Volumen 32, Nº 4.

Páginas 43-56
IDESIA (Chile) Septiembre-Noviembre, 2014

Mathematical modeling of the drying kinetics of the leaves of lemon

grass (Cymbopogon citratus Stapf) and its effects on quality
Modelación matemática de la cinética de secado de las hojas de hierba de limón
(Cymbopogon citratus Stapf) y sus efectos sobre la calidad
Paulo Carteri Coradi1*, Evandro de Castro Melo2, Rocinely Pereira da Rocha3

ABSTRACT

The aim of this study was evaluate the drying of the lemon grass plant (Cymbopogon citratus Stapf) at different air temperatures
(40 °C, 50 °C, 60 °C and 70 °C) to adjust the experimental data obtained with different mathematical models and assess the
quality of the plant after drying. A completely randomized design (CRD) was used with three drying replications for each speed
and temperature of the drying air. The essential oil content extracted from the dried plant at 0.8 m s–1 and 1.3 m s–1 with manual
control system was not affected by the drying process; the temperature of the drying air had a negative influence on the levels of
the essential oil of the plant; drying with automatic control decreased the essential oil content for all velocities studied compared
to the fresh plant; increments in the temperature of the drying air significantly reduced drying time. The mathematical model of
Two Terms is adequate to describe the drying process of lemon grass plant (Cymbopogon citratus Stapf); diffusion values i​​ ncreased
with increasing temperature of the drying air, while the value of activation energy was 62.84 kJ mol–1.
Key words: air, control, plant, velocity, temperature.

RESUMEN

El objetivo de este estudio fue evaluar el secado de la planta de hierba de limón (Cymbopogon citratus Stapf) a diferentes tempera-
turas de aire (40 °C, 50 °C, 60 °C y 70 °C) para ajustar los datos experimentales obtenidos con diferentes modelos matemáticos y
evaluar la calidad de la planta después del secado. Un diseño completamente al azar (DCA) se utilizó con tres repeticiones para
cada velocidad de secado y la temperatura del aire de secado. El contenido de aceite esencial extraído de la planta seca en 0,8 m
s–1 y 1,3 m s–1 con sistema de control manual no se vio afectado por el proceso de secado, la temperatura del aire de secado tuvo
una influencia negativa sobre la reducción de los niveles del aceite esencial de la planta, el secado con control automático de
disminución del contenido de aceite esencial para todas las velocidades estudiado en comparación la planta fresca; incrementa
el valor de la temperatura del aire de secado ha reducido significativamente el equipo de secado, el modelo matemático de Dos
Términos es adecuada para describir el proceso de secado de la planta de hierba de limón (Cymbopogon citratus Stapf), los
valores de difusión aumentó con el aumento de temperatura del aire de secado, mientras que el valor de la energía de activación
es 62.84 kJ mol–1.
Palabras clave: aire, control, velocidad, temperatura.

Introduction availability. The drying process may also contribute

to regular supply and facilitate the marketing of
Lemon grass (Cymbopogon citratus Stapf) is plants, because it facilitates transport and storage
widely cultivated in Brazil and utilized for medicinal (Castro & Ferreira, 2001). In the literature several
purposes, especially as tea, and industries are investing methods are mentioned to analyze the drying of
in it due to its essential oil. The growing demand for hygroscopic products (theoretical, empirical and semi-
medicinal species indicates the emergence of a market empirical). The empirical method is a method based
with high potential for consumption, requiring raw on experimental data and dimensionless analysis. The
material of high quality, with regular supply and easy empirical models of drying show a direct relationship

1 Federal University of Mato Grosso do Sul, Campus of Chapadão do Sul, Brazil.

2 Federal University of Viçosa, Department of Agricultural Engineering, Brazil.
3 Federal University of Viçosa, Department of Agricultural Engineering, Brazil.
* Corresponding Author: paulo.coradi@ufms.br

Fecha de Recepción: 23 Mayo, 2014.

Fecha de Aceptación: 21 Agosto, 2014.
44 IDESIA (Chile) Volumen 32, Nº 4, Septiembre-Noviembre, 2014

