# WikiJournal Preprints/Practical applications of moisture sorption models for predicting the drying characteristics and shelf-life of malted and/or fermented FARO 44 rice plus soybean-based complementary foods

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First submitted: 31 Jul 2023 Reviewer comments
QID: Q121359712
Suggested (provisional) preprint citation format: Charles Bristone; Charles Ariahu; Julius Kwagh-hal Ikya; Mike Ojotu Eke. "Practical applications of moisture sorption models for predicting the drying characteristics and shelf-life of malted and/or fermented FARO 44 rice plus soybean-based complementary foods". WikiJournal Preprints. Wikidata Q121359712.
License: CC-BY-SA 4.0 License and the GFDL
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## Article information

Authors: Charles Bristone, Chukuma Charles Ariahu, Julius Kwagh-hal Ikya, Mike Ojotu Eke
* ↑ Department of Food Science and Technology, Faculty of Engineering, University of Maiduguri, Borno State, Nigeria, P. M. B.1069
* ↑ bristonecharles@yahoo.com

## Abstract

The aim of this study is to examine practical use of BET and GAB models for studying the drying characteristics and shelf-life of malted and/or fermented rice plus soybean based complementary foods as well as to employ double logarithmic polynomial (DLP) equation to generate statistical significance between the sorption data. FARO 44 rice cultivar and soybean were obtained from the National Cereal Research Institute and Agric Seed Store House, respectively. Rice was processed into flours and further formulated with processed soybean flour, to provide 16% protein in each of the mixtures. The ratio of rice to soybean was calculated by the material balance equation and the experiment was a 2 x 2 completely randomized design. In this study, the equilibrium moisture contents of the formulated foods were determined gravimetrically at 20, 30, 40 and 50 $^o$C. The data generated are subjected to a one-way analysis of variance and also modelled. The net isosteric heat showing the drying effect and the shelf-life of the formulated foods were predicted. The results of the study showed that the equilibrium moisture contents, GAB and BET monomolecular moisture contents, enthalpy values of monolayer, heat of sorption of multilayer, total surface area of solids, net isosteric heat of desorption and the shelf-life of the formulated products ranged from 0.20 to 30.60 g H$_2$O/g solids, 2.244 to 7.676 (Mg) g H$_2$O/g solids, 2.284 to 4.612 (Mb) g H$_2$O/g solids, 40.947 to 64.752 kJ/mol, 31.419 to 42.246 kJ/mol, 80.24 to 162.02 m$^2$/g solids, 0.449 to 14.200 kJ/mol and 1059 to 1992523 days, respectively. The sorption study agreed with BET and GAB models’ concepts. Isotherms were observed to be temperature dependent and also showed slight formation of hysteresis. The monolayer moisture values varied and also energy constants are temperature dependent. The r$^2$ and RMS values justified the sorption parameters. The non-fermented formulated rice-based products are more hygroscopic than the other samples. Also, the malted-fermented rice-based product exhibited the highest thermostable characteristics (limited changes in energy constants) than the other samples. Drastic reduction of shelf-life was observed with increase in temperatures, packaging permeability, type of package etc. The isotherms within the BET region are essential for the shelf-life prediction of these products at simulated temperatures and relative humidity studied which are averages for the humid and dry regions and it reveals adequate storage stability (long-keeping) for these products. From this study, a well packaged dehydrated food product would permanently be stable in an appropriate storage environment.
Keywords: adsorption, desorption, storage, monolayer, multilayer, moisture

## Glossary

Adsorption: to take in moisture or gas.
Complementary foods: infants or babies’ foods which are often used to support babies’ breast feeding, usually at the age of six month until the child adopt solid foods. It can be given to invalid or an adult may also take it.
Critical water activity: water activity at which undesirable change occurs in foods or products, below critical water activity food is most stable and will have a very long shelf life or will not expire if stored properly.
Desorption: to give out moisture or gas
Equilibrium moisture: water or moisture in food that is at the state of balance or stability with the surrounding water vapour (relative humidity).
Fermentation; technology that utilizes the growth and metabolic activities of microorganisms for the transformation of food materials, most often break down of larger molecules to smaller ones
Hysteresis: difference between adsorption and desorption
Isotherm: moisture sorption curve on a graph.
Malt: germinated grain containing sufficient enzymes and modified-starch endosperm (maltose).
Malting: a controlled sprouting process of grain or germination of grain to yield malt.
Monolayer: the first one moisture layer of food, also called monomolecular layer, which is made up of a non-reactive moisture because of high binding energy capacity
Multilayers: many of the moisture layer that over-lay on top of monolayer, also called multimolecular layers.
Shelf life: the time during which a product will maintain desired physical, chemical, microbiological and sensory stability as well as to comply with nutritional labelling.
Sorption: either adsorption (absorption) or desorption or both
Water activity: water intensity or potentials of food, it is the ratio of the vapor pressure of water in the solid to the vapor pressure of pure water at the same temperature.

## Introduction

Moisture sorption isotherms (curves) describe the relationship between water activity and moisture content at a specified temperature and is unique to every food. This means the desorption (drying) and adsorption (rehydration) properties of one particular food differs with one another. Traditional complementary foods such as ogi (akamu), agidi, kunu (koko), kunun zaki etc and those of the new rice-based formulated food products have high moisture and can spoil easily if not dried after fermentation. Researchers in many parts of Africa have attempted to dry and convert some of them into instant food powders, which can be reconstituted with water as other conventional infant foods. Previously, we successfully produced instant Ogi powders. Nonetheless, drying alone is not enough for food which is intended to be packaged, transported, marketed or kept in shops for sale without evaluating their sorption behaviours through which knowledge of their drying characteristics or storage stability under low or high temperatures and relative humidity could be ascertained.
Water or moisture is recognized as being very important, if not critical to the stability of most products. Controlling of moisture within a product, by some method of drying or by chemically/structurally binding such as salting or sugaring has long been used by man for preservation. These do not only control microbial spoilage but also chemical and physical stability. Moisture content determination is essential in meeting product nutritional labelling regulations, specifying recipes and monitoring processes. However, moisture content alone is not a reliable predictor of engineering processes or microbiological as well as chemical responses such as oxidation, browning or deterioration etc. which occur in food during processing or storage. Hence the search for the knowledge of moisture sorption study and the best-simplest model that could describe the process. Limitations of moisture content measurement as an indicator of safety and quality are attributed to differences in the intensity which water associates with other food components. The water content of a safe product varies from one product to another. But using only moisture content alone, it will be impossible to know the available moisture in a product that would support process, reaction or microbial growth which may influences product quality and stability;.
Moisture sorption isotherms and the equations that describe these relationships are important for the solution of many engineering problems of foods. According to the authors and as reported earlier by Labuza et al., Rizvi and also Rockland and Stewart. Moisture sorption isotherms are useful thermodynamic tools for determining information about water and food substances and provide information to assess food processing operations such as drying, mixing, packaging and storage. Many researchers across the globe reported applications of moisture sorption isotherms. Aqua lab reported that a moisture sorption isotherm is a powerful tool for predicting the shelf life of food. Moisture sorption isotherm can be used to find critical water activity values where changes such as caking, clumping, loss of texture occur etc. Similarly, it can monitor product responses to ingredient and formulation changes, estimation of accurate shelf life, creation of mixing models, performing of packaging calculations and obtain the monolayer moisture value where a product is most stable during storage. According to Akubor, moisture sorption isotherm is being used to investigate structural features of food (surface area, pore volume, pore size distribution, crystallinity). Such data are useful for selecting appropriate storage conditions and packaging systems that optimize or minimize retention of both sensory and nutritional qualities of food. Food sorption isotherms vary with different temperatures, processing methods and give insight into the food moisture binding energy.
The knowledge of moisture sorption isotherms is very important for the analysis and design of several transformation processes of foods (e.g., in drying). It is important for understanding the physicochemical changes involved in the production processes which can assist in calculating the driving force (potential) in many mass transfer operations as well as predict ingredients' behaviour upon mixing. Also, the appropriate packaging material for food stability during processing or upon storage. The malting and fermentation processes are important for bulk reduction of gruel and thereby increase nutrients density for infants. Also, for reducing the pH in food and increase its storage stability by mitigating microbiological proliferation and biochemical processes which favour food spoilage. Rice and soybean combination has been used by earlier researchers to formulate diets that would alleviate nutritional challenges;. Nowadays, rice among many other cereal grains is the most receiving global attention for human consumption. FARO 44 rice among a series of rice varieties released in African sub-region has the most unique properties. These properties have satisfied both farmers’ and consumers’ preferences. High germination capacity, early maturity (110-120 days), optimum production capacity under low management, high yield (7 to 10 tonnes per hectare on a normal basis), high resistance to blast, pests and diseases etc. are farmers’ desired traits of FARO 44 rice. Consumers desired traits exhibited by FARO 44 rice include minimum breakages during milling as well as good cooking and adequate nutritional quality;;. These sorption properties together with the improved rice cultivar and the formulated food products have not been investigated. Notwithstanding, there is paucity of sorption research that incorporate both the drying characteristics and the shelf-life study, especially as single product is affected by malting and/or fermentation.

