Moisture Sorption Isotherms of Foods: Experimental Methodology, Mathematical Analysis, and Practical Applications

  • C. Caballero-Cerón
  • J. A. Guerrero-BeltránEmail author
  • H. Mújica-Paz
  • J. A. Torres
  • J. Welti-ChanesEmail author
Part of the Food Engineering Series book series (FSES)


Knowing the moisture content of a product is insufficient to predict its stability, making it necessary to also know its water activity (aw), a thermodynamic property describing the interactions between water molecules and the food matrix. Moisture sorption isotherms, i.e., the relationship between moisture content and aw at constant pressure and temperature describing the sorption process of water molecules into a specific material, are useful when identifying optimal food dehydration and storage conditions. Moisture sorption properties affect physicochemical and biological phenomena such as enzymatic degradation, microbial activity, food microstructure, sensory quality deterioration, nutrient losses, and other changes limiting the shelf life of food products. Some of these phenomena are associated with water mobility, which is also related with the phase transitions from a “glass” or amorphous to a “rubbery” state. Glass transition is a second order phase transition associated with time, temperature, and moisture content. When fresh foods are dried, water removal leaves behind an amorphous material. A desirable final product moisture level is one that corresponds to a glass transition temperature (Tg) higher than the product storage temperature. Therefore, knowing Tg helps in setting the food storage and/or process conditions required to retain textural properties and to predict the shelf life of low and intermediate moisture content foods.


Moisture sorption isotherms Mathematical analysis Experimental methodology 



Gibb’s free energy value






Constant of Halsey equation


Average standard error


Water activity


Water activity values estimated with the model


Experimental water activity values


Constant of Halsey equation


Brunauer-Emmett-Teller equation


Adsorbent constant, interaction energy constant


Dynamic dew point isotherm method


Dried solids


Differential scanning calorimetry


Dynamic vapor sorption method

F, G, and H

Constants of Lewicki equation


Guggenheim, Anderson, and De Boer equation


Condensation heat of pure water (J mol-1)


Total sorption heat of the monolayer (J mol-1)


Total sorption heat of subsequent water layers (J mol-1)


Interaction energy constant

k and n

Constants of Henderson equation


Linearized portion slope of the sorption isotherm in the range of interest


Measurements of deviation between predicted data


Isosteric heat of sorption


Slope in the lineal relationship of ln aw against the inverse absolute temperature


Isosteric heat of sorption


Ideal gas constant


Ideal gas constant


Coefficient of determination


Relative humidity


Measurements of deviation between experimental data


Absolute temperature


Isokinetic temperature


Glass transition temperature


Harmonic temperature


Moisture content


Average moisture content values

Xi, calc.

Calculated moisture content values

Xi, exp

Experimental moisture content values


Monolayer moisture values



The authors acknowledge the financial support from Tecnológico de Monterrey (Research Chair Funds CAT-00200 and Nutrigenómica), and author Claudia Caballero-Cerón thanks for the financial support for her graduate studies to CONACYT and Tecnológico de Monterrey.


