity or humidity ratio is defined as mass of water vapor associated with unit mass of dry air. Absolute humidity is

6 6 Drying Technologies for Foods dimensionless quantity. However, the units are often quoted as kg of water vapor per kg of dry air H = (7) where, p w = Partial pressure of water vapor, kpa p a = Partial pressure of dry air, kpa M w = Molecular weight of water = 18 g/mol M a = Molecular weight of air = 29 g/mol R = Gas Constant = 8.3l4 J/K mol T = Temperature, K = = (1 ) = (8) Relative humidity (RH) It is defined as the ratio of mass of water vapor (M v ) present in the moist air to the total mass of water vapor (M vs ) required to saturate it at the same temperature. It can also be defined as the ratio of partial pressure of water vapor in air-vapor mixture to that of pressure of water vapor of saturated air at same temperature. It is denoted as RH and is expressed in percentage. = = (9) where, p ws = Partial pressure of water vapor at saturation, kpa

7 Fundamentals of Drying Saturation humidity (H s ) Saturation humidity is a water holding capacity of air at a particular temperature that increases with increase in temperature. In other words, it can be defined as maximum quantity of water which air can hold before vapor starts condensing back to liquid water at a constant temperature. = (1 ) (10) Humid heat (C p ) It is the heat capacity of moist air. It is defined as amount of heat required to raise the temperature of one kg dry air along with its associated water vapor by 1 o C at constant pressure. Humid heat can be estimated from the following equation. = + = (11) where, C p dry air = Specific heat of dry air = kj/kg o C C p water = Specific heat of water vapor = 1.88kJ/kg o C Humid volume (V H ) Humid volume (also called as specific volume of air) is the volume occupied by unit mass of dry air and its associated vapor. Humid volume is inversely propositional to density. = ( )( ) (12) where, T = Temperature of air, K

8 8 Drying Technologies for Foods Psychrometric chart Psychrometric chart is graphical representation of thermodynamic properties of air. The properties of air water vapor mixture are useful in number of processes. Psychrometric chart is very useful to determine psychrometric properties without calculating the same using various equations. Development of equations to determine these properties is sometimes inconvenient and quiet tedious. So, to avoid calculations psychrometric chart is very helful. It is a plot between humidity ratio (ordinate) and dry bulb temperature (abscissa) with a series of curves representing values of percentage relative humidity superimposed. It is constructed for a standard atmospheric pressure of bar, corresponding to pressure at mean sea level. A typical layout of psychrometric chart is shown in Fig. 2. Knowing any two values of air properties helps in finding the remaining properties directly from the chart. Fig. 2: Diagrammatic representation of psychrometric chart 3.3 Water activity (a w ) Water is an important constituent of most of the foods. The availability of water for microbial growth, germination of spores, enzymatic activity and chemical reactions is one of the most critical factors which affect the quality, safety and shelf life of food. This availability of water is depicted as water activity (a w ). Water activity is a thermodynamic property and is defined as the ratio of partial vapor pressure of water in the food (P f ) to the vapor pressure of pure water (p pw ) at the same temperature.

9 Fundamentals of Drying 9 = (13) The relative humidity of air is expressed as ratio of partial vapor pressure of water present in air (p w ) to the vapor pressure of pure water (p pw ) at the same temperature. = x 100 (14) If the food is in equilibrium with air, then p f = p w, and water activity can be expressed in terms of equilibrium relative humidity (ERH). = 100 (15) There is a minimum a w requirement for a specific microorganism for its growth or germination of spores, some examples are listed in Table 1. Besides microbial damage, which typically occurs at a w > 0.70, water activity also influences phenomenas such as oxidation, non-enzymatic browning (Maillard reactions) and enzymatic reactions which requires much lower a w. General nature of the deterioration reaction rates as a function of a w for food systems is shown in Figure 3. Reducing a w can inhibit microbial growth and checks the deteriorative reactions. Water activity can be reduced by different preservation techniques such as dehydration or by adding water-binding agents like sugars, glycerol, or salt. Fig. 3: Food deterioration rate as a function of water activity

