Vitae
ISSN: 0121-4004
[email protected]
Universidad de Antioquia
Colombia
VÁQUIRO, Henry A.; VILLA-VÉLEZ, Harvey A.; TELIS-ROMERO, Javier; GABAS, Ana L.
PHYSICAL PROPERTIES OF APPLE SEEDS AS A FUNCTION OF MOISTURE CONTENT
Vitae, vol. 19, núm. 1, enero-abril, 2012, pp. S397-S399
Universidad de Antioquia
Medellín, Colombia
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S397
Vitae 19 (Supl. 1); 2012
PHYSICAL PROPERTIES OF APPLE SEEDS AS A FUNCTION
OF MOISTURE CONTENT
PROPIEDADES FÍSICAS DE SEMILLAS DE MANZANA EN FUNCIÓN DEL CONTENIDO
DE HUMEDAD
Henry A. VÁQUIRO1, Harvey A. VILLA-VÉLEZ2, Javier TELIS-ROMERO2, Ana L. GABAS3*
ABSTRACT
The objective of this work was to determine the physical properties of apple as a function of the volumetric
moisture content at 28 °C. The particle size, true density and bulk density were determined experimentally.
The bulk porosity was calculated. The particle size, true density and bulk density values decreased, while
the bulk porosity values increased with decreasing moisture content. Three classical empirical models
were fitted to physical properties. The parabolic model showed better statistical fitting parameters.
Keywords: Particle size, density, porosity, mathematical models.
RESUMEN
El objetivo del presente trabajo fue determinar las propiedades físicas de semillas de manzana en función
del contenido de humedad volumétrico a 28°C. El tamaño de partícula, densidad real y aparente fueron
determinados experimentalmente. La porosidad aparente fue calculada. Los valores del tamaño de
partícula, la densidad real y aparente disminuyeron, mientras que los valores de la porosidad aparente se
incrementaron cuando el contenido de humedad disminuyó. Tres modelos clásicos fueron utilizados para
modelar las propiedades físicas, siendo el modelo parabólico el que obtuvo mejor evaluación estadística.
Palabras clave: tamaño de partícula, densidad, porosidad, modelos matemáticos.
INTRODUCTION
Fruit production, besides meeting the fresh
consumption market, provides raw material for
various industries such as those producing fresh
or concentrated juice. Tons of wastes are generated due to separation of the seeds, during the
juice extraction, which are highly perishable (1, 2).
Dehydration would be a useful means of increasing its shelf-life for later use (3). Knowledge of the
particle size, bulk density, true density and bulk
porosity is essential for an adequate design of the
equipment used to handle the material. The particle
size can be determined in terms of its equivalent
diameter, defined as a function of the volume. The
bulk density is an important parameter to design
storage systems, and the porosity, obtained from
the bulk and true densities, is essential to calculate
the pressure drop in the airflow system (4, 5). Its
values can be used to predict the frictional pressure
drop of the beds, with material of any size and also
with broad size distribution. In this paper, studies
were carried out to supplement the data found in
the literature with respect to the physical properties
of apple seeds, and develop mathematical models
as a function of the volumetric moisture content.
1
Facultad de Ingeniería Agronómica. Universidad del Tolima. Ibagué, Colombia.
2
Departamento de Engenharia e Tecnologia de Alimentos. Universidade Estadual Paulista. São José do Rio Preto. São Paulo, Brasil.
3
Faculdade de Zootecnia e Engenharia de Alimentos. Universidade de São Paulo (FZEA-USP). Pirassununga, São Paulo, Brasil.
*
Corresponding author: [email protected]
S398
Vitae 19 (Supl. 1); 2012
MATERIAL AND METHODS
Raw material
Apple (Malus domestica Borb cv. Gala) seeds
used to the experimental procedures were obtained
directly from fruit juice production lines, from industries in São José do Rio Preto, SP, Brazil. The
seeds were manually separated from the waste and
washed with distilled water to remove the remaining pulp, and stored at 5°C until use.
Sample preparation
Apple seed were dried with hot air at 80°C and
2.6 m/s. Seed samples were collected at different
drying times in order to obtain eight different
moisture contents (6). The moisture content of
dried samples was homogenized by wrapping the
seeds in plastic film and holding them at 5°C during 24 h. After that, the seeds were kept at room
temperature (~28°C) to determine the moisture
content and physical properties.