  1. Aguerre RJ, Suárez C, Viollaz PE (1986) Enthalpy-entropy compensation in sorption phenomena: application to the prediction of the effect of temperature on food isotherms. J Food Sci 51:1547–1549Google Scholar
  2. Akanbi CT, Adeyemi RS, Ojo A (2006) Drying characteristics and sorption isotherm of tomato slices. J Food Eng 73:157–163Google Scholar
  3. Al-Muhtaseb AH, McMinn WAM, Magee TRA (2002) Moisture sorption isotherm characteristics of food products: a review. Trans IChemE 80:118–128Google Scholar
  4. Al-Muhtaseb AH, McMinn WAM, Magee TRA (2004) Water sorption isotherms of starch powders. Part 1: Mathematical description of experimental data. J Food Eng 61:297–307Google Scholar
  5. Apostolopoulos D, Gilbert SG (1990) Water sorption of coffee solubles by frontal inverse gas chromatography: thermodynamic considerations. J Food Sci 55:475–477Google Scholar
  6. Arlabosse P, Rodier E, Ferrasse JH, Chavez S, Lecomte D (2003) Comparison between static and dynamic methods for sorption isotherm measurements. Dry Tech 21:479–497Google Scholar
  7. Arslan N, Toğrul H (2005) Modeling of water sorption isotherms of macaroni stored in a chamber under controlled humidity and thermodynamic approach. J Food Eng 69:133–145Google Scholar
  8. Ayranci E, Duman O (2005) Moisture sorption isotherms of cowpea (Vigna unguiculata L. Walp) and its protein isolate at 10, 20 and 30 °C. J Food Eng 70:83–91Google Scholar
  9. Basu S, Shivhare US, Mujumdar AS (2006) Models for sorption isotherms for foods: a review. Dry Tech 24:917–930Google Scholar
  10. Baucour P, Daudin J (2000) Development of a new method for fast measurement of water sorption isotherms in the high humidity range validation on gelatin gel. J Food Eng 44:97–107Google Scholar
  11. Belarbi A, Aymard C, Meot JM, Themelin A, Reynes M (2000) Water desorption isotherms for eleven varieties of dates. J Food Eng 43:103–107Google Scholar
  12. Bell LN, Labuza TP (2000) Moisture sorption: practical aspects of isotherm measurement and use, 2nd edn. American Association of Cereal Chemists, St. Paul, MNGoogle Scholar
  13. Benedetti PDCD, Pedro MAM, Telis-Romero J, Telis VRN (2011) Influence of encapsulating materials on water sorption isotherms of vacuum-dried persimmon pulp powder. J Food Process Preserv 35:423–431Google Scholar
  14. Beristain CI, Garcia HS, Azuara E (1996) Enthalpy-entropy compensation in food vapor adsorption. J Food Eng 30:3–4Google Scholar
  15. Bhandari BR, Adhikari B (2008) Water activity in food processing and preservation. In: Chen XD, Arun SM (eds) Drying technologies in food processing. Blackwell Publishing Ltd., West Sussex, pp 55–89Google Scholar
  16. Bourlieu C, Guillard V, Vallès-Pamiès B, Guilbert S, Gontard N (2009) Edible moisture barriers: how to assess of their potential and limits in food products shelf-life extension? Crit Rev Food Sci Nutr 49:474–499Google Scholar
  17. Brunauer S, Emmett PH, Teller E (1938) Adsorption of gases in multimolecular layers. J Am Chem Soc 60:309–319Google Scholar
  18. Carter B, Fontana A (2008) Dynamic dewpoint isotherm versus other moisture sorption isotherm methods. Application note. Decagon Devices, Pullman, WAGoogle Scholar
  19. Carter BP, Schmidt SJ (2012) Developments in glass transition determination in foods using moisture sorption isotherms. Food Chem 132:1693. doi: 10.1016/j.foodchem.2011.06.022 Google Scholar
  20. Chotyakul N, Velazquez G, Torres JA (2011) Assessment of the uncertainty in thermal food processing decisions based on microbial safety objectives. J Food Eng 102:247–256Google Scholar
  21. Chotyakul N, Pérez Lamela C, Torres JA (2012) Effect of model parameter variability on the uncertainty of refrigerated microbial shelf-life estimates. J Food Process Eng 35:829. doi: 10.1111/j.1745-4530.2010.00631.x Google Scholar
  22. Corey ME, Kerr WL, Mulligan JH, Lavelli V (2011) Phytochemical stability in dried apple and green tea functional products as related to moisture properties. LWT Food Sci Technol 44:67–74Google Scholar