10 10 Drying Technologies for Foods Table 1: Minimum water activity for microbial growth and spore germination a w Microorganisms Bacteria Molds Yeast Products 0.97 Clostridium botulinum E Fresh meat, fruits and vegetables, Psuedomonas fluorescens canned fruits & vegetables, cooked sausages 0.95 Escherichia coli Clostridium perfringens Salmonella spp. Vibrio cholera 0.94 Clostridium botulinum A, BVibrio Stachybotrys atra Some cheeses (Cheddar, Swiss, parahaemolyticus Muenster), cured meat (ham), bread, sweetened condensed milk, fermented sausages, chocolate syrups 0.93 Bacillus cereus Rhizopus nigricans 0.92 Listeria monocytogenes 0.91 Bacillus subtilis 0.90 Staphylococcus aureus (anaerobic) Trichothecium roseum Saccharomycescerevisiae 0.88 Candida 0.87 Staphylococcus aureus (aerobic) 0.85 Aspergillus clavatus Dry pasta, spices, rice, confections, 0.84 Byssochlamys nivea wheat, whole egg powder, chewing 0.83 Penicillium expansum gum, flour, dry beans, cookies, Penicillium islandicum Debaryomyceshansenii crackers, bread crusts, breakfast Penicillium viridicatum cereals, dry pet food, peanut butter 0.82 Aspergillus fumigatus Aspergillus parasiticus (Contd.)

11 Fundamentals of Drying 11 a w Microorganisms Bacteria Molds Yeast Products 0.81 Penicillium cyclopium Penicillium patulum 0.80 Saccharomyces bailii 0.79 Penicillium martensli 0.78 Aspergillus flavus 0.77 Aspergillus niger Marmalade, Jam, marzipan, glacé Aspergillus ochraceous fruits, molasses, dried figs, heavily 0.75 Aspergillus restrictus salted fish Aspergillus candidus 0.71 Eurotium chevalieri 0.70 Eurotium amstelodami Dried fruits, nuts, snack bars, 0.62 Saccharomyces rouxii snack cakes, corn syrup, 0.61 Monascus bisporus marshmallow 0.60 No microbial proliferation 0.50 No microbial proliferation Dry pasta, spices, rice, noodles, honey, toffees 0.40 No microbial proliferation Whole egg powder, cocoa, dry beans 0.30 No microbial proliferation Cookies, crackers, bread crusts, breakfast cereals, dry pet food, peanut butter <0.20 No microbial proliferation Whole milk powder, dried vegetables, freeze dried corn

12 12 Drying Technologies for Foods Water activity is temperature dependent and change in water activity is due to change in water binding, dissociation of water, solubility of solutes in water, or the state of the matrix. The effect of temperature on the water activity of a food is product specific. Some products (e.g. pet foods, soup mix, juices) shows an increase in water activity with increasing temperature where as others (e.g. cookies, foods with crystalline salt and sugar) decrease a w with increasing temperature, while most high moisture foods such as chocolate syrup, sausages, have negligible change with temperature. Based on water activity also foods can be classified (Table 2). Foods with water activity above 0.85 are termed as high moisture foods and require refrigeration or another barrier to control the growth of pathogens. Foods with water activity between 0.60 and 0.85 are classified as intermediate moisture foods. These do not require refrigeration to control pathogens, but have a limited shelf-life because of spoilage, primarily by yeast and mold. And the foods with a water activity below 0.60 have an extended shelf-life, even without refrigeration. These foods are called low moisture foods. Some examples of the foods discussed above are shown in Table 2. Table 2: Classification of foods based on water activity Water Activity Classification Examples Requirements > 0.85 High Moisture Foods Meat, milk, fruits, Requires refrigeration or fresh fish another barrier to control the growth of pathogens 0.60 and 0.85 Intermediate Moisture Cakes, jams jellies, Does not require Foods pastries, flour, refrigeration to control heavily salted fish pathogens. Limited shelflife because of spoilage, primarily by yeast and mold < 0.60 Low Moisture Foods Milk powder, cereals Extended shelf-life, even without refrigeration 3.4 Equilibrium moisture content and sorption isotherms The moisture content at which vapor pressure of water present in food equals that of surroundings is termed as equilibrium moisture content (EMC). A plot of EMC versus relative humidity at a given temperature is termed as sorption isotherm. When food products attains EMC by losing moisture to the surroundings, it is known as desorption EMC. Whereas, when it is attained by gaining moisture from the surroundings it is known as adsorption EMC. Extent of sorption of water or desorption from food product depends on vapor pressure of water present in food sample and in surroundings. The difference between desorption and adsorption is known as hysteresis.

