Measurement and Modeling of Moisture Sorption Isotherm of Litchi (Litchi Chinensis Sonn.)

Abstract

The equilibrium moisture contents of litchi (Litchi Chinensis Sonn.) were experimentally determined using the dynamic method at temperatures of 30, 40, and 50°C over a range of relative humidity values of 12 to 95%. Five models were tested to fit the experimental isotherm data of litchi. The GAB model fitted the best to experimental isotherm data. The agreement between experimental and predicted values of this model is excellent (RMSE 1.8 to 3.4%). The isosteric heats of sorption water were also determined from the equilibrium data using the Clausius-Clapeyron equation and it was found to be a function of equilibrium moisture content.

Keywords:

• Litchi
• Sorption isotherm
• Dynamic method
• Modeling
• Isosteric heat of sorption

INTRODUCTION

Litchi (Litchi Chinensis Sonn.) is a tropical fruit and it is grown mainly in northern Thailand and northern Vietnam. This fruit is consumed as fresh and dried product. It is a seasonal fruit and drying of the fresh fruit during harvesting season ensures the year round taste of litchi. Furthermore, dried fruits as an alternative to fresh fruits are becoming popular because of the taste and flavor of the dried fruits. Once dried, this product is on sale for consumption and storage. For proper handling of drying process and storage of litchi, it is essential to know its sorption isotherm.

Moisture sorption isotherms describe the relationship between the equilibrium moisture content and relative humidity at a constant temperature.[1] The moisture sorption isotherm is an extremely useful tool for food scientists and technologists because it is required for predicting shelf life stability, predicting moisture changes during storage, selecting and designing packaging systems and modeling of drying and optimization of drying equipment.

Based on the authors' knowledge, there is no information available on sorption isotherms of litchi for its use in drying, packaging and storage. The objective of this study was to conduct experimental measurement of isotherms for litchi at various temperatures and relative humilities, to fit the moisture isotherms data to sorption isotherm models and to calculate the net isosteric heat of sorption from the experimental data and develop an equation for the net isosteric heat of sorption as a function of moisture content.

MATHEMATICAL MODELS OF SORPTION ISOTHERMS

Chen and Morey[2–3] evaluated four models: the modified Henderson model, modified Chung- Pfost model, the modified Halsey model and the modified Oswin model for fitting the sorption isotherms data from 18 grains and seed crops. Sun and Woods[4] reviewed more than 200 EMC/ERH purely empirical equations developed for cereal grains and food materials. But no single equation accurately describes the EMC/ERH relationships for various crops over a broad range of the relative humidity and temperature and also there is no universal equation for sorption isotherms of agricultural and food materials.

Numerous mathematical models for isotherms of food and food materials are available. Some of these are based on theory of sorption mechanism and others are either semi-theoretical or purely empirical. Van den Berg and Bruin[5] have classified 77 such equations, and Chirife and Iglesias[6] reviewed 23 such isotherm equations. None of these equations described adequately the sorption isotherms over the whole range of relative humidity and for all types of food material tested. Lomauro et al.[7] evaluated two two-parameter equations and one three-parameter equation for 163 food materials including fruits, vegetables, spices and starchy foods. They found that the three-parameter Guggenheim, Anderson and de Boer (GAB) equation[8] described the sorption isotherms for most food better than two parameters equations. Kuye and Ariri[9] tested the applicapability of nine sorption models to 30 isotherm data of some Nigerian foods and they also found that the GAB model fits well most of the data.

Recently the GAB model has been proposed by food engineers as the universal model to fit the sorption data for all foods. Lomauro et al.[7] reported that moisture sorption of foods can be described by more than one sorption model and the GAB gives the best fit for more than 50% of the fruits, meats and vegetables analyzed. But Chen and Jayas[10] repeated that GAB model could not be used to describe the sorption isotherms of starchy grains. Furthermore, it is difficult to extend the model by adding a temperature term.

Mir and Nath[11] fitted five isotherm models (BET, GAB, Henderson, Oswin and Smith) to the sorption isotherm data of three types of mango bars (plain mango bar, mango-coconut bar and mango-soya protein concentrate bar). The BET and GAB models were found to predict well the moisture content only for the plain mango bar whereas the Oswin model was applicable to all the three types of the mango bars. Hossain et al.[12] developed six two-parameter and one-three parameter models to fit the observed data of pineapple and the modified BET model was found to be the best model for pineapple.

Lahsasni et al.[13] determined the equilibrium moisture contents of prickly pear fruit using the gravimetric static method at three temperatures of 30, 40, and 50 °C over a range of relative humidity values from 5 to 90%. The sorption curves of prickly pear fruit decreased with increase in temperature at constant relative humidity. The GAB, modified Halsey, modified Chung-Pfost, modified Oswin and modified Henderson models were tested to fit the experimental data. The GAB model was found to be the most suitable for describing the sorption curves.

