Sorption Isotherms and Moisture Diffusivity in Fried Cassava-Shrimp Chips

Abstract

Equilibrium moisture sorption isotherms of fried cassava-shrimp chips were investigated by measuring water activity at 20, 30, and 40°C for modeling transient diffusion of moisture. The sorption isotherms followed a type III shape in water activity range of 0.1–0.9 showing negligible influence of temperature, and were best represented by the GAB, Henderson, and modified Henderson equations. Effective moisture diffusivity of chips based on analytical solution of Fick's law ranged from 0.8 × 10⁻¹¹ to 2.1 × 10⁻¹⁰ m²/s during exposure to fixed relative humidity (50, 70, and 90%) and temperature (20, 30, and 40°C) environments. An Arrhenius type relationship adequately described the dependence of effective moisture diffusivity both on temperature and relative humidity, and led to good agreement between experimental and estimated transient moisture sorption data.

Keywords:

• Fried cassava-shrimp chips
• Sorption isotherms
• Moisture diffusivity
• Thailand

Introduction

Fried cassava-shrimp chips (Khao Kriap) are popular snack foods in Thailand and other Southeast Asian countries. They are prepared traditionally by gelatinizing the dough formed from a mixture of tapioca flour, water, and flavoring with spices. Other nutritional ingredients such as fish, shrimp, or vegetables are usually added to produce various types of chips.1 The dough is rolled and cut into thin slices for drying subsequently to produce an intermediate product. Frying of slices in hot oil transforms them into expanded and light textured cassava-shrimp chips. Fried cassava-shrimp chips are classified as quick fried snack foods based on the process technology associated with their manufacture.2 Therefore, the quality of chips may be adversely affected by the presence of oxygen and moisture during storage. Oxygen promotes the oxidation of the oils absorbed during frying and results in rancid off-flavor. In addition, moisture gain by the chips during storage may destroy the crisp texture and lead to rejection by consumers.3

Moisture exchange between the food and the environment is one of the basic physical phenomena occurring in foods during processing and storage.4 5 The properties of foods are mainly affected by the amount of water present in any location in the foods. Water activity affects microbial spoilage, enzymatic reactions, and lipid oxidation as well as moisture sorption rate in food products.6 Normally, the relationship between equilibrium moisture content (m _e ) and water activity (a _w ) is presented in the form of either adsorption or desorption isotherm and described in terms of mathematical models. For example, Palou et al.7 described the moisture sorption characteristics of cookies and corn snacks with Peleg's and GAB models. Lewicki8 developed a three-parameter equation for moisture isotherms and fitted to thirty-one food sorption isotherms. Moisture sorption isotherms of composite foods filled with chocolate were determined and fitted with GAB equation by Kim et al.9 In addition, many researchers have studied moisture transfer in food materials in conjunction with equilibrium moisture isotherms. For example, Lomauro et al.4 reported moisture transfer properties of dry and semi-moist foods. Sorption and diffusion properties of peeled almond were determined by Ruiz-Bevia’ et al.10 Phoungchandang and Woods11 presented desorption isotherms and moisture diffusion during drying for whole peeled banana.

Fried cassava-shrimp chips are known to deteriorate during storage mainly by moisture gain. In order to optimize the shelf-life of the fried cassava-shrimp chips, data on moisture sorption isotherms and diffusion characteristics are needed. However, no such information is available for fried cassava-shrimp chips in the published studies. Therefore, the main objectives of this study were the determination of moisture sorption isotherms of fried cassava-shrimp chips and modeling of moisture transfer during storage at different temperatures and relative humidities.

Materials and Methods

Sample Preparation

Commercially available fried cassava-shrimp chips (Manora® brand) were used in this study. The average major ingredients of the chips were fresh shrimp (35%), cassava flour (45%), garlic (5%), pepper (1.5%), and monosodium glutamate (1%). The chips were obtained directly from a local food processor (Manora Foods Industry Co., Ltd., Bangkok, Thailand). The information on proximate composition of chips was also available.

The samples were conditioned by exposing to ambient air approximately at 25–30°C and 65–70% relative humidity (RH), and in a humidity controlled chamber (WTC Binder, Germany) at 30°C and 90% RH to attain intermediate and high moisture contents, respectively based on predetermined weight gains. Finally the chips were ground using an electric food blender and stored in glass jars at ambient temperature for three days to attain equilibrium conditions prior to determining m _e and a _w .