13 Fundamentals of Drying 13 The shape of isotherm is unique for each product due to differences in capillary effect, colligative effects of dissolved components such as salt and sugars as well as surface interactions. Moisture sorption isotherms are sigmoidal in shape for most foods, however, the foods that contain large amounts of sugar or small soluble molecules and are not rich in polymeric materials have a J-type isotherm (Fennema, 1996) as shown in Fig. 4. MC MC a w aw Fig. 4: Different shapes of sorption isotherms An isotherm can typically be divided into three regions A, B, C where each zone is an indicator of distinct water binding mechanisms at individual sites on the solid matrix (Fig. 5). Region A corresponds to hydration monolayer where water is tightly bound to the sites and is unavailable for reaction. In region B, the water molecules are less firmly bound to the sites compared to first zone and is confined to smaller capillaries. Water in region C is called free or solvent water. Water in this region is loosely held in voids, large capillaries, crevices and is available for reactions. Fig. 5: Typical sorption isotherm

14 14 Drying Technologies for Foods Measurement and Mathematical Modeling of Isotherms Different techniques have been used for measurement of sorption isotherms which are classified as, gravimetric, manometric and hygrometric methods (Jangam & Mujumdar, 2010). Gravimetric method is most commonly used and it involves measurement of mass change in continuous or periodic manner. The manometric method involves measurement of vapor pressure of water in equilibrium with the food product using sensitive manometers. In the hygrometric method relative humidity of air surrounding the food material at particular moisture content is measured. Besides these methods the sorption isotherms have also been described using mathematical models. Some of the widely used models along with their application in food are presented in Table 3. Some models have been derived theoretically based on thermodynamic concepts while others are an extended or modified form of these models. 4 Drying Kinetics 4.1 Rate of drying Drying rate is function of moisture content of product. The drying process based on drying rate can be divided into three periods: constant rate drying period, first falling rate and second falling rate period as shown in Figure 6. Period Period Fig. 6: A drying rate curve showing constant and falling rate period

15 Fundamentals of Drying 15 Table 3: Mathematical models of sorption isotherms Type of model Equation Details Food Products Reference Langmuir equation C is a constant Pear Park et al. (2001) Garden mint leaves Park et al. (2002) Brunauer-Emmett- C is a dimension-less Apples Kaymak-Ertekin & Gedik Teller (BET) parameter depending (2004) equation on heat of sorption for mono-layer region Dried tomato Iguedjtal et al. (2008) Blueberry Vega et al. (2009) Oswin equation K and N constant Dried tomato pulp Goula et al. (2008) Apple Moraes et al. (2008) Yam Montes et al. (2009) Smith model k 1 and k 2 are constants Mango pulp Da Silva et al. (2002) Walnut kernels Togrul & Arslan (2007) Cashew apple Alcântara et al. (2009) Halsey equation A is constant Pear osmotically dehydrated Park et al. (2001) pear Banana pulp Gouveia et al. (2004) Chung-Pfost Cocoa beans Shivhare et al. (2014) equation Modified A, B and C are constants Rough rice San Martin et al. (2001) Henderson equation

16 16 Drying Technologies for Foods Type of model Equation Details Food Products Reference Guggenheim- C and K are dimensionless Mango pulp Da Silva et al. (2002) Anderson-Boer parameters depending Passion fruit peel Oliveira et al. (2006) (GAB) equation; on heat of sorption Dried tomato pulp Goula et al. (2008) modification for mono and multiof BET equation layer region Lewicki model A and b are constants Cassava flour Suppakul (2006) Peleg model k 1 and k 2 are constants Pistachio nut Hayoglu & Faruk (2007) Instant green tea Sinija & Mishra (2008)

17 Fundamentals of Drying Constant rate period The process AB in drying rate curve represents the constant rate drying period. In constant rate drying, the surface of the food behaves as free water surface. The rate of evaporation of water from the surface is equal to the moisture migration from the interior of the product to its surface. This period continues till critical moisture content is reached. The constant drying period is governed fully by external heat and mass transfer as the surface of the product is always covered with the film of free water. The product temperature is usually at the wet bulb temperature of the drying air. Drying of washed seeds takes place in constant rate period. However, most of the foods and agricultural products do not show constant rate falling period. During constant rate period, the drying rate depends on i) Difference in temperature of air and wetted surface at constant air velocity and relative humidity, ii) ii) Difference in humidity between the air stream and the wet surface at constant air velocity and temperature, and Air velocity at constant temperature and relative humidity Critical moisture content (CMC): Point B on plot represents critical moisture content. It is the moisture content of the product at which constant rate drying period ceases and falling rate period begins. The critical moisture content depends on type of product and its thickness Falling rate period Most of the agricultural products are dried in falling rate drying period. The rate of drying is controlled by moisture diffusion towards the surface and further removal of moisture from the free surface. Falling rate period is divided into two zones: first falling rate free period and second falling rate period as shown in Fig. 6 by process BC and CD in drying curve respectively. a) First falling rate period First falling rate period is unsaturated surface drying. As drying proceeds, the wet surface area decreases as a result of which drying rate also decreases. The cause of falling rate drying period can be explained by the fact that the rate at which surface moisture is evaporated from the drying surface is more than the rate at which moisture is migrated from the interior to the surface. The reduction of wet surface to zero is end of the first falling rate period.