## Materials and Methods

Sources of raw materials and preliminary handlings
About 120 kg of FARO 44 was obtained from the National Cereals Research Institute, Badeggi, Bida, Niger State. This was dry-cleaned and destoned using de-stoner (De-Stoner, Hunan Sunfied Machinery Co., Ltd, Model: TQS 320, China) as described by Danbaba et al.,. Also, sixty-five (65 kg) kilogram of soybean (Glycine max) was procured from Agric Seed Store House, Gire market, Gire Local Government, Adamawa State. The soybean was sorted and washed with clean water. It was steeped, dried, toasted and de-husked as described by Iwe and Badau et al.. The kernel was milled into flour in a hammer mill and let to pass through a 0.8 mm mesh size screen (Christy Hunt Agricultural Ltd, Foxhills Ind. Est Scunthorpe, Model DE DN15 8QW, South Humbers, England) as described by Badau et al..
Malting and milling of rice
After cleaning, the paddy was divided into two equal lots. The first lot was malted while the second lot was left un-malted as described by Ariahu et al. and Gernah et al.. Malting of paddy was carried out with slight modification. Paddy was washed twice with clean water. The cleaned paddy rice was steeped inside sufficient clean water to cover the surface of the grains completely. It was kept at 29 ± 2 $^o$C with good air circulation for 24 hours. The steeping process was interrupted after every 6 hours by draining. An “air-rest” period of one hour each for every interruption was provided until the grain reached about 42% moisture content. The steeped paddy was then drained and wrapped in a wet jute bag to provide about 3 to 5 cm depth. FARO 44 grain was germinated for 43 hours at 29 ± 1 $^o$C (Figure 1). The short period of germination was timed and was done to counter technical difficulties during the de-husking of malted rice as experienced during pre-trials. After drying of germinated grains at 29 ± 2 $^o$C under constant air circulations and turning of paddy for 48 hours, the germinated dried grains were polished by detaching the roots and rootlet.
About 40 kg of cleaned and dried paddy for each lot was de-husked using a Greep Rice Mill (Model-MBLN-115, China). The malted and non-malted paddy were dried at 40 $^o$C in an air draft oven (air flow rate 140, Oven BS, Model OV-160, Gallen Kamp, England). After de-husking, the grains were finally dried again at 40 $^o$C in an air flow thermostat oven until constant weight was obtained. Then all the rice (malted and un-malted rice) was milled using a hammer miller and let to pass through a 0.8 mm sieve (Christy Hunt Agricultural Ltd, Foxhills Ind. Est Scunthorpe, Model DE DN15 8QW, South Humbers, England) as described by Badau et al..
Accelerated natural fermentation
The rice flours obtained from malted and non-malted paddy were each divided into two sub-lots. A sub-lot of each was subjected to accelerated natural fermentation as described by Ariahu et al.. After fermentation, the pastes were spread on drying trays (Figure 1) and dried to constant weights in an air draft oven at 40 $^o$C (Airflow safety thermostat oven with air flow rate 140, Oven BS, Model OV-160, Gallen Kamp, England) as reported by Nielsen. Finally, it was milled and let to pass through a 0.8 mm sieve, where each sub-lots yield malted-fermented rice (MFR), malted-non-fermented rice (MNFR), non-malted-fermented rice (NMFR) and non-malted-non fermented rice (NMNFR).
Product formulation
The product formulation aimed at obtaining 16 g protein of each test product. The various amounts were obtained by materials balance based on the proximate compositions of the food materials determined as described by AOAC, and to comply with recommendations of the protein advisory group (PAG) as described by WFP. The flours at appropriate ratios were blended in a dry mixer, parked in self-sealing polythene bags and placed in dry and cleaned plastic containers which were stored on dry shelves. Four test products comprising non-malted-non-fermented rice + soybean (NMNFRS), malted-non-fermented rice + soybean (MNFRS), non-malted-fermented rice + soybean (NMFRS) and malted-fermented rice + soybean (MFRS) were obtained. A 2 x 2 completely randomized experimental design was used as described by Gomez and Gomez.
Determination of equilibrium moisture contents
Equilibrium moisture contents were determined gravimetrically by placing the samples to an atmosphere of known relative humidity controlled by saturated sulphuric acid solutions prepared with concentrations of 10, 20, 30, 40, 50, 60, 70 and 80% in desiccators (Desiccators, Moncrieff, Parth, England). The prepared concentrations of sulphuric acid solutions at constant temperatures of 20, 30, 40 and 50 $^o$C created an avenue for the calculated water activities.
Gravimetrically, quadruplets samples of 0.5 g each were weighted with analytical balance (Mettler Toledo B144 College Precision Balance Max 151 G, Mettler Toledo, Model: B154. Switzerland) and were placed in a petri dish with a diameter of 3 cm in thermostatic incubators (Electrothermal Incubator, Searchtech Instrument, Model DNP-9032 and Gallenkamp Economy Incubator, Gallenkamp, Model 3A 4038, England) until equilibrium weight is established. When required for the desorption study, the dried sample was rewetted by sprinkling with 0.5 ml of distilled water using a hypodermic sterile syringe as described by Ariahu et al.. Samples were placed at constant temperature in an incubator and were weighted until a weight change of about < ± 0.001 g was recorded on two consecutive weighs when the samples were assumed to be at equilibrium. The equilibrium moisture content of each sample was calculated as described by Diosady et al. and Sengev et al.. Equilibration using sulphuric acid concentration is fast (within 2 to 3 days). We have checked the weights of sorbates and found that two to three days equilibrations are not different from two weeks except if precautions are not taken when opening and closing of dictators.
Modelling of sorption isotherms
The equilibrium moisture content generated were subjected to a one-way analysis of variance (ANOVA) using IBM SPSS statistics version 22 and mean values were separated by Duncan’s Multiple Range Test (DMRT) at a 5% significant level. The Brunauer-Emmett-Teller (BET) model, Guggenheim-Anderson and De Boer (GAB) model and double logarithmic polynomial (DLP) equations (equations 8, 9 and 14 respectively) were fitted into the equilibrium moisture data using non-linear regression methods (Decagon Devices Inc. MAT 2.0.11.0). Isosteric heat of sorption was determined by employing the use of Prism (GraphPad, Software Inc. version 8.2) and shelf-life study as described by Robertson.
BET model sorption parameters of malted and/or fermented FARO 44 rice plus soybean-based complementary foods have been determined as described by Van den Berg and Rahman using:
$BETEmc=M_{b}C_{b}{\boldsymbol {\alpha }}/(1-{\boldsymbol {\alpha }})[1+(C_{b}-1)]{\boldsymbol {\alpha }}$ (8)
Where:
BET = Brunauer, Emmett and Teller;
E$_{mc}$ = Equilibrium moisture content (g H$_2$O/100 g solids);
M$_b$ = BET monomolecular moisture content (g H$_2$O/100 g solids);
C$_b$ = Energy constant related to the net heat of sorption and
a$_w$ = Water activity (dimensionless).
GAB model was used to determine sorption parameters of malted and/or fermented FARO 44 rice plus soybean-based complementary foods as described by Van den Berg, Rahman and Quirijns et al. using:
$GABEmc=M_{g}Ck\alpha /{\bigl1-k\alpha {\bigr )}{\bigl1-k\alpha +Ck\alpha {\bigr )}$ (9)
Where:
GAB = Guggenheim-Anderson-de Boer;
E$_{mc}$ = Equilibrium moisture content in g H$_2$O/100 g solids;
a$_w$ = Water activity (dimensionless);
M$_g$ = GAB monomolecular moisture content (g/g, d.b.) in g H$_2$O/100 g solids;
K = Constant in the range of less than 1 (i.e., < 1) and
C = Constant in the range of 1 to 2000.
Both (C and K) are sorption constants which related to the energies of interaction between the first and the further sorb molecules at the individual sorption sites. The temperature dependence is included in the constants (C and K), such that:
$C=\exp$ q$_1$/q$_m$=C$_0$exp{\textstyle q_{1}/q_{m}=C_{0}\exp } ${\bigl\vartriangle H_{c}{\bigr )}/RT{\bigr )}$ = C$_0$exp{\textstyle C_{0}\exp } ${\biglH_{n}-H_{m}{\bigr )}/RT{\bigr )}$ (10)
$K=\exp q_{L}/q_{m}=K_{0}\exp$${\bigl\vartriangle H_{k}{\bigr )}/RT{\bigr )}$ = $K_{0}\exp {\biglH_{L}-H_{n}{\bigr )}/RT{\bigr )}$ (11)
$\vartriangle H_{c}=H_{n}-H_{m}$ (12)
$\vartriangle H_{k}=H_{L}-H_{n}$ (13)
Where:
∆H$_c$ = Difference in enthalpy between monomolecular and multi-molecular layer (kJ/mol);
∆H$_k$ = Difference in enthalpy between bulk liquid and multi-molecular layer (kJ/mol);
H$_m$ = Molar sorption enthalpy of the monomolecular layer (kJ/mol);
H$_n$ = Molar sorption enthalpy of the multi-molecular layer on top of the monomolecular layer (kJ/mol);
H$_L$ = Molar sorption enthalpy of the bulk liquid (kJ/mol);
T = Absolute temperature (K);
R = Molar gas constant (0.008314 kJ/mol K);
q$_1$ = Partition function of molecule in monomolecular layer;
q$_L$ = Partition function of molecule in bulk liquid;
q$_m$ = Partition function of molecule in multi-molecular layer; and
C$_o$ and K$_o$ = Entropic accommodation factors.
A polynomial equation was also used to calculate sorption parameters of malted and/or fermented FARO 44 rice plus soybean-based complementary foods as reported by Bonner and Kenny and Igbabul et al. using:
$DLPEmc$=$b_{3}$.$ln$(-$ln$(χ))$^3$+$b_{2}$.$ln$(-$ln$(χ))$^2$+$b_{1}$.$ln$(-$ln$(χ))+$b_{0}$ (14)
Where:
DLP = Double log polynomial equation;
E$_{mc}$ = Moisture content in g H$_2$O/100 g solids;
b$_{3,}$ b$_{2,}$ b$_{1,}$ b$_o$ = Isotherms model parameters (empirical constants); and
χ = ln(-ln(aw)) or water activity.
The monolayer values obtained were used to calculate the total surface area of the sorbent using:
$S_{0}$=${\bigl$$1$/$M_{s}$${\bigr )}$$N_{0}AM_{0}$ (15)
Where:
S$_o$ =Apparent surface area of the sorbent (m$^2$/g solids);
M$_s$ =Relative molecular mass of water (18 g/g mol);
N$_o$ = Avogadro’s number (6.023 x 10$^{23}$ molecules/mol);
A = Apparent surface area of one water molecule (1.05 x 10$^{-19}$ m$^2$); and
M$_o$ = Monomolecular moisture content (g H$_2$O/g solids).
The drying characteristic study employed the net isosteric heat of sorption. An algorithm was employed using numerical precision created by the Prism which divide range into 1000-line segments. A linear standard curve was used and x minimum and maximum values (2, 4, 6, 8, 10 and 12% moisture, also temperatures of 20, 30, 40 and 50 $^o$C) was considered for the computation. For sample NMNFRS at 20 $^o$C, 2% moisture correspond to water activity of 0.159103890951915 etc. at 95% confidence interval. The water activity values obtained for all the samples were converted to natural logarithm values and plotted against temperatures employed (i.e., their respective reciprocal of absolute temperatures (1/T)) using linear regression analysis (Figure 4).
The heats of moisture adsorption and desorption of the formulated food products were determined from equilibrium sorption data using the Integrated Clausius–Clapeyron equation:
$ln$$\alpha _{\omega }$=$C_{s}$$_t$ - Δ$H$$_{st}$ / $R1/T$ (16)
Where:
ΔH$_{st}$= Net isosteric heat of sorption;
H$_1$ = Isosteric heat of sorption (kJ/mol);
H$_v$ = Latent heat of vaporization of pure water (kJ/mol);
T = Absolute temperature ($^o$C);
R = Molar gas constant (0.008314 kJ/mol $^o$C); and
C$_{st}$= Constant related to entropy of sorption (Note: ΔH$_{st}$= − R × slope).
Net isosteric heat of sorption was plotted against moisture content of the formulated food products (Figure 5).
To predict the shelf life of the formulated food products, the water vapour permeability (water vapour permeance/film thickness) of the packaging materials was determined (predicted) using standard test methodology of the American Society for Testing and Materials (ASTM) International, adopted and as described by Gaikwad which employed Arrhenius type equation:
$P$$_2$=$P$$_{1e}$ $E$$_a$ ${\bigl1$/$T$$_1$ - $1$/$T$$_2$${\bigr )}$/$R$ (17)
Where:
E$_a$ = activation energy (kJ/mol);
R = universal gas constant (0.008314 kJ/mol. k);
T$_1$ = initial temperature ($^o$K) of the initial packaging permeability P$_1$ (g/m$^2$.day.mmHg); and
T$_2$ = predicting temperature ($^o$K) predicting the packaging permeability P$_2$ (g/m$^2$.day.mmHg).
Relative humidity was also taken into consideration using the least square fit. Hence, a working isotherm (straight line equation) derived from the isotherms of the formulated products was employed for predicting the shelf life of the formulated products as described by Sherma et al. and Robertson using:
$M=Y+b_{\alpha }\omega$ (18)
Where:
b = slope, Y = intercept at water activity equal (α$_ω$ = 0) to zero, which represent initial moisture content (M$_i$) at a given water activity or relative humidity. The above straight-line equation was used to estimate the initial moisture content (M$_i$), Critical moisture content (M$_c$) and equilibrium moisture content (M$_e$) at their respective water activity. Hence, shelf life was predicted using:
$ln$ ${\biglM_{e}-M_{i}/M_{e}-M_{c}{\bigr )}=B/X\times A/W_{s}\times P_{0}/b\times t_{s}$ (19)
Where:
B/χ = Water vapour permeability (g/m$^2$.day.mmHg) of test packaging material;
A = surface area (m$^2$) of package;
M$_i$ = initial moisture content (g H$_2$O/g solids);
M$_e$ = equilibrium moisture content (g H$_2$O/g solids) at specified storage relative humidity and temperature (from moisture sorption isotherm;
M$_c$ = critical moisture content (g H$_2$O/g solids);
P$_o$ = vapour pressure of pure water (mmHg) at storage temperature (from data book);
W$_s$ = weight (g) of dry food material in package;
b = slope (g H$_2$O/100 g solids) of straight line of moisture sorption isotherm within the BET region; and
t$_s$ = time (days) to reach M$_c$ (on set of spoilage or storage life) at the specified conditions.

