A Survey of Temperature Effects on GAB Monolayer in Foods and Minimum Integral Entropies of Sorption: a Review

Vol.:(0123456789) 1 3 https://doi.org/10.1007/s11947-021-02740-w

REVIEW ARTICLE A Survey of Temperature Effects on GAB Monolayer in Foods and Minimum Integral Entropies of Sorption: a Review

Héctor A. Iglesias1 · Rosa Baeza2   · Jorge Chirife2

Received: 12 July 2021 / Accepted: 19 November 2021

© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021

Abstract Some aspects of GAB monolayer values in foods were reviewed. Literature data on the stoichiometry of water sorption by proteins and other biopolymers were re-analyzed and a good linear correlation (r2 = 0.8431) between the number of polar groups and the GAB monolayer was obtained. This helps to corroborate the hypothesis that each polar group initially adsorbs a water molecule. A survey of GAB monolayers at various temperatures in more than 70 different food products indicated that for most of them – although not all – an increase in temperature produced a decrease in the value of moisture content (g water/100 g solids) corresponding to the monolayer. However, in an appreciable number of cases, it was observed that the monolayer remained constant or increased with temperature. The relationship between the minimum integral entropy (MIE) and the GAB monolayer was studied using literature data. For 38 different food products, the regression curve (r2 = 0.9038) between the moisture content corresponding to MIE and GAB monolayer was close to the 45° diagonal, suggesting that

GAB values matched the position of minimum integral entropy. However, for a wide variety of other products, the moisture of the MIE was located above that of the monolayer.

Keywords  GAB monolayer · Water sorption · Isotherms · Minimum integral entropies · Thermodynamic properties ·

Temperature effect Introduction A fundamental characteristic of food materials which influ- ences almost every aspect of the dehydration process and the storage stability of food products is its water sorption iso- therm. Measurement and modeling of sorption isotherms of food materials has attracted numerous researchers because of their application in relation to the stability and design of food dehydration operations. Comprehensive reviews on sorption behavior of foods have been published, and several empirical and semi-empirical equations have been proposed for the correlation of the equilibrium moisture content of food materials (Basu et al., 2006; Peleg, 2020).

Early in 1979, Boquet et al. studied the fitting abilities of various three-parameter literature isotherm equations to describe 39 food isotherms of meats, milk products, proteins, starchy foods, and vegetables. The best equation was that of Hailwood and Horrobin (1946), which was developed in attempt to interpret the water sorption isotherms of proteins.

The remarkably good ability of Hailwood-Horrobin’s equa- tion to fit experimental sorption data in foods led Boquet et al. (1979) to call it a “universal” equation to describe the sorption isotherms of water in food. Later, Boquet et al. (1980) were able to demonstrate that Hailwood-Horrobin’s equation was mathematically identical to GAB equation.

In the past, the well-known BET (Brunauer, Emmet and

Teller) sorption isotherm was the model that had the greatest application to water sorption by foods and foodstuffs (Basu et al., 2006; Iglesias & Chirife, 1976; Labuza, 1968; Timmermann et  al., 2001). One well-familiar constant obtained from BET equation was the monolayer moisture content which, as noted by Timmermann et al. (2001), was found to be a reasonable guide with respect to various aspects of

* Rosa Baeza

rosa_baeza@uca.edu.ar 1 Departamento de Industrias, Facultad de Ciencias Exactas y

Naturales, Universidad de Buenos Aires, Ciudad de Buenos

Aires, 1428 Buenos Aires, Argentina 2 Facultad de Ingeniería y Ciencias Agrarias, Pontificia

Universidad Católica Argentina (UCA), CABA, Av. Alicia

Moreau de Justo 1300 (C1107AAZ), Buenos Aires, Argentina

/ Published online: 13 January 2022 Food and Bioprocess Technology (2022) 15:717–733

1 3 interest in low-moisture foods (Iglesias & Chirife, 1982,

1984; Karel, 1973). In the past two decades, the Guggen- heim, Anderson, and de Boer (GAB) isotherm equation was widely used to describe the sorption behavior of many types of foods (Van den Berg, 1981; Basu et al., 2006; Quirijins et al., 2005; Lomauro et al., 1984). Having a reasonably small number of parameters (three), the GAB equation has been found to adequately represent the experimental data in the range of water activity of most practical interest in foods. The use of the GAB equation in foods is now almost universally used by laboratories around the world (Singh &

Singh, 1996; Quirijns et al., 2005; Peleg, 2020).

The thermodynamics of the water vapor-foodstuff equilib- rium also provides valuable information into structural mat- ters and energy requirements, but also tools to analyze the consistency of the experimental data (Iglesias et al., 1976;

Nunes & Rotstein, 1991). Rizvi and Benado (1983) have reviewed the applicability of thermodynamic properties to dehydrated foods and concluded that thermodynamic cal- culations yielded important insights regarding the structure of sorbed water.

Stability is greatly influenced by the moisture sorption characteristics of the product. The thermodynamics of water sorption in dried foodstuffs has also drawn interest because some authors suggested that it helps to understand better the stability of reduced moisture foods (Beristain et al., 2002;

Bonilla et al., 2010).

The present review is concerned with some aspects related to the GAB monolayer values and specifically the fol- lowing: its physical meaning, a survey of literature data on the effect of temperature on monolayers, and a comparison of literature data on location of minimum integral entropy (MIE) and GAB monolayer values in order to verify if both coincide at the same moisture content.

Results and Discussion The Meaning of GAB Monolayer Value

As mentioned before, the Guggenheim, Anderson and de

Boer (GAB) isotherm equation has been the most widely discussed moisture sorption model in the literature to describe the sorption behavior of foods (Basu et al., 2006;

Iglesias & Chirife, 1995; Peleg, 2020; Timmermann et al.,

2001). The GAB model’s most familiar presentation is in the form of (Eq. 1): where M is the equilibrium moisture content (g water/100 g dry solids); Mo is the monolayer water content (g (1)

퐌= 퐌퐨.퐂.퐊.퐚퐰 [(1 −퐊.퐚퐰)(1 −퐊.퐚퐰+ 퐂.퐊.퐚퐰)] water/100 g dry solids), aw is the water activity, and C and

K are constants.

Several authors reported that the monolayer value obtained from BET equation is always less than that obtained from the

GAB equation (Kaymak-Ertekin & Sultanoglu, 2001; McMinn and Magee (2003); Palou et al., 1997). Timmermann et al. (2001) analyzed the dilemma about the differences between the values of BET and GAB monolayer values and demonstrated that GAB monolayer moisture content is more representative than BET’s one.

In a recent review, Peleg (2020) stated “that the notion that foods have a physical water monolayer has been widely used in the food literature, but the issue of whether there really exists a water monolayer in foods has never been adequately settled”. It has been suggested, however, that water vapor molecules interact with hydrophilic groups which in foods and biomaterials are abundant. Peleg (2020) stated that this description of the sorption phenomenon is most likely correct although he pointed out that the water monolayer existence is still unproven and perhaps should be treated as a conjecture rather than a hypothesis.

As early as 1945, Pauling advanced that the water sorp- tion monolayer of proteins can be thought in terms of the attachment of one water molecule to each polar group of the side chains of the amino acids in the protein. In his analysis,

Pauling (1945) used BET monolayer values reported by Bull (1944), and the agreement with the number of polar groups of the proteins was roughly satisfactory. Timmermann et al. (2001) noted that in Pauling’s analysis, the monolayer values were in most cases lower than the number of polar groups.

They replaced BET values by recalculated GAB monolayer values and incorporated casein, a protein not considered by

Pauling (1945), and showed that the rough agreement noted by Pauling was now certainly improved.

We used the data collected by Timmermann et al. (2001) and added a few new data on number of polar groups and

GAB monolayer values corresponding to insulin, plakaal- bumin, and wheat and potato starch (Mac Laren & Rowen,

1951; Timmermann et al., 2001). A good linear correlation between the number of polar groups and the GAB monolayer was found, as shown in Fig. 1. The obtained linear regres- sion (r2 = 0.8431) was very close to the line of 45° indicat- ing a good agreement between number of water molecules calculated to exist in a GAB monolayer, and the number of polar side chains existed. Thus, and in agreement with vari- ous works (Gely & Giner, 2000; Quirijins et al., 2005), it may be reasonable to accept that GAB monolayer value pro- vides information about the amount of water that is strongly adsorbed to active sites, suggesting that each polar group ini- tially sorbs one molecule of water. A good linear correlation between the number of polar groups and the GAB monolayer is not perhaps enough to prove a given physical model. Peleg (2020) indicated that the supposition of a critical number of

718 Food and Bioprocess Technology (2022) 15:717–733

1 3 hydrophilic sites would have to be supported by independ- ent physical evidence. However, as stated by Pérez-Alonso et al. (2006), the “value of the monolayer is of particular interest since it indicates the amount of water that is strongly adsorbed to specific sites and is considered as the optimum value at which a food is more stable. And this fact has a high practical value regardless of its physical significance”.

It is to note that the well-known difference between the water sorption behavior of amorphous and crystalline sugars (Iglesias & Chirife, 1978) offers an example that the num- ber of hydrophilic groups alone is insufficient to explain the water sorption pattern.

Effect of Temperature on GAB Monolayer Values A review of a large amount of literature data on GAB mon- olayer values was carried out, but only those articles that reported values at three or more temperatures were chosen for the present survey. In most examples shown in the lit- erature, the GAB equation has been used independently for each temperature, generating a set of values for C, Mo, and k estimated from experimental data for each temperature condition.