18 18 Drying Technologies for Foods b) Second falling rate period In this period, sub surface evaporation takes place and drying continues till equilibrium moisture content is reached. Different mechanisms have been proposed for describing drying in capillary porous products. i) Capillary flow: Liquid diffusion due to surface forces ii) iii) iv) Liquid diffusion: Liquid movement due to difference in moisture concentration Surface diffusion: Liquid movement due to moisture diffusion on the pores surfaces Vapor diffusion: Vapor movement due to vapor pressure difference v) Thermal diffusion: Vapor movement due to temperature difference vi) Hydrodynamic flow: Liquid and vapor movement due to total pressure difference 4.2 Drying time calculation Drying time is the time required to reduce the moisture content of food product from initial to desired moisture content level. It is possible to estimate drying time if values of both initial moisture content and critical moisture content are known. By definition, rate of drying is given as = (16) where, R = rate of drying (kg of water per kg dry solid per unit time); m s is mass of dry solids; and represents rate of change of moisture content on a dry basis. The negative sign indicates decrease in moisture content. For constant rate period, rate of drying (R c )is constant and hence, Eq. (16) can be written as = Integrating within limits of initial (X i ) and and critical (X c ) moisture content total constant rate drying period (t c ) is given as = 0 (17) (18)

19 Fundamentals of Drying 19 = ( ) (19) For falling rate period, rate of drying is represented as = (20) In falling rate period, drying process is controlled by diffusion through capillaries and drying rate constantly decreases so drying rate (R f ) can be represented by Eq. (21) = + (21) Hence, 1 = 1 + & 2 = 2 + (22) where, a is the slope of line and b is its intercept, X 1 and X 2 are the initial and final moisture content for the first falling rate period (process BC ) Substituting Eq. (21) in Eq. (20) = 0 2 = (23) 1 + = ln 1 + (24) 2 + Using Eq. (22) slope a can be calculated as = (25) Substituting Eq. (25) in Eq. (24), falling rate drying time becomes = (26) As the falling rate period can be represented by a straight line from X c to X e, (equilibrium moisture content) and where X 1 < X c and X 2 < X c, then the drying rate and gradient at any moisture content X are given as = ( ) (27) = (28)

20 20 Drying Technologies for Foods Substituting Eq. 28 in Eq. 27 yields = ( ) (29) t f = ( ) ( 1 2 ) ln 1 2 (30) = ( ) ln 1 2 (31) Total drying time (t) can be calculated as = + Therefore, = ( ) + ( ) ln 1 2 (32) 4.3 Heat transfer in drying The rate of migration of the moisture from the solid to the surroundings controls the overall drying rate. Heat transfer in drying may take place by all the three modes: conduction, convection and radiation. In case of convection drying, the effects of conduction and radiation are assumed to be negligible. If m is the rate of moisture evaporation, the quantity of heat (q) required for evaporation can be calculated using Eq. (33). = (33) where, = latent heat of evaporation, kj/kg Also, the heat transfer rate (q) is given by = h ( ) (34) Hence, = h ( ) (35) where, h s = Heat transfer coefficient (kj/m 2 o C) T a = Temperature of drying air ( o C) T s = Temperature of interface of drying solid and air ( o C)