  23. Duarte Goneli AL, Corrêa PC, Horta De Oliveira GH, Ferreira Gomes C, Mendes Botelho F (2010) Water sorption isotherms and thermodynamic properties of pearl millet grain. Int J Food Sci Technol 45:828–838Google Scholar
  24. Eim VS, Rosselló C, Femenia A, Simal S (2011) Moisture sorption isotherms and thermodynamic properties of carrot. Int J Food Eng 7(3):1. doi: 10.2202/1556-3758.1804 Google Scholar
  25. Escobedo-Avellaneda Z, Pérez-Pérez MC, Bárcenas-Pozos ME, Welti-Chanes J (2011a) Moisture adsorption isotherms of freeze-dried and air-dried Mexican red sauce. J Food Process Eng 34:1931–1945Google Scholar
  26. Escobedo-Avellaneda Z, Velazquez G, Torres JA, Welti-Chanes J (2011b) Inclusion of the variability of model parameters on shelf-life estimations for low and intermediate moisture vegetables. LWT Food Sci Technol 47:364–370Google Scholar
  27. Ferro-Fontan C, Chirife J, Sancho E, Iglesias HA (1982) Analysis of a model for water sorption phenomena in foods. J Food Sci 47:1590–1594Google Scholar
  28. Furmaniak S, Terzyk AP, Gołembiewski R, Gauden PA, Czepirski L (2009) Searching the most optimal model of water sorption on foodstuffs in the whole range of relative humidity. Food Res Int 42:1203–1214Google Scholar
  29. Gabas AL, Telis-Romero J, Menegalli FC (1999) Thermodynamic models for water sorption by grape skin and pulp. Dry Tech 17:962–974Google Scholar
  30. Gabas AL, Menegali FC, Telis-Romero J (2000) Water sorption enthalpy-entropy compensation based on isotherms of plum skin and pulp. J Food Sci 65:680–684Google Scholar
  31. Goula AM, Karapantsios TD, Achilias DS, Adamopoulos KG (2008) Water sorption isotherms and glass transition temperature of spray dried tomato pulp. J Food Eng 85:73–83Google Scholar
  32. Greenspan L (1977) Humidity fixed points of binary saturated aqueous solutions. J Res Natl Bur Stand 81a:89–112Google Scholar
  33. Halsey G (1948) Physical adsorption in non-uniform surfaces. J Chem Phys 16:931Google Scholar
  34. Henderson SM (1952) A basic concept of equilibrium moisture. Agric Eng 33:29–35Google Scholar
  35. Hossain MD, Bala BK, Hossain MA, Mondol MRA (2001) Sorption isotherms and heat of sorption of pineapple. J Food Eng 48:103–107Google Scholar
  36. Iglesias HA, Chirife J (1976) Equilibrium moisture contents of air dried beef. Dependence on drying temperature. Int J Food Sci Technol 11:565–573Google Scholar
  37. Iglesias HA, Chirife J (1982) Handbook of food isotherms. Academic, New York, NYGoogle Scholar
  38. Jamali A, Kouhila M, Mohamed LA, Jaouhari JT, Idimam AI, Abdenouri N (2006) Sorption isotherms of Chenopodium ambrosioides leaves at three temperatures. J Food Eng 72:77–84Google Scholar
  39. Johnson P-NT, Brennan JG (2000) Moisture sorption isotherm characteristics of plantain (Musa, AAB). J Food Eng 44:79–84Google Scholar
  40. Jouppila K, Roos YH (1997) Water sorption isotherms of freeze-dried milk products: applicability of linear and non-linear regression analysis in modeling. Int J Food Sci Technol 32:459–471Google Scholar
  41. Katekawa ME, Silva MA (2007) On the influence of glass transition on shrinkage in convective drying of fruits: a case study of banana drying. Dry Tech 25:1659–1666Google Scholar
  42. Kaya S, Kahyaoglu T (2007) Moisture sorption and thermodynamic properties of safflower petals and tarragon. J Food Eng 78:413–421Google Scholar
  43. Kaymak-Ertekin F, Gedik A (2003) Sorption isotherms and isosteric heat of sorption for grapes, apricots, apples and potatoes. LWT Food Sci Technol 37:429–438Google Scholar
  44. Kaymak-Ertekin F, Sultanoğlu M (2001) Moisture sorption isotherm characteristics of peppers. J Food Eng 47:225–231Google Scholar
  45. Kim HK, Song Y, Yam KL (1991) Water sorption characteristics of dried red peppers (Capsicum annum L.). Int J Food Sci Technol 29:339–345Google Scholar
