0960–3085/02/$10.00+0.00 # Institution of Chemical Engineers Trans IChemE, Vol 80, Part C, June 2002
MOISTURE SORPTION ISOTHERM CHARACTERISTICS OF FOOD PRODUCTS: A REVIEW
. AL-MUHTASEB, W. A. M. McMINN and T. R. A. MAGEE
Food Process Engineering Research Group, School of Chemical Engineering, Queen’s University Belfast, Northern Ireland, UK.
nowledge of the sorption properties of foods is of great importance in food dehydration, especially in the quantitative approach to the prediction of the shelf life of dried foods. Equations for modelling water sorption isotherms are of special interest for many aspects of food preservation by dehydration, including evaluation of the thermodynamic functions of the water sorbed in foods. Knowledge of the thermodynamic properties associated with sorption behaviour of water in foods is important to dehydration in several respects, especially in the design and optimization of unit operation. Keywords: sorption isotherm; water activity; hysteresis; mathematical models; isosteric heat of sorption.
INTRODUCTION Controlling the moisture content during the processing of foods is an ancient method of preservation. This is achieved by either removing water, or binding it such that the food becomes stable to both microbial and chemical deterioration1. For this reason much attention has been given to the sorption properties of foods. Sorption characteristics have, and are currently being examined in light of their in uence on the storage stability of dehydrated products, as well as their effect on the diffusion of water vapour2. Walter3 in 1924 was probably the rst researcher to relate relative water vapour pressure to microbial growth, the main cause of food spoilage. A decade afterwards, Scott4 and Salwin5 independently applied this relationship and introduced the concept of water activity (aw). This is a term indicating the ‘quality’ of the water content of food. It describes the degree of ‘boundness’ of water and hence, its availability to participate in physical, chemical, and microbiological reactions. Since then, experimental and theoretical studies of the water associated with foods have been intensi ed in an attempt to understand and interpret water behaviour. Such endeavours have been fraught with dif culties because foods are heterogeneous mixtures of soluble organic and inorganic materials6. The properties of water, in relation to biological system, can be classi ed into three categories6. (1) Structural Aspects: the position and orientation of water molecules in relation to each other and to macromolecules; (2) Dynamic Aspects: molecular motions of water and their contribution to the hydrodynamic properties of the system; (3) Thermodynamic Aspects: water in equilibrium with its surroundings, at a certain relative humidity and temperature. 118
WATER ACTIVITY Water, the most abundant constituent of natural foods, has many roles in food processing and, while the chemistry is simple, the impact on food reactions and food quality is greater than any other chemical component7. Karel8 considered water to be the most important plasticizer ‘mobility enhancer’ for hydrophilic food component, i.e. its low molecular weight leads to a large increase in mobility, due to increased free volume (the volume of the polymerplasticizer mixture that is not occupied by molecules) and decreased local viscosity9. In biological systems, such as foods, water is believed to exist with either unhindered or hindered mobility, referred to as free and bound water, respectively. The amount of water held by the food product, under a speci c set of conditions, is traditionally referred to as the water-holding or water-binding capacity of the material. The often ill-de ned term, ‘bound water’ is usually considered as that portion of water held in the material which exhibits physical properties signi cantly different from those of free, or bulk, water10. It has been suggested that the water is bound to stronger hydrogen bond acceptors than liquid water (possibly with favoured hydrogen bond angles) as well as water-solvating nonpolar groups. According to Luck11, bound water has a reduced solubility for other compounds, causes a reduction in the diffusion of water-soluble solutes in the sorbent, and exhibits a decrease in diffusion coef cient with decreasing moisture content. The decreased diffusion velocity impedes drying processes because of slower diffusion of water to the surface. Some of the characteristics of bound water are lower vapour pressure, high binding energy as measured during dehydration, reduced mobility as seen by nuclear magnetic resonance (NMR), unfreezability at low temperature, and unavailability as a solvent12. Although each of these characteristics has been used to de ne bound water, each gives a
MOISTURE SORPTION ISOTHERM CHARACTERISTICS
different value for the amount of water which is bound. As a result of this, as well as the complexities and interactions of the binding forces involved, no universal de nition of bound water has been adopted. The concept of water activity, that is used most commonly by researchers in the food industry, can be de ned as: aw ? p= p0 ?
relative humidiy 100 …1?
Figure 2. Five types of van der Waals adsorption isotherm13.
where p is the partial pressure of water in the food (atm), and p0 the vapour pressure of pure water at the same temperature (atm). MOISTURE SORPTION ISOTHERM The relationship between total moisture content and the water activity of the food, over a range of values, and at a constant temperature, yields a moisture sorption isotherm when expressed graphically. This isotherm curve can be obtained in one of two ways (see Figure 1): (i) an adsorption isotherm is obtained by placing a completely dry material into various atmospheres of increasing relative humidity and measuring the weight gain due to water uptake; (ii) a desorption isotherm is found by placing an initially wet material under the same relative humidities, and measuring the loss in weight2. The adsorption and desorption processes are not fully reversible, therefore a distinction can be made between the adsorption and desorption isotherms by determining whether the moisture levels within the product are increasing indicating wetting, or whether the moisture is gradually lowering to reach equilibrium with its surroundings, implying that the product is being dried. On the basis of the van der Waals adsorption of gases on various solid substrates, Brunauer et al.13 classi ed adsorption isotherms into ve general types (see Figure 2). Type I is the Langmuir, and Type II the sigmoid shaped adsorption isotherm; however, no special names have been attached to the other three types. Types II and III are closely related to Types IV and V, except that the maximum adsorption occurs at a pressure lower than the vapour pressure of the gas. If,
Figure 1. Generalized sorption isotherm for food products91.
however, the solid is porous so that it has an internal surface, then the thickness of the adsorbed layer on the walls of the pores is necessarily limited by the width of the pores. The form of the isotherm is modi ed correspondingly; instead of Type II and III, Type IV and V exist14. Moisture sorption isotherms of most foods are nonlinear, generally sigmoidal in shape, and have been classi ed as Type II isotherms. Caurie15 suggested that most of the water in fresh food exerts a vapour pressure very close to that of pure water, i.e. unity. This vapour pressure level is maintained until the moisture content of the food decreases to about 22%. The moisture level is then no longer able to sustain the vapour pressure of the food at unity, and therefore, begins to show a lowered vapour pressure, as if in solution. The changes with atmospheric humidity of this last fraction (22%) of water in dehydrated foods result in the characteristic sigmoid shape of water sorption isotherms. Rowland16 suggested that the direct plasticizing effect of increasing moisture content at constant temperature is equivalent to the effect of increasing temperature at constant moisture and leads to increased segmental mobility of chains in amorphous regions of glassy and partially crystalline polymers. Foods rich in soluble components, such as sugars, however, have been found to show Type III behaviour, this is due to the solubility of sugars in water17. Chinachoti and Steinberg18 found that sucrose added to starch gels sharply increased the sorption of water at water activities higher than 0.85. The sorption isotherm characteristics of many food products have been determined experimentally (see Table 1), and have been further characterized according to the Brunauer et al.13 classi cation; a number of examples are presented in Table 2. For interpretation purposes, the generalized moisture sorption isotherm for a hypothetical food system may be divided into three main regions, as detailed in Figure 1. Region A represents strongly bound water with an enthalpy of vaporization considerably higher than that of pure water. A typical case is sorption of water onto highly hydrophilic biopolymers such proteins and polysaccharides. The moisture content theoretically, represents the adsorption of the rst layer of water molecules. Usually, water molecules in this region are unfreezable and are not available for chemical reactions or as plasticizers. Most dried food products are empirically observed to display their greatest stability at moisture contents comparable to the monolayer moisture content19.
Trans IChemE, Vol 80, Part C, June 2002
AL-MUHTASEB et al.
