Equilibrium Sorption Isotherms and Isosteric Heat of Rose Hip Fruits (Rosa Eglanteria)

Abstract

For sorptional data to be useful in simulation and design purposes, they must be represented by equations valid in the conditions usually found in industrial practice. In this regard sorptional models that include the influence of temperature on desorption and sorption equilibrium values are most valuable. In this article, water desorption and sorption isotherms of rose hip fruits (Rosa Eglanteria) were experimentally determined by the gravimetric method, and from these the isosteric heat of sorption was calculated. According to the ANOVA test carried out for this fruits, no significant differences were found between experimental desorption and adsorption isotherms. Seven models were tested to mathematically represent the moisture content as a function of water activity (a_w) in the a_w range of 0.11 to 0.85 and temperatures of 20, 40, and 60°C, for further use in process simulation.

The five-parameter GAB model was most accurate, with an MRE of −2,9 % and R² = 0.989. The values obtained for the isosteric heat of sorption were fitted with a previous published equation, with an MRE% = −0.05. The isosteric heat of sorption derived from the GAB five parameters equation, for the corresponding monolayer moisture content, only differed by 1.25% with the calculated in this paper.

Keywords:

• Rose hip fruits
• Equilibrium moisture isotherms
• Isosteric heat
• Experimental and simulation

INTRODUCTION

Water is an essential component of most fruits and plays an important role in food preservation.[1] Knowledge of the relationship between water content in a foodstuff, and the equilibrium relative humidity of the surrounding atmosphere, or food water activity is very useful to predict drying endpoint for food stability, to design new products, and to improve dehydration processes through design and optimization with adequate models.[2,3] Adsorption isotherms are also practical to provide information during storage handling of dehydrated products and during product reconstitution. Another key property is the isosteric heat of sorption of bound water in the food, which is higher than that for pure water and constitutes the minimum energy demand for dehydration. For this purpose equilibrium isotherms and heat of sorption curves are particularly useful when expressed as equations valid in practical conditions that can be incorporated in simulation models to improve and/or optimize dehydration processes and equipment. In this regard, models relating equilibrium moisture content or heat of sorption with water activity and temperature are especially useful.

There is a good literature reserve of equations relating water content with water activity, many of them including the influence of temperature.[4,5,6,7,8,9,10,11] However, despite various efforts, no equation is of true general use since water activity depends on food composition and of the interaction of several components with water in thermodynamic equilibrium conditions.[2] That is, different foods with the same chemical composition are expected to have different equilibrium moisture contents if their physical structures are not alike. Moreover, in a given food, not all the range of water activity corresponds to sorptional mechanisms, because at very high water activity water may be held in capillaries, or exist in dilute solutions.[12]

By this concept, fruits of diverse varieties kept at the same water activity may present variable moisture contents. Therefore, equilibrium data must be available even for chemically similar fruits to verify the applicability of existing equations and, eventually, to determine specific parameters for each cultivar. The objectives of this work were to obtain experimental equilibrium moistures for rose hip as a function of water activity for three temperatures, to compare the values with predictions from selected isotherm equations taken from literature sources and to calculate and model the sorption isosteric heat derived from the equilibrium data.

MATERIALS AND METHODS

Raw Material

Desorption

Fresh fruit, kept for 24 hours at 0°C in forced-air cold stores were used. According to their refractometric soluble solid content, Rose hip fruits were classified as fruit of 16 °Brix. This is a typical value for freshly harvested fruits in the Andean Patagonic Valleys at Parallel 42°, Argentina.

Adsorption

The raw material employed was the same as those used for desorption. Samples were dehydrated first at 70°C in vacuum oven until constant weight and then placed in a desiccator containing silica gel to allow the fruit to equilibrate any residual moisture gradient before being used.

Initial moisture and dry matter contents

From the classified sample, 50 fruits were cut in small pieces and mixed. Three replicates 5 g each, randomly selected, were placed in vacuum oven set at a temperature of 70°C with an absolute pressure of 10 mm Hg up to constant weight. Weights were determined using an analytical balance. Moisture and dry solids content are averages of the replicates and presented in Table 1.