  46. Kingsly ARP, Ileleji KE (2009) Sorption isotherm of corn distillers dried grains with solubles (DDGS) and its prediction using chemical composition. Food Chem 116:939–946Google Scholar
  47. Kühn I (1964) A new theoretical analysis of adsorption phenomena. Introductory part: the characteristic expression of the main regular types of adsorption isotherms by single simple equation. J Coll Sci 19:685–698Google Scholar
  48. Labuza TP, Altunakar B (2007) Water activity prediction and moisture sorption isotherms. In: Barbosa-Cánovas GV, Fontana AJ, Schmidt SJ, Labuza TP (eds) Water activity in foods: Fundamentals and applications. IFT/Blackwell, Ames, IA, pp 109–154Google Scholar
  49. Lemus-Mondaca R, Betoret N, Vega-Galvéz A, Lara-Aravena E (2009) Dehydration characteristics of papaya (Carica pubescens): determination of equilibrium moisture content and diffusion coefficient. J Food Process Eng 32:645–663Google Scholar
  50. Lewicki PP (1998) A three parameter equation for food moisture sorption isotherms. J Food Process Eng 21:127–144Google Scholar
  51. Lewicki PP (2000) Raoult’s law based food water sorption isotherm. J Food Eng 43:31–40Google Scholar
  52. Li QE, Schmidt SJ (2011) Use of ramping and equilibrium water vapor sorption methods to determine the critical relative humidity at which the glassy to rubbery transition occurs in polydextrose. J Food Sci 76:149–157Google Scholar
  53. Lim LT, Tang J, He J (1995) Moisture sorption characteristics of freeze dried blueberries. J Food Sci 60:810–814Google Scholar
  54. Liu P, Yu L, Wang X, Li D, Chen L, Li X (2010) Glass transition temperature of starches with different amylose/amylopectin ratios. J Cereal Sci 51:388–391Google Scholar
  55. López-Malo A, Palou E, Argaiz A (1994) Measurement of water activity of saturated salt solutions at various temperatures. In: Argaiz A, López-Malo A, Palou E, Corte P (eds) Proceeding of the session, ISOPOW Practicum II. Universidad de las Américas Puebla, Puebla, pp 113–116Google Scholar
  56. McMinn WAM, Magee TRA (2003) Thermodynamic properties of moisture sorption of potato. J Food Eng 60:157–165Google Scholar
  57. McMinn WAM, Al-Muhtaseb AH, Magee TRA (2003) Moisture sorption characteristics of starch gels. Part 1: Mathematical description of experimental data. J Food Process Eng 26:323–338Google Scholar
  58. McMinn WAM, Al-Muhtaseb AH, Magee TRA (2004) Assessment of two- and three-parameter Lewicki models for description of sorption phenomena of starch materials. J Sci Food Agric 84:1695–1700Google Scholar
  59. Medeiros ML, Ayrosa AMIB, Pitombo RNM, Lannes SCS (2006) Sorption isotherms of cocoa and cupuassu products. J Food Eng 73:402–406Google Scholar
  60. Menkov ND (2000) Moisture sorption isotherms of lentil seeds at several temperatures. J Food Eng 44:205–211Google Scholar
  61. Menkov ND, Durakova AG, Krasteva A (2004) Moisture sorption isotherms of walnut flour at several temperatures. Biotechnol Biotechnol Equip 18:201–206Google Scholar
  62. Menkov ND, Durakova AG, Krasteva A (2005) Moisture sorption isotherms of common bean flour at several temperatures. Electron J Environ Agric Food Chem 4:892–898Google Scholar
  63. Mohamed LA, Kouhila M, Jamali A, Lahsasni S, Mahrouz M (2005) Moisture sorption isotherms and heat of sorption of bitter orange leaves (Citrus aurantium). J Food Eng 67:491–498Google Scholar
  64. Moraga G, Martıínez-Navarrete N, Chiralt A (2004) Water sorption isotherms and glass transition in strawberries: influence of pretreatment. J Food Eng 62:315–321Google Scholar
  65. Moraga G, Martıínez-Navarrete N, Chiralt A (2006) Water sorption isotherms and phase transitions in kiwifruit. J Food Eng 72:147–156Google Scholar
  66. Moraga G, Talens P, Moraga MJ, Martínez-Navarrete N (2011) Implication of water activity and glass transition on the mechanical and optical properties of freeze-dried apple and banana slices. J Food Eng 106:212–219Google Scholar