Table 1. Summary of moisture sorption isotherm characteristics of food materials.
Material Starchy foods Corn Potato Wheat Flour Rice Sorghum Starch gel High protein foods Beef Chicken, raw Chicken, cooked Eggs Milk Macadamia nuts Cheese Yoghurt Fruits Banana Pineapple Apple Apricots Raisins Vegetables Green pepper Lentil Tomato Onion Sugar Beet Root Carrot Celery Cabbage
A=D D A and D A A and D A A and D A D A A A A A A
T, ? C 10–60 10–80 20–50 20 10–35 20–50 30–50 5–60 5–60 17–60 2–40 20–60 25 5–45 25–60 25–60 20–30 15–60 20–35 30–60 5–60 30–60 20–40 35–50 30–60 5–60 37
Researchers Chen and Clayton92, Kumar93, Iglesias and Chirife65, Iglesias and Chirife94, Duras and Hiver95. Mazza 96, Labuza97, Lomauro et al.32, Diamante and Murno98, Wang and Brennan37, Kiranoudis et al.38, McLauglin and Magee39, McMinn and Magee40. Becker and Sallans99, Hubbard et al.100, Bushuk and Winkler101. Taylor102, Wolf et al.52, Iglesias and Chirife65. Iglesias and Chirife94. Fish103, Saravacos and Stinch eld26, McMinn104. Salwin5, Iglesias and Chirife65. Labuza97. Wolf et al.105, Iglesias and Chirife94. Iglesias and Chirife94. Berlin et al.106, Labuza et al.72, Linko et al.82, Labuza97. Palipane and Driscoll24. Salwin5, Wolf et al.105, Iglesias and Chirife65, Lomauro et al.32. Wolf et al.105, Kim and Bhowmik81. Wolf et al.105, Iglesias and Chirife65. Wolf et al.105, Hossain et al.107. Wolf et al.52, Iglesias and Chirife65, Roman et al.108, Roman et al.109. Maroulis et al.110, Samaniego et al.111. Saravacos et al.16, Maroulis et al.110, Tsami et al.29. Lomauro et al.32, Kiranoudis et al.38, Kaymak-Ertekin and Sultanoglu41. Wolf et al.105, Menkov80. Kiranoudis et al.38. Salwin5, Samaniego-Esguerra et al.111, Kiranoudis et al.38, Adam et al.112. Iglesias et al.58. Taylor102, Kiranoudis et al.38. Wolf et al.105. Mizrahi et al.113.
and D and and and and D D D D
A A and D D A and D A and D A and D A and D D A D A A A
A: adsorption; D: desorption; T: temperature range.
Region B, represents water molecules which are less rmly bound, initially as multilayers above the monolayer. In this region, water is held in the solid matrix by capillary condensation. This water is available as a solvent for low-molecularweight solutes and for some biochemical reactions. The quantity of water present in the material that does not freeze at the normal freezing point usually is within this region. In region C or above, excess water is present in macro-capillaries or as part of the uid phase in high moisture materials This exhibits nearly all the properties of bulk water, and thus is capable of acting as a solvent. Microbial growth becomes a major deteriorative reaction in this region20,21. The variation in sorption properties of foods reported in the literature is caused by biological variation in foods, pretreatment of food, and differences in experimental techniques adopted (gravimetric, manometric or hygrometric)22.
Table 2. Types of van der Waals adsorption isotherms observed for different food materials. van der Waals adsorption isotherm Type II
EFFECT OF TEMPERATURE ON SORPTION ISOTHERMS The effect of temperature on the sorption isotherm is of great importance given that foods are exposed to a range of temperatures during storage and processing and water activity changes with temperature. Temperature affects the mobilityof water molecules and the dynamic equilibrium between the vapour and adsorbed phases. In general, researchers have found that if the water activity is maintained constant, an increase in temperature causes a decrease in the amount of sorbed water. Iglesias and Chirife23 considered this to indicate that the food is becoming less hygroscopic. Palipane and Driscoll24 suggested that at higher temperatures some water molecules are activated to energy levels that allow them to break away from their sorption sites, thus decreasing the equilibrium moisture content. A deviation from this behaviour, however, has been shown by certain sugars (glucose) and other low molecular weight food constituents (salt), which become more hygroscopic at higher temperatures due to their ability to dissolve in water25. Saravacos et al.22 observed the intersection of the 20? C and 30? C isotherm curves of sultana raisins at a water activity of approximately 0.78. This was also reported by Saravacos and Stinch eld26 for model systems containing starch and glucose. Similar effects of temperature on the isotherm characteristics have been observed by Audu et al.27 for sugars, and Weisser et al.28 for sugar alcohol.Tsami et al.29 found similar results for dried fruits, up to a water activity of 0.55–0.7. However, for water Trans IChemE, Vol 80, Part C, June 2002
Food materials Starch Gel , Corn94, Potato37, Macadamia nuts24, Carrot38, Tomato, Green pepper, Potato39,40, Lentil seeds80, Onion112, Green pepper41, Chestnut114, Hazelnut115, Cocoa beans116. Pineapple105, Banana65, sugars27, Apple108, Sugar alcohol28, Sucros-Starch18,55, Raisins16, Apricot110,111, Pineapple107, Cured beef117.
MOISTURE SORPTION ISOTHERM CHARACTERISTICS activity values greater than 0.7, there was an inversion of the effect of temperature (equilibrium moisture content increased with temperature). This phenomenon was attributedto the fact that, in general, at low aw values the sorption of water is due mainly to the biopolymers, with an increase of temperature having the normal effect of lowering the isotherm. However, as aw is raised beyond the intermediate region, water begins to be sorbed by the sugars and other low molecular weight constituents (offsets the effect of temperature). The result is an increasing of the moisture content, i.e. intersection of the isotherms25. The intersection point depends on the composition of the food and the solubility of sugars26. MEASUREMENT OF SORPTION ISOTHERMS Many methods are available for determining water sorption isotherms30. These methods can be classi ed into three categories: (1) gravimetric; (2) manometric; (3) hygrometric. ° gravimetric method: involves the measurement of weight changes. Weight changes can be determined both continuously and discontinuously in dynamic or static systems (i.e. air may be circulated or stagnant). Continuous methods employ the use of electro-balances or quartz spring balances. In the discontinuous systems, salt or sulphuric acid solutions are placed in vacuum or atmospheric systems with the food material, to give a measure of the equilibrium relative humidity. ° manometric method: measures the vapour pressure of water in the vapour space surrounding the food. To improve accuracy the uid selected for the manometer is often oil instead of mercury. The whole system is maintained at constant temperature and the food sample will lose water to equilibrate with the vapour space. This will be indicated by the difference in height on the manometer. ° hygrometric method: measures the equilibrium relative humidity of air in contact with a food material, at a given moisture content. Dew-point hygrometers detect the condensation of cooling water vapour. Electric hygrometers measure the change in conductance or capacitance of hygrosensors. Most hygrosensors are coated with a hygroscopic salt, such as LiCl, which absorbs moisture from the food sample. A static gravimetric technique was developed and standardized in the Water Activity Group of the European COST 90 project31. Moisture sorption data for food products published in the literature have been obtained by applying this technique at various temperatures and water activities for its following advantages32–41: (1) determining the exact dry weight of the sample; (2) minimizing temperature uctuation between samples and their surroundings or the source of water vapour; (3) registering the weight change of the sample in equilibrium with the respective water vapour pressures; (4) achieving hygroscopic and thermal equilibrium between samples and water vapour source. MOISTURE SORPTION HYSTERESIS In the eld of water vapour sorption by a solid sorbent, moisture sorption hysteresis is the phenomena by which two Trans IChemE, Vol 80, Part C, June 2002
