
Research Article

Mathematical Modelling of Thin Layer Drying of Salak

S.P. Ong
and
C.L. Law


ABSTRACT

Thin layer drying kinetics of salak (Salacca edulis) in hot air drying was investigated for temperature range of 50 to 80°C. Salak fruits were prepared in two forms; slices with membrane layer and slices without membrane layer on surface. A mathematical model was determined to describe the moisture reduction process during isothermal drying. Theoretical model of Fick’s second law, six semitheoretical models and one empirical model that commonly employed in food dehydration were evaluated. Results showed that the MidilliKucuk equation gave the best prediction to the drying kinetics evidenced by coefficient of determination, R^{2} ranging from 0.99760.9993. A new approach was used for the estimation of drying rate and the commencement point of second fallingrate period by using a semitheoretical model. Diffusivity coefficients of moisture transfer were found ranging from 4.19x10^{11} to 2.58x10^{10} m^{2} sec^{1}. It appears that moisture diffusion is the controlling mechanism of the thin layer drying and it is an increasing function of temperature. Activation energy was determined at 45.27 and 39.78 kJ mol^{1} for sample with and without surface membrane, respectively. Higher activation energy indicates that the membrane layer is a strong barrier to moisture movement across the sample surface. 




INTRODUCTION
Salak (Salacca edulis) or also known as snake fruit belongs to Arecaceae
family. This palm is native in Indonesia and Malaysia. Nevertheless, cultivation
of salak palm can also be found in Thailand and Philippines recently (AbadGarcía
et al., 2007). Salak fruit is a good source for dietary fibres and
carbohydrate (Lestari et al., 2003). This peculiar
fruit tastes sweet to subacid like combination of pineapple and jackfruit at
its ripe stage but immature fruit tastes sour and astringent. Despite the unique
smell and taste, salak contains valuable bioactive antioxidants such as vitamin
A, vitamin C and phenolic compounds (Setiawan et al.,
2001; Leong and Shui, 2002;
Shui and Leong, 2005; Leontowicz et al., 2007).
However, salak has a short shelf life of less than a week due to rapid ripening
and degradation of the bioactive ingredients.
Drying is one of the common methods used to preserve agricultural products.
Removal of moisture from produces may deactivate enzymes or microorganisms that
often cause undesired chemical reaction and lead to quality deterioration (Jayaraman
and Das Gupta, 2006). Drying kinetics is important in the analysis of moisture
migration process in a solid material. Many thermophysical properties and transport
properties that are usually integrated in a drying model can be determined from
the analysis of drying kinetics (MarinosKouris and Maroulis,
2006). Moreover, movement of moisture within a food material during drying
is a complex process with various diffusion mechanisms. Variation in composition
and complicated biopolymer structure of the food material may result in unique
drying characteristic for different food product (Zogzas
et al., 1996). Study on the drying kinetics may allow understanding
of the controlling mechanism during drying and hence influence of drying parameters
on dryer design and dried product quality can be determined.
Nemerous studies have been conducted to the drying kinetics and product quality
of foodstuffs that undergoing isothermal convective drying, for instance garlic,
pumpkin, grapes, apple and orange skin (Madamba et al.,
1996; Sawhney et al., 1999; Doymaz,
2007; Kaya et al., 2007). However, to date
there is no literature report on the drying kinetics of salak fruit which is a
good source for dietary antioxidant but unexploited. On the other hand, several
mathematical models have been proposed for the evaluation of moisture transport
behavior by either applying theoretical (Fick’s second law of diffusion),
semitheoretical and empirical modelling (Crank, 1975;
Jayas et al., 1991; Kabganian et al., 2002;
Demir et al., 2007; Midilli
et al., 2002; Doymaz, 2005). Theoretical model
can be used to get an insight on the mechanism of moisture transfer during the
fallingrate period in drying. However, simplified assumptions such as constant
diffusivity and onedimension liquid diffusion sometimes resulted in inadequate
prediction to the moisture distribution. Meanwhile, a semitheoretical model may
not able to explain the exact mechanism of moisture transport but it often gives
good estimation by incorporating lump values of other effects into the model parameters.
The objective of this study is to investigate the kinetics of thin layer drying of salak and to determine mathematical model for the moisture distribution profile of the convective hot air drying. This study also aims to extend the use of semitheoretical model in the estimation of drying rate at different drying temperature and determination of commencement point of second falling rate period. MATERIALS AND METHODS Sample preparation: Salak fruits (Salacca edulis) were purchased from a local fruit supplier. Fruits with similar size (ca. 57x5 cm) and skin colour were selected for all experiments to ensure consistency in the samples used. Fresh fruits were kept in refrigerator at about 10°C with storage period not longer than seven days. Salak slices (3x2x2 mm) were prepared in two forms, with surface membrane and without surface membrane. Sample without surface membrane was prepared by removing the membrane layer manually from the fruit surface before slicing. Drying experiments: Convective hot air drying experiments were performed by using an oven with forced air circulation (Memmert, UFP500, Germany). Heating elements were integrated evenly around the four inner walls to create uniform temperature distribution inside the chamber. Fresh air was preheated in a prewarming chamber and continuously added to the air inside the chamber. Meanwhile, exhaust air was discharged through an opening situated in the middle of back wall. Four levels of hot air temperature (50, 60, 70 and 80°C) were used. Samples (about 100 g) were arranged on flat perforated trays (65x35 cm with 1 cm diameter openings) and placed in the middle section of the oven. The weight of the sample was recorded periodically during the drying with 15 min interval in the first 2 h, 30 min interval in the subsequent next 2 h and hourly thereafter by using a digital balance (Adventurer OHAUS, AR3130, USA). Experiment was terminated when constant weight was obtained in three consecutive measurements. The moisture content obtained at this stage was marked as the Equilibrium Moisture Content (EMC). Dry Matter (DW) weight of the material was determined by drying the sample in oven at 105°C for 24 h.
Mathematical modelling
Moisture ratio: Moisture content was determined as a dimensionless
parameter denoted as Moisture Ratio (MR). Equation 1 relates
the sample moisture content in real time (X_{t}) to the initial moisture
content (X_{o}) and equilibrium moisture content (X_{e}) (Akpinar
et al., 2003):
Theoretical model: Fick’s second law was solved analytically for
diffusion in a plane sheet by assuming onedimension diffusion and constant
diffusivity (Crank, 1975). Ten terms (n = 10) from the
Fick’s series in Eq. 2 was used to estimate the moisture
content by conducting nonlinear regression analysis using Microsoft Excel SOLVER
tool (Microsoft Office Professional 2003, USA). Effective diffusivity constant
(D_{eff}) and sample thickness (L) are the model parameters.
Semitheoretical and empirical model: Semitheoretical and empirical models that commonly applied for fruits and vegetables drying were adopted from literatures as shown in Table 1. Three statistical parameters, coefficient of determination (R^{2}), Chisquare (χ^{2}) and Root Mean Square Error (RMSE), were used to assess the goodness of fit of the models to experiment data.
Drying rate and fallingrate period: Drying rate at a given temperature
was estimated by using first derivation of MidilliKucuk model equation while
gradient of the drying rate was calculated by conducting second derivation to
the same model.
Table 1: 
Semitheoretical and empirical models 