between average moisture content and drying time. Department at the Federal University of Viçosa-UFV
However, this method omits the fundamentals of the (Minas Gerais, Brazil). The lemon grass was harvested
drying process and its parameters have no physical between 8:00 and 9:00 am and the samples were taken
meaning, therefore it does not provide an accurate immediately to the laboratory for selection, moisture
view of the important processes that occur during content determination and cooled in refrigerated
the phenomenon while describing the drying curves chamber at 5 °C for subsequent drying. A fixed-
for certain experimental conditions. The model of bed dryer with upward air flow was used, which
Thompson et al. (1968) has traditionally been used in contained 4 perforated trays with upward air flow
studies of drying agricultural products and foodstuffs. and three electrical resistances for heating the drying
Much emphasis has been given to developing semi- air (Figure 1). Another experiment was conducted
theoretical models for achieving harmony between by varying the temperature of the drying air (40,
theory and ease of use. Such models are generally 50, 60 and 70 °C). Each drying test was performed
based on Newton’s Law of Cooling applied to mass using 250 g of lemon grass leaves, making a layer of
transfer. When applying this law it is assumed that 5 cm thick in the drying chamber. The leaves were
conditions are isothermal and resistance to moisture cut in 2 cm lengths and the drying air temperature
transfer is confined only to the surface of the product was kept at 50 °C, because essential oil content and
(Brooker et al., 1992). Among semi-theoretical models, active principle concentration are high at this length
the model of two terms, the Henderson and Pabis, and temperature, as described by Martinazzo et al.
Lewis, Page and Modified Page and Panchariya et (2010). Only one of the dryer trays, dryer chamber
al. (2002) have been widely used. Currently, research three, was filled with lemon grass leaves (Figure 1a).
on the study of the kinetics of thin layer drying is The reason for not completely filling all trays was due
performed with various agricultural products such to the amount of plant sample available. The control
as seeds, grains, fruits and some plant species with of the temperature and velocity of drying air were
economic importance. The conditions of the drying done with an automatic controller as described by
process that fit different models to each specific Prates et al. (2011). The dryer’s manual control was
situation are observed. Panchariya et al. (2002) set by regulation (opening and closing) of the diaphragm
various equations to the drying process of black tea (Figure 1b). Temperature data was taken with the use
and concluded that the model of Lewis reproduced best of thermocouples previously calibrated and placed in
experimental data of thin layer drying in temperature pre-set points of the dryer. Drying air velocity was
ranges from 80 to 120 °C. However, Demir et al. tracked by an anemometer (0.8 m s1, 1.3 m s–1 and
(2004), evaluating different mathematical models for 1.8 m s–1). The data of temperature and velocity of
drying of laurel (Laurus nobilis L.), found the Page drying air were taken in an automatic data acquisition
model to be the one that best described the process, system that recorded their values in a microcomputer.
while Doymaz (2006), who evaluated drying of The moisture content of the samples was determined
leaves of dill (Anethum graveolens L.) and parsley using the gravimetric method recommended by ASAE
(Petroselinum crispum L.), defined the Midilli model Standards (2000).
as the most suitable to describe the drying curves at
temperatures of 40 to 70 °C. The aim of the present 2.2. Determination of oil essential content
study is to fit mathematical models and evaluate
the quality of plants using thin layer drying and the After drying, samples were packed in
experimental data obtained in drying leaves of lemon polyethylene bags (40 μm) and stored in a refrigerated
grass Cymbopogon citratus (DC) Stapf at different chamber at 5 ºC until being submitted to extraction
drying air temperatures. of the essential oil. The essential oil was extracted
by hydro distillation utilizing Clevenger equipment
Material and Methods adapted to a round-bottomed two liter flask.

2.1. Drying of lemon grass 2.3. Mathematical modeling

The species (Cymbopogon citratus (D.C.). Stapf) The drying curves were fitted to the experimental
utilized for the drying tests was cultivated at the data using thirteen different semi-empirical and
experimental area of the Agricultural Engineering empirical equations detailed below.
 Mathematical modeling of the drying kinetics of the leaves of lemon grass (Cymbopogon citratus Stapf)… 45

Equation Model
RU = exp ( −k ⋅t ) Newton (1)

(
RU = exp −k ⋅ t n ) Page (2)

RU = exp ( −(k ⋅ t)n ) Page Modified (3)

( (
RU = exp − a − a 2 + 4 ⋅ b ⋅t )
1/2
) / 2⋅b Thompson (4)

U – Ue 8 ∞ 1 t ⎤
RU = = ∑ n−0 exp ⎡⎢ −(2n + 1)π D Eight Diffusion Terms (5)
Ui – Ue π (2n + 1) ⎣ 4L ⎥⎦
RU = a ⋅ exp(−k ⋅t) Henderson and Pabis (6)
RU = a exp ( −kt ) + c Logarithmic (7)

RU = a ⋅ exp ( −ko ⋅t ) + b ⋅ exp ( −k1 ⋅t ) Two Terms (8)

RU = a ⋅ exp ( −k ⋅t ) + (1− a ) exp ( −k ⋅ a ⋅t ) Two Exponential Terms (9)

RU = 1+ a t + b t 2 Wang and Singh (10)

