Reis et al 2017 Frutos de acerola

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ISSN: 1984-5529 
 
Jaboticabal 
v.45, n.2, p.130–136, 2017 
http://dx.doi.org/10.15361/1984-5529.2017v45n2p130-136 
130 
 
Desorption isotherms of acerola fruits variety 'Okinawa' 
 
Isotermas de dessorção em frutos de acerola variedade ‘Okinawa’ 
 
Daíse Souza REIS1; Acácio FIGUEIREDO NETO2; Josenara Daiane de Souza COSTA3; Francisco de 
Assis Cardoso ALMEIDA4; Josivanda Palmeira Gomes GOUVÊIA5 
 
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: 08-07-2015; Aceito em: 23-10-2016 
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 oC 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 sub-
globose, 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 there-
fore 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 
Científica, Jaboticabal, v.45, n.2, p.130-136, 2017 ISSN: 1984-5529 
 
131 
 
(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 pres-
sure 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 envi-
ronment, 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 equa-
tions, 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 compo-
nents of fruits and the equilibrium moisture at a spe-
cific 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 equi-
librium 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 poten-
tial 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 irri-
gated 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 solarradiation (SR) and daily sunshine hours (SH) during the acerola harvest season, 2012. 
Month 
T 
(°C) 
RH 
(%) 
R 
(mm) 
SR 
(MJ m-2 day-1) 
SH 
 (h day-1) 
August 24.30 63.98 2 21.05 8.1 
September 26.40 57.11 0 23.36 9.5 
October 27.70 56.36 0 26.08 9.7 
Average 26.13 59.15 - 23.47 9.1 
 
Table 2 - Characterization of acerola fruits, variety 'Okinawa', produced in the semiarid region of the São 
Francisco River Valley, 2012. 
 
Mass 
(g) 
Longitudinal 
diameter (cm) 
Transverse 
diameter (cm) 
Soluble solids 
(ºBrix) 
Vitamin C 
(mg/100g) 
Acerola ‘Okinawa’ 9.2 2.3 2.75 12 3,600 
 
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, circle-
shaped 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 0.001 g. Then, 
they were taken to a greenhouse at 60 oC 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 oC. After reading the Wa, 
the samples were removed from the equipment, 
weighed on an analytical balance HR-200 and placed in 
Científica, Jaboticabal, v.45, n.2, p.130-136, 2017 ISSN: 1984-5529 
 
132 
 
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 equilib-
rium 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 iso-
therms 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 con-
stants 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 
GAB 
 
(2) 
BET 
 
(3) 
OSWIN 
 
(4) 
SMITH 
 
(5) 
HALSEY 
 
(6) 
 
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 (R2), 
estimated standard deviation (SE ) and standard 
deviation P(%), according to Equations 7 and 8. 
𝑃 =
100
𝑛
∑
|𝑉𝑒𝑥𝑝 − 𝑉𝑝|
𝑉𝑒𝑥𝑝
𝑛
𝑖=1
 (7) 
 
 
(8) 
 
Where: 
P - standard deviation (%); 
SE - estimated standard deviation (%); 
Vexp - value obtained experimentally (decimal) 
Vp - 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. 
  WaKCWaKWaK
WaKCXm
Xe


11












1
1
)( )1(1
)( )( )1(1
1
 
N
NN
WaCWaC
WaNWaN
Wa
WaC
Xm
Xe
B
Wa
Wa
AXe 







1
  WaMaMbXe  1ln





 

)(ln Wa
A
Xe







 


DF
VV
SE
p
2
exp )(
Científica, Jaboticabal, v.45, n.2, p.130-136, 2017 ISSN: 1984-5529 
 
133 
 
Table 4 - Wa and Xe values of acerola for different temperatures. 
Temperature (ºC) 
30 40 50 
Wa Xe Wa Xe Wa Xe 
0.485 0.120 0.491 0.231 0.593 0.143 
0.533 0.161 0.505 0.267 0.617 0.180 
0.559 0.199 0.517 0.290 0.660 0.241 
0.567 0.231 0.530 0.353 0.698 0.306 
0.593 0.292 0.551 0.380 0.787 0.473 
0.650 0.420 0.636 0.433 0.876 0.694 
 0.691 0.619 
 