21 Fundamentals of Drying 21 Conclusion Drying is one of the most important unit operations in food processing industry. Inappropriate application of heat and mass transfer rates lead to under or over drying of the food resulting in quality problems without major increase in the drying kinetics. Understanding the principles of drying enables one to make appropriate decision in selection of drying process. An attempt is made here to provide general information on the fundamental principles and basic terminology used in the drying process. Different models and calculation procedures cited in literature has also been reviewed in this chapter. References Alcântara, S., Almeida, F., Silva, F. and Gomes, J. (2009). Adsorption isotherms of the dry cashew Apple. Revista Brasileira de Engenharia Agrícola e Ambiental, 13 (1): Da Silva, M., Gouveia, J. and Almeida, F. (2002). Desorption and isosteric heat of mango pulp. Revista Brasileira de Engenharia Agrícola e Ambiental, 6 (1): Fennema, O.R. (1996). Water and Ice. In: O.R. Fennema (Ed.), Food Chemistry. Marcel Dekker, Inc., New York, Basel, Hong Kong, pp Goula, A., Karapantsios, T., Achilias, D. and Adamopoulos, K. (2008). Water sorption isotherms and glass transition temperature of spray dried tomato pulp. Journal of Food Engineering, 85 (1) : Gouveia, J., Nascimento, J., Almeida, F., Silva, M., Farias, E. and Silva, F. (2004). Mathematical models for adjustment of desorption isotherms of banana variety silver. Engenharia Agrý cola, 24 (3) : Hayoglu, I. and Faruk, O. (2007). Water sorption isotherms of pistachio nut paste. International Journal of Food Science and Technology, 42 (2) : Iguedjtal, T., Louka, N. and Allaf, K. (2008). Sorption isotherms of potato slices dried and texturized by controlled sudden decompression. Journal of Food Engineering, 85(2): Jangam, S.V. and Mujumdar, A.S. (2010). Basic concepts and definition. In: S.V. Jangam, C.L. Law, A.S. Mujumdar (Eds.), Drying of Foods, Vegetables and Fruits, vol.1, ISBN , Published in Singapore, pp Kaymak-Ertekin, F. and Gedik, A. (2004). Sorption isotherms and isosteric heat of sorption for grapes, apricots, apples and potatoes. Lebensmittel Technologie, 37(4): Martin, M.B.S., Mate, J.I., Fernandez, T. and Virseda, P. (2001). Modelling adsorption equilibrium moisture characteristics of rough rice. Drying Technology, 19(3-4): Montes, E., Torres, R., Andrade, R., Pérez, O., Marimon, J. and Meza, I. (2009). Models of desorption isotherms of yam (Dioscorea rotundata). Dyna, 76 (157): Moraes, M.A., Rosa G.S. and Pinto, L.A. (2008). Moisture sorption isotherms and thermodynamic properties of apple Fuji and garlic. International Journal of Food Science and Technology, 43 (10): Oliveira, M., Campos, A., Dantas, J., Gomes, J. and Silva, F. (2006). Desorption isotherms of passion fruit peel (Passiflora edulis Sims): experimental determination and mathematical model evaluation. Ciência Rural, 36 (5): Park, K., Bin, A. and Brod, F. (2001). Sorption isotherms data and mathematical models for pear bartlett (Pyrus sp.) with and without osmotic dehydration. Ciência e Tecnologia de Alimentos, 21 (1):73-77.

22 22 Drying Technologies for Foods Park, K., Vohnikova, Z. and Brod, F. (2002). Evaluation of drying parameters and desorption isotherms of garden mint leaves (Mentha crispa L.). Journal of Food Engineering, 51 (3) : Prajapati, V.K., Nema, P.K. and Rathore, S.S. (2011). Effect of pretreatment and drying methods on quality of value-added dried aonla (Emblica officinalis Gaertn) shreds. Journal of Food Science Technology, 48(1) : San Martin M.B., Mate J.I., Fernandez T. and Verseda P. (2001). Modeling adsorption equilibrium moisture characteristics of rough rice. Drying Technology, 19: Shivhare, U.S., Arora, S., Ahmed, J., and Raghavan, G.S.V. (2004). Moisture adsorption isotherm for mushroom. Lebensmittel Technologie, 37: Sinija, V.R. and Mishra, H.N. (2008). Moisture sorption isotherms and heat of sorption of instant (soluble) green tea powder and green tea granules. Journal of Food Engineering, 86 (4) : Smith, P.G. (2011). Introduction to Food Process Engineering. 2 nd edition, Springer New York Dordrecht Heidelberg London. Suppakul, P. (2006). Moisture sorption characteristics of cassava flour film, In: Proceedings of 15th IAPRI World Conference on Packaging, Tokyo, Japan, pp Togrul, H. and Arslan, N. (2007). Moisture sorption isotherms and thermodynamic properties of walnut kernels. Journal of Stored Products Research, 43(3): Vega, A., López, J., Miranda, M., Di Scala, K., Yagnam, F. and Uribe E. (2009). Mathematical modelling of moisture sorption isotherms and determination of isosteric heat of blueberry variety O Neil. International Journal of Food Science and Technology, 44(10):