different paths exist between the adsorption and desorption isotherms42. In general, if the amount of water per unit mass of solid is plotted as the ordinate and the corresponding relative vapour pressure as the abscissa, the desorption isotherm lies above the adsorption isotherm and a closed hysteresis loop is formed. This is illustrated in Figure 1. The extent of hysteresis is related to the nature and state of the components in a food. It may re ect their structural and conformational rearrangment, which alters the accessibility of energetically favourable polar sites, and thus, may hinder the movement of moisture17. The effect of hysteresis on food is important, even though it can be relatively low in magnitude. Labuza et al.43 showed that lipid oxidation occurs 3–6 times faster in foods prepared by desorption than in those prepared by adsorption at constant aw. Labuza et al.44 suggested that, although more expensive, the preparation of intermediate moisture foods via adsorption following desorption, rather than desorption alone, might be justi ed in terms of increased shelf life. Theories of Sorption Hysteresis Several theories have been formulated to explain the phenomenon of hysteresis, and to date, no theory has given a complete insight into the several mechanisms and no quantitative prediction of hysteresis is available in the literature45. The interpretations proposed for sorption hysteresis can be classi ed into one, or more, of the following categories25,46: ° hysteresis on porous solids: this is observed in materials such as fruits, where the theory is based on capillary condensation; ° hysteresis on non-porous solids: this is observed in materials such as protein, where the theory is based on partial chemisorption, surface impurities, or phase changes; ° hysteresis on non-rigid solids: this is observed in materials such as starchy food, where the theory is based on changes in structure, as these changes hinder penetration of the adsorbate. Several theories have been postulated to explain hysteresis on porous solids. Without exception, the explanations were established on the basis of the capillary condensation phenomena, and therefore, interpretation of hysteresis can be realized in terms of the Kelvin equation40. Kapsalis42 reviewed the theories, and accordingly, established the following classi cation: ° incomplete wetting theory: suggests a variation in the contact angles between the solid and liquid during adsorption and desorption; ° ink bottle theory: explains hysteresis on the basis of the characteristic sorbent structure, i.e. large-diameter pores with narrow passages, simulated by an ‘ink bottle’; ° open-pore theory: extends the ink-bottle theory to include consideration of multi-layer adsorption and, hence, a variation in the pore menisci shape. It has been realized that a capillary condensation mechanism alone is not capable of explaining the presence of hysteresis in some food materials (ginger, coriander, cooked chicken and raw chicken), this is due to the fact that the hysteresis loop extends to low water activities; in
AL-MUHTASEB et al.
this region the capillary condensation mechanism is unlikely to operate47. Iglesias and Chirife48 recognized that it is not possible to give a single explanation of the hysteresis phenomena in foods; this is due to the fact that food is a complex combination of various constituents, which can, not only sorb water independently but also, interact amongst themselves. In a discussion on hysteresis, Hill49 stated that the adsorption branch represents the true equilibrium up to a certain point in the isotherm, and that the desorption branch never represents the true equilibrium. It was noted that for porous materials, such as foods, the region on the adsorption branch that represents equilibrium is limited or non-existent. This is due to the wide distribution of pore sizes rendering it impossible to determine, with any certainty, where capillary effects begin to exert a signi cant in uence in vapour pressure lowering; for the smallest pores it probably occurs in the early stages of the adsorption process. Among the factors that play a role in hysteresis is the nature of the pore size distribution, and the driving force involved in changing the water activity17,50. Gregg and Sing14 disagreed with Hill, considering that the desorption branch, having the lower pressure and hence the lower chemical potential, to more closely represent to equilibrium. Kapsalis42 commented on this controversial point by stating that, in general, the type of changes encountered upon adsorption and desorption will depend on the initial state of the sorbent (amorphose versus crystalline), the transition taking place during adsorption, and the speed of desorption. Rao51 attributed the elimination of hysteresis to the elastic properties of organogels. During adsorption, the capillary pores of the adsorbent become elastic and swell. Upon desorption, the removal of water causes shrinkage and general collapse of the capillary porous structure. Alteration of structure causes subsequent elimination of hysteresis due to the absence of capillary condensation. Types of Hysteresis A variety of hysteresis loop shapes have been observed in food systems. Wolf et al.52 reported wide differences in the magnitude, shape and extent of hysteresis of dehydrated foods; the characteristics are dependent on the type of food and the temperature. Variations can be grouped into three general categories, as shown in Figure 325: ° high-sugar and high pectin foods—this phenomena is pronounced in the lower moisture content region53; ° high-protein foods—hysteresis begins at high water activity, in the capillary condensation region, and extends over the isotherm to zero water activity; ° starchy foods—a large loop is reported, with the maximum deviation between the curves occuring at about aw 0.7 (or within the capillary condensation region )54. Investigations have indicated decreased total hysteresis and limited loop span along isotherms developed at elevated temperatures48. Chinachoti and Steinberg55 found hysteresis in sugar containing starch up to a water activity of 0.6, and Bolin56 up to 0.3 in raisins (very high sugar content). Tsami et al.29 observed signi cant hysteresis below 0.5–0.6 in fruits, and suggested that the absence of hysteresis at high temperature was due to the dissolution of sugars. Wolf et al.52 found a decrease of the hysteresis magnitude with
Figure 3. Examples of sorption hysteresis in foods42.
increasing temperature for pork, apple and rice. A similar behaviour was found by Benson and Richardson57 for ethyl alcohol sorption onto egg albumin. Although McLaughlin and Magee39 and McMinn and Magee40 found a decrease in the total hysteresis with increasing temperature for potato, Wang and Brennan37 observed an increase in the total hysteresis with increasing temperature (for potato). MATHEMATICAL DESCRIPTION OF MOISTURE SORPTION ISOTHERMS Although several mathematical models exist to describe water sorption isotherms of food materials2,58, no one equation gives accurate results throughout the whole range of water activities, and for all types of foods59. Labuza50 noted that no sorption isotherm model could t data over the entire range of relative humidity because water is associated with the food matrix by different mechanisms in different water activity regions. Of the large number of models available in the literature60, some of those more commonly used are discussed below. The Brunauer-Emmett-Teller (BET) Equation The Brunauer, Emmett and Teller (BET) sorption equation, formulated in 1938, represents a fundamental milestone in the interpretation of multilayer sorption isotherms, particularly Type II and III61; it provides an estimation of the monolayer value of moisture adsorbed on the surface. The monolayer moisture content of many foods has been Trans IChemE, Vol 80, Part C, June 2002
MOISTURE SORPTION ISOTHERM CHARACTERISTICS reported to correspond with the physical and chemical stability of dehydrated foods47,62. However, in almost all cases the so-called BET plots are only linear over the lower relative pressure region (aw) of the sorbate (0.05 < aw < 0.35). The theory behind the BET equation has been faulted on many grounds, including the assumptions that: (1) the rate of condensation on the rst layer is equal to the rate of evaporation from the second layer; (2) the binding energy of all of the adsorbate on the rst layer is equal; (3) the binding energy of the other layers is equal to those of the pure adsorbate. However, the equation has been useful in de ning an optimum moisture content for drying and storage stability of foods, and in the estimation of the surface area of a food19. The BET equation is generally expressed in the form: M Caw ? M0 …1 ? aw ?…1 ? aw ? Caw ? …2?
to the logarithm of the difference between the aw of the sample and pure water. The Smith model can be written as: where M is the moisture content (kg=kg dry solid), A the quantity of water in the rst sorbed fraction, and B the quantity of water in the multilayer moisture fraction. Henderson Equation One of the most widely used models relating water activity to the amount of water sorbed is the Henderson equation67. This can be written as: ? ?1=B ln…1 ? aw ? M? …5? ?A where M is the moisture content (kg=kg dry solid), A and B are constants. A linearized plot of ln[? ln(1 7 aw)] versus moisture content has been reported to give rise to three ‘localized isotherms’68,69 which do not necessarily provide any precise information on the physical state of water, as was originally thought67. Oswin Equation Oswin developed an empirical model which is a series expansion for sigmoid shaped curves, and can be written as: ? ?B aw M?A …6? 1 ? aw
M ? A ? B log…1 ? aw ?