Table 1 Characteristics of fruits and salts utilized to obtain atmospheres of known equilibrium relative humidity or a_w.

Fruit	°Brix	dry Moisture basis	% Dry solids
Fresh rose hip	16.0 ± 1.3	1.198 ± 0.049	45.5 ± 1.71
Dehydrated rose hip	—	0.043 ± 0.003	95.7 ± 3.6
Salts and their aw in saturated solutions
Salt	aw at 20°C	aw at 40°C	aw at 60°C
Lithium chloride	0.11	0.11	0.11
Potassium acetate	0.23	0.20	0.175
Magnesium chloride	0.33	0.32	0.30
Potassium carbonate	0.43	0.42	0.42
Magnesium nitrate	0.558	0.49	0.43
Sodium bromide	0.565	0.52	0.50
Potassium iodide	0.699	0.66	0.62
Sodium chloride	0.754	0.745	0.741
Potassium chloride	0.85	0.82	0.807

Equilibrium isotherms

They were determined according to the gravimetric method suggested by the European Cooperative Project, COST′90.[13] The experimental apparatus consisted of three natural convection ovens set to controlled temperatures of 20, 40, and 60 ± 0.5°C. In each oven, nine sealed containers were placed, each with a specific saturated salt solution that provides a constant relative humidity, as shown in Table 1. Three small subsamples of 2 g were placed in each container, being them initially wet for desorption tests and dry for adsorption experiments. The sample was obtained from a set of 50 selected fruits processed as indicated in the preceding section. Initial and successive weights were obtained in analytical balance, by removing the sample from the oven at the times recommended by COST^··90. Equilibrium was considered to be attained after finding three consecutive weights within the balance error. Equilibrium moisture content was calculated by differences of the first and last weight, considering constant the dry matter content. Results reported are average of the three subsamples of each container at any of the temperatures tested.

RESULTS AND DISCUSSION

Desorption

In Fig. 1, experimental values obtained for the equilibrium moisture contents in rose hip are plotted as a function of water activity for the three temperatures tested during desorption. Van den Berg and Bruin[14] have revised 77 equations for food isotherms, and find that some were related with the BET or GAB models while others belonged to the empirical category, with 2 or 3 parameters at constant temperature. Authors recommended the GAB equation for having parameters with physical meaning and good predictions up to a_w = 0.90, and indicated that one or two of the three GAB can be temperature-dependent, through Arrhenius-type relationships. In turn, Lomauro et al.[15] have used 88 experimental isotherms belonging to dairy products, coffee, tea, dry fruits, oilseeds, spices and starch-rich foods. Among other conclusions, they found that the GAB model for physical adsorption in multilayers accurately predicted some 75% of the isotherms to which it was fitted, but the experimental data were limited to a temperature of 25°C and to an a_w range of 0.24–0.96. On the other hand, van den Berg[16] listed a series of requirements for isotherm equations: (a) The experimental curve must be mathematically described for practical applications as drying, packaging and storage. (b) The equation must be relatively simple with a limited number of parameters. (c) The parameters must have physical meaning, (d) The parameters must be temperature-dependent. (e) The equation must allow for correction to account for hysteresis effects.

Figure 1 Experimental equilibrium moistures expressed on a dry basis (Xdb) as a function of water activity (a_w) for rose hip fruits during desorption, and the predictions of the five-parameter GAB model fitted in this work.

Upon these recommendations and in order to model the behavior of equilibrium isotherms, the models of: Crapiste and Rotstein;[17] Three and five-parameter GAB; Ratti;[8] Iglesias and Chirife;[18] Strohman and Yoerger[19] and Pfost et al.,[28] previously used in other fruits, were tested (The corresponding mathematical expressions are presented in Table 2). Using the non-linear regression feature of the Systat v.5.02 statistical software for Windows, the parameters fitted for the seven models applied to the data at 40 and 60°C are presented in Table 2. In addition, and to evaluate the behavior of models, an analysis of maximum, minimum and average percentage errors was carried out, together with statistical parameters of average residual and standard percentage error. These were calculated as:

(1)

(2)

Where y_i corresponds to experimental values, and y_ic to those predicted; the symbol n stands for the number of observations. Results are presented in Table 3. As indicated in Table 3, the model giving the best account of experimental data is the five-parameter GAB. Therefore, Fig. 1 also includes predicted curves by this GAB model. As indicated before, the parameters were fitted to data measured at 40 and 60°C. Using the model so developed, the curve at 20°C was extrapolated with acceptable accuracy to predict the corresponding observed values (Fig. 1).