The moisture content was analyzed using the
vacuum oven method (7) and expressed according to
the mass (Xww , kg/kg) and volumetric (Xvw , kg/m3)
moisture contents, the latter being calculated using
equation 1.
Equation 1.
where rw is the water density (kg/m3) and rt the
true density of the seeds (kg/m 3) (4).
The true density (r t, m3/kg), defined as the
ratio between the mass and the true volume of the
material.
The bulk density (rb, m3/kg) was calculated as
the ratio of the sample mass to a known volume.
Calibration was carried out using sucrose powder
(food grade) which has well-known true and bulk
densities (6, 8) in a cylindrical container with a
height to diameter ratio of 1.333 (0.200 m height
0.150 m diameter). The container was filled with
the seed sample using a funnel fixed 0.3 m above
the rim of the container. After discharging the seed,
the sample was carefully leveled with the rim of
the container using a plastic ruler, and the material
remaining in the container weighed on an electronic
balance with a precision of 1 mg. The bulk density
was determined using three replicates.
The bulk porosity is the parameter indicating
the amount of pores in the bulk of the materials
and is calculated from the bulk and the true density
using equation 3.
Equation 3.
where eb is the bulk porosity (volumetric fraction
of air in the bed) (6).
Empirical models for the physical properties
Three typical models were applied in the prediction of physical properties. The models are
described as:
Experimental procedure
Model 1 = a + b Xww
Equation 4.
Five hundred apple seeds were randomly chosen
and used to measure the average volume (1). The
true volumes (Vsph, m3) of the seeds at different
moisture contents were determined by the liquid
displacement method (samples weighing approximately 100 to 150 g), using toluene as the liquid
medium (8). An electronic balance with an accuracy
of 1 mg was used to determine the weight.
The equivalent spherical diameter was determined using the experimental value obtained for
the volume, according to equation 2.
Model 2 = a + bXvw + c(Xvw )2
Equation 5.
Model 3 = a + bXvw + clnXvw
Equation 6.
Equation 2.
where dsph is the equivalent spherical diameter (m)
and Vsph the volume (m 3).
where Xvw is the moisture content (w.b.) and a, b
and c are the empirical constants.
The identification of model parameters was
performed using the ‘solver’ tool of MS Excel®.
The coefficient of determination (R 2) was used to
evaluate the goodness of the estimations provided
by the models.
RESULTS AND DISCUSSION
The experimental datafor physical properties
of apple seeds as shown in table 1. The physical
S399
Vitae 19 (Supl. 1); 2012
properties of apple seeds (table 2) were estimated
by using the parabolic model (equation 2) since
it appeared as the best option from fitting of the
experimental and estimated data (R 2 > 0.97).
Table 1. Particle size (dsph), bulk density (rb), true density (rt) and porosity (eb) of apple seeds at different values of
moisture content*.
*
dsph
ñt
(kg/m3)
rb
(kg/m3)
Xww
(kg/kg)
Xvw
(kg/m3)
0.498
0.552
7.30
(0.27)
709.9
(6.9)
1232.4
(0.2)
0.424
0.442
0.496
7.25
(0.02)
706.9
(11.7)
1232.7
(15.0)
0.427
0.367
0.418
7.22
(0.00)
704.8
(7.8)
1231.1
(9.5)
0.427
0.296
0.342
7.16
(0.20)
700.1
(10.1)
1228.7
(1.4)
0.430
0.258
0.301
7.13
(0.10)
697.8
(6.8)
1226.9
(0.2)
0.431
-3
(× 10 m)
eb
0.218
0.256
7.12
(0.02)
696.3
(11.9)
1224.4
(14.9)
0.431
0.190
0.224
7.09
(0.00)
693.1
(8.1)
1222.5
(9.4)
0.433
0.158
0.187
7.08
(0.02)
691.6
(10.4)
1219.6
(0.2)
0.433
Standard deviations of three replicates.
Table 2. Parameters values of the physical properties of apple seeds using the parabolic model.
Physical property
Equations as a function of the moisture volumetric fraction
d sph × 10-3 (m)
0.992
rb (kg/m 3)
0.994
ñt (kg/m 3)
0.998
eb
0.978
CONCLUSIONS
The particle size, bulk density and true density
values decreased with decreasing moisture content,
while the bulk porosity values increased with decreasing moisture content. The parabolic model was
the best model to represent the physical properties
of the apple seeds.
3.
4.
5.
6.
7.
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