  67. Moreira R, Chenlo F, Vázquez MJ, Cameán P (2005) Sorption isotherms of turnip top leaves and stems in the temperature range from 298 to 328 K. J Food Eng 71:193–199Google Scholar
  68. Moreira R, Chenlo F, Torres MD, Vallejo N (2008) Thermodynamic analysis of experimental sorption isotherms of loquat and quince fruits. J Food Eng 88:514–521Google Scholar
  69. Moreira R, Chenlo F, Torres MD (2009) Simplified algorithm for the prediction of water sorption isotherms of fruits, vegetables and legumes based upon chemical composition. J Food Eng 94(3–4):334–343Google Scholar
  70. Myhara RM, Taylor MS, Slominski BA, Al-Bulushi I (1998) Moisture sorption isotherms and chemical composition of Omani dates. J Food Eng 37:471–479Google Scholar
  71. Oswin CR (1946) The kinetics of package life. III. The isotherm. J Soc Chem Ind 65(12):419–421Google Scholar
  72. Peleg M (1993) Assessment of a semi-empirical four parameter general model for sigmoid moisture sorption isotherms. J Food Process Eng 16:21–37Google Scholar
  73. Pott I, Neidhart S, Mühlbauer W, Carle R (2005) Quality improvement of non-sulphited mango slices by drying at high temperatures. Innov Food Sci Emerg Technol 6:412–419Google Scholar
  74. Quirijns EJ, van Boxtel AJB, van Loon WKP, van Straten G (2005) Sorption isotherms, GAB parameters and isosteric heat of sorption. J Sci Food Agric 85:1805–1814Google Scholar
  75. Rahman MS (1995) Food properties handbook. CRC, Boca Raton, FLGoogle Scholar
  76. Rahman MS (2009) Food stability beyond water activity and glass transition: macro-micro region concept in the state diagram. Int J Food Prop 12:726–740Google Scholar
  77. Rahman MS, Al-Belushi RH (2006) Dynamic isopiestic method (DIM): measuring moisture sorption isotherm of freeze-dried garlic powder and other potential uses of DIM. Int J Food Prop 9:421–437Google Scholar
  78. Rahman MS, Kasapis S, Guizani N, Al-Amri OS (2003) State diagram of tuna meat: freezing curve and glass transition. J Food Eng 57:321–326Google Scholar
  79. Rockland LR (1960) Saturated salt solutions for static control of relative humidity between 5° and 40°C. Anal Chem 32:1375–1376Google Scholar
  80. Roman-Gutierrez AD, Guilbert S, Cuq B (2002) Distribution of water between wheat flour components: a dynamic water vapor adsorption study. J Cereal Sci 36:347–355Google Scholar
  81. Ruiz-López II, Herman-Lara E (2009) Statistical indices for the selection of food sorption isotherm models statistical indices for the selection of food sorption isotherm models. Dry Tech 27:726–738Google Scholar
  82. Sá MM, Sereno AM (1994) Glass transition and state diagrams for typical natural fruits and vegetables. Thermochim Acta 246:285–297Google Scholar
  83. Schmidt SJ, Lee JW (2012) Comparison between water vapor sorption isotherms obtained using the new dynamic dewpoint isotherm method and those obtained using the standard saturated salt slurry method. Int J Food Prop 15:236–248Google Scholar
  84. Sharma P, Singh RRB, Singh AK, Patel AA, Patil GR (2009) Sorption isotherms and thermodynamics of water sorption of ready-to-use Basundi mix. LWT Food Sci Technol 4:441–445Google Scholar
  85. Singh PC, Singh RK (1996) Application of GAB model for water sorption isotherms of food products. J Food Process Preserv 20:203–220Google Scholar
  86. Smith SE (1947) The sorption of water vapor by high polymers. J Am Chem Soc 69:646–651Google Scholar
  87. Spackman CCW, Schmidt SJ (2010) Characterizing the physical state and textural stability of sugar gum pastes. Food Chem 119:490–499Google Scholar
  88. Spiess WEL, Wolf W (1987) Critical evaluation of methods to determine moisture sorption isotherms. In: Rockland LR, Beuchat LR (eds) Water activity: theory and applications to food. Institute of Food Technologists, Chicago, IL, pp 215–233Google Scholar
  89. Talla A, Jannot Y, Elambo Nkeg G, Puiggali J-R (2005) Experimental determination and modeling of sorption isotherms of tropical fruits: banana, mango, and pineapple experimental determination and modeling of sorption isotherms of tropical. Dry Tech 23:1477–1498Google Scholar