Table 1 summarizes data on GAB monolayer values (% dry basis) at several temperatures (mostly in the range

20–50 °C) for more than seventy food items. The raw mate- rials compiled in present work were the following: seeds (various), gums (guar gum, locust bean, tragacanth gum, xanthan gum), maltodextrin, ethnical foods (grape leather (pestil), Gulabjamun mix, Cheese-Puri mix) cassava, cassava bagasse, cassava flour, cocoa beans, fish meal, grape leather, several nuts, mushroom, potato flakes, sweet potato flakes, potatoes, Japanese noodles, loquat fruit, quince fruit, yogurt powder, blueberry powder, blueberry pomace, barley, rice flour, chestnut, cookies, corn snacks, corn, rice crackers, baobab leaf, red peppers, faba bean protein, paprika, “pin- hao” flour, mango mix powder, soy protein isolate, apples, cottonseed kernel, cottonseed protein isolate, microencapsu- lated canola oil, microencapsulated chia oil, microencapsu- lated natural colorant, microencapsulated paprika oleoresin, microencapsulated beet root juice, microencapsulated Swiss cheese bioaroma powder, fish meal, tamarind seed mucilage, chia seed mucilage, microencapsulated rosemary oil, tea, parmesan cheese, pineapple powders, mushrooms, cookies, casein, bulgur, chitosan, orange juice, cowpeas, and whey protein concentrate.

The effect of temperature on GAB monolayer values for selected products (from data in Table 1) is illustrated in

Figs. 2 through 9. The criteria used to group food products in the different figures had two objectives: (a) to illustrate that GAB monolayer not always decrease with increasing temperature (as usually stated in literature), but also may remain constant or increase, and (b) to avoid overlapping of data that would otherwise occur making the graphs very difficult to interpret.

The monolayer values shown in these figures do not pre- sent error bars because the vast majority of surveyed papers did not provide it. Only in a few cases did the authors report error bars for monolayers. For example, Alpizar-Reyes et al. (2016) indicated that relative error bands of GAB monolayers ranged from ± 4.5 to ± 5.9% for tamarind seed mucilage; Escalona-García et al. (2016) indicated values between ± 1.5% and ± 3.0% for microencapsulated chia oil in whey protein concentrate, and Torres et al. (2012) reported values of ± 1.1 to ± 3.2% for several gums (CMC, guar gum, locust bean gum, and others).

As frequently reported in literature, GAB monolayer moisture content decreases with increasing temperature for most – but not all – products surveyed. The rate of GAB monolayer change with temperature was found to be strongly dependent on the product. This can be observed by compar- ing the behavior of sweet potato flakes (Fig. 4) and paprika (Fig. 7) which show a steep decline, with others such as malting barley (Fig. 2), yogurt powder (Fig. 3), Jasmine rice crackers (Fig. 4), guar gum (Fig. 6), and Japanese noodles (Fig. 7) exhibit a more moderate decrease.

Other products show that GAB monolayer was independ- ent (or nearly) of temperature. This is the case for cookies and corn snacks (Fig. 2), tragacanth gum, locust bean, malto- dextrin DE10 (Fig. 5), microencapsulated paprika oleoresin (Fig. 6), CMC (Fig. 7), apple, pineapple powders, cottonseed protein isolate (Fig. 8), and tea and apples (Fig. 9). Finally, there are also products in which GAB monolayer increases

0 200 400 600 800 0 200 400 600 800 GAB monolayer (mol water/105g polymer r2 = 0.8431 line 45 °

Number polar groups (= mol water/105 g polymer) Fig. 1   Comparison of GAB monolayer values with number of polar groups in various proteins and potato and wheat starch. Data points correspond to collagen, gelatin, seroalbumin, wool, lactoblob. crist., idem freeze dried, egg albumin coagulated, egg albumin freeze dried, egg albumin not f. dried, c-zein, b-zein, salmin, casein, insulin, plakalbumin, wheat starch, potato starch. (from Timmermann et al.,

2001; McLaren & Rowen, 1951) 719 Food and Bioprocess Technology (2022) 15:717–733

1 3 Table 1   Literature data on GAB monolayer values in foods and foodstuffs at various temperatures

Product Composition/ description Adsorption/ desorption

Temperature, °C GAB, monolayer, % dry basis Reference

Camellia oleífera seeds Shelled Adsorption 20 30 40

2.60 3.10 2.65 Xing et al. (2012) Unshelled Equil. time 15–21 days

Adsorption 20 30 40 2.91 2.97 2.73 Gum Arabic Adsorption

25 35 40 8.11 9.97 11.0 Pérez-Alonso et al. (2006)

Mezquite gum (1) Adsorption 25 35 40 8.35 7.32 5.72

Maltodextrin, DE10 Adsorption 25 35 40 7.35 6.99 6.96

Cassava bagasse Composition: carbo- hydrates 72.8%; fat

6.2%; ash 11.6%; protein 9.4% Equil. time 28 days Adsorption

20 30 40 50 55 65 70 75 80 5.61 5.24 4.64 4.03 3.86

3.65 3.49 3.40 3.27 Carregari Polachini et al. (2016)

Cassava Adsorption 30 45 60 6.16 5.59 3.66 Koua et al. (2012)

Desorption 30 45 60 6.96 5.36 4.21 Encapsulated Swiss cheese bioaroma powder

Encapsulated in MD DE20 and Capsul Adsorption 15 25

35 45 13.76 17.8 24.0 32.0 Silva et al. (2015) Microencapsulated chia oil

Encapsulants: WPC and mesquite gum Equil. time 20–25 days

Adsorption 25 35 40 6.32 5.58 5.18 Escalona-García et al. (2016)

Cocoa beans Desorption 30 45 60 6.06 5.35 5.08 Koua et al. (2016)

Microencapsulated natural colorant Encapsulants Arabic gum: maltodextrin

Equil. time 20–25 days Adsorption 20 35 40 6.34 3.78

2.83 Pavón-García et al. (2011) Mesquite gum: malto- dextrin

Equil. time 20–25 days Adsorption 20 35 40 6.77 3.70

2.83 Microencapsulated paprika oleoresin Encapsulant: starch capsul

Equil. time 40–55 days Adsorption 25 35 45 6.50 6.40

6.39 Rascón et al. (2015) Microencapsulated beetroot juice

Encapsulant: Arabic gum Adsorption 25 35 40 4.69 4.30

3.64 Guadarrama-Lezama et al. (2014a) Fish meal From anchovy

Time to equil. 21 days Sorption 25 35 45 6.03 5.45

4.22 Vivanco and Mendieta Taboada (1998) 720 Food and Bioprocess Technology (2022) 15:717–733

1 3 Table 1   (continued) Product Composition/ description

Adsorption/ desorption Temperature, °C GAB, monolayer, % dry basis

Reference Grape leather (pestil) Grape juice and starch

Time to equil. 21 28 days Adsorption 15 25 35 10.34

13.98 8.39 Kaya and Kahyaoglu (2005) Gulabjamun mix

Mix of: milk powder, refined wheat flour, semolina, baking powder, citric acid

Sorption Time to equil.

40 days 10 25 40 3.17 3.14 3.10 Pushpadass et al. (2013)

Gums (several) CMC Time to equil. 56 days Adsorption

20 35 50 65 9.1 8.1 7.7 6.9 Torres et al. (2012) Guar gum

20 35 50 65 3.2 2.8 2.5 2.0 Locust bean 20 35 50 65

4.1 3.8 3.4 3.0 Tragacanth gum 20 35 50 65 5.0 4.9

4.5 3.8 Xanthan gum 20 35 50 65 7.7 7.4 7.0 6.1 Macadamia nuts

Adsorption 25 35 45 1.43 1.35 1.02 Domínguez et al. (2007)

Microencapsulated canola oil Encapsulant: whey protein concentrate

Adsorption 15 25 35 5.44 4.37 3.98 Bonilla et al. (2010)

Encapsulant: soy pro- tein isolate Adsorption 15 25

35 5.68 4.88 4.43 Encapsulant: mesquite gum Adsorption

15 25 35 6.61 5.56 5.04 Mesquite gum (2) Desorption

25 35 45 10.59 8.08 6.27 Beristain et al. (1999) Oyster mushroom (Pleu- rotus ostreatus)

Adsorption 25 35 45 5.2 4.5 3.9 Pascual-Pineda et al. (2020)

Parmesan cheese (grated) Sorption 16 24 32 40 48 56

64 5.71 4.92 4.86 4.52 4.36 4.76 4.13 Faria Freitas et al. (2016)

Pineapple powder (freeze dried) Added with maltodex- trin

Adsorption 20 30 40 50 6.8 6.0 6.2 6.2 Viganó et al. (2012)

721 Food and Bioprocess Technology (2022) 15:717–733

1 3 Table 1   (continued) Product Composition/ description

Adsorption/ desorption Temperature, °C GAB, monolayer, % dry basis

Reference Potato flakes Equil. time. 15 days Adsorption

15 20 25 30 4.75 4.27 3.96 3.42 Carvalho Lago and Zapata

Noreña (2015) Sweet potato flakes Equil. time 15 days

Adsorption 15 20 25 30 10.35 9.46 7.57 6.37 Carvalho Lago and Zapata

Noreña (2015) Potato Equil. time 21 days Adsorption

30 45 60 6.16 5.26 3.66 McMinn and Magee (2003) Desorption

30 45 60 6.96 5.59 4.21 Tamarind seed mucilage Equil. time 21–25 days

Adsorption 20 30 40 9.99 11.32 11.99 Alpizar-Reyes et al. (2016)