where M is the moisture content (kg=kg dry solid), M0 is monolayer moisture content (kg=kg dry solid), aw is the water activity, and C is a constant related to the net heat of sorption. The estimation of the constants is based on linearization of equation (2). In their study on the reliability of the methods used to evaluate the constants, Iglesias et al.63 proposed that a weighted least squares analysis is necessary and should be applied when the linear BET plot is studied. Halsey Equation The following equation, developed by Halsey64, provides an expression for condensation of multilayers at a relatively large distance from the surface: aw ? exp…?A=RT yr ? …3?
where A and r are constants, y ? M=M0, R is the universal gas constant (8.314 kJ mol? 1 K? 1), and T is the absolute temperature (K). Halsey assumed that the potential energy of a molecule varies as the inverse rth power of its distance from the surface. He also stated that the magnitude of the parameter r characterizes the type of interaction between the vapour and the solid. This equation was shown by Halsey64 to be a good representation of adsorption data that conform to Type I, II, or IIII isotherms19. Iglesias et al.58 and Iglesias and Chirife65 reported that the Halsey equation could be used to describe 220 experimental sorption isotherms of 69 different foods in the range of 0.1 < aw < 0.8. Smith Equation Smith developed an empirical model to describe the nal curved portion of the water sorption isotherm of a high molecular weight bio-polymer. He theorized that there are two fractions of water sorbed onto a dry surface; the rst exhibits a higher than normal heat of condensation and would be expected to follow the Langmuir model. Smith based his model on the second fraction, which can form only after the rst fraction has been sorbed. He considered the second fraction to consist of multilayers of condensed water molecules, which effectively prevent any possible evaporation of the initial layer. He theorized that the moisture content in the second fraction was proportional Trans IChemE, Vol 80, Part C, June 2002
where M is the moisture content (kg=kg dry solid), A and B are constants. Boquet et al.71 considered the Oswin equation to be the best one for describing the isotherms of starchy food, and a reasonably good t for meat and vegetables. This equation was also used by Labuza et al.72 to relate the moisture contents of non-fat dry milk up to aw ? 0.5. Guggenheim-Anderson-de Boer (GAB) Equation The three parameters GAB equation, derived independently by Guggenheim73, Anderson74, and de Boer75 is a semi-theoretical, multimolecular, localized, homogeneous adsorption model. It has been suggested to be the most versatile sorption model available in the literature and has been adopted by a group of West European food researchers60,76. It can be written as: M? M0 CKaw …1 ? Kaw ?…1 ? Kaw ? CKaw ? …7?
where M is the moisture content (kg=kg dry solid), M0 is the monolayer moisture content; C and K are constants related to the energies of interaction between the rst and further molecules at the individual sorption sites. Theoretically they are related to the sorption enthalpies60: ? ? H ? Hn C ? c0 exp m …8? RT ? ? H1 ? Hn K ? k0 exp …9? RT where c0 and k0 are entropic accommodation factors; Hm, Hn and H1 are the molar sorption enthalpies of the monolayer,
AL-MUHTASEB et al. GAB model gave a good t for over 75% of the food isotherms (starchy foods, fruits, vegetables and meat products), while the Oswin model described 57% of the food isotherms. Linko et al.82 reported that the Halsey model gave a good t for the experimental isotherms of dried milk products. Starch-containing foods83 have also shown to be well described in their sorption behaviour by this equation. In their comparison between Henderson and Halsey models, Chirife and Iglesias84 found that the Henderson model was less versatile than the Halsey model. ISOSTERIC HEAT OF SORPTION Knowledge of the differential heat of sorption is of a great importance when designing equipment for dehydration processes. This is due to the fact that the heat of vaporization of sorbed water may increase to values above the heat of vaporization of pure water as food is dehydrated to low moisture levels85. A differential heat of sorption greater than the heat of vaporization, primarily indicates that the energy of interaction between the sorbate and sorption sites is greater than the energy that holds the sorbate molecules together in the liquid state. Consequently, the level of moisture content at which the differential heat of sorption approaches the heat of vaporization of pure water is often taken as indicative of the amount of ‘bound’ water existing in the food86. Two methods are available for measurement of the differential heat of sorption. The rst is direct calorimetric measurement of the heat evolved, and the second is application of the Clausius-Clayperon equation on the isosteric equilibrium pressures at different temperatures (the ‘isosteric’ heat of sorption). Sorption calorimetry is dif cult because of the technique needed for precise measurement of the small quantities of heat evolved. For this reason, calorimetrical measured heats of sorption are much less common than those calculated from the sorption isotherm, however, they offer a higher degree of accuracy when determined with care19. The net isosteric heat (qst) is de ned as the total heat of sorption in the food minus the heat of vaporizationof water, at the system temperature29. Conventionally , qst is a positive quantity when heat is evolved during adsorption, and negative when heat is absorbed during desorption. The heat of adsorption is a measure of the energy released on sorption,
multilayers and bulk liquid, respectively (kJ mol? 1). The GAB model represents a re ned extension of the BET theory, postulating that the state of the sorbate molecules in the second and higher layers is equal, but different from that in the liquid-like state. This assumption introduces an additional degree of freedom (an additional constant, K) by which the GAB model gains its greater versatility. Incorporation of the parameter K, however, assumes that multilayer molecules have interactions with the sorbent that range in energy levels somewhere between those of the monolayer molecules and the bulk liquid. If K is less than unity, lower sorption than that demanded by the BET model is predicted; this allows the GAB isotherm to be successful up to high water activities (i.e. aw ? 0.9). In the special case where K ? 1, the GAB equation reduces to the BET equation (if K > 1, the sorption isotherm will become in nite at a value of aw less than unity, which is physically unsound)77. The major advantages of the GAB model are78: ° viable theoretical background77 since it is a further re nement of the Langmuir and BET theories of physical adsorption; ° good description of sorption behaviour of almost all foods from a water activity of zero to 0.9; ° parameters (c0, k0, Hm, Hn, and H1) have a physical meaning (as previously detailed) in terms of the sorption processes; ° describes the greater part of the temperature effect on isotherms by means of Arrhenius type equations. Table 3 provides a summary of the moisture sorption isotherms models adopted by researchers for a variety of food materials. Even though, both BET and GAB isotherm models are closely related, by postulating that the states of water molecules in the second and higher layers are of equal magnitude but different from that in the liquid state, it has been found that GAB parameters are more representative than the corresponding BET parameters79. Of the models assessed, McLauglin and Magee39 reported that the GAB model gave the best t for the sorption isotherms of potatoes. A similar nding was reported by Wang and Brennan37 for potato, Kiranoudis et al.38 for potato, carrot, tomato, green pepper and onion, and Menkov80 for lentil seeds. Kim and Bhowmik81 reported that the Hasley and GAB models gave good ts for the experimental isotherms of yoghurt. Lomauro et al.32 reported that the
Table 3. Summary of moisture sorption isotherm models used to t experimental data. Model GAB aw range 0.05–0.95
Food materials Protein , Starch , Casein, Potato starch 76, Fish90, Starchy food32, Raisins22, Raisins, Figs, and apricot110, Protein and starch food77, Potato37, Red pepper120, Macadamia nuts24, Pasta products121, Carrot, tomato, onion, and green pepper38, Yoghurt powder81, Potato39,40, Amaranth starch122, Lentil seeds80, Onion112, Pineapple107, Rice, Turkey, Chicken, Tomato, Potato starch, and Wheat starch 79, Chestnut114 Hazelnut115, Cured beef117. Protein123, Chicken48, Peanut akes62, Potato37,39, Lentil seed80, Onion112, Pineapple107, Rice, Turkey, Chicken, Tomato, Potato starch, and Wheat starch 79. Starchy food, Proteins, Meats, and Fruits84, Milk82, Potato83,37,39, Raisin16, Yoghurt powder81, Lentil seeds80, Hazelnut115, Chestnut114, Cured beef117, Cocoa beans116 Proteins123, Meats, and Fruits71, Starch food32, Potato37,39, Lentil seed80, Onion112, Hazelnut115, Chestnut114, Cured beef117 Wheat99, Corn starch124, Soy our, Beef, and Casein125,126, Pineapple107, Hazelnut115, Chestnut114, Cocoa beans116 Different food product69, Starchy food, Proteins, Meats, and Fruits84, Potato37, Lentil seeds80, Onion112, Pineapple107, Chestnut114, Cocoa beans116
BET Halsey Oswin Smith Henderson
0.05–0.35 0.05–0.8 0.05–0.9 0.3–0.9 0.05–0.8
Trans IChemE, Vol 80, Part C, June 2002
MOISTURE SORPTION ISOTHERM CHARACTERISTICS and the heat of desorption the energy requirement to break the intermolecular forces between the molecules of water vapour and the surface of adsorbent17. Thus, the heat of sorption is considered as indicative of the intermolecular attractive forces between the sorption sites and water vapour37. For the most part, the heat of desorption has been observed to present a higher magnitude than the corresponding heat of adsorption37–40,87–89. Iglesias and Chirife48 considered this to be due to structural modi cations which takes place during desorption; this modi es the over-all energy of binding of the sorbate through co-operative binding or to entrapment effects. This picture of the phenomena not only explains the difference between the adsorption and desorption heat curves, but it is also capable of explaining the difference between the moisture content of the adsorption and the desorption branch of the isotherm for a given water activity. Iglesias and Chirife87 concluded that the heats of change involved in irreversible processes are small compared with the overall energy changes, so they may be neglected in a general qualitativedescription, or in the estimation of the heat requirements for the dehydration process. On the basis of thermodynamic principles, the net isosteric heat of sorption may be determined from the equation: qst ? ?R @…ln aw ? @…1=T ? …10?
