Desorption isotherms of acerola fruits variety 'Okinawa'

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1 ISSN: Jaboticabal v.45, n.2, p , Desorption isotherms of acerola fruits variety 'Okinawa' Isotermas de dessorção em frutos de acerola variedade Okinawa Daíse Souza REIS 1 ; Acácio FIGUEIREDO NETO 2 ; Josenara Daiane de Souza COSTA 3 ; Francisco de Assis Cardoso ALMEIDA 4 ; Josivanda Palmeira Gomes GOUVÊIA 5 1 Autor para correspondência; Engenheira Agrícola e Ambiental. Universidade Federal do Vale do São Francisco, Campus Juazeiro. Laboratório de Armazenamento e Produtos Agrícolas. Av. Antônio Carlos Magalhães, 510 Juazeiro - BA Brasil. dayse29@hotmail.com 2 Professor D.Sc da Unidade Acadêmica de Engenharia Agrícola. Universidade Federal do Vale do São Francisco, Campus Juazeiro. figueiredoacacio@gmail.com 3 Engenheira Agrícola e Ambiental. Mestranda em Engenharia Agrícola e Ambiental. Universidade Federal de Campina Grande. Josenara.costa@gmail.com 4 Professor da Unidade Acadêmica de Engenharia Agrícola. Universidade Federal de Campina Grande. almeida@deag.ufcg.edu.br 5 Professora da Unidade Acadêmica de Engenharia Agrícola. Universidade Federal de Campina Grande. josivanda@gmail.com Recebido em: ; Aceito em: Abstract The cultivation of acerola in Brazil is growing. The acerola fruit is known to have several properties concurrent with where it is grown. The determination of the water activity of biological products becomes essential in studies on drying, storage and packaging processes since the higher the water activity of a product, the higher the susceptibility to attacks by microorganisms. This study aimed to evaluate desorption isotherms of acerola fruits (Malpighia glabra L.) for the temperatures 30, 40 and 50 C by the indirect static method. The experimental data were adjusted to the mathematical models BET, GAB, Halsey, and Oswin and Smith. Analyses of residues, coefficient of determination, relative standard deviation and estimated standard deviation were calculated for each adjusted model and used to evaluate the model that best adjusted to desorption isotherms. Based on the results obtained, the Smith's model represented isotherms with a higher precision for this variety of acerola. Additional keywords: drying; Malpighia glabra L.; mathematical models. Resumo O cultivo de acerola no Brasil tem-se apresentado cada vez mais crescente. O fruto da aceroleira é conhecido por apresentar várias propriedades concomitantes com o local onde é cultivada. A determinação da atividade de água dos produtos biológicos torna-se indispensável nos estudos dos processos de secagem, armazenagem e embalagem, uma vez que, quanto maior a atividade de água de um produto, mais propenso ele está ao ataque de microrganismos. Este trabalho teve como objetivo estudar as isotermas de dessorção em frutos de acerola (Malpighia glabra L.) para as temperaturas de 30, 40 e 50 o C pelo método estático indireto. Aos dados experimentais foram ajustados os modelos matemáticos de BET, GAB, Halsey, Oswin e Smith. A análise dos resíduos, do coeficiente de determinação, do erro médio relativo e do erro médio estimado, calculada para cada modelo ajustado, foi usada para se avaliar o modelo que melhor se ajustou às isotermas de dessorção. Com base nos resultados obtidos, o modelo de Smith representou essas isotermas com maior precisão para esta variedade de acerola. Palavras-chave adicionais: Malpighia glabra L.; modelos matemáticos; secagem. Introduction Acerola (Malpighia glabra L.) is a small tropical tree which grows and produces fruits rich in vitamin C (Manica et al., 2003). In Brazil, it is planted in all regions. Pernambuco, Ceará and Bahia are the major producing states, concentrating 70% of the national production (Figueiredo Neto et al., 2014). Acerola fruits are drupes with variable size, shape and weight. The shape can be oval or subglobose, with a lobed shape. It is considered a highly perishable fruit. It is marketed for the manufacture of frozen pulp and consumption in natura, interesting not only the regional market, but also other parts of the country where the fruit is scarce. As most fruits, much of the acerola crop is wasted because it is marketed in natura. It is therefore very important to provide information about other possibilities of using this fruit, being evident the need for a process which enables storage and marketing for a longer period. One of the most important procedures for the preservation of foods by decreasing its water activity is drying, considering that the fruit is composed of more than 80% of water 130