Table 2 Parameters obtained for regression of experimental data for the seven models tested.

	Parameters
Models	C1	C2	C3	C4	C5	C6
Crapiste and Rotstein[6]	185.088	1.087E + 10	−0.59	4.661
GAB 3 parameters	0.7E + 07	1.15E + 02	1.9
GAB 5 parameters	0.0887	3.392	554.08	0.394	110.439
Xm = C1 ; C0  = C2 ; ΔHc  = C3
K0  = C4 ; ΔHk  = C5
Iglesias and Chirife[8]	3.423	−0.0017	−1.11
Pfost et al.[10]	2900	−205	4.948
Ratti[11]	1.32	−0.165	2.59	−0.07	−1.903	−2.08
Strohman and Yoerger[13]	4.897	−4.813	0.824	−4.74
C1 , C2 , C3 , C4 , C5 , and C6 , are the constant parameters in the models used; aw is the water activity; T the absolute temperature; R the general gas constant, Pws the saturation vapor pressure; and, Xdb the moisture content in dry basis.

Table 3 Error analysis for obtaining parameters of the different models evaluated in Table 2 with corresponding regression coefficients.

Model	Maximum error %	Minimum error %	MRE %	Standard error %	Average residual %	R^2
Crapiste and Rotstein[6]	173.3	−94.8	−32.4	21.6	17.5	0.905
3 parameters GAB	67.2	−54.9	−19.4	12.6	9.4	0.937
5 parameters GAB	8.0	−11.7	− 2.9	3.2	2.9	0.989
Iglesias and Chirife[8]	75.0	−97.0	−1.5	8.9	7.4	0.961
Pfost et al.[10]	103.7	−27.3	8.2	12.6	11.2	0.902
Ratti[11]	66.3	−63.8	1.9	9.5	8.7	0.931
Strohman and Yoerger[13]	94.6	−20.6	.6	11.8	10.7	0.961

The trend of the results obtained (Fig. 1) is similar to those from published data by other authors in other fruits.[17,20,19,21,22,23,24] In the same figure, the equilibrium moisture is observed to increase at constant a_w for decreasing temperature, as indicated by Chirife et al.[25] and Giner.[3] Chirife et al.[25] has indicated that adsorption is favored by lower temperatures because of its exothermic nature. The equilibrium moisture content of fruits for a water activity threshold of 0.7 is particularly important because most microorganisms cannot grow in this condition. However, complete stability cannot be ensured at this water activity because other processes as enzymic and Maillard browning may be active and would require further drying or refrigerated to keep color and nutritive properties.[26,1] Nonetheless, setting a water activity of 0.7, safe moisture contents for microbial stability can be obtained from Fig. 1 to be 0.235 at 20°C; 0.216 at 40°C and 0.203 decimal, dry basis at 60°C. Therefore, as safe moisture contents increase for decreasing temperature, dehydrated fruit kept in refrigerated storage would require less dehydration for microbial stability (For instance, using the selected model at 10°C for a water activity of 0.7 gives a safe moisture content of 0.247 decimal, dry basis). This analysis shows the benefits of refrigerated storage for dehydrated foods, which is interesting when considering advantages and disadvantages of specific facilities for packaging and storing dehydrated foods.[3]