Kaymak-Ertekin and Gedik[14] determined the moisture isotherms of grapes, apricots, apples and potatoes at 30, 45, and 60°C using the standard static-gravimetric method. Six two-parameter and five three-parameter sorption models were tested to fit the experimental data. The Halsey equation gave the best fit to the experimental data for all the materials tested over the range of temperatures and water activities investigated. The GAB model gave also the closest fit to the sorption data for potatoes and grapes.

MATERIALS AND METHODS

Determination of Equilibrium Moisture Content of Litchi

Equilibrium moisture contents of litchi were determined experimentally in the Department of Physics, Silpakorn University, Nakhon Pathom, Thailand using the dynamic method. To determine the equilibrium moisture contents, three sets of equipment were constructed and each set consists of a hot air chamber containing six sample boxes in three trays. The sample box was essentially an airtight plastic box containing saturated salt solution to maintain constant relative humidity inside the sample box. Each sample box is divided by plastic wall into two sections for holding two samples separately and simultaneously. The sample boxes were half filled with salt solution. The samples were placed inside the perforated sample containers of 3 cm diameter and 2 cm height and the sample boxes were placed on the perforated plastic supports just above the salt solution. Two small electric fans were fitted to circulate the air inside the sample box to accelerate moisture transfer between the samples and air inside the sample box. The sample boxes were placed inside the hot air chamber. The hot air chamber was equipped with a 3 kW electrical heater and an electronic temperature controller to maintain the temperature and the relative humidity was maintained by saturated salt solution.

In conducting the experiments, 50 g of the flesh of litchi was placed inside the sample containers located inside the sample boxes and the sample boxes were placed inside the hot air chamber. The samples were weighed regularly until they reached equilibrium. The final moisture contents of the product were determined by the standard oven method (temperature of 103°C for 24 hours). The selected temperatures for sorption isotherm determination were 30, 40, and 50°C and the water activity was 0.12 to 0.95.

The models selected to fit the sorption isotherms of litchi are shown in Table 1. These models were selected based on their effectiveness for describing isotherms of several food and plant materials and simplicity of computation. The temperature effect in the GAB model is included as:

(1)

Table 1 Selected isotherm models for fitting experimental data

No.	Model name	Mathematical expression
1.	Day and Nelson model
2.	Modified Halsey model
3.	Modified Chung-Pfost model
4.	Modified Oswin model
5.	GAB model

The parameters of the models were determined using Marquardt-Levenberg optimization methods. Reduced mean relative error (RMRE), value of the root mean square error (RMSE) and randomness of residuals (ei) were computed.

Determination of the Isosteric Heat of Sorption

The net isosteric heat of sorption can be used to determine the energy requirements of drying and it provides useful information on the state of water in food products. The moisture content level of a material at which the net isosteric heat of sorption reaches the value of the latent heat of sorption is often considered as an indication of the amount bound water existing in the food.[15–16] Several researchers have determined isosteric heats of sorption of food materials such fruits, vegetables, fish, meat and spices.[12,16,17–20] Heat of sorption phenomena can be explained by Clausius-Clayperon equation[16,20] as follows:

(2)

Integrating Eq. (2), assuming that the isosteric heat of sorption (Q_st ) is independent of temperature, gives the following equation:

(3)

The value of Q_st is calculated from the slope of the Eq. (3).

RESULTS AND DISCUSSIONS

Sorption isotherms (points) of litchi at three temperature levels of 30, 40, and 50 °C, in the range of 12–95% relative humidity values are shown in Fig. 1. The isotherm curves have sigmoid shape and similar patterns. Figure 1 shows that the EMC values decreased with the increase in temperature at all levels of relative humidity. The kinetic energy associated with water molecules present in litchi increased with increasing temperature. This in turn, resulted in decreasing attractive forces, and consequently, escapes of water molecules. This led to a decrease in EMC values with increase in temperature at a given relative humidity. Several researches[12,20,22–25] have reported similar trends for food materials.

Figure 1 Measured sorption isotherms (points) for litchi at the temperature levels of 30, 40, and 50°C.

Computed parameters and their coefficients of determination for sorption isotherms of litchi are shown in Table 2. The characteristic parameters of the GAB model are shown in Table 3. Among the isotherm models tested, GAB model fitted the best to the experimental isotherm data of litchi for the temperature levels of 30, 40, and 50°C. The GAB model was the best among the five fitted models with the lowest values of standard error of estimate (RMSE) and mean relative error (RMRE), and the highest value of coefficient of determination. The modified Oswin model was next to the GAB model in terms of standard error of estimate and mean relative error, and the highest value of coefficient of determination. The predicted and observed equilibrium moisture contents are shown in Fig. 2 for the GAB model and the modified Oswin model. The agreement between the observed and predicted values is very good. Figure 3 shows the residuals of the predicted equilibrium moisture contents for the GAB model and the modified Oswin model and the residuals for both the models are random in pattern. Hence, the GAB model and the modified Oswin model are acceptable.