Chia seeds mucilage Equil. time 20–25 days Adsorption

25 35 40 7.93 5.33 4.05 Velázquez-Gutiérrez et al. (2014)

Loquat fruit Equil. time 56 days Sorption 20 35 50

65 16.3 13.6 12.1 9.9 Moreira et al. (2008) Quince fruit

Equilib. time 56 days Sorption 20 45 65 11.5 8.02 4.35

Moreira et al. (2008) Dehydrated yacon bagasse Protein 2.32%, lipids

0.35%; Ash 4.0%; fiber 22.2%; CH 67.4% Sorption 20

30 40 50 1.2 1.0 0.7 0.6 Carvalho Lago and Zapata Noreña (2015)

Yogurt powder, spray dried Added with sugar and maltodextrin before drying

Sorption 20 30 40 50 4.88 4.54 3.86 3.52 Seth et al. (2018)

Cheese-Puri mix Prepared from wheat flour, cheddar cheese, milk powder

Adsorption 25 35 45 2.05 2.50 2.49 Thanuja and Ravindra (2012)

Blueberry juice powder Added with whey protein isolate

Adsorption 20 35 50 10.5 8.7 8.6 Tao et al. (2017)

Blueberry fruit (mashed) Adsorption 20 35 50 9.6 7.2

6.3 Tao et al. (2017) Blueberry pomace Adsorption 20

35 50 4.5 4.2 4.1 Tao et al. (2017) Cassava flour Equil. time 19–25 days

Adsorption 25 30 35 7.31 7.28 6.32 Ayala-Aponte (2016)

Malting barley Desorption 20 30 40 50 10.18 9.29 8.51

8.13 Gely and Pagano (2012) Rice flour DVS: very short equil. time

Adsorption 5 23 45 7.9 7.3 6.6 Sandoval et al. (2011)

722 Food and Bioprocess Technology (2022) 15:717–733

1 3 Table 1   (continued) Product Composition/ description

Adsorption/ desorption Temperature, °C GAB, monolayer, % dry basis

Reference Chestnut Desorption 20 30 40 50 6.08 6.05

6.02 6.00 Vázquez et al. (2001) Cookies Adsorption

“Habaneras” 25 35 45 4.58 4.53 4.15 Palou et al. (1997)

“Ricanelas” 25 35 45 4.09 4.09 3.91 “Animalitos” 25

35 45 4.41 4.11 3.97 Corn snacks Adsorption Doritos

25 35 45 3.26 3.06 3.00 Palou et al. (1997) Tostitos

25 35 45 3.71 3.77 3.45 Jasmine rice crackers Sorption

30 45 60 5.94 5.60 5.01 Siripatrawan and Jantawat (2006)

Kuka (baobab leaf) Equil. time 15–18 days Adsorption

Desorption 34 37 45 34 37 45 4.83 3.94 3.68 9.35 8.41

5.78 Ajisegiri et al. (1994) Macadamia in-shell nuts

Equil. time 42 days Adsorption 10 20 30 40 4.14 3.85

3.60 3.37 Palipane and Driscoll (1993) Desorption 10

20 30 40 5.56 4.94 4.42 3.92 Red peppers Equil. time. > 21 days

Adsorption 30 45 60 9.96 9.95 8.6 Kaymak-Ertekin and

Sultanoglu (2001) Desorption 30 45 60 11.3 9.0 6.7

Sesame seed (whole) Equil. time 28 days Sorption 15

25 35 3.09 2.66 1.89 Kaya and Kahyaoglu (2006) Dehulled sesame seed

Equil. time 28 days Sorption 15 25 35 2.44 2.62 2.15

Dehulled-roasted sesame seed Equil. time 28 days Sorption

15 25 35 1.82 1.64 1.74 Faba bean protein Adsorption

25 35 40 5.52 4.55 4.32 Alpizar-Reyes et al. (2018)

Microencapsulated chili extract Equil. time 15–20 days

Adsorption 25 35 40 12.49 10.58 7.70 Guadarrama-Lezama et al. (2014b)

723 Food and Bioprocess Technology (2022) 15:717–733

1 3 Table 1   (continued) Product Composition/ description

Adsorption/ desorption Temperature, °C GAB, monolayer, % dry basis

Reference Paprika Adsorption 30 40 50 60 10.04 7.54

4.42 3.78 Shirkole et al. (2019) Pinhao flour (seeds of

Araucaria angustifolia) Equil. time 30–40 days Adsorption

10 20 30 40 6.60 6.04 5.77 5.17 Cladera-Olivera et al. (2011)

Rosemary oil microen- capsulated with Arabic gum Adsorption

15 25 35 45 12.42 11.52 10.29 8.42 Silva et al. (2014)

Mango mix powder (mixed with MD DE 17–20) Equil. time 28–35 days

Adsorption 20 30 40 50 5.53 4.33 3.45 2.79 Cano-Higuita et al. (2013)

Japane noodles (Udon) Desorption 20 30 40 7.88 7.38

6.83 Inazu et al. (2001) Soy Protein Isolate Adsorption

15 25 35 5.68 4.88 4.43 Bonilla et al. (2010) Whey protein Concen- trate

Adsorption 15 25 35 5.44 4.37 3.98 Mesquite gum Adsorption

15 25 35 6.61 5.56 5.04 Tea Equil. time 3–17 days Adsorption

25 35 45 4.40 4.20 4.19 Arslan and Togrul (2006) Orange juice, s. dried

Adsorption 20 30 40 50 12.6 10.9 10.2 9.8 Sormoli and Langrish (2014)

Pistacho nuts paste Equil. time 50–60 days Adsorption

20 30 40 2.23 2.18 2.43 Maskan and Gogus (1997) Green beans

20 30 40 7.09 6.51 5.31 Samaniego-Esguerra et al. (1991)

Casein acid, from buf- falo milk Adsorption 25 35 45

5.60 4.70 4.55 Sawhney et al. (2011) Bulgur Equil. time 7 days

Adsorption 20 30 40 5.03 3.69 2.55 Erbas et al. (2015)

Apples, golden delicious Equil. time 9–16 days Desorption

30 40 50 60 12.1 12.9 12.2 12.6 Mbarek and Mihoubi (2018)

Cottonseed protein isolate Adsorption 15 25 35 45 3.93

3.61 3.47 3.29 Tunc and Duman (2007) Equil. equilibrium

724 Food and Bioprocess Technology (2022) 15:717–733

1 3 with increasing temperature, such as fish meal (Fig. 3), microencapsulated cheese bioaroma, microencapsulated allspice oil (Fig. 8), and passion fruit juice microcapsules (Fig. 9).

In summary, although in most cases shown in Table 1 and also in literature (Gely & Giner, 2000; Quirijns et al., 2005;

Domínguez et al., 2007) GAB monolayers decrease with increasing temperature, it cannot be taken for granted since as shown here, GAB monolayers can also remain constant or even increase with increasing temperature.

Iglesias and Chirife (1984) analyzed the effect of tem- perature on BET monolayer values of foods and reported

BET values mostly decreased with increasing temperature.

They proposed the following empirical model to correlate

BET values with temperature: (2) In MoBET = p + a.T, where ­MoBET is BET monolayer moisture content (g water/100 g dry solid), T is temperature (°C), and p and a are constants. Iglesias and Chirife (1984) noted that the relative effect of temperature on BET values was very different for different foods. For example, BET values in some fruits (banana, pineapple, peach) decreased by about

21–35% between 25 and 40 °C, while in eggs the decrease was only 3% over the same temperature interval. In some cases, Eq. (1) failed to reproduce the behavior of BET val- ues with temperature. Iglesias and Chirife (1984) suggested that the relative variation of BET values with temperature was dependent on the physicochemical nature of the food as well as the time needed to reach sorption equilibrium. In turn, the equilibrium time dependence was determined by the experimental device utilized to construct the isotherm.

This reasoning can also be applied to the results here reviewed. Most cases shown in Table 1 were derived from

10 20 30 40 50 60 0 5 10 Temperature, °C GAB monolayer value, % d.b.

Cookies (H) Cookies (R) Cookies (A) Corn snacks (D)

Corn snacks (T) Blueberry juice powder Cassava flour

Malting barley Fig. 2   Effect of temperature on GAB monolayer value. Cookies and corn snacks: from data reported by Palou et  al. (1997); blueberry juice powder: from data reported by Tao et al. (2017); cassava flour: from data reported by Ayala-Aponte (2016); malting barley: from data reported by Gely and Pagano (2012)

0 20 40 60 0 5 10 15 20 Temperature, °C GAB monolayer value, % d.b.

Cocoa beans Fismeal Parmesan cheese Yogurt powder Loquat fruit

Quince fruit Tamarind seed mucilage Fig. 3   Effect of temperature on GAB monolayer value. Cocoa beans: from data reported by Koua et  al. (2016); fishmeal: from data reported by Vivanco and Mendieta Taboada (1998); Parmesan cheese: from data reported by Faria Freitas et al. (2016); yogurt pow- der: from data reported by Seth et al. (2018); loquat fruit: from data reported by Moreira et al. (2008); quince fruit: from data reported by

Moreira et al. (2008) Fig. 4   Effect of temperature on

GAB monolayer value. Potato: from data reported by McMinn and Magee (2003); potato flakes: from data reported by

Carvalho Lago et al. (2015); sweet potato flakes: from data reported by Carvalho Lago et al. (2015); Jasmine rice crackers: from data reported by Siripatrawan and Jantawat (2006); corn: from data reported by Gely and Giner (2000); macadamia nuts: from data by

Domínguez et al. (2007) 0 10 20 30 40 50 60 70 0 2

4 6 8 10 12 Temperature, °C GAB monolayer value, % d.b.