Table 5 - Parameter estimates of acerola desorption isotherms of empirical models, coefficient of 
determination (R2) and standard deviation (P). 
Model Parameters 
Temperature (ºC) 
30 40 50 
BET 
Xm 0.446 5.402 9.118 
C 39.03 0.042 0.015 
N 3 3 3 
P (%) 1.420 7.500 19.23 
R2 (%) 96.66 92.67 81.89 
SE 0.021 0.034 0.088 
Residue distribution Random 
GAB 
Xm 0.573 0.019 9.749 
C 10.41 2.405 0.013 
K 0.381 1.060 0.747 
P (%) 0.600 6.390 5.350 
R2 (%) 99.44 94.63 98.79 
SE 0.015 0.030 0.023 
Residue distribution Tendentious 
HALSEY 
A 0.948 0.240 0.090 
B 3.523 0.855 1.119 
P (%) 1.050 6.790 9.160 
R2 (%) 97.78 94.75 96.77 
SE 0.014 0.030 0.041 
Residue distribution Tendentious 
OSWIN 
A 0.684 0.289 0.150 
B 0.155 0.910 0.794 
P (%) 0.710 6.570 8.330 
R2 (%) 99.02 94.80 97.37 
SE 0.013 0.030 0.037 
Residue distribution Tendentious 
SMITH 
Ma 0.469 63.283 0.455 
Mb 0.345 -0.150 -0.247 
P (%) 1.590 5.920 2.800 
R2 (%) 95.39 94.75 99.71 
SE 0.013 0.030 0.011 
Residue distribution Random 
 
Científica, Jaboticabal, v.45, n.2, p.130-136, 2017 ISSN: 1984-5529 
 
134 
 
Table 5 shows the constants estimated for the 
models GAB, BET, and Oswin, Smith and Halsey, 
coefficients of determination (R2) 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 (R2 = 81.89% and P = 19.23%), 
well represented the experimental data. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1 - Residual values (Y axis) for the mathematical equations analyzed at three temperatures in function 
of the predicted values (X axis). 
Valores preditos
V
al
or
es
 re
sid
ua
is
-0,07
-0,06
-0,05
-0,04
-0,03
-0,02
-0,01
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,05 0,15 0,25 0,35 0,45 0,55 0,65 0,75
B E T
Valores preditos
Va
lor
es
 re
sid
ua
is
-0,07
-0,06
-0,05
-0,04
-0,03
-0,02
-0,01
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,05 0,15 0,25 0,35 0,45 0,55 0,65 0,75
G A B
Valores preditos
V
al
or
es
 re
si
du
ai
s
-0,07
-0,06
-0,05
-0,04
-0,03
-0,02
-0,01
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,05 0,15 0,25 0,35 0,45 0,55 0,65 0,75
Oswin
Valores preditos
V
alo
re
s r
es
id
ua
is
-0,07
-0,06
-0,05
-0,04
-0,03
-0,02
-0,01
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,05 0,15 0,25 0,35 0,45 0,55 0,65 0,75
Smith
Valores preditos
Va
lor
es
 R
es
idu
ais
-0,07
-0,06
-0,05
-0,04
-0,03
-0,02
-0,01
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,05 0,15 0,25 0,35 0,45 0,55 0,65 0,75
Halsey
○ 30 ºC ∆ 40 ºC □ 50 
ºC 
0.07 
 
 
 
 
 
0.00 
 
 
 
 
 
-0.07 
 
 
0.07 
 
 
 
 
 
0.00 
 
 
 
 
 
-0.07 
 
 
0.07 
 
 
 
 
 
0.00 
 
 
 
 
 
-0.07 
 
 
0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 
0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 
Científica, Jaboticabal, v.45, n.2, p.130-136, 2017 ISSN: 1984-5529 
 
135 
 
 
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 (R2) 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. 
 
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. 
Atividade de água (decimal)
Um
ida
de
 de
 eq
uil
íbr
io,
 b.
s. 
(de
cim
al)
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0
30ºC
40ºC
50ºC
Smith Model: Xe = Mb – Ma Ln (1 – Wa) 
1.0 
 
0.8 
 
0.6 
 
0.4 
 
0.2 
 
0.0 
0.0 0.2 0.4 0.6 0.8 1.0 
 
Científica, Jaboticabal, v.45, n.2, p.130-136, 2017 ISSN: 1984-5529 
 
136 
 
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