2 (Rodrigues et al., 2002; Silva et al., 2002). The water content of any product when in equilibrium with the storage environment is called equilibrium moisture content. The equilibrium moisture content assesses the loss or gain of water under determined conditions of temperature and relative humidity. It is directly related to the drying and storage processes of agricultural products (Sousa et al., 2014). According to Costa (2010), equilibrium moisture content is achieved when the partial pressure of water vapor inside the product equals the partial pressure of the air vapor that surrounds it. The equilibrium moisture content of biological products, by determining drying isotherms, is related to the size of dryers. Agricultural products interact with the environment, releasing or absorbing water, tending to a balance between its water content and environment humidity. In an equilibrium condition, the humidity relations can be expressed by mathematical equations, which are known as sorption isotherms or hygroscopic equilibrium curves (Argenta, 2015). Isotherms can be defined as curves describing the relation of balance between the quantity of water sorbed by the constituent components of fruits and the equilibrium moisture at a specific temperature (Chaves et al., 2015). Water activity is important for the processing of agricultural products and their conservation because it is associated to the availability of free water for the growth of microorganisms and other reactions that promote the deterioration of the product (Resende et al., 2006). However, empirical models are used for the determination of isotherms representing such equilibrium relation since no theoretical model has been able to accurately estimate the equilibrium moisture content for a range of temperature and relative humidity (Costa et al., 2013). Given the above and considering the potential commercialization of this fruit, especially for the agricultural industry, the objective of this study is to determine moisture desorption isotherms of acerola, variety 'Okinawa', for the temperatures 30, 40 and 50 C and adjust the models proposed in the literature to experimental data. Material and methods The study was conducted in laboratory. The raw material used was acerola (Malpighia glabra L.), variety 'Okinawa', from a property located at the irrigated project Nilo Coelho in Petrolina, Pernambuco (PE) state, where the fruits were harvested in the penultimate quarter of 2012 (Table 1). Approximately 300 acerola fruits, variety 'Okinawa', were manually collected, separated and packaged in containers to avoid unwanted damage. After harvesting, the fruits were transported to the laboratory where they were washed and characterized as shown in Table 2, eliminating malformed and damaged fruits. Table 1 Monthly averages of the daily mean air temperature (T), air relative humidity (RH), total rainfall (R), daily solar radiation (SR) and daily sunshine hours (SH) during the acerola harvest season, T RH R SR SH Month ( C) (%) (mm) (MJ m -2 day -1 ) (h day -1 ) August September October Average Table 2 - Characterization of acerola fruits, variety 'Okinawa', produced in the semiarid region of the São Francisco River Valley, Mass (g) Longitudinal diameter (cm) Transverse diameter (cm) Soluble solids (ºBrix) Vitamin C (mg/100g) Acerola Okinawa ,600 Desorption isotherms were determined by the indirect static method based on the study by Capriste & Rotstein (1982) using the equipment Thermoconstanter Novasina TH-200. For the sample preparation, circleshaped acerola fruits were used weighting approximately 9.0 g. They were placed in the plastic cells provided by the equipment and weighed in an analytical balance with a precision of g. Then, they were taken to a greenhouse at 60 o C for 6 hours in order to lose moisture. After this period, samples were removed from the oven and placed in a desiccator. Then, the plastic cells containing the samples were placed into the Thermoconstanter Novasina TH-200 for readings of water activity (Wa). The readings were obtained for the temperatures 30, 40 and 50 o C. After reading the Wa, the samples were removed from the equipment, weighed on an analytical balance HR-200 and placed in 131