Potato Potato flakes Sweet potato flakes Corn Macadamia nuts

Jasmine rice crackers 725 Food and Bioprocess Technology (2022) 15:717–733

1 3 sorption isotherms determined using the known gravimetric method, in which food samples were placed into glass/plas- tic desiccators containing different saturated salt solutions.

Desiccators were then placed in constant temperature incu- bators at the desired temperature (usually between 20 and

50 °C) until the equilibrium moisture content was reached.

The equilibration time reported ranged between about 15 and 50 days. Water activity equilibration for these periods of time at relatively high temperatures may cause physical and chemical deterioration of the sample which is reflected in available sorption sites. These reactions may consist in non- enzymatic browning, denaturation, crosslinking, and interac- tion of the native or denatured proteins with oxidized lipids or carbohydrates, as well as structural modifications induced by temperature. Thus, a modification in the availability of hydrophilic sites for water binding by one or several of the above mechanisms leads to modification of GAB monolayer values when increasing temperature: a decrease, an increase, or a constancy.

Romani et al. (2015) studied the effect of storage time of packed biscuits at 35 °C for up to 92 days, and the adsorption isotherm was determined using a rapid Dynamic Dewpoint isotherm (DDI), whose equilibration times was far smaller than in the traditional static gravimetric technique. The resulting adsorption isotherms of stored biscuits, observed by means of DDI method, were affected by previous stor- age time at 35 °C. The monolayer moisture content (BET monolayer in this case) significantly increased from 1.473 to 2.080 g water/100 g db, from the beginning to the end of storage. The authors ascribed the increase of monolayer values during biscuit storage to an increase of active sites for

Fig. 5   Effect of temperature on GAB monolayer value.

C. oleifera seeds, unshelled: from data reported by Xing et al. (2012); C. oleífera seeds, shelled: from data reported by

Xing et al. (2012); gum Arabic: from data reported by Pérez- Alonso et al. (2006); mesquite gum (1): from data reported by Pérez-Alonso et al. (2006);

Maltodextrin DE10: from data reported by Pérez-Alonso et al. (2006); locust gum: from data reported by Torres et al. (2021); tragacanth gum: from data reported by Torres et al. (2012); mesquite gum (2): from data reported by Beristain et al. (1999)

10 20 30 40 50 0 2 4 6 8 10 12 14 Temperature, °C GAB monolayer, % d.b.

C. oleifera seeds, unshelled C.oleifera seeds, shelled

Gum arabic Mesquite gum (1) Maltodextrin DE10 Locust bean

Tragacanth gum Mesquite gum (2) 0 10 20 30 40 50 60

0 2 4 6 8 10 Temperature, °C GAB monolayer value, % d.b. encapsulated chia oil encapsulated paprika oleoresin encapsulated beet root juice encapsulated canola oil

CMC Guar gum Fig. 6   Effect of temperature on GAB monolayer value. Microencap- sulated chia oil: from data reported by Escalona-García et al. (2016); microencapsulated paprika oleoresin: from data reported by Rascón et al. (2015); microencapsulated beetroot juice: from data reported by

Guadarrama-Lezama et al. (2014a, b); microencapsulated canola oil: from data reported by Bonilla et al. (2010); CMC: from data reported by Torres et al. (2012); guar gum: from data reported by Torres et al. (2012)

0 10 20 30 40 50 60 0 5 10 Temperature, °C GAB monolayer value, % d.b.

Mango mix powder Japanese noodles Paprika Potato flakes

CMC Blueberry pomace Fig. 7   Effect of temperature on GAB monolayer value. Mango mix powder (mixed with MD): From data reported by Cano-Higuita et al. (2013); Japanese noodles: from data reported by Inazu et al. (2001); paprika: from data reported by Shirkole et al. (2019); potato flakes: from data reported by Carvalho-Lago et  al. (2015); CMC: from data reported by Torres et al. (2012); blueberry pomace: from data reported by Tao et al. (2017)

726 Food and Bioprocess Technology (2022) 15:717–733

1 3 water binding, as a consequence of chemical and physical changes of its main components (egg, starch, sugars, lipid, protein) induced by product ageing.

Iglesias and Chirife (1978) determined the water adsorp- tion isotherms at 30 °C of precooked beef previously dried at three different temperatures: 30 °C, 55 °C, and 70 °C, respectively. They found that the higher the drying tempera- ture, the lower was the sorption capacity of dried beef and reported that quantity of water contained in the BET mon- olayer was affected by the previous drying temperature of

30, 55, or 70 °C reducing from 5.4 to 5.1 and 4.5 (non-fat % dry basis) respectively.

Generally, the GAB model is used independently for each temperature, generating a set of values for C, Mo, and

K estimated from experimental data for each temperature.

Another alternative is the introduction of a temperature- dependent expression for the parameters, yielding a bigger amount of constants to be estimated with the whole set of isotherms (Staudt et al., 2013). Accordingly, various authors (Martín-Santos et al., 2012; Quirijns et al., 2005;

Shirkole et al., 2019) have proposed that Mo was related to temperature by using the following Arrhenius-type equation: where Mo′ is a pre-exponential factor and ΔHm is an Arrhenius- type energy factor. However, the complex experimental behavior (decrease, constancy or increase) of GAB mon- olayers with temperature (Figs. 2–10) may not be adequately predicted with Eq. (3).

Integral Entropies of Sorption and GAB Monolayer The thermodynamics of water vapor sorption in foods has attracted interest because it may provide a more thorough interpretation of the sorption phenomenon and assists in understanding the mechanism (Beristain et al., 2002).

It is well known that the stability of low moisture foods depends on great measure on its moisture sorption charac- teristics, and some researchers considered (Bonilla et al.,

2010) that the thermodynamics of water vapor sorption may also propose a scientific criterion for the prediction of the stability and storage life of dehydrated foods. In recent years, the study of water sorption thermodynamics in dehydrated products has been the subject of several studies (3)

Mo = Mo exp (ΔHm∕RT) 0 10 20 30 40 50 60 0 5 10 15

20 25 Temperature, °C GAB monolayer value, % d.b.

Microenc.allspice e. oil (1) Microenc.allspice e. oil (2)

Apple Cottonseed protein isolate Pineapple powder freeze-dried encapsulated cheese bioaroma

Fig. 8   Effect of temperature on GAB monolayer. Microencapsulated allspice essential oil (1) with WPC 66% + mesquite gum 17% + MD

17%: from data reported by Sánchez-Sáenz et  al. (2011); microen- capsulated allspice essential oil (2) with WPC 17% + mesquite gum

17% + MD 66%: from data reported by Sánchez-Saenz et al. (2011); apple (golden delicious): from data reported by Mbarek and Mihoubi (2018); cottonseed kernel: from data reported by Tunc and Dumar (2007); cottonseed protein isolate: from data reported by Tunc and

Dumar (2007); pineapple powder (freeze-dried): from data reported by Viganó et al. (2012); pineapple powder (vacuum dried): from data reported by Viganó et al. (2012)

0 10 20 30 40 50 60 70 0 5 10 15 GAB Monolayer, % d.b.

Tea Orange juice Bulgur Pistacho nuts paste Temperature, °C

Passion fruit juice microcapsules Fig. 9   Effect of temperature on GAB monolayer. Tea: from data reported by Arslan and Togrul (2006); orange juice (spray-dried): from data reported by Sormoli and Langrish (2014); safflower petal: from data reported by Kaya and Kahyaoglu (2007); apples (golden delicious): from data reported by Mbarek and Mihoubi (2018); bul- gur: from data reported by Erbas et al. (2015); pistachio nuts paste: from data reported by Maskan and Gogus (1997); passion fruit juice microcapsules: from data reported by Carrillo-Navas et al. (2011)

727 Food and Bioprocess Technology (2022) 15:717–733

1 3 (Pérez-Alonso et al., 2006; Silva et al., 2015; Escalona- García et al., 2016; Faria Freitas et al., 2016; Viganó et al.,.

2012; Xiao & Tong, 2013; Moreira et al., 2008) and many others. Various studies reported that a plot of integral entropy curve versus moisture content of various foods showed a well-defined minimum and interpreted that it is the moisture content corresponding to a monolayer, since a complete monolayer corresponds to a small number of configurations of the system (Beristain et al., 1994; Bertuzzi et al., 2003; Nunes & Rotstein, 1991; Xing et al., 2012).

Many authors indicated that the decrease in entropy is asso- ciated with the loss of mobility of the water molecules fol- lowed by an increase in entropy as the water regains mobil- ity by forming several “layers.” The integral entropy can be interpreted qualitatively in terms of the order/disorder and randomness of the adsorbed water molecules and could be assumed to coincide with the moisture content required to form a monolayer where strong bonds between the adsorb- ate and adsorbent occurred. Literature reports used the point of minimum integral entropy as a tool to predict the maximum stability point of dehydrated foods (Bonilla et al.,

2010). This will be discussed later in this review.

The thermodynamic analysis of sorption needs the knowledge of isotherms at different temperatures, and three isotherms in the range 20–40 °C or 25–45 °C have been mostly used. The analysis of the thermodynamic functions of water sorption in foods has been described in detail by many authors (Beristain et al., 1994; Kumagai et al., 1994;

Xing et al., 2012) and includes the Gibbs free energy (ΔG), where T is the absolute temperature (K); R, the universal gas constant (J ­mol−1 ­K−1); and aw is the water activity. A change on free energy as a result of water sorption is usually accom- panied by changes on both the enthalpy and the entropy. Both differential and integral enthalpies (ΔH) and entropy (ΔS) may then be calculated. Sorption enthalpy is a molar dif- ferential quantity derived from the temperature dependence of the isotherm, in contrast to the integral enthalpy which is the average energy for all the water molecules already bound at that level. The respective differential and integral entro- pies are obtained from the differential and integral enthalp- ies, respectively. Pérez-Alonso et al. (2006), Tolaba et al. (1997), Domínguez et al. (2007), Bonilla et al. (2010), and

Rodríguez-Bernal et al. (2015) – among others – described the calculation of differential and integral thermodynamic functions in water sorption in foodstuffs.