Table 4. Isoteric heat of sorption of food materials. Material Apple Apricots Beef Carrot Celery Cheese Chicken Corn Eggs Milk Onion Peppers Pineapple Potato Sugar beet Raisins Rice Squid Starch (potato) Starch (maize) Tapioca Tomato qst (kJ kg? 1) 83.34–1112 ? 55.56–277.8 356–1374 566.7–1594.4 144–325 365–780 249–2661.7 111–425.5 95.3–490.9 34–395 222.2–2111.3 722.2–1961.1 277.8–1666.8 461.1–1933.3 36.7–611.2 ? 55.5–944.5 142.3–445.1 313–778 0–373.8 ? 14.5–64.5 83.34–888.9 411.1–2383.3 Researcher
Roman et al. . Tsami et al.89. Iglesias and Chirife23. Kiranoudis et al.38. Iglesias and Chirife23. Iglesias and Chirife23. Iglesias and Chirife23. Cenkowski et al.127, Iglesias and Chirife23. Iglesias and Chirife23. Iglesias and Chirife23. Kiranoudis et al.38, Adam et al.112. Kiranoudis et al.38 and Kaymak-Ertekin and Sultanoglu41. Iglesias et al.48, Hossain et al.107. Wang and Brennan37, Kiranoudis et al.38, McLaughlin and Magee39, McMinn and Magee40. Iglesias et al.48, Iglesias and Chirife23. Saravacos et al.22, Tsami et al.89. Iglesias and Chirife23, Cenkowski et al.127. Castanon and Barral128. Iglesias and Chirife23. Iglesias and Chirife23. Soekarto and Steinberg129. Kiranoudis et al.38.
where qst is the net isosteric heat of sorption at constant moisture content (kJ mol? 1 water). This relationship was derived from the ClausiusClayperon equation, applied to the system and pure water with the following assumptions87–88: (1) the heat of vaporization of pure water and excess heat of sorption do not change with temperature; (2) the moisture content of the system remains constant. Labuza et al. mentioned that these assumptions could be met for a pure system at low temperature, however, for complex systems like food, irreversible changes can occur in the binding properties of the system. The main advantage of the equation is that it gives the heat of adsorption and desorption for food materials which is necessary to estimate the heat load during the drying of food materials45. Values of isosteric heat of sorption, obtained by adopting the Clausius-Clayperon equation, have been reported in the literature for several foods, including meat products, vegetables and fruits (see Table 4). The net isosteric heat of sorption decreases considerably when the moisture content is increased. In an attempt to describe the relationship between the net isosteric heat of sorption and the moisture content, Tsami et al.29 proposed an empirical exponential correlation, which can be written as: qst ? q0 exp…?X =X0 ? …11?
these parameters have been reported in the literature for several foods (see Table 5). CONCLUSIONS Moisture content control is an inherent feature of many food-processing operations. Moisture sorption isotherms have an important role to play in the quantitative approach to the prediction of the shelf life of dried foods due to their sensitivity to moisture changes. The existence of hysteresis loops in the moisture sorption isotherms of food is indicative of a non-equilibrium state, no matter how reproducible the data. Equations for tting water sorption isotherms in foods are of special interest in many aspects of food preservation by dehydration; including the prediction of drying times and shelf life of a dried product in a packaging material. Besides this practical interest, the isotherm equation is also needed
Table 5. Characteristic parameters for equation (11) for food materials. Material Adsorption data Apricot Potato Raisin Desorption data Apricot Carrot Green pepper Onion Potato Raisin Tomato q0 X0 (kg=kg (kJ mol? 1) dry solid) 10.3 44 94.7 109 40.5 61.1 65 74.6 56 131 114.2 0.06 0.08 0.03 0.03 0.2 0.19 0.18 0.08 0.09 0.03 0.12 Researcher Tsami et al.89. McMinn and Magee40. Tsami et al.89. Tsami et al.89. Kiranoudis et al.38. Kiranoudis et al.38. Kiranoudis et al.38. Kiranoudis et al.38, McMinn and Magee40. Tsami et al.89. Kiranoudis et al.38.
where q0 is the net isosteric heat of sorption of the rst molecules of water in the food (kJ mol? 1), X is the equilibrium moisture content, (kg=kg dry solid), and X0 is the characteristic moisture content of the food material, (kg=kg dry solid). q0 provides important information on both the physiochemical interactions of water with the major food constituents and the state of water within the food system, and it is an invaluable parameter, for estimation of the energy requirements (q0, X0) during drying40. Values of Trans IChemE, Vol 80, Part C, June 2002
AL-MUHTASEB et al.