## Result and Discussion
###### Equilibrium moisture sorption of the formulated food products

The equilibrium moisture adsorption and desorption of malted and/or fermented FARO 44 rice plus soybean-based complementary foods at 20, 30, 40 and 50 $^o$C are shown in Tables 1, 2, 3, 4 and respectively. The water activity of sulphuric acid solutions used as reported by Sahin and Samnu.
Regardless of temperature change, the adsorption and desorption of moisture contents ranged from 0.20 to 29.25 and 0.30 to 30.60 g H$_2$O/g solids respectively. The result of moisture sorption mostly showed a significant difference (p < 0.05) especially at higher than lower water activity. Those which did not vary significantly (p > 0.05) most often differ by less than or equal to 0.0001 g of sorbate. The temperature dependency of the moisture sorption was observed to be evident. Equilibrium moisture contents decreased at lower water activity with increasing temperature (i.e., at 40 and 50 $^o$C). This is in agreement with many sorption studies that equilibrium moisture content at constant water activity decreased as temperature increased. However, contrary to the results obtained at a higher water activity of about 0.8 to 0.9, because of sudden inversions; equilibrium moisture contents increased as temperature increased. It was earlier mentioned to occur as a result of changes in water binding, water dissociation or solubility of the solute. A similar trend was also reported to occur in many foods at a water activity of higher than 0.7. This was also observed on sorghum-based food products. In addition, at a water activity of about 0.5 to 0.7, a sudden increase of equilibrium moisture contents throughout the sorption process was observed. This was in agreement with many reports and it may indicate the beginning of the capillary condensation region where water molecules tend to be free. A similar trend of a sharp increase of moisture, at about water activity beyond 0.6 and 0.7. In most cases, higher equilibrium moisture contents (more hygroscopic) were observed in sample NMNFRS and MNFRS than the other formulations. Also, higher moisture desorption than adsorption at the same water activity was observed throughout this study. A study by Mathlouthi in a model food system within the water activity range of 0.32 – 0.93 caused degradation of vitamin C as a result of moisture differences between adsorption and desorption. Thus, constant moisture or water activity shifts in food as a result of temperature change would enhance food susceptibility to microbial or chemical degradation.
Table 1. Equilibrium moisture sorption (g H$_2$O/g solids) of the formulated food products at 20 $^o$C :
| Water activity | NMNFRS | MNFRS | NMFRS | MFRS |
| | | Adsorption | | |
| 0.0048 | 0.55$^{bc}$ ± 0.19 | 0.50$^{bc}$ ± 0.38 | 1.30$^a$ ± 0.35 | 0.95$^{ab}$ ± 0.34 |
| 0.0422 | 0.57$^{cd}$ ± 0.19 | 0.52$^d$ ± 0.38 | 1.35$^a$ ± 0.35 | 1.10$^{ab}$ ± 0.20 |
| 0.1573 | 2.50$^b$ ± 0.48 | 4.90$^a$ ± 2.56 | 2.65$^b$ ± 0.41 | 3.45$^{ab}$ ± 0.50 |
| 0.3442 | 4.35$^{ab}$ ± 0.87 | 4.95$^a$ ± 2.51 | 3.85$^{ab}$ ± 0.19 | 3.85$^{ab}$ ± 0.19 |
| 0.5599 | 6.45$^b$ ± 1.00 | 7.45$^{ab}$ ± 0.64 | 8.45$^a$ ± 1.06 | 7.40$^{ab}$ ± 0.95 |
| 0.7491 | 11.50$^{de}$ ± 0.42 | 12.65$^{cd}$ ± 1.45 | 14.35$^a$ ± 0.8 | 14.15$^b$ ± 0.55 |
| 0.8796 | 17.15$^b$ ± 0.82 | 17.35$^{ab}$ ± 0.60 | 17.90$^{ab}$ ± 0.77 | 17.95$^{ab}$ ± 2.37 |
| 0.9558 | 23.28$^{ab}$ ± 0.82 | 24.90$^a$ ± 0.66 | 23.90$^{ab}$ ± 0.38 | 25.00$^a$ ± 1.97 |
| | | Desorption | | |
| 0.0048 | 0.75$^{bc}$ ± 0.19 | 0.65$^c$ ± 0.30 | 1.35$^a$ ± 0.30 | 1.10$^{ab}$ ± 0.26 |
| 0.0422 | 0.90$^d$ ± 0.12 | 0.95$^{cd}$ ± 0.41 | 1.65$^a$ ± 0.30 | 1.50$^{ab}$ ± 0.20 |
| 0.1573 | 3.10$^b$ ± 0.48 | 5.50$^a$ ± 2.56 | 3.25$^b$ ± 0.41 | 4.50$^{ab}$ ± 0.50 |
| 0.3442 | 4.95$^{ab}$ ± 0.87 | 5.60$^a$ ± 2.45 | 4.45$^{ab}$ ± 0.19 | 5.45$^a$ ± 0.19 |
| 0.5599 | 7.05$^b$ ± 1.00 | 8.05$^{ab}$ ± 0.64 | 9.00$^a$ ± 1.08 | 8.00$^{ab}$ ± 0.95 |
| 0.7491 | 12.10$^{cd}$ ± 0.42 | 13.20$^c$ ± 1.49 | 14.75$^b$ ± 0.55 | 15.60$^a$ ± 1.13 |
| 0.8796 | 17.75$^b$ ± 0.82 | 17.95$^{ab}$ ± 0.60 | 18.50$^{ab}$ ± 0.77 | 18.45$^{ab}$ ± 2.39 |
| 0.9558 | 23.90$^{ab}$ ± 0.77 | 25.50$^a$ ± 0.66 | 24.50$^{ab}$ ± 0.38 | 25.60$^a$ ± 1.97 |
| Mean values in a raw with common superscripts are not significantly (p > 0.05) different. Each value is a mean ± SD of quadruplicate determinations. NMNFRS: Non-malted-non-fermented rice + soybean, MNFRS: Malted-non-fermented rice + soybean, NMFRS: Non-malted-fermented rice + soybean, MFRS: Malted-fermented rice + soybean. |||||
Table 2. Equilibrium moisture sorption (g H$_2$O/g solids) of the formulated food products at 30 $^o$C :
| Water activity | NMNFRS | MNFRS | NMFRS | MFRS |
| | | Adsorption | | |
| 0.0059 | 0.55$^a$ ± 0.10 | 0.50 $^a$ ± 0.12 | 0.30$^a$ ± 0.12 | 0.45$^a$ ± 0.19 |
| 0.0470 | 0.55$^a$ ± 0.19 | 0.51$^a$ ± 0.30 | 0.55$^a$ ± 0.10 | 0.70$^a$ ± 0.12 |
| 0.1677 | 2.20$^a$ ± 0.16 | 2.45$^{ab}$ ± 0.38 | 2.80$^{ab}$ ± 0.91 | 3.10$^a$ ± 0.62 |
| 0.3574 | 4.05$^a$ ± 0.66 | 3.70$^b$ ± 0.60 | 4.00$^a$ ± 0.00 | 4.00$^a$ ± 0.00 |
| 0.5711 | 5.40$^c$ ± 0.46 | 6.00$^{bc}$ ± 0.00 | 6.20$^{bc}$ ± 0.40 | 6.50$^{ab}$ ± 1.00 |
| 0.7549 | 11.70$^a$ ± 0.12 | 11.40$^{ab}$ ± 0.67 | 11.25$^{ab}$ ± 0.72 | 11.35$^{ab}$ ± 0.53 |
| 0.8814 | 16.45$^{ab}$ ± 1.56 | 17.85$^a$ ± 0.57 | 17.65$^a$ ± 1.91 | 16.60$^{ab}$ ± 1.21 |
| 0.9562 | 28.10$^a$ ± 0.81 | 26.10$^c$ ± 0.26 | 28.20$^a$ ± 0.16 | 26.45$^{bc}$ ± 0.34 |
| | | Desorption | | |
| 0.0059 | 0.70$^a$ ± 0.12 | 0.70$^a$ ± 0.12 | 0.50$^a$ ± 0.12 | 0.65$^a$ ± 0.19 |
| 0.0470 | 0.95$^a$ ± 0.19 | 2.05$^a$ ± 1.10 | 2.75$^a$ ± 3.50 | 1.10$^a$ ± 0.12 |
| 0.1677 | 2.85$^b$ ± 0.25 | 3.05$^{ab}$ ± 0.38 | 3.40$^{ab}$ ± 0.91 | 3.70$^a$ ± 0.62 |
| 0.3574 | 4.65$^a$ ± 0.66 | 4.30$^b$ ± 0.60 | 4.60$^a$ ± 0.00 | 4.60$^a$ ± 0.00 |
| 0.5711 | 6.00$^c$ ± 0.46 | 6.60$^{bc}$ ± 0.00 | 6.80$^{bc}$ ± 0.40 | 7.10$^{ab}$ ± 1.00 |
| 0.7549 | 12.05$^a$ ± 0.57 | 12.00$^a$ ± 0.67 | 11.85$^a$ ± 0.72 | 11.95$^a$ ± 0.53 |
| 0.8814 | 17.05$^{ab}$ ± 1.56 | 18.45$^a$ ± 0.57 | 18.25$^{ab}$ ± 1.91 | 17.20$^{ab}$ ± 1.21 |
| 0.9562 | 28.70$^a$ ± 0.81 | 26.70$^c$ ± 0.26 | 28.80$^a$ ± 0.16 | 27.05$^{bc}$ ± 0.34 |
| Mean values in a raw with common superscripts are not significantly (p > 0.05) different. Each value is a mean ± SD of quadruplicate determinations. NMNFRS: Non-malted-non-fermented rice + soybean, MNFRS: Malted-non-fermented rice + soybean, NMFRS: Non-malted-fermented rice + soybean, MFRS: Malted-fermented rice + soybean. |||||
Table 3. Equilibrium moisture sorption (g H$_2$O/g solids) of the formulated food products at 40 $^o$C :
| Water activity | NMNFRS | MNFRS | NMFRS | MFRS |
| | | Adsorption | | |
| 0.0071 | 0.20$^a$ ± 0.00 | 0.20$^a$ ± 0.00 | 0.20$^a$ ± 0.00 | 0.20$^a$ ± 0.00 |
| 0.0521 | 1.00$^{ab}$ ± 0.16 | 0.75$^b$ ± 0.25 | 1.00$^{ab}$ ± 0.16 | 1.25$^a$ ± 0.34 |
| 0.1781 | 2.60$^{cd}$ ± 0.16 | 2.55$^d$ ± 0.19 | 2.50$^d$ ± 0.26 | 2.90$^{abc}$ ± 0.26 |
| 0.3702 | 3.65$^a$ ± 0.19 | 3.55$^a$ ± 0.53 | 3.65$^a$ ± 0.41 | 3.15$^a$ ± 0.10 |
| 0.5816 | 5.55$^a$ ± 0.30 | 5.80$^a$ ± 0.92 | 5.60$^a$ ± 0.23 | 5.30$^a$ ± 0.58 |
| 0.7604 | 8.80$^{bc}$ ± 0.16 | 9.20$^a$ ± 0.16 | 8.00$^d$ ± 0.16 | 8.00$^d$ ± 0.16 |
| 0.8831 | 19.45$^a$ ± 0.19 | 18.65$^b$ ± 0.19 | 18.25$^c$ ± 0.19 | 16.45$^d$ ± 0.19 |
| 0.9565 | 28.50$^a$ ± 0.26 | 24.70$^c$ ± 0.26 | 26.10$^b$ ± 0.26 | 24.70$^c$ ± 0.26 |
| | | Desorption | | |
| 0.0071 | 0.85$^a$ ± 0.19 | 0.65$^{ab}$ ± 0.19 | 0.55$^b$ ± 0.10 | 0.85$^a$ ± 0.19 |
| 0.0521 | 1.95$^{ab}$ ± 0.19 | 1.80$^{ab}$ ± 0.16 | 1.90$^{ab}$ ± 0.12 | 2.00$^{ab}$ ± 0.16 |
| 0.1781 | 3.20$^{ab}$ ± 0.16 | 3.20$^{ab}$ ± 0.16 | 3.45$^{ab}$ ± 0.34 | 3.30$^{ab}$ ± 0.26 |
| 0.3702 | 3.95$^d$ ± 0.19 | 4.60$^{ab}$ ± 0.16 | 4.40$^c$ ± 0.16 | 3.40$^e$ ± 0.16 |
| 0.5816 | 6.15$^b$ ± 0.19 | 6.95$^a$ ± 0.19 | 6.15$^b$ ± 0.19 | 6.15$^b$ ± 0.19 |
| 0.7604 | 9.50$^{ab}$ ± 0.26 | 9.90$^a$ ± 0.26 | 8.70$^c$ ± 0.26 | 8.70$^c$ ± 0.26 |
| 0.8831 | 20.10$^a$ ± 0.26 | 19.30$^b$ ± 0.26 | 18.90$^b$ ± 0.26 | 17.10$^c$ ± 0.26 |
| 0.9565 | 29.30$^a$ ± 0.26 | 24.30$^d$ ± 0.26 | 26.90$^b$ ± 0.26 | 25.50$^c$ ± 0.26 |
| Mean values in a raw with common superscripts are not significantly (p > 0.05) different. Each value is a mean ± SD of quadruplicate determinations. NMNFRS: Non-malted-non-fermented rice + soybean, MNFRS: Malted-non-fermented rice + soybean, NMFRS: Non-malted-fermented rice + soybean, MFRS: Malted-fermented rice + soybean. |||||
Table 4. Equilibrium moisture sorption (g H$_2$O/g solids) of the formulated food products at 50 $^o$C :
| Water activity | NMNFRS | MNFRS | NMFRS | MFRS |
| | | Adsorption | | |
| 0.0085 | 0.20$^a$ ± 0.00 | 0.20$^a$ ± 0.00 | 0.20$^a$ ± 0.00 | 0.20$^a$ ± 0.00 |
| 0.0575 | 0.55$^{ab}$ ± 0.25 | 0.70$^{ab}$ ± 0.26 | 0.65$^{ab}$ ± 0.25 | 0.40$^b$ ± 0.00 |
| 0.1887 | 1.90$^{ab}$ ± 0.26 | 1.80$^{ab}$ ± 0.54 | 2.00$^{ab}$ ± 0.16 | 2.10$^a$ ± 0.35 |
| 0.3827 | 3.80$^a$ ± 0.59 | 3.75$^a$ ± 0.66 | 3.55$^a$ ± 0.53 | 3.10$^a$ ± 0.12 |
| 0.5914 | 6.45$^a$ ± 0.25 | 6.00$^{ab}$ ± 0.57 | 6.26$^{ab}$ ± 0.10 | 6.15$^{ab}$ ± 0.64 |
| 0.7655 | 10.75$^a$ ± 0.44 | 10.05$^{ab}$ ± 0.64 | 10.40$^a$ ± 0.91 | 9.15$^{bc}$ ± 0.19 |
| 0.8848 | 18.45$^b$ ± 0.30 | 16.00$^c$ ± 0.28 | 15.30$^c$ ± 0.26 | 19.40$^{ab}$ ± 0.37 |
| 0.9570 | 29.25$^a$ ± 2.07 | 29.20$^a$ ± 0.81 | 24.45$^c$ ± 0.66 | 27.10$^b$ ± 0.90 |
| | | Desorption | | |
| 0.0085 | 0.30$^b$ ± 0.12 | 0.55$^a$ ± 0.10 | 0.60$^a$ ± 0.16 | 0.55$^a$ ± 0.10 |
| 0.0575 | 1.30$^a$ ± 0.12 | 1.50$^a$ ± 0.20 | 1.50$^a$ ± 0.20 | 1.25$^a$ ± 0.10 |
| 0.1887 | 2.85$^a$ ± 0.35 | 2.40$^b$ ± 0.37 | 2.65$^{ab}$ ± 0.19 | 2.80$^{ab}$ ± 0.16 |
| 0.3827 | 4.65$^{ab}$ ± 0.44 | 4.90$^a$ ± 0.12 | 4.25$^{bc}$ ± 0.34 | 3.60$^d$ ± 0.16 |
| 0.5914 | 7.00$^{ab}$ ± 0.43 | 6.75$^{ab}$ ± 0.72 | 6.75$^{ab}$ ± 0.25 | 6.65$^{ab}$ ± 0.84 |
| 0.7655 | 11.40$^a$ ± 0.43 | 10.60$^{abc}$ ± 0.67 | 11.15$^{ab}$ ± 0.82 | 9.75$^c$ ± 0.19 |
| 0.8848 | 19.00$^b$ ± 0.28 | 16.75$^c$ ± 0.30 | 20.95$^a$ ± 0.25 | 19.40$^b$ ± 0.69 |
| 0.9570 | 30.60$^a$ ± 0.16 | 30.10$^{ab}$ ± 0.26 | 25.45$^d$ ± 0.25 | 28.00$^c$ ± 0.37 |
| Mean values in a raw with common superscripts are not significantly (p > 0.05) different. Each value is a mean ± SD of quadruplicate determinations. NMNFRS: Non-malted-non-fermented rice + soybean, MNFRS: Malted-non-fermented rice + soybean, NMFRS: Non-malted-fermented rice + soybean, MFRS: Malted-fermented rice + soybean. |||||
Moisture sorption isotherms of the formulated food products
Moisture sorption isotherms are shown in Figure 2 and 3. These isotherms have been observed to correspond with many sorption studies of agricultural products and as described by many researchers. The shapes of the isotherms are in agreement with the earlier classification and description Brunauer et al. and as reported by Andrade et al. as sigmoidal (type 2); similar in resemblance with the Greek letter symbol sigma (ς). Similarly, this phenomenon has been reported in the literature for cereal-based products, whole yellow dent corn, energy sorghum and many other agricultural products.
Regardless of temperature change, the desorption isotherms are slightly above adsorption isotherms throughout. As earlier reported (Rahman; Sahin and Samnu,, such a phenomenon (hysteresis) is a normal sorption process which usually occurs in hygroscopic products (agricultural products). Mathlouthi elucidates that the filling and emptying of moisture in capillaries of food does not follow the same kinetics and changes in the structure of some food constituents subjected to various water activity are the main causes of hysteresis. There are many sorption theories of hysteresis in literature which tried to explain how such a phenomenon occur. After studying many theories of hysteresis, research workers concluded that it is impossible to give a single explanation of the hysteresis phenomena in foods;. But in this study, one can infer vapour pressure, capillary or other optimal conditions for desorption than in adsorption might have been the major contributing factors for higher moisture desorption than adsorption. Hysteresis which is the difference between adsorption and desorption isotherms appeared distinctly close to the midpoints of the isotherms (curves). Samples MFRS and NMFRS at 20 and 50 $^o$C respectively, exhibited higher hysteresis than any other sample. Different loop shapes of hysteresis have been reported to depend on the composition of the product, temperature, storage time and the number of successive adsorption and desorption (Sahin and Samnu,. Rahman and Andrade et al. highlighted the effect and variety of hysteresis loop shapes of different foods, which also correlates with these FARO 44 products. Though there were many differences between adsorption and desorption isotherms in this study, no much clear difference in features was observed at the hydration monolayer nor region of free water of the isotherms, probably due to the skewness of the regression. A previous report has supported the argument that hysteresis in high sugar or high pectin foods mainly occurs in the monomolecular region. In this study, the effect of fermentation, malting, heat treatment and composition of the mixtures might have influenced hysteresis in other regions of the isotherms, especially in malted or fermented ones. It was observed that sorption isotherms at about the water activity of 0.8 to 0.9 showed a decrease in hysteresis as temperature increased except sample NMFRS. Also, changes in water binding, dissociation or dissolution of sugar at higher temperatures might have influenced the slight shift in hysteresis at higher water activity. There is a likelihood then, the effect of hysteresis may transient the sorption regions. As reported earlier (Quirijns et al.,, many times effects of hysteresis may complicate thermodynamic data derived from sorption isotherms. From this study, hysterical effects at levels of low water activity are remarkable for browning reaction, oxidation, loss of nutritional and sensory qualities as well as the growth of Osmophilic yeasts. However, not much in most of the samples.
BET, GAB and DLP model parameters of the formulated food products