As indicated by Bonilla et al. (2010), changes in the inte- gral entropy have been calculated from. (4)

ΔG = ΔGo + R T ln(aw) (5) (Δ퐒퐢퐧퐭)퐓= −(Δ퐇퐢퐧퐭)퐓−Δ퐆) 퐓

A large number of literature studies reported a mini- mum of integral entropy versus moisture content and were reviewed to verify whether or not such minimum actually occurs close to the GAB monolayer. Only those studies that reported both the integral minimum entropy and the GAB values were chosen for this review, and about fifty eligible articles with appropriate data were used.

As mentioned above, the net integral entropy of water adsorption usually decreases gradually with increasing

0 5 10 15 0 5 10 15 GAB monolayer (aver), g/100 g d.b.

Moisture at M.I.E, g/100 g d.b. line of 45 ° r2 = 0.9089

Fig. 10   Correlation between moisture content of minimum integral entropy (MIE) and GAB monolayer. borocotó fruit, medium phase; from data of Rodríguez-Bernal et  al., 2015)–Camelia oleifera shelled (from data of Xing et al., 2012); C. oleífera unshelled; (from data of Xing et al.,

2012); Arabic gum (from data of Xing et al. (2012); paprika oleoresin encapsulated in modified starch,(from data of Rascón et al. (2015); multi- ple extract microencapsulated in Arabic gum, mesquite gum, and malto- dextrin (from data of Pavón-García et  al., 2015); Xanthan gum (from data of Torres et al., 2012); Macadam nut (from data of Domínguez et al. (2007); mesquite gum (from data of Bonilla et al., 2010); millet grains, var. Exborno, adsorption (from data of Aviara et al., 2016); millet grains var. Ex Borno, desorption (from data of Aviara et al., 2016); millet grains var. Sosat C88, adsorption (from data of Aviara et al., 2016); whey pro- tein isolate (from data of Bonilla et al., 2010); oyster mushroom, freeze- dried (from data of Pascual-Pineda et al., 2020); Parmesan cheese,grated, storage and drying (from data of Faria Freites et al., 2016); pineapple powder spray-dried, and vacuum dried (from data of Viganó et al., 2012); sweet potato flakes (from data of Carvalho-Lago et al., 2015); Yogurt freeze-dried (from data of Azuara-Nieto & Beristain, 2007); sesame seed dehulled and roasted (from data of Kaya & Kahyaoglu, 2006); cocoa beans (from data of Koua et al., 2016); mango pulp, spray dried with maltodextrin or skimmed milk, (from data of Cano-Higuita et al.,

2013); pullulan (from data of Xiao & Tong, 2013); pullulan/alginate

60:40, (from data of Xiao & Tong, 2013); pullulan/alginate 40:60, (from data of Xiao & Tong, 2013); alginate (from data of Xiao & Tong, 2013); faba bean protein (from data of Alpízar-Reyes et al. (2018); sugar beet root (from data of Iglesias et al. (1976); Yogurt, concentrated and freeze- dried conc. (from data of Azuara & Beristain, 2007); sweetened yogurt, spray-dried (from data of Seth et al. (2018); potato, desorption (data from

McMinn & Magee, 2003) 728 Food and Bioprocess Technology (2022) 15:717–733

1 3 moisture content to a minimum value around the monolayer moisture content, and then increases with further increase in moisture content. Although the value of minimum entropy may be unique, there are food products with zones in which this minimum does not vary appreciably in a defined range of moisture (Beristain & Azuara, 1990). For example, Rascón et al. (2015) indicated that for paprika oleoresin encapsulated in Capsul (modified starch), this zone begins at moisture con- tents of 5.89 g water/100 g soluble solids and ends at 6.94 g water/100 g soluble solids. Bonilla et al. (2010) reported that for whey protein, microcapsules at 25 °C moisture content at minimum integral entropy were 6.38% (dry solids), but the moisture content range where integral entropy remained more or less constant was 5.10–6.52% (dry basis).

Figure 10 shows a plot of the moisture corresponding to MIE versus the GAB monolayer, for 39 pairs of values obtained from literature. Since these values were in most cases reported at 3 temperatures (mostly 25–45 °C), a mean value was used here. It can be seen that there is a linear relationship between both parameters, and the regression line is close to the 45° diagonal (Fig. 10) with a quite acceptable correlation coefficient (r2 = 0.9089). The relationship between the mois- ture content of both variables is given by Eq. (6): which indicates that the GAB monolayers are close to the moisture of MIE zone.

Delgado et al. (2014) noted that in some cases, the ther- modynamic analysis was not in accordance with the mon- olayer obtained with the GAB model, generally the mini- mum integral entropy point being higher than the GAB monolayer. This behavior was also observed in several products examined in the present review. Thirty-one pairs of literature values (not included in those shown in Fig. 10) are plotted in Fig. 11. The regression line is now far from the 45° diagonal, and the dispersion of the data is reflected in a lower value of r2 (0.8024). The relationship between the moisture content of both variables is given by Eq. (7): which indicates that for these products, the moisture at minimum integral entropy is considerably higher than GAB monolayer.

Some authors considered the minimum integral entropy to be the point of maximum stability (Pérez-Alonso et al.,

2006). However, when the moisture at the point of the mini- mum integral entropy is considerably higher than GAB monolayer, there is uncertainty regarding the validity of minimum entropy as a point of stability. (6) [ΔSint]min = 0.8935. GAB value + 0.8523 (7) [ΔSint]min = 1.448. GAB + 1.466

0 5 10 15 0 5 10 15 20 Moisture at MIE, g/100 g d.b.

GAB monolayer, g/100 g d.b. r2 = 0.8024 Line 45 ° Fig. 11   Correlation between moisture content of minimum inte- gral entropy (MIE) and GAB monolayer. Green coffee beans (data from Beristain et  al., 1994; green coffee beans (data from Estrada

Bahen, 2019); dehydrated yacon bagasse (data from Carvalho Lago

& Zapata Norena,  2015); tarragon (data from Kaya & Kahyaoglu,

2007); Winged bean seed (data from Fasina et al., 1999); soya bean (data from Aviara et  al., 2004); Sesame seed, whole (data from

Kaya & Kahyaoglu, 2006); sesame seed dehulled (data from Kaya

& Kahyaoglu, 2006); red onion microcapsules in maltodextrin (data from Pascual-Pineda et al., 2018); millet grain flour germinated (data from Sharama et al., 2018); millet grain flour non-germinated (data from Sharama et  al., 2018); encapsulated canola oil in soy protein isolate (data from Bonilla et  al., 2010); encapsulated canola oil in mesquite gum (data from Bonilla et al, 2010); tragacanth gum (data from Torres et  al., 2012); encapsulated natural colorant in Arabic gum 50% + maltodextrin 50% (data from Pavón-García et al., 2011); encapsulated natural colorant in mesquite gum 50% + maltodextrin

50% (data from Pavón-García et  al., 2011); defatted sesame meal (data from Al-Mahasneh et  al., 2007); Arabic gum 17% + mesquite gum 66% + maltodextrin 17% (data from Pérez-Alonso et al., 2006); alfalfa pellets (data from Fasina et  al., 1997); mesquite gum (data from Pérez-Alonso et  al., 2006); microencapsulated allspice essen- tial oil in whey protein conc.-mesquite gum & maltodextrin, (data from Sánchez-Saenz et  al.,  2011); sweet potato flakes (data from

Fasina,  2006); red onion microcapsules (data from Pascual-Pineda et al., 2018); soybean TGX (from data of Aviara et al., 2004); winged bean seed (data from Fasina et al., 1999); pestil (grape leather), (data from Kaya & Kahyaogluom, 2005); beet root microcapsules in Ara- bic gum, (data from Guadarrama-Lezama et  al., 2014a, b); pineap- ple powder with maltodextrin, vibro fluidized bed (data from data of Viganó et al., 2012); canola oil microencapsulated with soy pro- tein isolate, whey protein concentrate, or mesquite gum (data from

Bonilla et al., 2010); microcapsules passion fruit juice in Arabic gum

17% + mesquite gum 66% + maltodextrin 17% (from data of Carrillo- Navas et al. (2011); microcapsules passion fruit juice in Arabic gum

17% + mesquite gum 17% + maltodextrin 66% (from data of Carrillo- Navas et al. (2011)

729 Food and Bioprocess Technology (2022) 15:717–733

1 3 At this stage, we prefer not to consider stability aspects since “stability” is the sum of many changes such as micro- bial spoilage, oxidative, enzymatic and non-enzymatic reac- tions, texture, crispness, and other physical changes (sticki- ness, collapse, crystallization) associated with the glass transition (Roos, 1995). In turn, these changes depend on food moisture content in different ways. Nevertheless, some general comments on stability need to be made.