Effective diffusivity and activation energy: Effective diffusivity
constant (D_{eff}) can be determined from the linearized first term
from the Fick’s infinite equation as shown in Eq. 3 by
assuming that constant diffusivity applied to the internal moisture movement
during first fallingrate period.
Natural logarithm of MR was plotted versus t and D_{eff} can be determined
from the slope. Relationship between D_{eff} and temperature can be
evaluated with Arrhenius equation as shown in Eq. 4.
RESULTS AND DISCUSSION
Drying kinetics: Moisture content of samples at four levels of temperature
(50, 60, 70 and 80°C) were monitored over the drying period. Initial moisture
content of the salak fruits were recorded at 4.24±0.39 kg water kg DW^{1}.
Figure 1a and b show the moisture ratio
versus time for salak slices with and without surface membrane, respectively.
Both graphs show exponential trend for the drying curves and it can be observed
that the samples reached EMC in a shorter time at higher temperature. Many literatures
showed similar results when conducting hot air drying to agricultural products
such as red chillies, pineapple and potatoes (Arora et
al., 2006; Nicoleti et al., 2001; Rossello
et al., 1992). Higher drying temperature would result in higher drying
kinetics. However, membrane layer on the fruit surface is a barrier to moisture
transfer. Higher moisture content was found in salak with surface membrane when
compared with those without membrane at a given time period. Nevertheless, the
effect of surface barrier was less pronounce when drying process was conducted
at higher temperature. Moisture contents for both samples (with and without
membrane) were found close to each other for the hot air drying at temperature
80°C.
Mathematical modelling: Mathematical modelling of the drying curves
under various temperatures was conducted by using nonlinear regression analysis
coupled with generalized reduced gradient algorithm (GRG2). All the model constants
were calculated based on the iterative method and the statistical parameters
for the estimation are shown in Table 2. Based on the obtained
values for the three statistical parameters, it can be seen that MidilliKucuk
equation is the best model to describe the drying kinetics of salak slices at
all tested temperatures with R^{2}, χ^{2} and RMSE values
ranging from 0.99760.9993, 0.0001 0.0003 and 0.00680.0128, respectively.
 Fig. 1: 
Moisture ratio of salak slices at different temperature (a)
with surface membrane and (b) without surface membrane 
In agreement with other literatures, MidilliKucuk model often gave better
prediction on the moisture distribution profile among other semitheoretical
models (Ait Mohamed et al., 2005;
HacIhafIzoglu et al., 2008; Karaaslan and Tunçer,
2008). On the other hand, Fick’s equation (theoretical) resulted in
lower value of R^{2} as compared with semitheoretical models, while
the Wang and Singh model (empirical) presented the lowest R^{2} value
among the theoretical and semitheoretical models.
Drying rate and fallingrate period: High value of R^{2} and
low value of χ^{2} and RMSE obtained from the regression analyses
indicate that the MidilliKucuk model fitted well with the experiments data.
Thus, it can be used to represent the drying curve for salak slices under isothermal
drying and the drying rate can be calculated by applying first derivative to
the MidilliKucuk equation. Drying rate curves for salak slices with and without
surface membrane are shown in Fig. 2a and b,
respectively. It was observed hat there was no constantrate period in all drying
rate curves.
Table 2: 
Results of statistical parameters estimated from regression
analyses for temperature of 5080°C 