The BET, GAB and DLP model equations were fitted to the experimental sorption data by non-linear regression analysis as shown in Tables 5a and 5b. The GAB and BET monomolecular moisture contents (M$_g$ and M$_b$) regardless of temperature change varied from 2.244 to 7.676 and 2.284 to 4.612 g H$_2$O/g solids, respectively. In addition, the GAB energy constant (C) ranged from 1.972 to 49.425. The GAB constant (C) which measure the strength of water binding to the primary binding sites, is the ratio of the partition function of the molecule in a monolayer to that of the partition function of molecules in a multilayer;. On the other hand, K values ranged from 0.681 to 0.990. K which measures the entropic configuration (arrangement) and mobility of water molecules, is the ratio of the partition function of molecules in bulk liquid to the partition function of molecules sorbed in the multilayer;. The BET constant (C$_b$) also ranged from 3.253 to 141.917. Both BET and GAB energy constants are in agreement with their respective model concepts. C and C$_b$ values showed a strong temperature dependency than the K values. From vast literature which reported K values of foods including those compiled by Rahman are mostly between the range of 0.6 to nearly 1. The more the energy constants of a particular food differ from one temperature to the other, the more likely the instability of the food products.
Tables 5a and 5b showed the monolayer most strongly bound at the sorption sites. The monolayer at the desorption sites had higher water-binding capacity than the adsorption. This is also not far-fetched from the enthalpy energy the difference between the state of the multilayer during adsorption and desorption, probably caused by difference between distributions of water molecules over the polymer matrix during its swelling and shrinking as reported previously for entropy change. Also, effects of hysteresis as stated by other researchers in many theories of hysteresis are eminent. Samples MNFRS, MFRS, MFRS and MNFRS at 20, 30, 40 and 50 $^o$C respectively had the highest binding energy of water molecules at the desorption sites. While samples NMFRS, MNFRS, MNFRS and NMFRS at the same corresponding temperatures had the lowest binding energy (at sites). From these findings, the adsorption phenomenon contributed weakening of the molecular binding energy of MNFRS and NMFRS. The energy capacity is higher for desorption than adsorption except for NMFRS (1.972) which recorded the lowest, followed by MFRS (5.795) at 50 $^o$C (Table 5b). On average, the GAB C values of MFRS ranged from 8.985 (adsorption) to 20.444 (desorption). MFRS had the strongest monolayer energy binding capacity on average, followed by NMNFRS (C = 5.3125 to 19.287), MNFRS (C = 6.149 to 16.219) and NMNFRS (C = 4.878 to 12.440). In general, as temperature increased to 30 and 40 $^o$C, the GAB constant (C values) of most samples exhibited strong monolayer water molecules. But at 50 $^o$C (Table 5b) energy capacity was reduced, which agreed with the thermodynamics of sorption. The high temperature was known to decrease binding energy between molecules because of the increased excitation. As such, mutual distances between molecules would increase, resulting the weakening of their molecular attractive forces. Thus, causing molecules to break away (Quirijns et al.,. Van den Berg explained that decreasing binding energy shows an increasing residence time for the sorbed molecules in the first layer, meaning that at high temperature the character of the sorption process become less strongly localized. It can be seen; the energy capacity of sorption sites is important for keeping dehydrated food quality because food without binding energy is prone to moisture migration. It is as important as the food is in free moisture region which allows the entering or escaping of moisture. A food with zero energy binding capacity would mean food in a free-water region.
The K values of samples were mostly structured and the multilayer water molecules differed from the bulk liquid. It is also varied and was found to exhibit slight temperature dependency. Most values of K increased slightly as temperature increased. This phenomenon occurred because of temperature effects causing the movement of water molecules to the sorption sites. Thus, as temperature increased, multilayer properties of water molecules become less structured which corresponds with the molecules in the bulk liquid. Sample MNFRS (at 20, 30 and 40 $^o$C) had more (better) structured multilayer at the sorption sites, followed by NMFRS (50 $^o$C) at desorption sites. However, sample NMNFRS (30 $^o$C) had a less structured multilayer at desorption sites, followed by MFRS at desorption (40 $^o$C) and adsorption (50 $^o$C) sites. This means multilayer water molecules of samples NMNFRS and MFRS at those points are not well organized and had multilayer properties slightly comparable with bulk liquid molecules. Food with K value equal to or greater than 1, is an interpretation that that food is already predisposed to the movement of free water molecules according to GAB model assumptions. Observed entropy differences between the state of the multilayer adsorption and desorption are slight.
The coefficient of determination (r$^2$) and RMS of the DLP for the food products ranged from 0.982 to 1.000 and 0.166 to 1.193; GAB ranged from 0.986 to 1.000 and 0.062 to 1.100; and BET ranged from 0.823 to 1.00 and 0.026 to 0.785 respectively. Irrespective of temperature or sorption mode, the GAB model fitting parameters were better correlated (r$^2$ = 0.886 to 1.000), followed by DPL (r$^2$ = 0.982 to 1.000) and BET (r$^2$ = 0.823 to 1.000). GAB model has been reported earlier to be the best fit for predicting sorption isotherms of foods or agricultural products. The use of GAB and DLP equations for modelling was better justified at 30 $^o$C and also BET at 50 $^o$C, because there were good correlations at those points. A predictive equation (Double logarithmic polynomial) was employed to check how the sorption parameters of the sorption models vary statistically and it was found to correlate well. In general, the use of r$^2$ and RMS as determinants for model validation in this study's reviled BET model is better justified for the modelling of malted and/or fermented rice plus soybean-based complementary foods than the GAB model or DPL equation. However, an earlier report (Samapundo et al. stated that a good fit for a model to experimental data does not describe the quality of the sorption process but only the mathematics of the model. In addition, it only reveals or measures how closely the data points to the line of the best fit.
For dehydrated food to be stable for a long time under storage, available moisture must be removed from the food down to monolayer moisture level and prevent any subsequent moisture adsorption from the environment into the intended food made for storage. This process would be enough to preserve or retain the quality of the food materials for a long time, probably being shelf stable. Tables 5a and 5b indicated samples NMFRS and MNFRS had the highest GAB and BET monolayer moisture respectively and MFRS the lowest. The GAB monolayer moisture values of formulations were mostly higher than the BET monolayer moisture values and both mostly decreased as temperature increased. GAB and BET monolayer moisture desorption of foods were also observed to be mostly higher than adsorption. A similar trend was also reported and who also reported GAB and BET monolayer values decreased significantly with increasing temperature after studying about 100 foods and food components. Samupundo et al. reported that at higher temperatures water molecules do break away from sorption sites causing the decrease in monolayer moisture. However, Van den Berg and Rahman stated that monolayer moisture is not temperature dependent. Another study also found monolayer moisture decreased or increased with increasing temperature.
The monolayer moisture values of foods obtained in this study are slightly comparable to those found by Bonner and Kenney who modelled energy sorghum at 15 to 40 $^o$C, and found the range of GAB monolayer moisture values from 6.86 to 8.44% during desorption and 5.41 to 5.70% during adsorption by the dynamic dew-point method. GAB monolayer moisture values of whole yellow dent corn from 6.03 to 7.44% (adsorption) and 6.84 to 8.46% (desorption) at 25 to 37 $^o$C found by Samapundo et al. slightly match this study. Moraes et al. found GAB monolayer moisture for garlic from 5.0 to 5.6%, which is within the range of monolayer moisture values obtained. But slightly varied with BET monolayer moisture (3.0 to 5.0%). The result of the sorption study on whole black peppercorns by Yogendrarajah et al. yielded comparable GAB monolayer moisture of 3.49 to 4.78% during adsorption and 4.36 to 4.67% during desorption (22 to 37 $^o$C). Similar monolayer moisture values from 2.27 to 3.65 g H$_2$O/100 g solids for adsorption and 2.70 to 5.48 g H$_2$O/100 g for desorption (25 to 50 $^o$C) were obtained by Ariahu et al.. Their results correspond better with this study probably because of the similar adopted methodology. Syamaladevi et al. found comparable results of BET and GAB monolayer moisture of 4.5 and 7.4% respectively, for raspberry at room temperature (23 $^o$C) by the isopiestic method. Results obtained by Kim et al. vary slightly with the GAB monolayer moisture obtained. In their work, the monolayer moisture values of composite foods filled with chocolate was between 1 to 5% (20, 30 and 40 $^o$C). Many sorption studies that reviled monolayer values of foods and other agricultural products were found to correlate well with this study.
Much higher monolayer moisture values of agricultural products than the ones obtained in this study were also observed. Diosady et al. obtained higher monolayer moisture values of canola meals from 9.06 to 9.60% (10, 22 and 34 $^o$C). Another estimated GAB parameter by Kiranoudis et al. reviled monolayer moisture values of 8.70 to 21.20% db. for vegetables and 10.50 to 15.00% db. for fruits (30, 45 and 60 $^o$C) which are much higher than the results obtained, probably temperature disparity may be responsible. Also, at a much-elevated temperatures (from 20 to 70 $^o$C) than the ones used in this study, Goula et al. found much higher GAB monolayer values (20.00 to 21.30%) of spray-dried tomato pulp. Monolayer moisture of 9.73 g H$_2$O/100 g solids for vacuum-dried onion and 9.79 g H$_2$O/100 g solid for air-dried onion has been reported by Masud Alam and Nazrul Islam which are higher than the results obtained. BET and GAB monolayer moisture values between 5.19 to 14.60% and 5.92 to 16.42% respectively for African arrowroot lily (10 to 40 $^o$C) found by Igbabul et al. are also much higher. Regression methods also might have been the contributing factors which resulted in much significant difference in the results obtained. Moraes et al. also found higher monolayer moisture values of apples from 10.7 to 16.8% (GAB) and 10.6 to 14.8% (BET) (50, 60 and 70 $^o$C). High-temperature disparity was also observed and possibly the cause of much difference with the results obtained. Souza et al. carried sorption study (20, 26, 33, 38 and 44 $^o$C) for mango skin and obtained much higher GAB (1.114 × 10$^4$ to 2.940 × 10$^5$ kg/kg, d.b) and lower BET monolayer moisture values (5.712 × 10$^{-2}$ to 8.519 × 10$^{-2}$ kg/kg, d.b) compared to this report. The GAB and BET monolayer moisture values of more than 290 foods including food components compiled from relevant kinds of literatures by Rahman were observed to be mostly between the ranges of 0.98 to 33.3% and 0.74 to 13.50% for GAB and BET respectively. Also, three different regression methods used to compare the GAB monolayer moisture content of onion, green bean and apricot were found to be varied between 5.31 to 13.54%;. It is likely then, the reason for having higher monolayer moisture in fruits or vegetables than cereal-based foods may be attributed to many available sorption sites for the binding of water molecules. It is also possible that the use of higher temperatures for sorption study would not contribute decrease in monolayer moisture values as many reported and as expected by classical thermodynamic principles of sorption, but due to anomaly of mathematical regression analysis. Many researchers that modelled at higher temperatures could have obtained lower monolayer moisture contents than those modelled at lower temperatures using the same methodology. But it was not so as observed.
To elucidate, if the sorption sites are empty or partially empty, then it can easily pick up moisture to fill the empty sites. Hence, spoilage by microorganism or biochemical process. But if these sites are already filled up with moisture, the faster the deterioration or spoilage of food. Sorption sites of food may partially be empty of moisture if the food is well dried and this would promote keeping qualities of foods.
Table 5a. DLP, GAB and BET sorption isotherm regression parameters of the formulated food products :
| Adsorption | Adsorption | Adsorption | Adsorption | Adsorption | Desorption | Desorption | Desorption | Desorption |
| Products | NMNFRS | MNFRS | NMFRS | MFRS | NMNFRS | MNFRS | NMFRS | MFRS |
| | | | | 20 $^o$C | | | | |
| DLP | | | | | | | | |
| b$_o$ | 4.397 | 5.423 | 5.116 | 5.062 | 5.004 | 6.359 | 5.702 | 6.256 |
| b$_1$ | -4.632 | -4.556 | -5.472 | -5.141 | -4.704 | -4.445 | -5.505 | -5.225 |
| b$_2$ | 1.084 | 0.779 | 1.320 | 1.218 | 1.006 | 0.533 | 1.208 | 0.950 |
| b$_3$ | 0.194 | 0.071 | 0.370 | 0.260 | 0.175 | -0.012 | 0.336 | 0.204 |
| r$^2$ | 0.998 | 0.995 | 0.994 | 0.992 | 0.998 | 0.990 | 0.995 | 0.987 |
| RMS | 0.391 | 0.605 | 0.647 | 0.805 | 0.419 | 0.849 | 0.597 | 1.003 |
| GAB | | | | | | | | |
| M$_g$ | 4.578 | 4.467 | 7.676 | 5.486 | 4.604 | 4.673 | 6.687 | 5.461 |
| K | 0.851 | 0.681 | 0.753 | 0.828 | 0.852 | 0.855 | 0.780 | 0.827 |
| C | 4.664 | 10.431 | 2.440 | 4.449 | 7.505 | 18.933 | 4.166 | 10.910 |
| r$^2$ | 0.998 | 0.996 | 0.992 | 0.990 | 0.998 | 0.992 | 0.992 | 0.986 |
| RMS | 0.241 | 0.573 | 0.850 | 0.919 | 0.373 | 0.783 | 0.852 | 1.073 |
| BET | | | | | | | | |
| M$_b$ | 3.820 | 4.121 | 2.324 | 2.883 | 3.987 | 4.612 | 2.834 | 4.079 |
| C$_b$ | 5.827 | 9.869 | 141.917 | 26.837 | 8.818 | 15.179 | 86.604 | 21.521 |
| r$^2$ | 0.977 | 0.907 | 0.820 | 0.868 | 0.973 | 0.849 | 0.876 | 0.922 |
| RMS | 0.205 | 0.208 | 0.316 | 0.102 | 0.383 | 0.785 | 0.516 | 0.658 |
| | | | | 30 $^o$C | | | | |
| DLP | | | | | | | | |
| b$_o$ | 3.805 | 3.831 | 4.109 | 4.352 | 4.418 | 4.639 | 5.029 | 4.969 |
| b$_1$ | -3.831 | -4.448 | -4.039 | -3.913 | -3.829 | -4.304 | -3.774 | -3.978 |
| b$_2$ | 1.146 | 1.302 | 1.095 | 0.947 | 1.035 | 1.193 | 0.971 | 0.865 |
| b$_3$ | -0.042 | 0.132 | -0.035 | -0.027 | -0.078 | 0.087 | -0.095 | -0.046 |