There is no direct reason to explain why in a group of foods (Fig. 10), the moisture at the minimum integral entropy point is close to the GAB monolayer, but in another group of foods and foodstuffs (Fig. 11), the moisture at MIE is considerably higher than GAB monolayer. Admittedly, foods are heterogeneous mixtures of biopolymers, water, and solutes. Therefore, the positive or negative correlation between moisture of MIE and GAB monolayer is probably due to differences in composition and structure of food sys- tems examined. According to Viganó et al. (2012), foods with the same chemical composition and different micro- structure could show different moisture sorption behavior influencing the results. They studied the thermodynam- ics of water sorption by pineapple powders produced by vibro-fluidized drying (VFD), spray drying (SD), freeze drying (FD), or vacuum drying (VD) and reported that the moisture (and hence aw) at the minimum integral entropy depended on the drying method utilized; for example, it was 6.8% (db.) for VD and dramatically increased to 18.9% for VFD. They stated this difference is due to changes pro- duced in the product microstructure during dehydration and that powders produced by SD and VFD are more stable at changing aw because they presented minimum entropy at higher moisture contents. However, this statement should be taken with caution as it was not confirmed experimentally.

The GAB monolayer was less sensible than MIE to these microstructural changes. Comparing VFD and VD the GAB monolayer changed by about 67% while the MIE suffered a

178% change.

Sánchez-Saenz et al. (2011) studied the encapsulation of allspice oil in a mixture of whey protein concentrate, mes- quite gum, and maltodextrin and reported that conditions of maximum stability (minimum integral entropy) for micro- capsules corresponded to aw = 0.713 at 25 °C or 0.657 at

35 °C. It must be noted that aw 0.713 at 25 °C may allow growth of xerophilic fungi during storage, albeit slowly.

Similarly, Bonilla et al. (2010) encapsulated canola oil in soy protein isolate and reported that at 35 °C, the moisture condition for stability (minimum integral entropy) corre- sponded to aw = 0.71; again, this aw will also allow growth of some xerophilic fungi. Azuara-Nieto and Beristain-Guevara (2007) reported that minimum integral entropy predicted that at 30 °C, the maximum stability of powder whey protein will occur when stored at aw = 0.50, but they did not substan- tiate experimentally this statement.

More research is needed to determine whether the ther- modynamic approach helps to predict storage stability of foods and foodstuffs. Some works cited in this review experi- mentally confirmed the relationship between MIE and stabil- ity of the studied products. But in others, this was not the case, or it was not experimentally confirmed.

Conclusions Re-examination of old data on the stoichiometry of water sorption in proteins but with addition of some new values for other biopolymers confirmed there is a good correla- tion (r2 = 0.8413) between the number of water molecules calculated to exist in a GAB monolayer and the number of polar groups. This reconfirms the old Pauling’s hypothesis that each polar group initially sorbs one molecule of water.

A literature survey performed for more than 70 differ- ent food items allowed to collect GAB monolayer values at different temperatures. Although the decrease of GAB values with increasing temperature is the behavior usually reported in literature, it cannot be taken for granted since as shown here, the monolayer can also remain constant or even increase with increasing temperature.

The study of the relationship between the minimum integral entropy (MIE) and the GAB monolayer indicated that for 38 different foods, a good agreement was observed between the moisture content corresponding to the mini- mum integral entropy and the GAB monolayer. However, for other foods, the regression curve between both param- eters indicated that the moisture content corresponding to the minimum integral entropy was considerably higher than

GAB monolayer. The results of this review may help to sup- port the use of GAB monolayer value as adequate mois- ture content for many aspects of food stability. Also, it may promote additional research about the relation between the

GAB monolayer and the minimum integral entropy, as well as the real role of the latter in the prediction of stability of low-moisture foods.

Funding  Facultad de Ingeniería y Ciencias Agrarias, Pontificia Uni- versidad Católica Argentina and ANPCyT (project PICTO UCA 2017–

0071) provided financial support.

Declarations Competing Interests  The authors declare no competing interests.

References Ajisegiri, E. S., Sopade, P. A., & Abass, A. (1994). Moisture sorp- tion study on Nigerian foods: Kuka. Journal of Stored Products

Research, 30, 331–338.

730 Food and Bioprocess Technology (2022) 15:717–733

1 3 Al-Mahasneh, M. A., Rababah, T. M., & Yang, W. (2007). Moisture sorption thermodynamics of defatted sesame meal. Journal of

Food Engineering, 81, 735–740.

Alpizar-Reyes, E., Carrillo-Navas, H., Romero, R., Varela-Guerrero,

V., Alvarez-Ramırez, J., & Perez-Alonso, C. (2016). Thermo- dynamic sorption properties and glass transition temperature of tamarind seed mucilage (Tamarindus indica L.). Food and Bio- products Processing. https://​doi.​org/​10.​1016/j.​fbp.​2016.​11.​006

Alpizar-Reyes, E., Castanao, H., Carrillo-Navas, J., Alvarez-Ramírez,

R., Gallardo-Rivera, C., Pérez-Alonso, A., & Guadarrama- Lezama, Y. (2018). Thermodynamic sorption analysis and glass transition temperature of faba bean (Vicia faba L.) protein.

Journal of Food Science and Technology, 55, 935–943.

Arslan, N., & Togrul, H. (2006). The fitting of various models to water sorption isotherms of tea stored in a chamber under con- trolled temperature and humidity. Journal of Stored Products

Research, 42, 112–135.

Aviara, N. A., Ajibola, O. O., & Oni, S. A. (2004). Sorption equilib- rium and thermodynamic characteristics of soya bean. Biosys- tems Engineering, 87(2), 179–190.

Aviara, N. N., Marwan, U., & Ogbenjuwa, A. O. (2016). Effect of temperature and moisture sorption hysteresis on monolayer moisture content of selected crops determined using BET and

GAB models. Conference: NIAE Minna 2016.

Ayala-Aponte, A. A. (2016). Determination of moisture sorption iso- therms of Jasmine rice crackers using BET and GAB models.

DYNA, 83, 139–145.

Azuara-Nieto, E., & Beristain-Guevara, C. I. (2007). Thermody- namic and kinetic study of water adsorption on whey protein.

Revista Mexicana De Ingeniería Química, 6, 359–365.

Basu, S., Shivhare, U. S., & Mujumdar, A. S. (2006). Models for sorption isotherms for foods: A review. Drying Technology :

An International Journal, 24, 917–930.

Beristain, C. I., & Azuara, E. (1990). Maximum Stability in Dehy- drated Products. Ciencia (mexico), 41, 229–236.

Beristain, C. I., Diaz, R., García, H. S., & Azuara, E. (1994). Ther- modynamic behavior of green whole and decaffeinated coffee beans during adsorption. Drying Technology, 12, 1221–1233.

Beristain, C. I., Azuara, B., Garcia, H. S., & Vernon-Carter, E. J. (1999). Determination of moisture desorption enthalpy of mesquite gum with differential scanning calorimetry and ther- mogravimetric analysis. Drying Technology: An International

Journal, 17, 937–945.

Beristain, C. I., Azara, E., & Vernon-Carter, E. (2002). Thermody- namic analysis of the sorption process of mesquite gum. Chem.

Eng. Comm., 189, 115–123.

Bertuzzi, M. A., Armada, M., & Gottifredi, J. C. (2003). Thermody- namic analysis of water vapour sorption of edible starch based films. Food Sci Tech. Int., 9, 0115–0117.

Bonilla, I. E., Azuara, E., Beristain, C. I., & Vernon-Carter, E. J. (2010). Predicting suitable storage conditions for spray-dried microcapsules formed with different biopolymer matrices.

Food Hydrocolloids, 24, 633–640.

Boquet, R., Chirife, J., & Iglesias, H. A. (1979). Equations for fitting water sorption isotherms of foods. III. Evaluation of various three‐parameter model. Journal of Food Technology. https://​ doi.​org/​10.​1111/j.​1365-​2621.​1979.​tb008​96.x

Boquet, R., Chirife, J., & Iglesias, H. A. (1980). Technical note:

On the equivalence of isotherm equations. Journal of Food

Technology, 15, 345–349.

Bull, H. (1944). Adsorption of water vapor by proteins. Journal of

American Chemical Society, 66, 1499–1507.

Cano-Higuita, D. M., Villa-Vélez, H. A., Telis-Romero, J., Váquiro,

H. A., & Nicoletti-Telis, V. R. (2013). Influence of alterna- tive drying aids on water sorption of spray dried mango mix powders: A thermodynamic approach. Food and Bioproducts

Processing. https://​doi.​org/​10.​1016/j.​fbp.​2013.​10.​005

Carregari Polachini, T., Fachin, L., Betiol, L., Lopes-Filho, J. F., &

Telis-Romero, J. (2016). Water adsorption isotherms and ther- modynamic properties of cassava bagasse. Thermochimica

Acta.https://​doi.​org/​10.​1016/j.​tca.​2016.​03.​032

Carrillo-Navas, H., Gonzalez-Rodea, D. A., Cruz-Olivares, J., Barrera- Pichardo, J. F., Roman-Guerrero, A., & Perez-Alonso, C. (2011).

Storage stability and physicochemical properties of passion fruit juice microcapsules by spray-drying. Revista Mexicana de Ing- eniería Química, 10, 421–430.

Carvalho Lago, C., & Zapata Noreña, C. P. (2015). Thermodynamic analysis of sorption isotherms of dehydrated yacon (Smallanthus sonchifolius) bagasse. Food Bioscience, 12, 26–33.

Cladera-Olivera, F., Ferreira Marczak, L. M., Zapata Noreña, P., &

Pettermann, A. C. (2011). Modeling water adsorption isotherms of pinhão (araucaria angustifolia seeds) flour and thermody- namic analysis of the adsorption process. Journal of Food Pro- cess Engineering, 34, 826–843.