 Fig. 2: 
Drying rate curves for salak slices (a) with surface membrane
and (b) without surface membrane 
All drying experiments comprised of only fallingrate period. The rate of drying
fell steadily with time. It appears that higher drying rate was obtained at
high temperature and sample without surface membrane attained higher drying
rate when compared with those with membrane layer at a given temperature.
Many literatures suggested that moisture diffusion in solid material during
fallingrate period is diffusioncontrolled and moisture diffusion in first
fallingrate period is more prominent and significant as compared with diffusion
in second fallingrate period. This is because second fallingrate period is
the period of unsaturated surface evaporation and usually the amount of moisture
removed is relatively small but the time required may be long. Hence, moisture
diffusivity can be estimated from the first fallingrate period and the calculated
effective diffusivities are lump values over the range of moisture content (Geankoplis,
1993). Nevertheless, in most cases, the commencement of second fallingrate
period is difficult to be estimated from the drying rate curve due to unobvious
curve change especially when data points are closed to each other at low moisture
content.
Thus, plots for drying rate gradient against drying time were constructed by
applying second derivation to the MidilliKucuk model. Figure
3a and b show the curves for the dying rate gradient with
and without membrane layer, respectively. Overall, drying rate gradient was
found increased with time before reaching a constant value and decreased with
time thereafter. The obtained constant value is an indication of first fallingrate
period due to the characteristic of the first fallingrate curve which is usually
a straight line with slope.
 Fig. 3: 
Drying rate gradient for salak slices (a) with surface membrane
and (b) without surface membrane 
It appears that time period for the occurrence of the first fallingrate is
dependent on the temperature. For instance, the beginning points for the second
fallingrate period (also the end points for first fallingrate period) were
found at 120, 75, 60 and 45 min at temperature of 50, 60, 70 and 80°C, respectively,
for the drying of salak with membrane layer. It seems that at higher temperature
the first fallingrate period will be shorten.
Effective diffusivity and activation energy: Plots of lnMR versus t
for the four drying temperatures were constructed by using only the data fell
within the first fallingrate period and the results are shown in Fig.
4a and b. The constant diffusivity (D_{o}) and
activation energy (E_{a}) were determined from the yintercept and slope
of the linearized Arrhenius equation curve, respectively. Table
3 shows the summary of the D_{eff}, D_{o }and E_{a}.
The estimated D_{eff} ranging from 4.19x10^{11} to 2.58x10^{10}
m sec^{1} and the obtained values are fall within the range of values
reported in other literatures (Madamba et al., 1996;
Nicoleti et al., 2001; Biju Cletus and Carson,
2008; Garau et al., 2006).
 Fig. 4: 
Plot of lnMR versus t for salak slices (a) with surface membrane
and (b) without surface membrane 
Table 3: 
Effective diffusivity, constant diffusivity and activation
energy for salak with or without membrane 

Apparently, the effective diffusivity increased with drying temperature. On
the other hand, activation energy for sample with surface membrane was found
higher than those without surface membrane. This could be resulted by the existence
of the membrane on the sample surface that had become the resistance for the
moisture movement. Thus higher energy required to overcome the resistance.
CONCLUSION
Elevated air temperature resulted in higher drying kinetics. Effective diffusivity
constant was found increased with temperature and correlated well with the Arrhenius
equation. Higher activation energy showed that the surface membrane was a strong
barrier to moisture diffusion from internal to surrounding air. MidilliKucuk
model gave better prediction to the moisture distribution profile as compared
to other semitheoretical models.
ACKNOWLEDGMENTS The authors are grateful to the Ministry of Science, Technology and Innovation for the financial support through eScience funding and support from the University of Nottingham, Malaysia Campus.

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