| r$^2$ | 0.996 | 0.998 | 0.998 | 0.998 | 0.996 | 0.996 | 0.997 | 0.998 |
| RMS | 0.643 | 0.455 | 0.386 | 0.408 | 0.591 | 0.549 | 0.540 | 0.426 |
| GAB | | | | | | | | |
| M$_g$ | 3.323 | 4.151 | 3.521 | 3.493 | 3.405 | 3.812 | 3.480 | 3.688 |
| K | 0.924 | 0.888 | 0.918 | 0.909 | 0.922 | 0.899 | 0.920 | 0.904 |
| C | 6.747 | 3.668 | 7.394 | 9.989 | 12.198 | 14.217 | 43.581 | 15.647 |
| r$^2$ | 0.994 | 9.998 | 0.999 | 0.998 | 0.995 | 0.997 | 0.999 | 0.997 |
| RMS | 0.721 | 0.386 | 0.322 | 0.443 | 0.668 | 0.514 | 0.341 | 0.471 |
| BET | | | | | | | | |
| M$_b$ | 3.585 | 3.024 | 3.272 | 3.147 | 3.622 | 2.839 | 3.106 | 3.479 |
| C$_b$ | 4.843 | 7.452 | 7.829 | 10.839 | 8.697 | 47.993 | 58.457 | 15.060 |
| r$^2$ | 0.979 | 0.958 | 0.962 | 0.940 | 0.979 | 0.999 | 0.978 | 0.941 |
| RMS | 0.282 | 0.335 | 0.438 | 0.435 | 0.324 | 0.057 | 0.265 | 0.485 |
| NMNFRS: Non-malted-non-fermented rice + soybean, MNFRS: Malted-non-fermented rice + soybean, NMFRS: Non-malted-fermented rice + soybean, MFRS: Malted-fermented rice + soybean, r$^2$ = Coefficient of determination |||||||||
Table 5b. DLP, GAB and BET sorption isotherm regression parameters of the formulated food products :
| Adsorption | Adsorption | Adsorption | Adsorption | Adsorption | Desorption | Desorption | Desorption | Desorption |
| Product | NMNFS | MNFRS | NMFRS | MFRS | NMNFRS | MNFRS | NMFRS | MFRS |
| | | | | 40 $^o$C | | | | |
| DLP | | | | | | | | |
| b$_o$ | 3.063 | 3.119 | 3.071 | 3.090 | 3.943 | 4.444 | 4.193 | 3.887 |
| b$_1$ | 3.558 | -3.984 | -3.366 | -2.920 | -3.738 | -4.302 | -3.463 | -3.004 |
| b$_2$ | 1.916 | 1.886 | 1.691 | 1.512 | 1.391 | 1.180 | 1.056 | 1.044 |
| b$_3$ | 0.125 | 0.288 | 0.113 | 0.061 | -0.026 | 0.147 | -0.075 | -0.129 |
| r$^2$ | 0.987 | 0.985 | 0.983 | 0.990 | 0.987 | 0.982 | 0983 | 0.993 |
| RMS | 1.172 | 1.093 | 1.212 | 0.863 | 1.141 | 1.141 | 1.214 | 0.752 |
| GAB | | | | | | | | |
| M$_g$ | 3.379 | 4.013 | 3.119 | 2.717 | 3.243 | 3.827 | 3.123 | 2.768 |
| K | 0.927 | 0.888 | 0.925 | 0.933 | 0.932 | 0.887 | 0.927 | 0.939 |
| C | 4.478 | 2.903 | 6.169 | 13.891 | 19.832 | 11.995 | 27.429 | 49.425 |
| r$^2$ | 0.989 | 0.988 | 0.986 | 0.992 | 0.990 | 0.987 | 0.989 | 0.996 |
| RMS | 1.071 | 0.994 | 1.096 | 0.759 | 1.002 | 0.994 | 0.987 | 0.584 |
| BET | | | | | | | | |
| M$_b$ | 2.684 | 2.725 | 2.682 | 2.284 | 2.629 | 3.081 | 3.015 | 2.405 |
| C$_b$ | 12.364 | 9.582 | 11.717 | 27.962 | 57.946 | 25.719 | 30.879 | 81.595 |
| r$^2$ | 0.978 | 0.959 | 0.988 | 0.823 | 0.983 | 0.996 | 0.989 | 0.909 |
| RMS | 0.200 | 0.293 | 0.144 | 0.437 | 0.181 | 0.115 | 0.179 | 0.367 |
| | | | | 50 $^o$C | | | | |
| DLP | | | | | | | | |
| b$_o$ | 3.459 | 3.419 | 3.529 | 3.024 | 4.343 | 4.302 | 3.917 | 3.666 |
| b$_1$ | -4.098 | -3.211 | -3.698 | -2.636 | -3.952 | -3180 | -5.015 | -3.991 |
| b$_2$ | 1.320 | 0.981 | 0.976 | 1.260 | 1.092 | 0.822 | 1.642 | 1.374 |
| b$_3$ | -0.007 | -0.199 | 0.007 | -0.545 | -0.111 | -0.255 | 0.314 | 0.037 |
| r$^2$ | 0.999 | 1.000 | 1.000 | 0.994 | 0.999 | 0.999 | 0.984 | 0.991 |
| RMS | 0.282 | 0.216 | 0.166 | 0.543 | 0.297 | 0.270 | 1.193 | 0.924 |
| GAB | | | | | | | | |
| M$_g$ | 3.596 | 2.759 | 3.256 | 2.440 | 3.446 | 2.905 | 5.686 | 3.513 |
| K | 0.921 | 0.947 | 0.909 | 0.990 | 0.929 | 0.944 | 0.842 | 0.918 |
| C | 3.673 | 7.595 | 5.295 | 7.612 | 10.225 | 19.731 | 1.972 | 5.796 |
| r$^2$ | 1.000 | 0.999 | 0.999 | 0.996 | 1.000 | 0.998 | 0.987 | 0.994 |
| RMS | 0.113 | 0.360 | 0.321 | 0.426 | 0.062 | 0.477 | 1.100 | 0.791 |
| BET | | | | | | | | |
| M$_b$ | 3.516 | 3.355 | 2.895 | 2.504 | 3.352 | 3.500 | 2.808 | 2.471 |
| C$_b$ | 3.253 | 3.533 | 5.130 | 6.033 | 9.583 | 8.130 | 17.578 | 20.899 |
| r$^2$ | 0.998 | 0.999 | 0.998 | 0.965 | 1.000 | 0.972 | 0.992 | 0.974 |
| RMS | 0.074 | 0.081 | 0.074 | 0.261 | 0.026 | 0.342 | 0.162 | 0.235 |
| NMNFRS: Non-malted-non-fermented rice + soybean, MNFRS: Malted-non-fermented rice + soybean, NMFRS: Non-malted-fermented rice + soybean, MFRS: Malted-fermented rice + soybean, r$^2$ = Coefficient of determination. |||||||||
GAB molar sorption enthalpies of the formulated food products
GAB monomolecular enthalpy (Hm) and multi-molecular enthalpy (H$_n$) of sorption of malted and/or fermented rice plus soybean-based complementary foods are shown in Table 6. Irrespective of temperature or sorption mode, enthalpy values of monolayer varied from 40.947 to 64.752 kJ/mol, with NMFRS having the highest and MNFRS the lowest monolayer enthalpy of sorption at 20 and 50 $^o$C respectively. Monolayer heat of sorption showed temperature dependency. GAB monolayer enthalpy of sorption mostly decreased as temperature increased except for NMFRS during adsorption (20 $^o$C). This means high temperature resulted in the weakening of monolayer molecules hence lowering of molar heat of sorption. This also matched remarkably with the effect of higher temperature on BET and GAB energy constants. So, it is in line to say molar heat of sorption decreased with decreasing binding energy. This has a physical meaning and relates to the principles of thermodynamics. The differences in the magnitude of the monolayer enthalpies of NMNFRS in the adsorption and MFRS in the desorption mode consecutively (i.e., 20 to 30 $^o$C or 30 to 40 $^o$C or 40 to 50 $^o$C) followed the same trend and also in their desorption and adsorption, respectively.
The enthalpy of sorption has been investigated by many researchers. A study on sorghum-based complementary foods by Sengev et al. found monolayer enthalpy values (50.34 to 61.37 kJ/mol at 10, 20, 30 and 40 $^o$C) comparable with the results obtained. But Diosady et al. found higher monolayer enthalpy of 84.112 to 84.880 kJ/mol of canola meals (at 16 to 34 $^o$C) than the enthalpy values obtained. The use of lower temperatures in their study than this current work may be the contributing factor to many differences. This is because a study conducted at 25 to 50 $^o$C by Ariahu et al. reviled similar monolayer enthalpy of sorption (Crayfish = 53.40 to 77.29 kJ/mol). All their findings also indicated temperature dependency, which is in agreement with these current findings. Other data from literature on ΔH$_c$ and ΔH$_k$ of foods, can be obtained from Kiranoudis et al. and Quirijns, et al.. But the correlation was impossible with this study because specific enthalpy at a particular temperature has not been employed.
Multilayer heat of sorption also exhibited temperature dependency. It varied between 31.419 to 42.246 kJ/mol. At 20 $^o$C, sample NMFRS recorded the highest values of molar heat at desorption and the lowest at adsorption sites. The differences in the magnitude of the multilayer enthalpies of NMNFRS in the adsorption and MFRS in the desorption mode consecutively followed a similar trend and also in their desorption and adsorption modes, respectively. It follows a similar trend as the case of monolayer heat, except the magnitude of multilayer enthalpy of sorption was lower than the monolayer. As molecules of water sorb to the multilayer strength of binding energy capacity becomes weaker (less bound) thereby reducing the multilayer enthalpy. Hence lower heat of sorption is expected in multilayer because of the higher energy binding strength of monolayer. In a study conducted by Diosady et al. found slightly higher enthalpy (49.185 to 48.420 kJ/mol) of multilayer of canola meals than in this study. Study on complementary food by Sengev et al. also obtained slightly higher multilayer heat values (43.83 to 45.89 kJ/mol) as compared with this study. But a study by Ariahu et al. yielded slightly comparable results. However, in their study, some values (enthalpy of crayfish from 25.02 to 57.22 kJ/mol) were either slightly higher or lower as compared with this study.
Based on a report from the literature it was observed molar heat of sorption of water molecules may be as low as close to zero. Any point where there is low molar heat of sorption is an indication of high entropy which may be accompanied by a low binding energy of water molecules according to GAB model concepts. Low heat of sorption of a product may be an added advantage for dehydration. But a disadvantage for a dehydrated product, such that infinitesimal energy would facilitate their ease to pick-up moisture from the humid environment if not properly stored. Quirijns et al. in their study found a close range of GAB molar enthalpy to net isosteric heat of sorption. Hence, GAB molar enthalpy can be employed as a useful tool for estimating the drying process and it could be used to evaluate the operating cost of dehydration for FARO 44 products.
Table 6. GAB isotherm molar enthalpies (kJ/mol) of of the formulated food products :
| Products | 20 $^o$C | 30 $^o$C | 40 $^o$C | 50 $^o$C |
| Monolayer enthalpy of adsorption (H$_m$) |||||
| NMNFRS | 51.575 | 51.145 | 50.725 | 50.285 |
| MNFRS | 51.682 | 51.253 | 50.833 | 50.793 |
| NMFRS | 49.269 | 56.839 | 56.419 | 55.979 |
| MFRS | 55.676 | 55.246 | 54.826 | 54.386 |
| Monolayer enthalpy of desorption (H$_m$) |||||
| NMNFRS | 53.712 | 53.282 | 52.862 | 52.422 |
| MNFRS | 42.237 | 41.807 | 41.387 | 40.947 |
| NMFRS | 64.752 | 64.322 | 63.902 | 63.462 |
| MFRS | 47.258 | 46.838 | 46.418 | 45.978 |
| Multilayer enthalpy of adsorption (H$_n$) |||||
| NMNFRS | 42.205 | 41.775 | 41.355 | 40.915 |
| MNFRS | 41.805 | 41.376 | 40.956 | 40.516 |
| NMFRS | 31.419 | 38.989 | 38.569 | 38.129 |
| MFRS | 39.539 | 39.109 | 38.689 | 38.249 |
| Multilayer enthalpy of desorption (H$_n$) |||||
| NMNFRS | 41.964 | 41.534 | 41.114 | 40.674 |
| MNFRS | 41.847 | 41.417 | 40.997 | 40.557 |
| NMFRS | 42.246 | 41.816 | 41.396 | 40.956 |
| MFRS | 41.290 | 40.860 | 40.440 | 40.000 |
| NMNFRS: Non-malted-non-fermented rice + soybean, MNFRS: Malted-non-fermented rice + soybean, NMFRS: Non-malted-fermented rice + soybean, MFRS: Malted-fermented rice + soybean. |||||
Surface area of solids of the formulated food products
Table 7 showed the total surface area of solids. The total surface area of FARO 44 products varied from 80.24 to 162.02 m$^2$/g solids, with sample MNFRS recorded highest total surface area and MFRS the lowest at 20 $^o$C (desorption) and 40 $^o$C (adsorption) respectively. The total surface area of solids mostly decreased as temperature increased up to 40 $^o$C except for sample NMFRS values varied as temperature increased. Similar trends are also in agreement with the findings by Ariahu et al.. In their study, the total surface area of crayfish varied from 79.7 to 128.5 m$^2$/g solids as temperature increased (adsorption) and also decreased from 192.60 to 94.90 m$^2$/g solids as temperature increased (desorption). However, some values were either higher or lower than the ones obtained. Igbabul et al. found apparent surface area (182.34 to 513.34 m$^2$/g solids) of African arrowroot lily products decreased with increasing temperatures. The total surface area of solids in their study findings is much higher than the ones obtained in this study and those reported by Ariahu et al.. Another much higher total surface area value of solids was obtained by Moraes et al. on apple Fuji (196 to 315 m$^2$/g solids) and garlic (374.5 to 588 to m$^2$/g solids). Their findings showed decreasing of total surface area as temperature increased (50, 60 and 70 $^o$C).
Table 7. Total surface area of water binding (m$^2$/g solid) for solids of the formulated food products :
| Adsorption | NMNFRS | MNFRS | NMFRS | MFRS |
| 20 $^o$C | 134.20 | 144.77 | 81.64 | 101.28 |
| 30 $^o$C | 125.94 | 106.23 | 114.95 | 110.55 |
| 40 $^o$C | 94.29 | 95.73 | 94.22 | 80.24 |
| 50 $^o$C | 123.52 | 117.86 | 101.70 | 87.97 |
| Desorption | | | | |
| 20 $^o$C | 140.06 | 162.02 | 99.56 | 143.30 |
| 30 $^o$C | 127.24 | 99.73 | 109.13 | 122.22 |
| 40 $^o$C | 92.36 | 108.24 | 105.92 | 84.49 |
| 50 $^o$C | 117.76 | 122.96 | 98.65 | 86.81 |
| NMNFRS: Non-malted-non-fermented rice + soybean, MNFRS: Malted-non-fermented rice + soybean, NMFRS: Non-malted-fermented rice + soybean, MFRS: Malted-fermented rice + soybean. |||||
Net isosteric heat of sorption predicting drying characteristics of the formulated food products
The isosteres obtained from Clausius–Claperyon relationships between water activity and absolute temperature (Figures 4) at water contents of 2 to 12% and their respective isosteric heat of sorption are provided in Figure 5. The regression parameters are given in Tables 8 (adsorption) and 9 (desorption). The intercept which relates to the entropy of sorption ranged from - 0.745 to 0.511 (NMNFRS), 0.486 to 2.965 (MNFRS), 1.191 to 2.479 (NMFRS), 0.589 to 2.572 (MFRS) respectively. For the desorption mode, the intercept ranged from -0.931 to 0.235 (NMNFRS), 0.433 to 2.677 (MNFRS), 0.476 to 2.313 (NMFRS), and 1.245 to 3.610 (MFRS). The slopes which represent the magnitudes of net isosteric heats (ΔH$_{st}$) ranged from 0.043 to 5.695 kJ/mol (NMNFRS), 2.453 to 12.138 kJ/mol (MNFRS), 4.232 to 10.875 kJ/mol (NMFRS) and 2.685 to 11.099 kJ/mol (MFRS) respectively. Also, for the desorption mode, the net isosteric heat ranged from 0.449 to 5.363 kJ/mol (NMNFRS), 2.478 to 11.872 kJ/mol (MNFRS), 2.586 to 10.925 kJ/mol (NMFRS) and 4.490 to 14.200 kJ/mol (MFRS) respectively. The regression coefficients ranged from 0.795 to 0.991 for the adsorption plots and 0.880 to 962 for the Clausius–Claperyon desorption plots. It was observed that the data points of the second plots (i.e., from the linear regression parameters) decreased exponentially with increase in the moisture content of the food materials. Net isosteric heat of both adsorption and desorption isotherms as a function of moisture content for non-malted - non fermented rice + soybean decreased rapidly as moisture content increased. These rates of rapid decrease were observed higher in non-malted - non fermented rice + soybean, followed by malted - non fermented rice + soybean, malted –
fermented rice + soybean and non-malted fermented rice + soybean. Maximum net isosteric heat with slight variation among formulations was observed throughout except for non-malted - non fermented rice + soybean which was much lower.