Delgado, R. M., Luna-Bárcenas, G., Arámbula-Villa, G., Azuara, E.,

López-Peréa, P., & Salazar, R. (2014). Effect of water activity in tortilla and its relationship on the acrylamide content after frying.

Journal of Food Engineering, 143, 1–7.

Domínguez, I. L., Azuara, E., Vernon-Carter, E. J., & Beristain, C. I. (2007). Thermodynamic analysis of the effect of water activity on the stability of macadamia nut. Journal of Food Engineering,

81, 566–571.

Erbas, M., Aykın, E., Arslan, S., & Durak, A. N. (2015). Adsorption behaviour of bulgur. Food Chemistry, 195, 87–90.

Escalona-García, L. A., Pedroza-Islas, R., Natividad, R., Rodríguez- Huezo, M. E., Carrillo-Navas, H., & Pérez-Alonso, C. (2016).

Oxidation kinetics and thermodynamic analysis of chia oil microencapsulated in a whey protein concentrate-polysaccharide matrix. Journal of Food Engineering, 175, 93–103.

Estrada Bahen, E. B. (2019). Efecto de la humedad y actividad de agua sobre la producción de ocratoxina A por hongos toxigénicos en café. Thesis to obtain the Master's degree in Biosciences. Guer- rero, México.

Faria Freitas, M. L., de Carregari Polachini, T., Souza, A. C., & Telis- Romero, J. (2016). Sorption isotherms and thermodynamic prop- erties of grated Parmesan cheese. International Journal of Food

Science and Technology, 51, 250–259.

Fasina, O. O., Sokhansanj, S., & Tyler, R. (1997). Thermodynamics of moisture sorption in alfalfa pellets. Drying Technology: An

International Journal, 15, 1553–1570. https://​doi.​org/​10.​1080/​

07373​93970​89173​07 Fasina, O. O. (2006). Thermodynamic properties of sweet potato. Jour- nal of Food Engineering, 75, 149–155.

Fasina, O. O., Ajibola, O. O., & Tyler, R. T. (1999). Thermodynamics of moisture sorption in winged bean seed and gari. Journal of

Food Process Engineering, 22, 405–418.

Gely, M. C., & Giner, S. A. (2000). Water - corn equilibrium: tempera- ture dependency of the g.a.b. model parameters and calculation of the heat of sorption. Drying technology, 18, 1449–1464.

Gely, M. C., & Pagano, A. M. (2012). Moisture desorption isotherms and isosteric heat of sorption characteristics of malting barley (hordeum distichum l.). Latin American Applied Research, 42, 237–243.

Guadarrama-Lezama, A. Y., Cruz-Olivares, J., Martínez-Vargas, S. L.,

Carrillo-Navas, H., Guerrero, R., & Pérez-Alonso, C. (2014a).

Determination of the minimum integral entropy, water sorption and glass transition temperature to establishing critical storage conditions of beetroot juice microcapsules by spray drying.

Revista Mexicana De Ingeniería Química, 8(3), 405–441.

Guadarrama-Lezama, A. Y., Jaramillo-Flores, E., Gutiérrez-López, G.

F., Pérez-Alonso, C., Dorantes-Álvarez, L., & Alamilla-Beltrán,

731 Food and Bioprocess Technology (2022) 15:717–733

1 3 L. (2014b). Effects of storage temperature and water activity on the degradation of carotenoids contained in microencapsulated chili extract. Drying Technology: An International Journal, 32,

1435–1447.

Hailwood, A. J., & Horrobin, S. (1946). Absorption of water by poly- mers: Analysis in terms of a simple model. Transactions of the

Faraday Society, 42B, 84–89.

Iglesias, H. A., & Chirife, J. (1978). Delayed crystallization of amor- phous sucrose in humidified freeze-dried model systems. Journal of Food Technology, 13, 137–142.

Iglesias, H. A., & Chirife, J. (1976). Equilibrium moisture contents of air-dried beef. Dependence on drying temperature. Journal of

Food Technology, 11, 565–573.

Iglesias, H. A., Chirife, J., & Viollaz, P. (1976). Thermodynamics of water vapour sorption by sugar beet root. Journal of Food Tech- nology, 11, 91–101.

Iglesias, H. A., & Chirife, J. (1982). Handbook of food isotherms. Aca- demic Press.

Iglesias, H. A., & Chirife, J. (1984). Technical note: Correlation of

BET monolayer moisture content in foods with temperature.

Journal of Food Technology, 19, 503–506.

Iglesias, H. A., & Chirife, J. (1995). An alternative to the GAB model for the mathematical description of moisture sorption isotherms of foods. Food Research International., 28, 317–321.

Inazu, T., Iwasaki, K., & Furuta, T. (2001). Desorption isotherms for japanese noodle (udon). Drying Technology: An International

Journal, 19, 1375–1384.

Karel, M. (1973). Recent research and development in the field of low moisture and intermediate moisture foods. CRC Critical Reviews of Food Technology, 3, 329–345.

Kaya, S., & Kahyaoglu, T. (2006). Influence of dehulling and roasting process on the thermodynamics of moisture adsorption in sesame seed. Journal of Food Engineering, 76, 139–147.

Kaya, S., & Kahyaoglu, T. (2005). Thermodynamic properties and sorption equilibrium of pestil (grape leather). Journal of Food

Engineering, 71, 200–207.

Kaya, S., & Kahyaoglu, T. (2007). Moisture sorption and thermody- namic properties of safflower petals and tarragon. Journal of

Food Engineering, 78, 413–421.

Kaymak-Ertekin, F., & Sultanoglu, M. (2001). Moisture sorption iso- therm characteristics of peppers. Journal of Food Engineering,

47, 225–231.

Koua, B. K., Magloire, P., Koffi, E., Gbaha, P., & Toure, S. (2012).

Thermodynamic analysis of sorption isotherms of cassava (Mani- hot esculenta). Journal of Food Science and Technology, 2014,

1711–1723.

Koua, B. K., Magloire, P., Koffi, E., & Gbaha, P. (2016). Moisture desorption isotherms characteristics of cocoa beans. Pakistan

Journal of Food Science, 26, 143–152.

Kumagai, H., Iwase, M., Kumagai, H., Mizuno, A., & Yano, T. (1994).

Application of solution thermodynamics to the water sorption isotherms of food materials. Bioscience, Biotechnology, and Bio- chemistry, 58(3), 475–481.

Labuza, T. P. (1968). Sorption phenomena in foods. Food Technology,

23, 15–19.

Lomauro, C. J., Bakshi, A. S., & Labuza, T. P. (1984). Evaluation of food moisture sorption isotherm equations. Part I: Fruit, vegetable and meat products. Lebensmittel-Wissenschaft Und-Technologie,

18, 111–117.

Mac Laren, A. D., & Rowen, J. W. (1951). Water sorption by polymers and proteins. Journal of Polymer Science, VII, 289–324.

Martín-Santos, J., Vioque, M., & Gómez, R. (2012). Thermodynamic properties of moisture adsorption of whole wheat flour. Calcu- lation of net isosteric heat. International Journal of Food Sci- ence and Technology. https://​doi.​org/​10.​1111/j.​1365-​2621.​2012.​

02996-x McMinn, W. A. M., & Magee, T. R. A. (2003). Thermodynamic properties of moisture sorption of potato. Journal of Food

Engineering, 60, 157–165.

Maskan, M., & Gogus, F. (1997). The Fitting of Various Models to

Water Sorption Isotherms of Pistachio Nut Paste. Journal of

Food Engineering, 33, 227–237.

Mbarek, R., & Mihoubi, D. (2018). Thermodynamic properties and water desorption isotherms of Golden Delicious apples. Heat and Mass Transfer. https://​doi.​org/​10.​1007/​s00231-​018-​2527-8

Moreira, R., Chenlo, F., Torres, M. D., & Vallejo, N. (2008). Ther- modynamic analysis of experimental sorption isotherms of loquat and quince fruits. Journal of Food Engineering, 88,

514–521.

Nunes, R. V., & Rotstein, E. (1991). Thermodynamics of the water- foodstuff equilibrium. Drying Technology: An International

Journal, 9, 113–137.

Palipane, K. B., & Driscoll, R. H. (1993). Moisture sorption character- istics of in-shell macadamia nuts. Journal of Food Engineering,

18, 63–76.

Palou, E., López-Malo, A., & Argaiz, A. (1997). Effect of temperature on the moisture sorption isotherms of some cookies and corn snacks. Journal of Food Engineering, 31, 85–93.

Pascual-Pineda, L. A., Hernández-Marañon, H., Castillo-Morales, M.,

Uzárraga-Salazar, M., Rascón-Díaz, M. P., & Flores-Andrade, E. (2020). Effect of water activity on the stability of freeze-dried oyster mushroom (Pleurotus ostreatus) poder. Drying Technol- ogy, 39(989), 1002.

Pascual-Pineda, L. A., Rascón, M. P., Quintanilla-Carvajal, M. X.,

Castillo-Morales, M., Marín, U. R., & Flores-Andrade, E. (2018).

Effect of porous structure and spreading pressure on the storage stability of red onion microcapsules produced by spray freezing into liquid cryogenic and spray drying. Journal of Food Engi- neering, 245, 65–72.

Pauling, L. (1945). The adsorption of water by proteins. Journal of the

American Chemical Society, 67, 555–557.

Pavón-García, L. M. A., Pérez-Alonso, C., Orozco-Villafuerte, J.,

Pimentel-González, D. J., Rodríguez-Huezo, M. E., & Vernon- Carter, E. J. (2011). Storage stability of the natural colourant from Justicia spicigera microencapsulated in protective colloids blends by spray-drying. International Journal of Food Science and Technology, 46, 1428–1437.