  90. Timmermann EO, Chirife J, Iglesias HA (2001) Water sorption isotherms of foods and foodstuffs: BET or GAB parameters? J Food Eng 48:19–31Google Scholar
  91. Tonon RV, Baroni AF, Brabet C, Gibert O, Pallet D, Hubinger MD (2009) Water sorption and glass transition temperature of spray dried açai (Euterpe oleracea Mart.) juice. J Food Eng 94:215–221Google Scholar
  92. van den Berg C, Bruins S (1981) Water activity and its estimation in food systems: theoretical aspects. In: Rockland LR, Stewart GF (eds) Water activity: influence on food quality. Academic Press, Inc., New York, NY, pp 1–61Google Scholar
  93. Varghese KS, Ramachandrannair SV, Mishra HN (2008) Moisture sorption characteristics of curd (Indian yogurt) powder. Int J Dairy Technol 62:85–92Google Scholar
  94. Vega-Gálvez A, López J, Miranda M, DiScala K, Yagnam F, Uribe E (2009) Mathematical modeling of moisture sorption isotherms and determination of isosteric heat of blueberry variety O’Neil. Int J Food Sci Technol 44:2033–2041Google Scholar
  95. Viollaz PE, Rovedo CO (1999) Equilibrium sorption isotherms and thermodynamic properties of starch and gluten. J Food Eng 40:287–292Google Scholar
  96. Viswanathan R, Jayas DS, Hulasare RB (2003) Sorption isotherms of tomato slices and onion shreds. Biosyst Eng 86:465–472Google Scholar
  97. Welti-Chanes J, Pérez E, Guerrero-Beltrán JA, Alzamora SM, Vergara-Balderas F (2008) Applications of water activity management in the food industry. In: Barbosa-Canovas GV, Fontana AJ, Schmidt AR, Labuza TP (eds) Water: activity in foods. Blackwell Publishing Ltd., Oxford, UK, pp 341–357Google Scholar
  98. Xie F, Liu W-C, Liu P, Wang J, Halley PJ, Yu L (2010) Starch thermal transitions comparatively studied by DSC and MTDSC. Starch 62:350–357Google Scholar
  99. Yan Z, Sousa-Gallagher J, Oliveira FAR (2008a) Sorption isotherms and moisture sorption hysteresis of intermediate moisture content banana. J Food Eng 86:342–348Google Scholar
  100. Yan Z, Sousa-Gallagher MJ, Oliveira FAR (2008b) Effect of temperature and initial moisture content on sorption isotherms of banana dried by tunnel drier. Int J Food Sci Technol 43:1430–1436Google Scholar
  101. Yao W, Yu X, Lee JW, Yuan X, Schmidt SJ (2011) Measuring the deliquescence point of crystalline sucrose as a function of temperature using a new automatic isotherm generator. Int J Food Prop 14:882–893Google Scholar
  102. Yu X, Kappes SM, Bello-Pérez LA, Schmidt SJ (2008a) Investigating the moisture sorption behavior of amorphous sucrose using a dynamic humidity generating instrument. J Food Sci 73(1):25–35Google Scholar
  103. Yu X, Martin SE, Schmidt SJ (2008b) Exploring the problem of mold growth and the efficacy of various mold inhibitor methods during moisture sorption isotherm measurements. J Food Sci 73:69–81Google Scholar
  104. Yu X, Schmidt AR, Bello-Pérez LA, Schmidt SJ (2008c) Determination of the bulk moisture diffusion coefficient for corn starch using an automated water sorption instrument. J Agric Food Chem 56:50–58Google Scholar
  105. Yuan X, Carter BP, Schmidt SJ (2011) Determining the critical relative humidity at which the glassy to rubbery transition occurs in polydextrose using an automatic water vapor sorption instrument. J Food Sci 76(1):78–89Google Scholar

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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Centro de Biotecnología FEMSA, Escuela de Biotecnología y AlimentosTecnológico de MonterreyMonterreyMexico
  2. 2.Departamento de Ingeniería Química, Alimentos y AmbientalUniversidad de las Américas-PueblaCholulaMexico
  3. 3.Escuela de Ingeniería y CienciasTecnológico de MonterreyMonterreyMéxico
  4. 4.Food Process Engineering Group, Department of Food Science and TechnologyOregon State UniversityCorvallisUSA

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