The net isosteric heat of sorption is the minimum amount of energy required to remove (desorption) or add (adsorption) a given amount of water to a hygroscopic material. Similarly, net isosteric heat of sorption (ΔH$_{st}$) is the energy difference between total heat of sorption (H$_1$) and the heat of vaporization (H$_v$) . In practice during drying, small amount of heat or energy is enough to initiate drying and to remove the free water from solids, followed by a larger amount of heat application to remove the remaining strongly bound water from same solids (net isosteric heat increases with decreasing moisture, Figure 5). The resultant heats would account for the amount of heat required for drying. According to GAB model concepts, any residual moisture in the well-dried solids would account for those in the monolayer region which is difficult to be removed by ordinary drying process because of its very strongly bound nature (H-bonded water). Andrade et al. reported that this water is unfreeze-able and it is not available for chemical reactivity. So, it may not pose traits during storage since the moisture of the solids have reduced to monolayer. And if such drying process adequately have subjected the solids to reach level of monolayer moisture, then the product would have adequate keeping quality. As elucidates in another report, moisture contents in the monolayer are tightly bound to the solids, and so require high energy capacity to remove its water contents. As moisture content of the solids is increasing, the most active sites of solids become occupied and sorption occurs on the less active sites giving lower heat of sorption. Application of Clausius-Clapeyron equation for determining the differential heat of sorption is an alternative economical method to the calorimetric method of determining heat of sorption. The net enthalpy required for product dehydration. Report by Raman shows Clausius-Clapeyron isosteric method of determining heat of sorption often yield nearly same result as the calorimetric method. One of the disadvantages of this method is that it cannot account for heat offered by a specific temperature (e.g., 20 $^o$C) simply because of the regression analysis that often-employed range of temperatures. It can then be seen, drying is the practical application of desorption since water or moisture goes out of the solid materials of food.
Isosteric heat applies to desorption and is being used for studying the drying characteristics of foods under law-moisture. The net isosteric heat of sorption is a function of moisture content as reported by Yogendrarajah et al. and as observed in Figures 4 and 5. The dependency of the net isosteric heat of sorption on the equilibrium moisture content was fitted with linear regression. The data points of the second plots from the linear regression parameters decreased exponentially with increase in moisture content of the food materials until it approaches the latent heat of vaporization of pure water (ΔH$_{st}$ = 0 kJ/mol). A similar trend was reported in previous studies. This could be due to the different strengths of water binding. Initial occupation of the highly active polar sites on the surface could be difficult due to high interaction energy and subsequent filling of the less active sites could become possible with low energy. These findings have been observed to be in harmony with many agricultural products. The higher value of isosteric heat of sorption at values of low moisture content signifies high interactive energy between surface sites and moisture as the material approaches a monomolecular layer of water molecules. On the other hand, it may value the spontaneity of the food system and could help to identify the physical, chemical and microbiological stability of food.
Table 8: Linear regression parameters of Clausius-Clapeyron adsorption temperature dependence of the formulated food products :
| | | Moisture content (g/100 g food) | Moisture content (g/100 g food) | Moisture content (g/100 g food) | Moisture content (g/100 g food) | Moisture content (g/100 g food) | Moisture content (g/100 g food) |
| Products | | 2 | 4 | 6 | 8 | 10 | 12 |
| NMNFRS | Parameters | | | | | | |
| | Intercept | 0.511 | -0.364 | -0.745 | -0.652 | | |
| | Slope | -685 | -293 | -89 | -50 | | |
| | r$^2$ | 0.9415 | 0.974 | 0.964 | 0.933 | | |
| MNFRS | Intercept | 2.965 | 1.515 | 0.8510 | 0.637 | 0.543 | 0.486 |
| | Slope | -1460 | -880 | -584 | -447 | -361 | -295 |
| | r$^2$ | 0.884 | 0.884 | 0.870 | 0.823 | 0.750 | 0.636 |
| NMFRS | Intercept | 2.479 | 1.665 | 1.360 | 1.250 | 1.210 | 1.191 |
| | Slope | -1308 | -924 | -738 | -633 | -563 | -509 |
| | r$^2$ | 0.833 | 0.918 | 0.974 | 0.991 | 0.980 | 0.956 |
| MFRS | Intercept | 2.572 | 1.210 | 0.967 | 0.741 | 0.655 | 0.589 |
| | Slope | -1335 | -788 | -616 | -476 | -392 | -323 |
| | r$^2$ | 0.971 | 0.965 | 0.795 | 0.991 | 0.981 | 0.938 |
| NMNFRS = Non-malted-non-fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, r$^2$ = Coefficient of determination, I = Intercept coefficient. ||||||||
Table 9: Linear regression parameters of Clausius-Clapeyron desorption temperature dependence of the formulated food products :
| | | Moisture content (g/100 g food) | Moisture content (g/100 g food) | Moisture content (g/100 g food) | Moisture content (g/100 g food) | Moisture content (g/100 g food) | Moisture content (g/100 g food) |
| Products | | 2 | 4 | 6 | 8 | 10 | 12 |
| NMNFRS | Intercept | 0.245 | -0.621 | -0.931 | | | |
| | Slope | -645 | -242 | -54 | | | |
| | r$^2$ | 0.880 | 0.917 | 0.900 | | | |
| MNFRS | Intercept | 2.677 | 1.114 | 0.5975 | 0.433 | 0.436 | 0.453 |
| | Slope | -1428 | -792 | -531 | -404 | -344 | -298 |
| | r$^2$ | 0.883 | 0.911 | 0.876 | 0.916 | 0.975 | 0.964 |
| NMFRS | Intercept | 2.313 | 1.029 | 0.617 | 0.476 | 0.490 | 0.483 |
| | Slope | -1314 | -767 | -539 | -420 | -364 | -311 |
| | r$^2$ | 0.965 | 0.949 | 0.907 | 0.917 | 0.939 | 0.935 |
| MFRS | Intercept | 3.610 | 1.921 | 1.405 | 1.293 | 1.246 | 1.245 |
| | Slope | -1708 | -1036 | -776 | -666 | -591 | -540 |
| | r$^2$ | 0.909 | 0.888 | 0.880 | 0.939 | 0.962 | 0.960 |
| NMNFRS = Non-malted-non-fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, r$^2$ = Coefficient of determination, I = Intercept coefficient. ||||||||
Predicted shelf of the formulated food products
Tables 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 and 21 showed predictive shelf life of formulated food products in storage conditions of low-and high-density polyethene packages at temperatures of 20, 30 and 40 $^o$C and their corresponding relative humidity are 50 and 80% each. The predicted shelf life of formulated products varied irrespective of temperature, relative humidity or packaging material and also increased with an increase in temperature, relative humidity and in high-density polyethene package compared with the low-density polyethene package. The estimated shelf life of these formulated products ranged from 1059 (MFRS) to 1992523 days (NMNFRS), where their low-density polyethylene (LDPE) and high-density polyethene (HDPE) packages are placed within predictive storage conditions of 40 $^o$C/80% relative humidity and 20 $^o$C/80% relative humidity respectively.
In Table 10, where formulated products are predicted in LDPE package at the storage conditions of 20 $^o$C and 50% relative humidity, their shelf life ranged from 52063 (NMFRS) to 195706 days (NMNFRS). These results were observed to be lower than the other ones stored at 20 $^o$C (Tables 11, 12 and 13) with varying conditions of storage in terms of relative humidity or polyethene packages. In Table 11, where the products stored are in HDPE packages, with storage conditions are 20 $^o$C and 50% relative humidity, resulted in an estimated shelf life from the range of 408841 (NMFRS) to 1536846 days (NMNFRS), which was observed to be the second highest category in terms of predicted shelf-life durations. In Table 12, the estimated shelf life of the formulated products ranged from 140053 (NMFRS) to 349959 days (MFRS), which was predicted in an adequate storage standard LDPE within the storage conditions of 20 $^o$C and relative humidity of 80%, was observed to be the number third position other sets with estimated higher shelf-life durations. In Table 13, the predicted shelf life of formulated products in HDPE package with the storage conditions of 20 $^o$C and 80% relative humidity ranged from 644411 (NMFRS) to 1992523 days (NMNFRS). It was observed that this set had the highest estimated shelf life among all the various sets. At 20 $^o$C, irrespective of relative humidity or packaging materials, NMNFRS had the highest estimated shelf life, followed by samples MNFRS, MFRS and NMFRS.
At 30 $^o$C storage conditions, there were new trends. In Table 14, the predicted shelf life of the formulated products in LDPE (at 30 $^o$C/50% relative humidity) ranged from 23836 (MNFRS) to 45649 days (MFRS). Among those 30 $^o$C sets of storage conditions (Tables 14, 15 and 16), those in LDPE packages with 30 $^o$C and 50% relative humidity (Table 14) had the lowest estimated shelf life, followed by those in Tables 16, 17 and 15 respectively and their corresponding shelf life ranged from 93568 (MNFRS) to 291189 days (MFRS), 111281 (MNFRS) to 349426 days (MFRS) and 226448 (MNFRS) to 433669 days (MFRS). Generally, it was observed that at 30 $^o$C irrespective of packaging materials and relative humidity, sample MFRS had the highest estimated shelf life, followed by samples NMFRS, NMNFRS and MNFRS. This shows that fermentation a has great advantage over the keeping-qualities of foods, especially at slightly higher temperatures above 20 $^o$C.
At 40 $^o$C, there were also slight changes in trends. In Tables 18, 19, 20 and 21, the predicted shelf life of the formulated products ranged from 2311 (NMNFRS) to 24703 days (MFRS), 26372 (NMNFRS) to 281891 days (MFRS), 1059 (MFRS) to 6405 days (MNFRS) and 15718 (MFRS) to 95087 days (MNFRS) respectively. In Table 18, where LDPE packages are within predictive conditions of 40 $^o$C/50% relative humidity, samples MFRS had the highest estimated shelf life followed by samples MNFRS, NMFRS and NMNFRS. In Table 19, where the predictive conditions are 40 $^o$C/50% relative humidity and HDPE package usage, sample MFRS was observed to have the highest estimated shelf life, followed by samples NMFRS, MNFRS and NMNFRS. However, at the predictive conditions of 40 $^o$C, 80% relative humidity and the usage of LDPE packages (Table 20), showed the estimated shelf life of all the formulated products to be the lowest compared to all the various sets of conditions used for estimating their shelf life. Hence, sample MFRS was observed to be the lowest in terms of estimated shelf life, followed by samples NMNFRS, NMFRS and MNFRS. This means, storing these formulated products at 40 $^o$C, 80% relative humidity and stipulated usage of the LDPE package at that condition would be inappropriate. Therefore, it is advisable to avoid storing low-moisture foods at 40 $^o$C/80% relative humidity in the LDPE package. Alternatively, 20 to 30 $^o$C and low relative humidity is recommended to prevent rapid set on spoilage and avoidance of unnoticeable growth or proliferation of pathogenic microorganisms in foods which may be detrimental to the health of consumers if such foods are consumed. In Table 21 (at 40 $^o$C/80% relative humidity and HDPE packaging usage), there was no change of trends as compared to the influential storage conditions in Table 20 except in terms of the magnitude of the estimated shelf life of the formulated products, where the predicted shelf life of the formulated products (Table 21) compared to those in Table 20.
Generally, throughout the temperatures of 20 and 30 $^o$C, NMNFRS and MNFRS exhibited higher predicted shelf life respectively. At 40 $^o$C, their shelf life was observed to be higher except at 40 $^o$C and 80% relative humidity level in the LDPE package. Above 20 $^o$C, MFRS mostly exhibited higher levels of predicted shelf life irrespective of temperatures, relative humidity and the type of packaging material, whereas NMNFRS had the highest predicted shelf life throughout the 20 $^o$C set of packages.
Packaging of food is important for preserving food quality, reducing food wastage and minimizing the use of chemical additive for food preservation. Sorption isotherms are valuable for shelf-life prediction. Shelf-life studies can provide important information to product developers to ensure that the consumer will see a high-quality product for a significant period after production. Certainly, long shelf-life studies do not fit with the speed requirement and therefore accelerated studies or computer-simulated predictions have been developed as part of innovation, which often employed complex algorithms for solutions. Also, the rate at which reactions occur in foods, the effects of temperature, moisture and the immeasurable effect of other parameters on foods have become necessary factors contributing to the science of accelerated shelf-life studies. In this study, it is evident that the rate of permeation of water vapour or moisture as confirmed through the standard (grade one) low- or high-density polyethene would not pose a significant effect on the shelf life of the formulated food products if adequately packaged in grade one polyethene and stored within the standard reference condition. It becomes obvious that quick spoilage of low-moisture foods packaged in polyethene may be due to the poor quality of the polymers itself owing to failures of polymer manufacturers adhering to production standards. Such that storing foods in such substandard polymers would not offer moisture-free environmental protection and so predisposed food to deterioration. The long-time (days) in all the predicted shelf life was characterized by the permeability characteristics together with the working linear equations of the sorption isotherms described by Sherma et al., which means the time taken for moisture permeation through the barriers of the polyethene into the food material until an equilibrium is established between the food and the humidity of the storing environment, hence spoilage is set. Equilibrium moisture establishment between the food and the storage environment is critical for spoilage of low-moisture foods due to moisture adsorption by the food. Ideally, low-moisture foods are not expected to spoil in moisture-free environment where there are no other external conditions such as light interfering with the food.