Determination of Equilibrium Moisture Sorption Isotherms

The moisture sorption isotherms of fried cassava-shrimp chips were determined by direct measurement of a _w of samples conditioned to different moisture levels.6 Duplicate samples (weighing approximately 3 g) were used for a _w measurements at 20, 30, and 40°C by a CX-2 Water Activity System (Decagon Devices, Pullman, WA) providing ± 0.003 accuracy for its readings. Because the cooled mirror dew point technique which is the primary measurement method of relative humidity is applied to measure a _w , no calibration is necessary for this instrument according to its manual. However, the linear offset was verified before a _w measurements by standard saturated salt solutions corresponding to the a _w of about 0.1 (LiCl₂), 0.8 (NaCl), and 1.0 (distilled water) at each temperature to assure the correctness of readings. Moisture content determination was based on the drying of ground samples weighing approximately 5 g in an oven at 105°C overnight.12 Later moisture sorption isotherms were obtained from the relationships between a _w and moisture content.

Determination of Transient Moisture Diffusion in Chips

Fried cassava-shrimp chips weighing approximately 5 g were placed in five separate Petri dishes for exposure in a controlled environment chamber using nine different combinations of preselected temperature (20, 30, and 40°C) and RH (50, 70, and 90%). The weight gain by the samples was recorded at known time intervals, and used for calculating the moisture content during exposure. The initial moisture content of samples was determined by the oven method as described earlier. The thickness of 30 chips was also measured using a micrometer.

Data Analysis

Equilibrium Moisture Sorption Isotherm Models

The following five isotherm models were selected to check their applicability to represent the experimental data:

GAB equation13 14:

Henderson equation15:

Modified Henderson equation,13 16 and17:

Modified Halsey equation18:

Modified Oswin equation19:

All isotherm models were arranged to express m _e as a function of a _w . The parameters of the selected models were computed using nonlinear regression procedure available in SPSS.20 The goodness of fit of different models was investigated using three criteria13 21 described as mean sum of squares of residuals (MSE),13 mean relative percentage deviation (P)13 16 and the plot of residual pattern.

Determination of Moisture Diffusivity

The analytical solution of Fick's second law for the diffusion of moisture in one dimension across an infinite slab assuming uniform initial moisture content, constant surface moisture content in equilibrium with surrounding environment, negligible external resistance at the surface and constant diffusivity leads to Eq. (6)4 22:

It is also assumed that shrinkage in the product due to moisture adsorption is negligible. The values of effective moisture diffusivity, D in Eq. (6) were determined by a computer program for implementing nonlinear least-squares regression using Newton-Raphson method based on first 60 terms of the series solution.23

ResultS and Discussion

Composition of Fried Cassava-Shrimp Chips

Average proximate composition of fried cassava-shrimp chips was carbohydrates (54.3%), fat (27.2%), protein (10.2%), fiber (1.6%), and ash (3.4%) on dry basis as shown in Table 1. A comparison of the compositions of fried cassava-shrimp chips and commercially available potato and corn chips24 as shown in Table 1 indicated obvious similarities in the proportions of major components such as carbohydrates, fat, and protein.

Table 1 Proximate composition of experimental fried cassava-shrimp chips and selected commercially available chips (% dry basis)

Component	Cassava shrimp chips	Potato chips24	Corn chips21
Water	1.7	1.8	2.0
Protein	10.2	5.3	7.1
Fat	27.2	39.8	25.2
Carbohydrates	54.3	50.0	62.3
Fiber	1.6	3.1	0.6
Ash	3.4	—	0.9

Moisture Sorption Isotherms

The sorption isotherm data of fried cassava-shrimp chips at 20, 30, and 40°C are presented in Table 2. The isotherms (Fig. 1) exhibited a smooth shape resembling to type III classification,25 26 which is commonly obtained for foods with high fat content.27 Apparently, the equilibrium moisture content increased slowly over lower range of a _w and showed a steep rise thereafter at higher a _w levels most possibly because of hydrophobic nature of the chips due to their high fat content.27 It can be seen that the moisture sorption isotherms were not influenced by temperature over a _w range of 0.1–0.9. These results are similar to moisture adsorption isotherms reported previously in literature for foods such as garlic28 and pistachio nut paste.29

Figure 1. Moisture sorption isotherms of fried cassava-shrimp chips showing experimental data and fitted relationships based on GAB equation.