3 the greenhouse, proceeding to readings at intervals of 15 and 30 minutes. This process was repeated until the last water activity reading was equal to or greater than the penultimate. Thus, every water activity reading corresponded to a desorption isotherm curve point for the temperature studied. Dry mass was obtained by the mass at equilibrium taken to an oven at 100 C for 3 hours (AOAC, 1984). The equilibrium moisture content (dry basis) was calculated based on the difference between the mass of the sample in equilibrium and the dry mass (Equation 1). Xe = me - dm dm (1) Where: Xe - equilibrium moisture content on a dry basis (decimal); me - mass of the sample in equilibrium (g); dm - dry mass of the sample (g). To predict the behavior of desorption isotherms of acerola, the models GAB, BET, and Oswin, Smith & Halsey were tested, as shown in Table 3, for adjustment of desorption isotherms and the choosing of the model that best adjusted the data. The Quasi-Newton method of non-linear regression analysis was used to estimate the constants of the model (Xm, C, K, A, B, Mb and Ma) using the Statistica software, version 5.0. Table 3 - Models for adjustment of desorption isotherms of acerola. Modelo matemático Equação Xe XmC K Wa GAB (2) 1 K Wa1 K Wa C K Wa N N 1 Xe C Wa 1 ( N 1) ( Wa) N ( Wa) BET (3) N 1 Xm 1Wa 1 (1 C) Wa C ( Wa) Wa Xe A 1Wa B OSWIN (4) SMITH Xe Mb Ma ln 1Wa (5) A HALSEY Xe (6) ln ( Wa) Where: Xe equilibrium moisture content on a dry basis (decimal); Wa - water activity (decimal); N - number of molecular layers; Xm - moisture content of the molecular monolayer (decimal); C - BET constant related to the sorption heat of the molecular layer; A, B, Ma, Mb and K - adjust parameters. The criteria used to choose the best adjustment were the coefficient of determination (R 2 ), estimated standard deviation (SE ) and standard deviation P(%), according to Equations 7 and 8. n P = 100 n V exp V p SE i=1 V exp ( Vexp V p ) DF 2 (7) (8) Where: P - standard deviation (%); SE - estimated standard deviation (%); V exp - value obtained experimentally (decimal) V p - value predicted by the model (decimal); n - number of experimental data; DF - degree of freedom of the model; Results and discussions The data in Table 4, obtained experimentally, represent the equilibrium moisture content in function of water activity and temperature for acerola fruits. According to the values presented, it appears that the equilibrium moisture content increases with the increase in water activity. These results are consistent with what happens to most hygroscopic products, as noted by Gouveia et al. (1999), Silva et al. (2002) and Oliveira et al. (2009), who evaluated ginger, mango and pineapple isotherms, respectively. However, water activity (Wa) increased with the increase in temperature. This behavior differs from that obtained by Kechaou & Maalej (1999), who concluded that water activity decreases with the increase in temperature for banana fruits. 132

4 Table 4 - Wa and Xe values of acerola for different temperatures. Temperature (ºC) Wa Xe Wa Xe Wa Xe Table 5 - Parameter estimates of acerola desorption isotherms of empirical models, coefficient of determination (R 2 ) and standard deviation (P). Model BET GAB HALSEY OSWIN SMITH Parameters Temperature (ºC) Xm C N P (%) R 2 (%) SE Random Xm C K P (%) R 2 (%) SE Tendentious A B P (%) R 2 (%) SE Tendentious A B P (%) R 2 (%) SE Tendentious Ma Mb P (%) R 2 (%) SE Random 133