A shelf-life study reported by Anandito et al. reviled fish Koya packed in metalized plastic and stored at 30 °C was reduced with an increase in relative humidity (RH) and resulting in a shelf-life of fish Koya for 234 days at 75% relative humidity, 203 days at 80% relative humidity as well as 180 days at 85% relative humidity. Similarly, a study by Ekafitri et al. assessed shelf-life of the banana bars under storage conditions of 30 °C with relative humidity of 80% in three types of packaging (aluma, aluminium foil, and metalized plastic) within a period of 30 days and their findings of shelf life of banana bar products in aluminium foil pack were 511.15 days and aluma pack was 458.72 days, much longer than those packaged in metalized plastic which confirmed 80.95 days shelf life which is much lower compared to this current findings. Therefore, it is important to evaluate the integrity of packing materials before commencing a shelf-life study of any food as reviled in this study. Packaging materials have a shelf-life which upon degradation or decomposition would certainly reduce the expected shelf life of the packaged food material. Hence, it is expected that when determining or predicting the shelf-life of food, the packaging materials’ shelf-life should be taken into consideration because there is no ideal package that is not prone to deterioration or other environmental hazards which may influence permeation. All packaging materials including glasses and metals which are very rigid and have high resistance to environmental conditions, do decompose over time. Evaluating the packaging integrity would help to harmonize the results of researchers’ findings and provide or establish useful information on the shelf-life of foods.
Table 10. Predicted shelf life (at 20 $^o$C/50% RH) of formulated food products in low density polyethylene (LDPE) :
| Parameter | NMNFRS | MNFRS | NMFRS | MFRS |
| Initial moisture content Mi (gH$_2$O/g solids) | 2.10 | 2.80 | 2.25 | 3.60 |
| Equilibrium moisture content Me (gH$_2$O/g solids) | 6.36 | 6.48 | 5.41 | 7.10 |
| Critical moisture content Mc (gH$_2$O/g solids) | 5.25 | 5.45 | 3.45 | 6.15 |
| Slope of isotherms | 8.51 | 7.36 | 6.32 | 6.99 |
| Packaging permeability (g/m$^2$.day.mmHg) of LDPE at 20 $^o$C/50% RH | 0.0011 | 0.0011 | 0.0011 | 0.0011 |
| Packaging area A (m$^2$) | 0.0151 | 0.0151 | 0.0151 | 0.0151 |
| Weight of solids W (g) | 5 | 5 | 5 | 5 |
| Saturated vapour pressure (P$_o$) of pure H$_2$O (mmHg) at 20 $^o$C | 17.54 | 17.54 | 17.54 | 17.54 |
| Me - Mi/Me – Mc | 3.83 | 3.57 | 1.61 | 3.50 |
| 1n Me - Mi/Me – Mc | 1.34 | 1.27 | 1.61 | 1.25 |
| Shelf life (days) | 195706 | 160417 | 52063 | 149954 |
| NMNFRS = Non-malted-non fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted-fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, RH = Relative humidity. |||||
Table 11. Predicted shelf life (at 20 $^o$C/50% RH) of formulated food products in high density polyethylene (HDPE) :
| Parameter | NMNFRS | MNFRS | NMFRS | MFRS |
| Initial moisture content Mi (gH$_2$O/g solids) | 2.10 | 2.80 | 2.25 | 3.60 |
| Equilibrium moisture content Me (gH$_2$O/g solids) | 6.36 | 6.48 | 5.41 | 7.10 |
| Critical moisture content Mc (gH$_2$O/g solids) | 5.25 | 5.45 | 3.45 | 6.15 |
| Slope of isotherms | 8.51 | 7.36 | 6.32 | 6.99 |
| Packaging permeability (g/m$^2$.day.mmHg) of HDPE at 20 $^o$C/50% RH | 0.00014 | 0.00014 | 0.00014 | 0.00014 |
| Packaging area A (m$^2$) | 0.0151 | 0.0151 | 0.0151 | 0.0151 |
| Weight of solids W (g) | 5 | 5 | 5 | 5 |
| Saturated vapour pressure (P$_o$) of pure H$_2$O (mmHg) at 20 $^o$C | 17.54 | 17.54 | 17.54 | 17.54 |
| Me - Mi/Me – Mc | 3.83 | 3.57 | 1.61 | 3.50 |
| 1n Me - Mi/Me – Mc | 1.34 | 1.27 | 1.61 | 1.25 |
| Shelf life (days) | 1536846 | 1259730 | 408841 | 1177561 |
| NMNFRS = Non-malted-non fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted-fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, RH = Relative humidity. |||||
Table 12. Predicted shelf life (at 20 $^o$C/80% RH) of formulated food products in low density polyethylene (LDPE) :
| Parameter | NMNFRS | MNFRS | NMFRS | MFRS |
| Initial moisture content Mi (gH$_2$O/g solids) | 2.10 | 2.80 | 2.25 | 3.60 |
| Equilibrium moisture content Me (gH$_2$O/g solids) | 8.91 | 8.69 | 7.31 | 9.19 |
| Critical moisture content Mc (gH$_2$O/g solids) | 5.25 | 5.45 | 3.45 | 6.15 |
| Slope of isotherms | 8.51 | 7.36 | 6.32 | 6.99 |
| Packaging permeability (g/m$^2$.day.mmHg) of LDPE at 20 $^o$C/80% RH | 0.00023 | 0.00023 | 0.00023 | 0.0023 |
| Packaging area A (m$^2$) | 0.0151 | 0.0151 | 0.0151 | 0.0151 |
| Weight of solids W (g) | 5 | 5 | 5 | 5 |
| Saturated vapour pressure (P$_o$) of pure H$_2$O (mmHg) at 20 $^o$C | 17.54 | 17.54 | 17.54 | 17.54 |
| Me - Mi/Me – Mc | 1.86 | 1.82 | 1.31 | 1.84 |
| 1n Me - Mi/Me – Mc | 0.62 | 0.60 | 0.27 | 0.61 |
| Shelf life (days) | 433043 | 362443 | 140053 | 349959 |
| NMNFRS = Non-malted-non fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted-fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, RH = Relative humidity. |||||
Table 13. Predicted shelf life (at 20 $^o$C/80% RH) of formulated food products in high density polyethylene (HDPE) :
| Parameter | NMNFRS | MNFRS | NMFRS | MFRS |
| Initial moisture content Mi (gH$_2$O/g solids) | 2.10 | 2.80 | 2.25 | 3.60 |
| Equilibrium moisture content Me (gH$_2$O/g solids) | 8.91 | 8.69 | 7.31 | 9.19 |
| Critical moisture content Mc (gH$_2$O/g solids) | 5.25 | 5.45 | 3.45 | 6.15 |
| Slope of isotherms | 8.51 | 7.36 | 6.32 | 6.99 |
| Packaging permeability (g/m$^2$.day.mmHg) of HDPE at 20 $^o$C/80% RH | 0.00005 | 0.00005 | 0.00005 | 0.00005 |
| Packaging area A (m$^2$) | 0.0151 | 0.0151 | 0.0151 | 0.0151 |
| Weight of solids W (g) | 5 | 5 | 5 | 5 |
| Saturated vapour pressure (P$_o$) of pure H$_2$O (mmHg) at 20 $^o$C | 17.54 | 17.54 | 17.54 | 17.54 |
| Me - Mi/Me – Mc | 1.86 | 1.82 | 1.31 | 1.84 |
| 1n Me - Mi/Me – Mc | 0.62 | 0.60 | 0.27 | 0.61 |
| Shelf life (days) | 1992523 | 1667674 | 644411 | 1610234 |
| NMNFRS = Non-malted-non fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted-fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, RH = Relative humidity. |||||
Table 14. Predicted shelf life (at 30 $^o$C/50% RH) of formulated food products in low density polyethylene (LDPE) :
| Parameter | NMNFRS | MNFRS | NMFRS | MFRS |
| Initial moisture content Mi (gH$_2$O/g solids) | 2.40 | 3.00 | 2.60 | 2.55 |
| Equilibrium moisture content Me (gH$_2$O/g solids) | 4.35 | 4.17 | 4.62 | 4.95 |
| Critical moisture content Mc (gH$_2$O/g solids) | 3.90 | 3.90 | 4.20 | 4.35 |
| Slope of isotherms | 3.9 | 2.37 | 4.04 | 4.80 |
| Packaging permeability (g/m$^2$.day.mmHg) of LDPE at 30 $^o$C/50% RH | 0.00016 | 0.00016 | 0.00016 | 0.00016 |
| Packaging area A (m$^2$) | 0.0151 | 0.0151 | 0.0151 | 0.0151 |
| Weight of solids W (g) | 5 | 5 | 5 | 5 |
| Saturated vapour pressure (P$_o$) of pure H$_2$O (mmHg) at 30 $^o$C | 31.84 | 31.84 | 31.84 | 31.84 |
| Me - Mi/Me – Mc | 4.35 | 4.33 | 4.81 | 4.00 |
| 1n Me - Mi/Me – Mc | 1.50 | 1.47 | 1.57 | 1.39 |
| Shelf life (days) | 40025 | 23836 | 43397 | 45649 |
| NMNFRS = Non-malted-non fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted-fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, RH = Relative humidity.. |||||
Table 15. Predicted shelf life (at 30 $^o$C/50% RH) of formulated food products in high density polyethylene (HDPE) :
| Parameter | NMNFRS | MNFRS | NMFRS | MFRS |
| Initial moisture content Mi (gH$_2$O/g solids) | 2.40 | 3.00 | 2.60 | 2.55 |
| Equilibrium moisture content Me (gH$_2$O/g solids) | 4.35 | 4.17 | 4.62 | 4.95 |
| Critical moisture content Mc (gH$_2$O/g solids) | 3.90 | 3.90 | 4.20 | 4.35 |
| Slope of isotherms | 3.9 | 2.37 | 4.04 | 4.80 |
| Packaging permeability (g/m$^2$.day.mmHg) of HDPE at 30 $^o$C/50% RH | 0.00152 | 0.00152 | 0.00152 | 0.00152 |
| Packaging area A (m$^2$) | 0.0151 | 0.0151 | 0.0151 | 0.0151 |
| Weight of solids W (g) | 5 | 5 | 5 | 5 |
| Saturated vapour pressure (P$_o$) of pure H$_2$O (mmHg) at 30 $^o$C | 31.84 | 31.84 | 31.84 | 31.84 |
| Me - Mi/Me – Mc | 4.35 | 4.33 | 4.81 | 4.00 |
| 1n Me - Mi/Me – Mc | 1.50 | 1.47 | 1.57 | 1.39 |
| Shelf life (days) | 380240 | 226448 | 412272 | 433669 |
| NMNFRS = Non-malted-non fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted-fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, RH = Relative humidity.. |||||
Table 16. Predicted shelf life (at 30 $^o$C/80% RH) of formulated food products in low density polyethylene (LDPE) :
| Parameter | NMNFRS | MNFRS | NMFRS | MFRS |
| Initial moisture content Mi (gH$_2$O/g solids) | 2.40 | 3.00 | 2.60 | 2.25 |
| Equilibrium moisture content Me (gH$_2$O/g solids) | 5.52 | 5.69 | 5.83 | 6.39 |
| Critical moisture content Mc (gH$_2$O/g solids) | 3.90 | 3.90 | 4.20 | 4.35 |
| Slope of isotherms | 3.90 | 2.37 | 4.04 | 4.80 |
| Packaging permeability (g/m$^2$.day.mmHg) of LDPE at 30 $^o$C/80% RH | 0.00108 | 0.00108 | 0.00108 | 0.00108 |
| Packaging area A (m$^2$) | 0.0151 | 0.0151 | 0.0151 | 0.0151 |
| Weight of solids W (g) | 5 | 5 | 5 | 5 |
| Saturated vapour pressure (P$_o$) of pure H$_2$O (mmHg) at 30 $^o$C | 31.84 | 31.84 | 31.84 | 31.84 |
| Me - Mi/Me – Mc | 1.93 | 1.50 | 1.98 | 1.88 |
| 1n Me - Mi/Me – Mc | 0.66 | 0.41 | 0.68 | 0.63 |
| Shelf life (days) | 247857 | 93568 | 264535 | 291189 |
| NMNFRS = Non-malted-non fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted-fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, RH = Relative humidity.. |||||
Table 17. Predicted shelf life (at 30$^o$C/80% RH) of formulated food products in high density polyethylene (HDPE) :
| Parameter | NMNFRS | MNFRS | NMFRS | MFRS |
| Initial moisture content Mi (gH$_2$O/g solids) | 2.40 | 3.00 | 2.60 | 2.25 |
| Equilibrium moisture content Me (gH$_2$O/g solids) | 5.52 | 5.69 | 5.83 | 6.39 |
| Critical moisture content Mc (gH$_2$O/g solids) | 3.90 | 3.90 | 4.20 | 4.35 |
| Slope of isotherms | 3.90 | 2.37 | 4.04 | 4.80 |
| Packaging permeability (g/m$^2$.day.mmHg) of HDPE at 30 $^o$C/80% RH | 0.00009 | 0.00009 | 0.00009 | 0.00009 |
| Packaging area A (m$^2$) | 0.0151 | 0.0151 | 0.0151 | 0.0151 |
| Weight of solids W (g) | 5 | 5 | 5 | 5 |
| Saturated vapour pressure (P$_o$) of pure H$_2$O (mmHg) at 30 $^o$C | 31.84 | 31.84 | 31.84 | 31.84 |
| Me - Mi/Me – Mc | 1.93 | 1.50 | 1.98 | 1.88 |
| 1n Me - Mi/Me – Mc | 0.66 | 0.41 | 0.68 | 0.63 |
| Shelf life (days) | 297428 | 111281 | 317441 | 349426 |
| NMNFRS = Non-malted-non fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted-fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, RH = Relative humidity. |||||
Table 18. Predicted shelf life (at 40 $^o$C/50% RH) of formulated food products in low density polyethylene (LDPE) :
| Parameter | NMNFRS | MNFRS | NMFRS | MFRS |
| Initial moisture content Mi (gH$_2$O/g solids) | 3.60 | 2.70 | 2.60 | 2.55 |
| Equilibrium moisture content Me (gH$_2$O/g solids) | 3.86 | 4.22 | 4.05 | 4.67 |
| Critical moisture content Mc (gH$_2$O/g solids) | 3.80 | 3.90 | 2.99 | 4.35 |
| Slope of isotherms | 0.51 | 3.04 | 2.91 | 4.24 |
| Packaging permeability (g/m$^2$.day.mmHg) of LDPE at 40 $^o$C/50% RH | 0.00194 | 0.00194 | 0.00194 | 0.00194 |
| Packaging area A (m$^2$) | 0.0151 | 0.0151 | 0.0151 | 0.0151 |
| Weight of solids W (g) | 5 | 5 | 5 | 5 |
| Saturated vapour pressure (P$_o$) of pure H$_2$O (mmHg) at 40 $^o$C | 55.37 | 55.37 | 55.37 | 55.37 |
| Me - Mi/Me – Mc | 4.33 | 4.75 | 1.37 | 6.63 |
| 1n Me - Mi/Me – Mc | 1.47 | 1.56 | 0.31 | 1.89 |
| Shelf life (days) | 2311 | 14619 | 2781 | 24703 |
| NMNFRS = Non-malted-non fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted-fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, RH = Relative humidity. |||||
Table 19. Predicted shelf life (at 40 $^o$C/50% RH) of formulated food products in high density polyethylene (HDPE) :
| Parameter | NMNFRS | MNFRS | NMFRS | MFRS |
| Initial moisture content Mi (gH$_2$O/g solids) | 3.60 | 2.70 | 2.60 | 2.55 |
| Equilibrium moisture content Me (gH$_2$O/g solids) | 3.86 | 4.22 | 4.05 | 4.67 |
| Critical moisture content Mc (gH$_2$O/g solids) | 3.80 | 3.90 | 2.99 | 4.35 |
| Slope of isotherms | 0.51 | 3.04 | 2.91 | 4.24 |
| Packaging permeability (g/m$^2$.day.mmHg) of HDPE at 40 $^o$C/50% RH | 0.00017 | 0.00017 | 0.00017 | 0.00017 |
| Packaging area A (m$^2$) | 0.0151 | 0.0151 | 0.0151 | 0.0151 |
| Weight of solids W (g) | 5 | 5 | 5 | 5 |
| Saturated vapour pressure (P$_o$) of pure H$_2$O (mmHg) at 40 $^o$C | 55.37 | 55.37 | 55.37 | 55.37 |
| Me - Mi/Me – Mc | 4.33 | 4.75 | 1.37 | 6.63 |
| 1n Me - Mi/Me – Mc | 1.47 | 1.56 | 0.31 | 1.89 |
| Shelf life (days) | 26372 | 27986 | 31733 | 281891 |
| NMNFRS = Non-malted-non fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted-fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, RH = Relative humidity. |||||
Table 20. Predicted shelf life (at 40 $^o$C/80% RH) of formulated food products in low density polyethylene (LDPE) :
| Parameter | NMNFRS | MNFRS | NMFRS | MFRS |
| Initial moisture content Mi (gH$_2$O/g solids) | 3.60 | 2.70 | 2.90 | 2.50 |
| Equilibrium moisture content Me (gH$_2$O/g solids) | 4.00 | 5.13 | 4.93 | 2.96 |
| Critical moisture content Mc (gH$_2$O/g solids) | 3.80 | 3.90 | 3.75 | 2.75 |
| Slope of isotherms | 0.51 | 3.04 | 2.91 | 0.51 |
| Packaging permeability (g/m$^2$.day.mmHg) of LDPE at 40 $^o$C/80% RH | 0.00193 | 0.00193 | 0.00193 | 0.00193 |
| Packaging area A (m$^2$) | 0.0151 | 0.0151 | 0.0151 | 0.0151 |
| Weight of solids W (g) | 5 | 5 | 5 | 5 |
| Saturated vapour pressure (P$_o$) of pure H$_2$O (mmHg) at 40 $^o$C | 55.37 | 55.37 | 55.37 | 55.37 |
| Me - Mi/Me – Mc | 2.00 | 1.98 | 1.97 | 1.95 |
| 1n Me - Mi/Me – Mc | 0.69 | 0.68 | 0.68 | 0.67 |
| Shelf life (days) | 1090 | 6405 | 6131 | 1059 |
| NMNFRS = Non-malted-non fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted-fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, RH = Relative humidity. |||||
Table 21. Predicted shelf life (at 40 $^o$C/80% RH) of formulated food products in high density polyethylene (HDPE) :
| Parameter | NMNFRS | MNFRS | NMFRS | MFRS |
| Initial moisture content Mi (gH$_2$O/g solids) | 3.60 | 2.70 | 2.90 | 2.50 |
| Equilibrium moisture content Me (gH$_2$O/g solids) | 4.00 | 5.13 | 4.93 | 2.96 |
| Critical moisture content Mc (gH$_2$O/g solids) | 3.80 | 3.90 | 3.75 | 2.75 |
| Slope of isotherms | 0.51 | 3.04 | 2.91 | 0.51 |
| Packaging permeability (g/m$^2$.day.mmHg) of HDPE at 40 $^o$C/80% RH | 0.00013 | 0.00013 | 0.00013 | 0.00013 |
| Packaging area A (m$^2$) | 0.0151 | 0.0151 | 0.0151 | 0.0151 |
| Weight of solids W (g) | 5 | 5 | 5 | 5 |
| Saturated vapour pressure (P$_o$) of pure H$_2$O (mmHg) at 40 $^o$C | 55.37 | 55.37 | 55.37 | 55.37 |
| Me - Mi/Me – Mc | 2.00 | 1.98 | 1.97 | 1.95 |
| 1n Me - Mi/Me – Mc | 0.69 | 0.68 | 0.68 | 0.67 |
| Shelf life (days) | 16187 | 95087 | 91021 | 15718 |
| NMNFRS = Non-malted-non fermented rice + soybean flour, MNFRS = Malted-non fermented + soybean flour, NMFRS = Non-malted-fermented rice + soybean flour, MFRS = Malted-fermented rice + soybean flour, RH = Relative humidity. |||||