Table 2 Moisture content (m _e ) and water activity (a _w ) of fried cassava-shrimp chips

	a w
m e (% d.b.)	20°C	30°C	40°C
0.97	0.084	0.107	0.134
1.09	0.109	0.130	0.164
1.22	0.196	0.221	0.226
1.57	0.203	0.231	0.257
2.83	0.333	0.362	0.374
3.50	0.380	0.394	0.404
4.84	0.412	0.450	0.461
5.43	0.459	0.492	0.507
6.05	0.515	0.535	0.545
7.93	0.617	0.626	0.635
8.04	0.598	0.616	0.622
10.65	0.694	0.702	0.704
11.10	0.707	0.716	0.726
15.38	0.785	0.796	0.809
17.61	0.810	0.811	0.813
27.30	0.896	0.897	0.897
40.83	0.947	0.952	0.954

Analysis of variance showed that there were no significant differences (p < 0.05) between the experimental and estimated values of the equilibrium moisture contents for the selected five moisture sorption isotherm models. Also no significant differences were found among the equilibrium moisture contents estimated by all five models. However, the GAB, Henderson, and modified Henderson equations best described the sorption isotherms with relatively low values of standard error of estimation (SEE), MSE, and P along with high values of coefficient of determination (R ²) as showed in Table 3. The residuals from these models were also scattered randomly. In contrast, the fitting by the modified Oswin and modified Halsey equations resulted in residual plots exhibiting a pattern in data. Therefore, these models were considered inadequate for describing the sorption isotherms of fried cassava-shrimp chips. A comparison of experimental and estimated equilibrium moisture contents based on the GAB equation indicating a good overall fit is presented in Fig. 1.

Table 3 Parameters and related statistics for five moisture sorption models fitted to experimental data

	Parameters			Statistics
Model	A	B	C	R ^2	SEE	MSE	P (%)	Residual plot
1. GAB
20^oC(m m =4.83%db)	0.9387	—	1.8586	0.999	0.351	0.123	9.30	Random
30^oC(m m =5.51%db)	0.9234	—	1.1853	0.999	0.332	0.110	8.09	Random
40^oC(m m =5.43%db)	0.9238	—	1.1370	0.998	0.477	0.227	6.73	Random
2. Henderson
20^oC	0.2142	0.7093	—	0.996	0.684	0.468	16.80	Random
30^oC	0.2220	0.7058	—	0.998	0.497	0.247	11.92	Random
40^oC	0.2304	0.6987	—	0.997	0.596	0.356	9.73	Random
3. Modified Henderson	0.0004	0.7045	490.80	0.997	0.563	0.318	12.74	Random
4. Modified Oswin	6.7028	−0.0220	0.6563	0.989	1.126	1.267	25.68	Pattern
5. Modified Halsey	1.3555	−0.0054	2.2638	0.975	0.563	2.828	48.63	Pattern

Moisture Sorption Characteristics

The estimated values of D for fried cassava-shrimp chips based on the fitting of analytical series solution for infinite slab (Eq. (6)) to the experimental moisture sorption data are presented in Table 4. The equilibrium moisture contents (m _e ) of chips estimated by GAB equation (Eq. (1)) are also shown in Table 4. The D values ranged approximately from 0.8 × 10⁻¹¹ to 2.1 × 10⁻¹⁰ m²/s. Labuza6 reported that D values could range from 1.0 × 10⁻¹³ to 1.0 × 10⁻⁸ m²/s for most freeze-dried foods. Thus, the moisture diffusivity of fried cassava-shrimp chips fell within the normally expected range of D for other food products.

Table 4 Moisture diffusivity (D) of fried cassava-shrimp chips, mean relative percentage deviation (P), and R ² determined from moisture sorption experiments

RH (%)	T (°C)	m e	D(expt.) (×10^−11 m^2/s)	D(est.) (×10^−11 m^2/s)	P (%)	R ^2
50	20	5.66	0.84	0.69	1.63	0.983
50	30	5.16	1.24	1.78	2.83	0.992
50	40	4.98	5.06	4.34	1.49	0.992
70	20	11.00	6.82	7.43	5.40	0.970
70	30	10.66	13.18	12.55	2.51	0.991
70	40	10.38	21.32	20.50	1.01	0.999
90	20	28.32	5.53	5.48	5.27	0.985
90	30	27.84	6.88	6.60	8.06	0.932
90	40	27.34	7.44	7.85	6.34	0.964