5 Table 5 shows the constants estimated for the models GAB, BET, and Oswin, Smith and Halsey, coefficients of determination (R 2 ) and standard deviation (P). It is observed that the moisture content of the monolayer (Xm) of the BET equation increased with the increase in temperature. The parameter C, in the same equation, decreased with the increase in temperature. For the GAB model, Xm presented random variations within the studied temperature range. A similar result was obtained for the moisture content of the monolayer for desorption isotherms of guava regarding this model (Rodrigues et al., 2002). It was also verified (Table 5) that the parameter C decreased with the increase in temperature. A similar decrease was found by Moura et al. (2001) by drying cashew fruits. The divergence in the values of these parameters is probably due to differences in the stability, both physical and chemical, of these dehydrated products. Table 5 also shows that the results of the estimates for the parameters of desorption isotherms, varying according to temperature and considering the estimated constants, determination coefficients and the module of standard deviation relative to all models, except BET, at 50 C (R 2 = 81.89% and P = 19.23%), well represented the experimental data G A B B E T ,00 0, ,15 0,25 0,35 0,45 0,55 0,65 0,75 0,15 0,25 0,35 0,45 0,55 0,65 0, Halsey Oswin ,00 0, ,15 0,25 0,35 0,45 0,55 0,65 0, , ,25 0, , , , , Smith ,00-30 ºC 40 ºC , ,25 0, , ,55 0, ,75 Valores Residuais Figure 1 - Residual values (Y axis) for the mathematical equations analyzed at three temperatures in function of the predicted values (X axis). 134

6 The Smith's model had the smallest standard deviation in relation to the isotherms of acerola at 40 and 50 C. At that temperature (30 C), the coefficient of determination of the GAB model (99.44%) was higher than that of Smith (95.39%). The choice for the Smith's model as the best representation of the phenomenon under study is due to the joint analysis of coefficient of determination, standard deviation, estimated standard deviation and distribution of residues (random). It is supported by research conducted by Pereira et al. (2001), wherein, among the studied equations, the Smith's equation satisfactorily represented the desorption isotherm of avocado at 40 C by the hygrometric method. It appears that the models GAB, BET, and Oswin, Smith and Halsey satisfactorily described the adjustment of desorption isotherms of acerola for each temperature since the values of the coefficients of determination (R 2 ) were greater 90% and the relative standard deviations (E ) were below 10%, except for the BET model at 50 C. Analyzing the distribution of residual values (Figure 1) for the mathematical equations studied, it is possible to observe that, among the models studied, only BET and Smith equations present a random distribution of residuals (Table 5), suggesting that these equations can be used satisfactorily for the mathematical representation of equilibrium moisture content in function of water activity for Cajá fruits under the conditions studied. The desorption isotherms of acerola, variety 'Okinawa', adjusted by the Smith's model (Figure 2) for the temperatures 30, 40 and 50 C, present the characteristic shape of the equilibrium of a hygroscopic material, wherein the points corresponding to curves align along them. It is observed that the increase in water activity for each temperature results in an increase in equilibrium humidity. The desorption rate is higher at the beginning of the process, decreasing continuously as it approaches the equilibrium moisture content, a behavior that enables confirming an increase in desorption rate with the decrease in relative humidity. Umidade de equilíbrio, b.s. (decimal) 1.0 1, , , , ,2 30ºC 40ºC 50ºC Smith Model: Xe = Mb Ma Ln (1 Wa) 0.0 0, ,0 0, , , , ,0 Atividade de água (decimal) Figure 2 - Desorption isotherms of acerola (equilibrium unit, Y axis) at 30, 40 and 50 C as function of water activity. Furthermore, the equilibrium is achieved by a relatively fast increase in product temperature at the initial moments of the process. This is significant because the behavior of the temperature distribution curve show a good correspondence between drying rates and fruit heating rates during drying, particularly at the beginning of the process, wherein the decrease in moisture is easier. According to Oliveira et al. (2009), the shapes of isotherms obtained at the temperatures studied always follow the type III of BET classification, a J shape. Such shapes are typical of products with high concentrations of sugars and solutes and present little absorption by capillarity. Conclusions The desorption curves of acerola, variety of 'Okinawa', for the temperatures 30, 40 and 50ºC were best represented by the Smith's model. The choice for the Smith's model as the best representation of the phenomenon under study is made based on the joint analysis of the coefficient of determination, standard deviation, estimated standard deviation and distribution of residues (random). The dependence of isotherms on temperature can be perfectly expressed not only by Smith's model, but also by the BET model for the temperatures 30 and 40 C. 135

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