Table 2 The coefficients of the selected models, reduced mean relative error (RMRE), standard error of estimate (RMSE) and the coefficient of determination (R²) for litchi

Model	Temperature (°C)	Coefficients				RMRE (%)	RMSE (%)	R^2
		b0	b1	b2	b3
Day and Nelson	30, 40, 50	6.95 × 10^−7	1.569446	2.325110	−0.04768	9.1898	6.0813	0.9638
Modified Halsey	30, 40, 50	10.6609	−0.031676	2.417281		6.7559	3.6633	0.9746
Modified Chung-Pfost	30, 40, 50	154.3127	−11.31032	0.033847		7.4331	5.0929	0.9869
Modified Oswin	30, 40, 50	98.6643	−0.829739	3.091631		5.9899	3.5929	0.9874
GAB	30	41.0223	325.7558	0.7749		3.1673	2.9749	0.9869
	40	34.5295	114.3076	0.7887		5.6869	3.3663	0.9464
	50	32.6566	18.1243	0.7723		2.0829	1.8129	0.9848

Figure 2 (a) Predicted and measured sorption isotherms for litchi at the temperature levels of 30, 40, and 50°C (GAB model); and (b) predicted and measured sorption isotherms for litchi at the temperature levels of 30°C, 40°C and 50°C (Modified Oswin model).

Table 3 Characteristic parameters of the GAB model

b10	b20	h1	h2
6.25 × 10^−10	0.884055	16484.28261	−70.10988

Figure 3 (a) Residuals of the predicted equilibrium moisture contents (GAB model); and (b) residuals of the predicted equilibrium moisture contents (Modified Oswin model).

The plot of ln(rh) as a function of 1/T_ab at constant moisture content is shown in Figure 4. The slopes of the lines at constant moisture contents were determined by regression analysis to find the net isosteric heat of sorption of litchi. The heat of sorption for litchi at different moisture contents is presented in Fig. 5. The net isosteric heat of sorption was found to decrease exponentially with increase in moisture content. This trend is similar to those reported by other researchers for agricultural, food, and medicinal and aromatic plants.[12–13,17,26–32] The net isosteric heat of sorption was found to be a function of equilibrium moisture content and the following equation is developed:

(4)

Figure 4 Plot of ln (rh) as a function of 1/T_ab at constant moisture content.

Figure 5 Net isosteric heat of sorption (Q_st ) of litchi for different for different values of equilibrium moisture contents.

This relation shows that the net isosteric heat of sorption of litchi decreased exponentially with the increase of equilibrium moisture content.

CONCLUSIONS

The equilibrium moisture content isotherms of litchi were determined experimentally at the temperature levels of 30, 40, and 50°C and a relative humidity in the range of 12 to 95% using the dynamic method. The effects of temperature were found to be significant and the equilibrium moisture content increased with decreasing temperature at constant water activity. Five sorption isotherm models were used to fit the experimental data of litchi. Among the sorption models tested, the GAB model fitted the best to the experimental isotherms of litchi at 30, 40, and 50°C and the modified Oswin model was next to the GAB model. The best equation is suggested for its use in drying, storing and packaging. The heat of sorption of litchi is found to decreases with the increase of moisture content and it is an exponential function of moisture content. This equation is suggested for use in the computation of heat of sorption of litchi.

NOMENCLATURE

aw	=	water activity, decimal
b0,b1, b2, b3, b10, b20	=	parameters of isotherm equation
EMC	=	equilibrium moisture content, % db
ERH	=	equilibrium relative humidity, %
h1,h2	=	parameters of isotherm equation
k	=	constant of the solution of the Clausius-Clayperon equation
M	=	moisture content, % db
Me	=	equilibrium moisture content, % db
Qst	=	isosteric heat of sorption, kJ/mole
rh	=	relative humidity, %
R	=	coefficient of determination
R0	=	universal gas constant, 8.315 kJ/kg-mol-K
T	=	temperature, °C
Tab	=	temperature, K

ACKNOWLEDGMENTS

This research is a part of the research project SFB 564 (“Research for Sustainable Land Use and Rural Development in Mountainous Regions of Southeast Asia”), funded by Deutsche Forchungsgemeinschaft (DFG), Germany, and co-funded by the National Research Council of Thailand and the Ministry of Science, Technology and Environment, Vietnam. We gratefully acknowledge the financial support for this research. We would also like to thank the Silpakorn University Research and Development Institute for supporting the experimental work.