Pavón-García, L. M. A., Gallardo-Rivera, R., Roman-Guerrero, A.,

Carrillo-Navas, H., Rodríguez-Huezo, M. E., Guadarrama- Lezama, A. Y., & Perez-Alonso, C. (2015). Moisture sorption properties and storage stability conditions of a nutraceutical sys- tem microencapsulated by spray drying. Revista Mexicana De

Ingeniería Química, 8, 611–613.

Peleg, M. (2020). Models of sigmoid equilibrium moisture sorption iso- therms with and without the monolayer hypothesis. Food Engi- neering Reviews. https://​doi.​org/​10.​1007/​s12393-​019-​09207-x

Pérez-Alonso, C., Beristain, C. I., Lobato-Calleros, C., Rodríguez- Huezo, M. E., & Vernon-Carter, E. J. (2006). Thermodynamic analysis of the sorption isotherms of pure and blended carbo- hydrate polymers. Journal of Food Engineering, 77, 753–760.

Pushpadass, H. A., Emerald, F. M. E., Chaturvedi, B., & Rao, K. J. (2013). Moisture sorption behavior and thermodynamic proper- ties of gulabjamun mix heartwin. Journal of Food Processing and Preservation. https://​doi.​org/​10.​1111/​jfpp.​12199

Quirijns, E. J., van Boxtel, A. J. B., van Loon, W. K. P., & van Straten,

G. (2005). Sorption isotherms, GAB parameters and isosteric heat of sorption. Journal of the Science of Food and Agriculture,

85, 1805–1814.

Rascón, M. P., Bonilla, E., García, H. S., Salgado, M. A., González- Arnao, M. T., & Beristain, C. I. (2015). Tg and aw as criteria for the oxidative stability of spray-dried encapsulated paprika oleo- resin. European Food Research and Technology, 241, 217–225.

732 Food and Bioprocess Technology (2022) 15:717–733

1 3 Rizvi, S. S. H., & Benado, A. I. (1983). Thermodynamic analysis of drying foods. Drying Technology: An International Journal, 2,

471–502.

Rodríguez-Bernal, J. M., Flores-Andrade, E., Lizarazo-Morales, C., Bonilla,

E., Pascual-Pineda, L. A., Gutierréz-López, G., & Quintanilla- Carvajal, M. X. (2015). Moisture adsorption isotherms of the borojó fruit (Borojoa patinoi. Cuatrecasas) and gum arabic powders. Food and Bioproducts Processing, 94, 187–198.

Romani, S., Rocculi, P., Tappi, S., & Dalla Rosa, M. (2015). Mois- ture adsorption behaviour of biscuit during storage investigated by using a new Dynamic Dewpoint method. Food Chemistry. https://​doi.​org/​10.​1016/j.​foodc​hem.​2015.​06.​114

Roos, Y. (1995). Glass transitions in foods. Academic Press.

Samaniego-Esguerra, C. M., Boag, I. F., & Robertson, G. L. (1991).

Comparison of Regression Methods for Fitting the GAB Model to the Moisture Isotherms of some Dried Fruit and Vegetables.

Journal of Food Engineering, 13, 115–133.

Sánchez-Saenz, E. O., Pérez-Alonso, C., Cruz-Olivares, J., Román- Guerrero, A., Baéz-González, J. B., & Rodríguez-Huezo, M.

E. (2011). Establishing the most suitable storage conditions for microencapsulated allspice essential oil entrapped in blended biopolymers matrices. Drying Technology: An International

Journal, 29(8), 863–872.

Sandoval, A. J., Barreiro, J. A., & Muller, J. A. (2011). Determination of moisture adsorption isotherms of rice flour using a dynamic vapor sorption technique. Interciencia, 36, 848–852.

Sawhney, I. K., Sarkar, B. C., & Patil, G. R. (2011). Moisture sorption characteristics of dried acid casein from buffalo skim milk. LWT

- Food Science and Technology, 44, 502–510.

Seth, D., Dash, K. K., Mishra, H. N., & Deka, S. C. (2018). Thermody- namics of sorption isotherms and storage stability of spray dried sweetened yoghurt poder. Journal of Food Science and Technol- ogy. https://​doi.​org/​10.​1007/​s13197-​018-​3340-6

Sharama, N., Goyal, S. K., & Alam, T. (2018). Effect of Germination on the Functional and Moisture Sorption Properties of High–

Pressure-Processed Foxtail Millet Grain Flour. Food and Bio- process Technology, 11, 209–222.

Silva, E. K., Fernandes, R. V., Borges, S. V., Botrel, D. A., & Queiroz,

F. (2014). Water adsorption in rosemary essential oil microparti- cles: Kinetics, thermodynamics and storage conditions. Journal of Food Engineering. https://​doi.​org/​10.​1016/j.​jfood​eng.​2014.​

05.​003 Silva, E. K., Borges, S. V., Gomes da Costa, G. M., & Queiroz, F. (2015). Thermodynamic properties, kinetics and adsorption mechanisms of Swiss cheese bioaroma poder. Powder Technol- ogy, 272, 181–188.

Shirkole, S. S., Mujumdar, S., & Sutar, P. P. (2019). Studies on thermal stability of high-power short time microwave dried paprika (Cap- sicumannuum L.) considering the interaction of water molecules with sorption sites. Drying Technology, 39, 52–65.

Siripatrawan, U., & Jantawat, P. (2006). Determination of moisture sorption isotherms of jasmine rice crackers using BET and

GAB models. Food Science and Technology International, 12,

459–465.

Staudt, P. B., KechinskiI, C. P., Tessaro, I. C., Marczak, L. D. F.,

Soares, R. D. P., & Cardozo, N. S. M. (2013). A new method for predicting sorption isotherms at different temperatures using the BET model. Journal of Food Engineering, 114, 139–145.

Singh, P. C., & Singh, R. K. (1996). Application of GAB model for water sorption isotherms of food products. Journal of Food Pro- cessing and Preservation. https://​doi.​org/​10.​1111/j.​1745-​4549.​

1996.​tb007​43.x Sormoli, M., & Langrish, T. A. G. (2014). Moisture sorption isotherms and net isosteric heat of sorption for spray-dried pure orange juice powder. LWT - Food Science and Technology. https://​doi.​ org/​10.​1016/j.l

Tao, Y., Wu, Y., Yang, J., Jiang, N., Wang, Q., Toi Chu, D., Han, Y., &

Zhou, J. (2017). Thermodynamic sorption properties, water plas- ticizing effect and particle characteristics of blueberry powders produced from juices, fruits and pomaces. Powder Technology,

323, 208–218.

Thanuja, D., & Ravindra, M. R. (2012). Thermodynamic analysis of moisture sorption characteristics of cheese–puri mix. Journal of

Food Processing and Preservation, 38, 420–429.

Timmermann, E. O., Chirife, J., & Iglesias, H. A. (2001). Water sorp- tion isotherms of foods and foodstuffs: BET or GAB parameters?

Journal of Food Engineering, 48, 19–31.

Tolaba, M. P., Suárez, C., & Viollaz, P. (1997). Heats and entropies of sorp- tion of cereal grains: a comparison between integral and dif- ferential quantities. Drying Technology: An International Journal,

15, 137–150.

Torres, M. D., Moreira, R., Chenloa, F., & Vázquez, M. J. (2012).

Water adsorption isotherms of carboxymethyl cellulose, guar, locust bean, tragacanth and xanthan gums. Carbohydrate Poly- mers, 89, 592–598.

Tunc, S., & Duman, O. (2007). Thermodynamic properties and mois- ture adsorption isotherms of cottonseed protein isolate and dif- ferent forms of cottonseed simples. Journal of Food Engineering,

81, 133–143.

Van den Berg, C. (1981). Vapor sorption equilibria and other starch interactions: A physico-chemical approach. Doctoral Thesis.

Agricultural University.

Vázquez, G., Chenlo, F., & Moreira, R. (2001). Modelling of desorp- tion isotherms of chestnut: Influence of temperature and evalu- ation of isosteric heats. Drying Technology: An International

Journal, 19, 1189–1199.

Velázquez-Gutiérrez, S. K., Figueira, A. C., Rodríguez-Huezo, M. E.,

Roman-Guerrero, A., Carrillo-Navas, H., & Pérez-Alonso, C. (2014). Sorption isotherms, thermodynamic properties and glass transition temperature of mucilage extracted from chia seeds (Salvia hispanica L.). Carbohydrate Polymers. https://​doi.​org/​

10.​1016/j.​carbp​ol.​2014.​11.​068 Viganó, J., Ebner-Azuara, V., Telis Cesar, R. N., Beristain, I., Jiménez,

M., & Telis-Romero, J. (2012). Role of enthalpy and entropy in moisture sorption behavior of pineapple pulp powder produced by different drying method. Thermochimica Acta, 528, 63–71.

Vivanco, M., & Mendieta Taboada, O. (1998). Thermodynamic behav- ior of fish meal during adsorption. Drying Technology: An Inter- national Journal, 16(9–10), 1827–1842.

Xiao, Q., & Tong, Q. (2013). Thermodynamic properties of moisture sorption in pullulan–sodium alginate based edible films. Food

Research International, 54, 1605–1612.

Xing, C., Liu, X., Jin, Q., Li, J., Huang, J., Liu, Y., & Wang, X. (2012).

Moisture sorption thermodynamics of Camellia oleifera. Food

Biophysics, 7, 163–172.

Publisher's Note  Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

733 Food and Bioprocess Technology (2022) 15:717–733