16. Rowland. S. P., 1980, Water in Polymers (American Chemical Society, Washington DC, USA). 17. Rao, M. A. and Rizvi, S. S. H., 1995, Engineering Properties of Foods (Marcel Dekker Inc, New York, USA). 18. Chinachoti, P. and Steinberg, M. P., 1984, Interaction of sucrose with starch during dehydration as shown by water sorption, J Food Sci, 49: 1604. 19. Van den Berg, C., 1991, Food-water relations: progress and integration, comments and thoughts, Water Relations in Foods, Levine, H. and Slade, L. (ed) (Plenum Press, New York, USA). pp 21–28. 20. Aguilera, J. and Stanley, D. W., 1999, Microstructural Principles of Food Processing and Engineering (Aspen Publishers Inc, USA). 21. Toledo, R. T., 1991, Fundamentals of Food Process Engineering (Chapman and Hall, New York, USA). 22. Saravacos, G. D., Tsiourvas, D. A. and Tsami, E., 1986, Effect of temperature on the water adsorption isotherms of sultana raisins, J Food Sci, 51: 381–387. 23. Iglesias, H. A. and Chirife, C., 1982, Handbook of Isotherms (Academic Press, New York, USA). 24. Palipane, K. B. and Driscoll, R. H., 1992, Moisture sorption characteristics of inshell macadamia nuts, J Food Engng, 18: 63–76. 25. Kapsalis, J. G., 1987, In uences of hysteresis and temperature on moisture sorption isotherms, Water Activity: Theory and Applications to Food, Rockland, L. B. and Beuchat, L. R. (ed) (Marcel Dekker Inc, New York, USA), pp 173–213. 26. Saravacos, G. D. and Stinch eld, R. M., 1965, Effect of temperature and pressure on the sorption of water by freeze-dried food materials, J Food Sci, 30: 779–786. 27. Audu, T. O. K., Loncin, M. and Weisser, H., 1978, Sorption isotherms of sugars, Lebensm-Wiss-Technol, 11: 31. 28. Weisser, H., Weber, J. and Loncin, M., 1982, Water vapour sorption isotherms of sugar substitutes in the temperature range 25 to 80? C, Inter Zeits Lebens Technol, 33: 89. 29. Tsami, E., Maroulis, Z. B., Morunos-Kouris, D. and Saravacos, G. D., 1990, Heat of sorption of water in dried fruits, Int J Food Sci Technol, 25: 350–359. 30. Gal, S., 1981, Techniques for obtaining complete sorption isotherms, Water Activity: In uences on Food Quality, Rockland, L. B. and Stewart, G. F. (ed) (Academic Press, New York, USA), pp 89–154. 31. Wolf, W., Spiess, W. E. L. and Jung, G., 1985, Standardization of isotherm measurements, Properties of Water in Foods, Simatos, D. and Multon, J. L. (ed) (Martinus Nijhoff, The Netherlands), pp 661–679. 32. Lomauro, C. J., Bakshi, A. S. and Labuza, T. P., 1985, Evaluation of food moisture sorption isotherm equations. Part I. Fruit, vegetable and meat products, Lebensm-Wiss-Technol, 18: 111–117. 33. Carbonell, J. V ., Pinaga, F., Yusa, V . and Pena, J. L., 1986, The dehydration of paprika with ambient and heated air and the kinetics of colour dehydration during storage, J Food Engng, 5: 179–192. 34. Aguerre, R. J., Suarez, C. and Viollaz, P. E., 1989, New BET type multilayer sorption isotherms, Part II, Lebensm-Wiss-Technol, 22: 192–198. 35. Diamante, L. M. and Murno, P. A., 1990, Water desorption isotherms of two varieties of sweet potato, Int J Food Sci Technol, 25: 140–156. 36. Timmermann, E. O. and Chirife, J., 1991, The physical state of water sorbed at high activities in starch in terms of the GAB sorption equation, J Food Engng, 13: 171–196. 37. Wang, N. and Brennan, J. G., 1991, Moisture sorption isotherm characteristics of potatoes at four temperatures, J Food Engng, 14: 269–282. 38. Kiranoudis, C. T., Tsami, E., Maroulis, Z. B. and Morunos-Kouris, D., 1993, Equilibrium moisture content and heat of desorption of some vegetables, J Food Engng, 20: 55–74. 39. McLaughlin, C. P. and Magee, T. R. A., 1998, The determination of sorption isotherm and the isosteric heats of sorption for potatoes, J Food Engng, 35: 267–280. 40. McMinn, W. A. M. and Magee, T. R. A., 1999, Studies on the effect of temperature on the moisture sorption characteristics of potatoes, J Food Proc Engng, 22: 113–128. 41. Kaymak-Ertekin, F. and Sultanoglu, M., 2001, Moisture sorption isotherm characteristics of peppers, J Food Engng, 47: 225–231. 42. Kapsalis, J. G., 1981, Moisture sorption hysteresis, Water Activity: In uences on Food Quality, Rockland, L. B. and Stewart, G. F. (ed) (Academic Press, New York, USA), pp 143–177. 43. Labuza, T. P., McNally, L., Gallagher, D., Hawkes, J. and Hurtado, F., 1972, Stability of intermediate moisture foods. 1. Lipid oxidation, J Food Sci, 37: 154–159.
for evaluating the thermodynamic functions of the water sorbed in foods. To date, no one equation gives accurate results throughout the whole range of water activities, and for all types of foods. The thermodynamic properties of foods including enthalpy and entropy of sorption are essential for the design and optimization of unit operations, and further help the understanding and interpretation of sorption mechanisms and food-water interactions. NOMENCLATURE
A aw B C c0 Hm Hn H1 DHvap K k M M0 p, pi p0 qst r R T X X0 constant water activity constant constant entropic accommodation factor molar sorption enthalpies of monolayer, kJ mol? 1 molar sorption enthalpies of multilayers, kJ mol? 1 molar sorption enthalpies of bulk liquid, kJ mol? 1 latent heat of vaporization of pure water, kJ mol? 1 constant entropic accommodation factor moisture content, kg=kg dry solid monolayer moisture content, kg=kg dry solid water vapour pressure exerted by the food material, atm vapour pressure of the pure water at the equilibrium temperature of system, atm net isosteric heat of sorption, kJ mol? 1 constant universal gas constant, 8.314 kJ mol? 1 temperature, K equilibrium moisture content, kg=kg dry solid characteristic moisture content of the food material, kg=kg dry solid
1. Labuza, T. P., 1980, The effect of water activity on reaction kinetics of food deterioration, Food Technol, April: 36–59. 2. Labuza, T. P., 1968, Sorption phenomena in foods, Food Technol, 22: 15–24. 3. Walter, H., 1924, Zeitschrift Botanic, 16: 393. 4. Scott, N. F., 1957, Water relations of food spoilage microorganism, Advances in Food Research, Vol. III (Academic Press, New York, USA). 5. Salwin, H., 1959, De ning minimum moisture contents for foods, Food Technol, 13: 594–595. 6. Rizvi, S. S. H. and Benado, A. L., 1984, Thermodynamic properties of dehydrated foods, Food Technol, 38: 83–92. 7. Valentas, K. J., Rotstein, E. and Singh, P. R., 1997, Handbook of Food Engineering Practice (CRC Press, New York, USA). 8. Karel, M., 1985, Effects of water activity and water content on mobility of food components, and their effects on phase transitions in food systems, Properties of Water in Foods, Simatos, D. and Multon, J. L. (ed) (Martinus Nijhoff, The Netherlands), pp 153–169. 9. Slade, L. and Levine, H., 1991, Beyond water activity: Recent advances based on an alternative approach to the assessment of food quality and safety, Crit Rev in Food Sci and Nutr, 30: 115–360. 10. Berlin, E., 1981, Hydration of milk proteins, Water Activity: In uences on Food Quality, Rockland, L. B. and Stewart, G. F. (ed) (Academic Press, New York, USA), pp 467–488. 11. Luck, W. A. P., 1981, Structure of water in aqueous systems, Water Activity: In uences on Food Quality, Rockland, L. B. and Stewart, G. F. (ed) (Academic Press, New York, USA), pp 407–434. 12. Labuza, T. P. and Busk, C. G., 1979, An analysis of the water binding in gels, J Food Sci, 44: 1379–1385. 13. Brunauer, S., Deming, L. S., Deming, W. E. and Troller, E., 1940, On the theory of Van der Waals adsorption of gases, J Am Chem Soc, 62: 1723–1732. 14. Gregg, S. J. and Sing, K. S. W., 1967, Adsorption Surface Area and Porosity (Academic Press, New York, USA). 15. Caurie, M., 1970, A practical approach to water sorption isotherms and the basis for the determination of optimum moisture levels of dehydrated foods, J Food Technol, 6: 85–93.