It was also apparent from Table 4 that an increase in both air temperature and RH resulted in higher values of D signifying a corresponding increase in the rate of moisture sorption. The dependence of D on temperature was expressed using the Arrhenius equation30:

Fitting of Eq. (7) to experimental data at different RH levels indicated the R ² values higher than 0.9. Both E _a and A _a decreased with an increase in RH. Further, analysis showed that moisture diffusivity was best estimated by Eq. (7) (R ² > 0.96) using nonlinear regression based on the following relationships:

The activation energy, E _a decreased from about 70.3 to 13.8 kJ/mol when the RH increased from 50 to 90%. A comparison of experimental and estimated values of D based on Eq. (7) indicated a very good agreement as shown in Table 4. These results confirmed that diffusion of moisture in fried cassava-shrimp chips depended on both temperature and relative humidity of the surrounding environment. Previous studies have reported that moisture diffusion in banana,11 rough rice,31 and parboiled polished rice32 is mainly temperature dependent, and could be represented by the Arrhenius equation. Also it has been shown that both temperature and moisture content might have significant effects on the moisture diffusivity of some foods when fitting Arrhenius equation to the experimental data.33 Thus, the composition and porous structure of fried cassava-shrimp chips could be responsible for the dependence of moisture diffusivity both on temperature and RH.

Figures 2, 3, 4 show a close relationship between experimental and estimated values of moisture contents of fried cassava-shrimp chips during exposure to various constant RH and temperature conditions. These results revealed the validity of Eq. (6) to describe the moisture transfer characteristics of the chips. Because of the porous structure, high surface area and very small thickness of the chips, moisture diffusion was predominately across the chips, and the effect of moisture diffusion along the edges could be neglected. At any given RH, moisture absorption by the chips increased with an increase in temperature at all exposure times. However, higher moisture contents attained by the chips when exposed to 50% RH at 20°C as compared to 30°C in Fig. 2 were primarily due to higher initial moisture content of the samples. The values of mean relative percentage deviation (P) and R ² for various moisture absorption plots are presented in Table 4 to indicate the good overall fitting.

Figure 2. Comparison of experimental and estimated moisture contents of fried cassava-shrimp chips during storage at different temperatures and 50% RH.

Figure 3. Comparison of experimental and estimated moisture contents of fried cassava-shrimp chips during storage at different temperatures and 70% RH.

Figure 4. Comparison of experimental and estimated moisture contents of fried cassava-shrimp chips during storage at different temperatures and 90% RH.

Conclusions

Equilibrium moisture sorption isotherms and moisture transfer characteristics of fried cassava-shrimp chips were described accurately by the developed mathematical models. The moisture sorption isotherms resembled type III shape and exhibited little influence of temperature over the water activity (a _w ) range of 0.1–0.9. The GAB, Henderson, and modified Henderson equations estimated the equilibrium moisture content of chips as a function of a _w with good accuracy. Analytical solution of Fick's law for one-dimensional moisture diffusion in a semi-infinite slab could be used for estimating the sorption of moisture by fried cassava-shrimp chips during exposure to different temperature (T) and relative humidity (RH) environments. The effective moisture diffusivity (D) ranged from 2.1 × 10⁻¹⁰ to 0.8 × 10⁻¹¹ m²/s, and was well within the range of reported values for porous food products. In addition, Arrhenius type relationship existed between D and T at any given RH, and indicated a distinct decrease in the magnitude of equation parameters with increasing RH.

Nomenclature

A	=	Constant
A a	=	Constant (m2/s)
B	=	Constant
C	=	Constant
a w	=	Water activity (decimal)
D	=	Effective moisture diffusivity (m2/s)
E a	=	Activation energy (kJ/mol)
L	=	Half-thickness of the slab (m)
m	=	Moisture content at time t ((kg water/kg dry solid) × 100)
m o	=	Initial moisture content ((kg water/kg dry solid) × 100)
m e	=	Equilibrium moisture content ((kg water/kg dry solid) × 100)
m m	=	Monolayer moisture content ((kg water/kg dry solid) × 100)
MSE	=	Mean sum of squares of residuals
n	=	Number of terms
P	=	Mean relative percentage deviation
R	=	Universal gas constant (8.314 × 10−3 kJ/mol K)
R 2	=	Coefficient of determination
RH	=	Relative humidity (decimal)
SEE	=	Standard error of estimation
t	=	Time (s)
T C	=	Temperature (°C)
T K	=	Absolute temperature (K)