## Conclusion

BET, GAB and DLP equations were employed for the sorption study using nonlinear regression methods. Isotherms showed temperature dependency. The moisture sorption of the rice-based formulated products exhibited sigmoid-shaped isotherms (type 2). Slight hysteresis occurred. The adsorption and desorption phenomenon of the rice-based formulated food products at low water activity exhibited less sensitivity to the environmental storage conditions. NMNFRS and MNFRS are slightly more hygroscopic than NMFRS and MFRS. GAB and BET monolayer moisture contents and energy constant values mostly varied. But slightly showed temperature dependency. Molar sorption enthalpies and the apparent surface area of solids agreed with many classical findings. Sample MFRS showed the highest thermostable characteristics. The sorption parameters obtained in this study have exhibited adequate drying characteristics and hold the potential for long-keeping qualities of the new rice-based formulated food products.

### Acknowledgements

We thank the Canadian Government, who funded our previous research through the ‘Development of new rice-based products, by the Canadian International Development Agency and Africa Rice Centre under the project ‘Enhancing food security in Africa through the Improvement of rice post-harvest handling, marketing and the development of new rice-based products. Without which, it could have been impossible for feasible transition from our previous research to current ones. We also acknowledge the National Cereals Research Institute, Badeggi, for providing the rice variety (FARO 44), Anaso Sunday Sigismond (Deputy Director Technologist, Department of Food Science and Technology, University of Maiduguri) who supplied and prepared the sulphuric acid concentrations; and Dr. Zachary Cartwright (Lead Food Scientist, Meter Group, USA) who donated MAT 2.0.11.0 for the moisture sorption analysis.

### Competing interests

The authors declare no conflict of interest.