Trans IChemE, Vol 80, Part C, June 2002
MOISTURE SORPTION ISOTHERM CHARACTERISTICS
44. Labuza, T. P., Cassil, S. and Sinskey,A. J., 1972,Stabilityof intermediate moisture foods. 2. Microbiology, J Food Sci, 37: 160–166. 45. Rahman, S., 1995, Food Properties Handbook (CRC Press, Inc. New York, USA). 46. Arnell, J. C. and McDermot, H. L., 1957, Sorption hysteresis, Surface Activity, Vol. 2, Schulman, J. H. (ed) (Butterworth, London, UK). 47. Karel, M., 1973, Recent research and development in the eld of lowmoisture and intermediate-moisture foods, CRC Crit Rev Food Sci Technol, 3: 329–373. 48. Iglesias, H. A. and Chirife, C., 1976, Isosteric heat of water vapour sorption on dehydrated foods. Part II, Hysteresis and heat of sorption comparison with B.E.T. theory, Lebensm-Wiss-Technol, 9: 123–127. 49. Hill, P. E., 1949, Statistical mechanics of adsorption, V , Thermodynamics and heat of adsorption, J Chem Phys, 17: 520–535. 50. Labuza, T. P., 1975, Interpretation of sorption data in relation to the state of constituent water, Water Relations in Food, Duckworth, R. (ed) (Academic Press, New York, USA), pp 155–172. 51. Rao, K. S., 1942, Disapperance of the hysteresis loop. The role of elasticity of organogels in hysteresis in sorption. Sorption of water on some cereals, J Phys Chem, 45: 517. 52. Wolf, M., Walker, J. E. and Kapsalis, J. G., 1972, Water vapour sorption hysteresis in dehydrated foods, J Agr Food Chem, 20: 1073–1077. 53. Okos, M. R., Narsimhan, G., Singh, R. K. and Weitnauer, A. C., 1992, Food dehydration, Handbook of Food Engineering, Heldman, D. R. and Lund, D. B. (ed) (Marcel Dekker Inc, New York, USA), pp 437–562. 54. Benado, A. L. and Rizvi, S. S. H., 1985, Thermodynamic properties of water on rice as calculated from reversible and irreversible isotherms, J Food Sci, 50: 101. 55. Chinachoti, P. and Steinberg, M. P., 1986, Interaction of solutes with raw starch during desorption as shown by water retention, J Food Sci, 51: 450–452. 56. Bolin, J. R., 1980, Relation of moisture to water activity in prune and raisin, J Food Sci, 45: 1190. 57. Benson, S. W. and Richardson, R. L., 1955, A study of hysteresis in the sorption of polar gases by native and denatured proteins, J Am Chem Soc, 70: 2585. 58. Iglesias, H. A., Chirife, J. and Lombardi, J. L., 1975, An equation for correlating equilibrium moisture content in foods, Food Technol, 10: 289–294. 59. Iglesias, H. A. and Chirife, C., 1976, A model for describing the water sorption behavior of foods, J Food Sci, 41: 984–992. 60. Van den Berg, C. and Bruin, S., 1981,Water activity and its estimation in food systems, Water Activity: In uences on Food Quality, Rockland, L. B. & Stewart, G. F. (ed) (Academic Press, New York, USA), pp 147–177. 61. Timmermann, E. O., 1989, A BET-like three sorption stage isotherm, J Chem Soc Faraday Trans, 85: 1631–1645. 62. Hill, P. E. and Rizvi, S. S. H., 1982, Thermodynamic parameters and storage stability of drum dried peanut akes, Lebensm-Wiss-Technol, 15: 185–190. 63. Iglesias, H. A., Boquet, R. and Chirife, J., 1977, On the evaluation of BET constants from the BET isotherm equation, J Food Sci, 42: 1387– 1389. 64. Halsey, G., 1948, Physical adsorption on non-uniformsurfaces, J Chem Phys, 16: 931–937. 65. Iglesias, H. A. and Chirife, J., 1976, A model for describing the water sorption behaviour of foods, J Food Sci, 41: 984–992. 66. Smith, S. E., 1947, The sorption of water vapour by high polymers, J Am Chem Soc, 69: 646. 67. Henderson, S. M., 1952, A basic concept of equilibrium moisture, Agric Engng, 33: 29–32. 68. Rockland, L. B., 1969, Water activity and storage stability, Food Technol, 23: 1241–1251. 69. Iglesias, H. A. and Chirife, J., 1976, On the local isotherm concept and modes of moisture binding in food products, J Agric Food Chem, 24: 77–79. 70. Oswin, C. R., 1946, The kinetics of package life III. The Isotherm, J Chem Indust, 65: 419–421. 71. Boquet, R., Chirife, J. and Iglesias, H. A., 1978, Equations for tting water sorption isotherms of foods: II. Evaluation of various twoparameter models, J Food Technol, 13: 319–327. 72. Labuza, T. P., Mizrahi, S. and Karel, M., 1972, Mathematical models for optimization of exible lm packaging of foods for storage, Trans ASAE, 15: 150–155. 73. Guggenheim, E. A., 1966, Application of Statistical Mechanics (Clarendon Press, Oxford, UK).
74. Anderson, R. B., 1946, Modi cation of the B.E.Tequation, J Am Chem Soc, 68: 686–691. 75. de Boer, J. H., 1953, The Dynamical Character of Adsorption (Clarendon Press, Oxford, UK). 76. Bizot, H., 1983, Using the ‘GAB’ model to construct sorption isotherms, Physical Properties of Food, Jowitt et al. (ed) (Applied Science, New York, USA), pp 43–54. 77. Chirife, J., Timmermann, O., Iglesias, H. A. and Boquet, R., 1992, Some features of the parameter K of the GAB equation as applied to sorption isotherms of selected food materials, J Food Engng, 15: 75–82. 78. Van den Berg, C., 1984, Description of water activity of foods for engineering purposes by means of the GAB model of sorption, Engineering and Food, Vol. 1, McKenna, B. M. (ed) (Elsevier Applied Science, New York, USA), pp 311–321. 79. Timmermann, O., Chirife, J. and Iglesias, H. A., 2001, Water sorption isotherms of foods and foodstuffs: BET or GAB parameters? J Food Engng, 48: 19–31. 80. Menkov, N. D., 2000, Moisture sorption isotherms of lentil seeds at several temperatures, J Food Engng, 44: 205–211. 81. Kim, S. S. and Bhowmik, S. R., 1994, Moisture sorption isotherms of concentrated yoghurt and microwave dried yoghurt powder, J Food Engng, 21: 157–176. 82. Linko, P., Pollari, T., Harju, M. and Heikonen, M., 1981, Water sorption properties and the effect of moisture on structure of dried milk products, Lebensm-Wiss-Technol, 15: 26–30. 83. Crapiste, G. H. and Rotstein, E., 1982, Prediction of sorptional equilibrium data for starch-containing foodstuff, J Food Sci, 47: 1501–1507. 84. Chirife, J. and Iglesias, H. A., 1978, Equations for tting water sorption isotherms of foods: Part 1. A review, J Food Technol, 13: 159–174. 85. King, C. J., 1968, Rate of moisture sorption and desorption in porous, dried foodstuffs, Food Technol, 22: 509–514. 86. Duckworth, R. B., 1972, The properties of water around the surfaces of food colloids, Proc Inst Food Sci Technol, 5: 60–67. 87. Iglesias, H. A. and Chirife, C., 1976, Isosteric heat of water vapour sorption on dehydrated foods. Part I. Analysis of the differential heat curves, Lebensm-Wiss-Technol, 9: 119–122. 88. Rizvi, S. S. H., 1986, Thermodynamic properties of foods in dehydration, Engineering Properties of Foods, Rao, M. A. and Rizvi, S. S. H. (Marcel Dekker Inc, New York, USA), pp 223–309. 