Adsorption

Fig. 2 presents experimental equilibrium moisture contents obtained by adsorption for rose hip as a function of water activity at the three temperatures tested. Values so obtained are observed to be similar to those measured by desorption and, for this reason, an statistical analysis of variance (ANOVA) was carried out at a significance level of 5%. Values for desorption and adsorption were not found to be significantly different as can be seen in Table 4. On these grounds, the same model (five-parameter GAB) with the same parameters can describe equilibrium adsorption and desorption isotherms. Other authors have already stated that hysteresis may not appear in equilibrium isotherms for all foods.[27,28,5,29,30] Iglesias and Chirife[31] have published a thorough revision of equilibrium isotherms, and reported a marked hysteresis effect in various products such as apple, dextrin, pistachio, and sugar. Moreover, differences of equlibrium moisture contents caused by hysteresis in one research can be as considerable as the differences between the isotherms reported by various authors, as it is the case in coffee, colagen, figs, fish protein, peanut, milk, mushroom, and pears. Various hypothesis have been formulated to explain the hysteresis phenomenon. Labuza[32] has attributed it to sugar supersaturation, while Chinachoti and Steimberg[33] to the crystalline state of sugars. Tsami et al.[24] considered that hysteresis is caused by the change in composition of the product during storage and/or dehydration. However, as the sorption isotherms of some products having soluble solids as pear and figs do not show any considerable hysteresis, another hypothesis can be proposed,[30] which is related to non-equilibrium conditions of water inside the foods. Water diffusivity in foods is often lower than 5 × 10⁻⁹ m²/s, so either for samples losing moisture through the surface (dehydration) or adsorbing through it (rehydration), steep moisture gradients are established inside the food so equilibrium moisture can be different to that obtained in totally equilibrated samples, i.e., in samples with flat internal gradients. This may suggest that hysteresis may or may not appear in the same sample. Furthermore, in samples where the hysteresis effect is moderate, it can be masked by the experimental error of the method used. To this end, to minimize errors, samples used in the adsorption tests were allowed to reach equilibrium in a closed container for 24 hours. From the point of view of the product stability Fennema[1] proposes that in the presence of hysteresis the water activity ensuring microbial stability for the adsorption branch, of lower moisture content, would be not guarantee stability for the desorption branch, of higher moisture content, by molecular mobility considerations. Therefore, if a safe moisture content is calculated with the desorption branch of the isotherm, the water activity threshold used must be lower than that for adsorption.

Figure 2 Experimental equilibrium moisture contents, expressed on a dry basis (Xdb) as function of water activity, in rose hip fruits during adsorption and predictions of the five-parameter GAB model fitted in this work for desorption.

Table 4 Statistical analysis on experimental values of equilibrium moisture contents arrived at by desorption and adsorption.

ANOVA Desorption – adsorption
Data	Mean	Variance	N
Desorption	0.18237	0.01003	17
Adsorption	0.17278	0.0863	24
F = 0.09937; p = 0.75427
At a level of 0.05, means are not significantly different.

Isosteric Heat of Sorption

The isosteric heat of sorption Q, is the energy per unit mass required to remove water from a material and incorporates the binding energy between water molecules and the food dry matter.[34] Therefore, it is logically related to the amount of energy required in a dehydration process. The net isosteric heat of sorption q represents the difference of the heat of sorption Q and that for pure water evaporation Lw, and can be evaluated by means of the Clausius-Clapeyron equation, in method sometimes called Clausius-Clapeyron — sorption isotherm method,[3] which is expressed by:[34,35,36]

(3)

The derivative placed in the left hand side of Eq. (3) can be evaluated with a sorption isotherm model used to calculate q. Otherwise, if mathematical manipulations are complicated, or a model is not available, the value of q can be obtained from the slope of the ln a_w vs 1/T plot. Eq. (3) is based on the assumption that q is independent of temperature, despite it is not always true it is often accepted as such.[34,37] For this last method, the experimental sorption curve must be available at least for three temperatures. Based on the integrated form of Eq. (3), Mulet et al.[36] used an expression by Riedel[38] relating a_w with temperature and proposed a very simple expression to obtain q:

(4)

(5)

Being R the gas constant (8.314 kJ/kmol K), a_w1 and a_w2 water activities evaluated at temperatures T₁ and T₂ , respectively. A and b are regression parameters from Eq. (5). By combining Eqs. (4) and (5), Mulet et.al.[36] have obtained:

(6)

Where D = A R. Therefore, q is calculated at different moisture contents by repeated application of the ln a_w vs 1/T plot. Then, by further fitting of Eq. (6) to the data of Q vs Xbs, the parameters D and b are found. In Fig. 3, Q values, obtained from the equlibrium curves of moisture dry basis vs a_w (observed values), are plotted together with predictions by Eq. (6) using the parameters fitted in this work. Values of the parameters obtained in this work are: D = 799.56 kJ/kg and b = 7.662 kg dry solids/kg water. Maximum and minimum errors % were 1.31 and – 2.47, respectively, the mean relative error being, MRE % = −0.05.

Figure 3 Isosteric heat of sorption as a function of the moisture content for rose hip fruits, and predictions by Eq. (13).

In analysis carried out by Giner (3) and Mulet et.al.,[34] maximum values of Q are reported to be between 1.14 to 1.20 times the heat of vaporization of pure water. In this work, for the value obtained for the minimum moisture measured Xdb = 0.093, the ratio was 1.147, close to the conclusions by the previous authors. Moreover, the monolayer moisture content obtained by the five-parameter GAB model was of 0.0887 kg water/kg dry solid, and, from the same model, the monolayer heat of sorption can be obtained using the correlations for C and K from the five-parameter GAB model (Table 2), where:

(7)

While H_m and H_n are the monolayer and multilayer heats of sorption, respectively. If both expressions are combined in Eq. (7) by solving through the common parameter, H_n (33), the following is obtained:

(8)

By replacing the values from the fitting ΔHc and ΔHk (C₃ and C₅ in Table 2), and that for Lw in Eq. (8), H_m is found to be 2855.6 kJ/kg. In turn, from Eq. (6) used at the monolayer moisture, a value of 2820.3 kJ/kg is obtained which is within 1,25 % from that obtained by Eq. (8).

CONCLUSIONS

Equilibrium moisture contents were experimentally determined during water desorption and adsorption in rose hip fruits at 20, 40, and 60°C. By comparing adsorption and desorption values under the experimental conditions assessed here, no statistically significant hysteresis phenomenon was detected. For this reason, experimental values for adsorption and desorption were fitted with the same seven previously published models. Among the predictive models tested, the five-parameter GAB model was selected based on its best statistical parameters of goodness of fit for the prediction of experimental data of sorption in rose hip. The selected model mathematically represents experimental equilibrium moistures as a function of water activity and represented adequately effect of temperature in the range studied. Predictions at a temperature lower than used in the fitting gave an acceptable agreement as well. The experimental values mentioned above were used to calculate the isosteric heat of sorption for rose hip fruits. Values obtained were interpreted with a simple, previously published model, giving a satisfactory correlation. Moreover, the heat corresponding to the monolayer moisture content calculated in this work only differed by 1.25% from that obtained using the GAB model in the same conditions. Values of the heat of sorption to heat of vaporization obtained here are in agreement with published values for different fruits.

Notes

3. Giner, S.A. Diseño de secadoras continuas de trigo. Simulación de la transferencia de calor y materia y de perdidas de calidad. Tesis Doctoral. Departamento de Química e Ingeniería Química, Facultad de Ingeniería, Universidad Nacional de La Plata, La Plata, Argentina, 1999, Cap. 4; 1–39

8. Ratti, C. Diseño de Secaderos de Productos Frutihortícolas. Tesis Doctoral. Departamento de Química e Ingeniería Química. Planta Piloto de Ingeniería Química, Universidad Nacional del Sur, Bahía Blanca, Argentina, 1991; 27–57

20. Pfost, H.B.; Maurer, S.G.; Chung, D.S.; Milliken, G.A. Summarizing and Reporting Equilibrium Moisture Data for Grains, ASAE paper No. 76–3520. St. Joseph, Michigan, 1976

25. Chirife, J.; Resnik, S.; Suarez, C. Fundamentos de secado y almacenaje de granos. Curso de postgrado. Departamento de Industrias. Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires – Argentina, 1985