89. Tsami, E., 1991, Net isosteric heat of sorption in dried fruits, J Food Engng, 14: 327–335. 90. Labuza, T. P., Kaanane, A. and Chen, J. Y., 1985, Effect of temperature on the moisture sorption isotherms and water activity shift of two dehydrated foods, J Food Sci, 50: 385–391. 91. Heldman, D. R. and Lund, D. B., 1992, Handbook of Food Engineering (Marcel Dekker, New York, USA), pp 437–563. 92. Chen, C. S. and Clayton, J. T., 1971, The effect of temperature on sorption isotherms of biological materials, Trans ASAE, 14: 927–929. 93. Kumar, M., 1974, Water vapour adsorption on whole corn our, degermed corn our, and germ our, J Food Technol, 9: 433–444. 94. Iglesias, H. A. and Chirife, J., 1984, Technical note: Correlation of BET monolayer moisture content in foods with temperature, J Food Technol, 19: 503–506. 95. Duras, N. H. and Hiver, H. L., 1993, Adsorption of water on cereal bread type dietary bers, J Food Engng, 20: 17–43. 96. Mazza, G., 1982, Moisture sorption isotherms of potato slices, J Food Technol, 17: 47–54. 97. Labuza, T. P., 1984, Practical aspects of isotherm measurment and use, Moisture Sorptions (Am Assoc Cereal Chemists, St Paul, USA). 98. Diamante, L. M. and Murno, P. A., 1990, Water desorption isotherms of two varieties of sweet potato, Int J Food Sci Technol, 25: 140–156. 99. Becker, H. A. and Sallans, H. R., 1956, A study of the desorption isotherms of wheat at 25 and 50? C, Cereal Chem, 33: 79–91. 100. Hubbard, J. E., Earle, F. R. and Senti, F. R., 1957, Moisture relations in wheat and corn, Cereal Chem, 34: 422–433. 101. Bushuk, W. and Winkler, C. A., 1957, Sorption of water vapour on wheat our, starch and gluten, Cereal Chem, 34: 73–85. 102. Taylor, A. A., 1961, Determination of moisture equilibria in dehydrated foods, Food Technol, 15: 536–540. 103. Fish, B. P., 1958, Diffusion and thermodynamics of water in potato starch gel, Proc 1958 Conf on Fund Aspects of Dehydration of Foodstuffs, Soc Chem Ind, pp 24–36. 104. McMinn, W. A. M., 1996, Transport and Thermophysical Property Variations During the Convective Drying of Starch Materials, Doctoral thesis (Queen’s University Belfast, UK).
Trans IChemE, Vol 80, Part C, June 2002
AL-MUHTASEB et al.
120. Kim, H. K., Song, Y., Yam, K. L., 1991, Water sorption characteristic of dried red peppers, Int J Food Sci Technol, 29: 339–345. 121. Lagoudaki, M., Demertzis, P. G. and Kontominas, M. G., 1993, Moisture adsorption behaviour of pasta products, Lebensm-WissTechnol, 26: 512–516. 122. Calzetta Resio, A., Aguerre, R. J. and Suarez, C., 1999, Analysis of the sorptional characteristics of amaranth starch, J Food Engng, 42: 51–57. 123. McLaren, A. D. and Rowen, J. W., 1951, Water sorption by polymers and proteins, J Polymer Sci, 7: 289–324. 124. Lang, K. W., 1978, Application of a Mass Balance to Predict Water Binding by Formulated Foods. M.S. Thesis, University of Illinois, Urbana-Champaign, IL. 125. Lang, K. W. and Steinberg, M. P., 1981, Predicting water activity from 0.3 to 0.95 of a multicomponent food formulation, J Food Sci, 46: 670–672. 126. Lang, K. W. and Steinberg, M. P., 1981, Linearization of the water sorption isotherm for homogeneous ingredients over aw 0.3–0.95, J Food Sci, 46: 1450–1452. 127. Cenkowski, S., Jaya, D. S. and Dao, D., 1992, Latent heat of vaporization for selected foods and crops, Can Agric Engng, 34: 281. 128. Castanon, C. A. and Barral, A. O., 1988, Sorption isotherms of raw muscle, Food Sci Technol, 21: 212–215. 129. Soekarto, S. T. and Steinberg, M. P., 1981, Determination of binding energy for the three fractions of bound water, Water Activity: In uences on Food Quality, Rockland, L. B. and Stewart, G. F. (eds) (Academic Press, New York, USA), pp 265–279.
105. Wolf, W., Spiess, W. E. L. and Jung, G., 1973, DieWasserdampfsorptionsisothermen einiger in der literature bislangwening berucksichtiger lebensmittel, Lebensm-Wiss-Technol, 6: 94–98. 106. Berlin, E., Kliman, P. G. and Pallansch, M. J., 1970, Changes in state of water in proteinaceous systems, J Colloid Inter Sci, 34: 488–494. 107. Hossain, M. D., Bala, B. K., Hossain, M. A. and Mondol, M. R. A., 2001, Sorption isotherms and heat of sorption of pineapple, J Food Engng, 48: 103–107. 108. Roman, G. N., Rotstein, E. and Urbician, M. J., 1979, Kinetics of water vapour desorption from apples, J Food Sci, 44: 193–197. 109. Roman, G. N., Urbician, M. J. and Rotstein, E., 1982, Moisture equilibria in apples at several temperatures: Experimental data and theoretical considerations, J Food Sci, 47: 1484–1488. 110. Maroulis, Z. B., Tsami, E., Marinos-Kouris, D. and Saravacos, G. D., 1988, Application of the GAB model to the moisture sorption isotherms for dried fruits, J Food Engng, 7: 63–78. 111. Smaniego-Esguerra, C. M., Boag, I. F. and Roberston, G. L., 1991, Comparison of regression methods for tting the GAB model to the moisture isotherms of some dried fruit and vegetables, J Food Engng, 13: 115–133. 112. Adam, E., Muhlbauer, W., Esper, A., Wolf, W. and Spie, W., 2000, Effect of temperature on water sorption equilibrium of onion, Drying Technol, 18: 2117–2129. 113. Mizrahi, S., Labuza, T. P. and Karel, M., 1970, Feasibility of accelerated tests for browning in dehydrated cabbage, J Food Sci, 35: 799. 114. Vazques, G., Chenlo, F. and Moreira, R., 2001, Modelling of desorption isotherms of chestnut: In uence of temperature and evaluation of isosteric heats, Drying Technol, 19: 1189–1199. 115. Guzey, D., Ozdemir, M., Seyhan, F., Dogan, H. and Devres, O., 2001, Adsorption isotherms of raw and roasted hazelnuts, Drying Technol, 19: 691–699. 116. Sandoval, A. J. and Barreiro, J. A., 2002, Water sorption isotherms of non-fermented cocoa beans, J Food Engng, 51: 119–123. 117. Degado, A. E. and Da-Wen Sun, 2002, Desorption isotherms of cooked and crured beef and pork, J Food Engng, 51: 163–170. 118. Grigera, J. R. and Berendson, H. J. C., 1979, The molecular details of collagen hydration, Biopolymers, 18: 47–57. 119. Van den Berg, C., 1981, Vapour Sorption Equilibria and Other WaterStarch Interactions; A Physico Chemical Approach, Doctoral thesis (Agricultural University, Wageningen, The Netherlands).
Correspondence concerning this paper should be addressed to Professor T. R. A. Magee, School of Chemical Engineering, Queen’s University Belfast, David Keir Building, Belfast, BT9 5AG, Northern Ireland, UK. E-mail: firstname.lastname@example.org The manuscript was received 9 July 2001 and accepted for publication after revision 11 March 2002.
Trans IChemE, Vol 80, Part C, June 2002