Henderson and
RU = a ⋅ exp ( −k ⋅t ) + b ⋅ exp ( −ko ⋅t ) + c ⋅ exp ( −k1 ⋅t ) (11)
Pabis Modified
( )
RU = a ⋅ exp −k ⋅t n + b ⋅t Midilli (12)

( ) (
RU = a ⋅exp −k ⋅t + 1− a ⋅exp −k ⋅ b⋅t ) ( ) Diffusion approximation (13)

where The hygroscopic moisture equilibrium (Ue) was

RU : Moisture ratio, dimensionless; determined by equation 15 proposed by Corrêa et
t : drying time, h; al. (2002) for medicinal plants, with its parameters
k, ko, k1 : drying constant, h-1; determined by the desorption process.
a, b, c, n : model coefficients;
n : number of terms of the equation; 1
Ue = (15)
D : diffusion coefficient, m2 s-1; (a.T + URc )
b

L : product thickness, m
where
To determine the ratios of moisture during T: air temperature, °C;
drying air under different conditions we used the UR: relative humidity, decimal
following expression: a, b, c: constants that depend on the nature of the
product.
U * − Ue* In the case of lemon grass: a = –1.0484, b = –0.0221
RU = (14) and c = –0.0628.
Ui* − Ue*
It is usual to consider the value of the diffusion
where coefficient constant or linearly dependent on the
U* : water content of product (% d.b.); temperature of the drying air. This relationship was
Ui* : initial water content of the product (% d.b.); expressed by the Arrhenius model (Park et al., 2002).
Ue* : equilibrium water content of the product (%
E ⎞
d.b.). D = Aexp ⎛ − (16)
⎝ RT ⎠
46 IDESIA (Chile) Volumen 32, Nº 4, Septiembre-Noviembre, 2014

Figure 1. Front view (a) and frontal section (b) of dryer.

where (P) and the average estimated error (SE), and verified
A: constant (m2 s–1); by the behavior of the distribution of residuals. The
E: activation energy (kJ kmol–1); relative average error and the average error estimated
R: universal gas constant (8.314 kJ kmol–1 K–1); for each model were calculated according to the
Tabs: absolute temperature (K). following expressions, respectively:

The coefficients of the Arrhenius expression

100 Y − Ŷ
were linearized by applying the logarithm of the
form:
P=
n
∑ Y
(18)

∑ (Y − Ŷ )
E 1 2
LnD = LnA − (17) (19)
RT Ta SE =
GLR
Data was analyzed using analysis of variance where
and regression by F test, adopting the 5% level of Y: experimentally observed value;
significance. Ŷ : value calculated by the model;
N: number of experimental observations;
2.4. Statistical analysis GLR: degrees of freedom of the model (the
number of observations minus the number of
The quantitative and qualitative factors were model parameters).
analyzed using the program SISVAR® 4.3 and
the results were compared by Tukey tests, using Results and Discussion
5% probability. The experimental design was
a completely randomized design (CRD) with 3.1. Drying velocity and essential oil content
three tests for each drying air velocity and drying
temperature. To adjust the mathematical models Table 1 shows the moisture content of fresh
analyses nonlinear regressions were performed plant and from dried samples, acquired during the
using the Quasi-Newton method in the computer drying process using manual and automatic control
program STATISTICA 7.0®. To check the degree of of air velocity, respectively. It also reports the mean
fit of each model the significance of the regression of air temperature and total time of drying, with
coefficient was evaluated by t-tests, adopting the 5% their standard deviations for the drying treatments
level of probability, the magnitude of the coefficient with air velocity of 0.8 m s–1, 1.3 m s–1 and 1.8
of determination (R2), the mean relative error values​​ m s–1. The velocity of the drying air is one of the
 Mathematical modeling of the drying kinetics of the leaves of lemon grass (Cymbopogon citratus Stapf)… 47

Table 1. Parameters evaluated during the drying process of lemon grass using manual and automatic control of air velocity.

Drying air velocity Moisture content Moisture content

Drying time (min) Temperature (ºC)
(m s–1) of fresh plant (d.b.) of dried plant (d.b)
Manual control
0.8 3.12 ± 0.31 0.13 ± 0.01 220 ± 20 50.3 ± 0.96
1.3 3.12 ± 0.31 0.11 ± 0.01 200 ± 10 49.9 ± 1.23
1.8 3.12 ± 0.31 0.12 ± 0.02 190 ± 10 50.2 ± 0.87
Automatic control
0.8 3.12 ± 0.31 0.11 ± 0.09 220 ± 20 50.4 ± 0.97
1.3 3.12 ± 0.31 0.11 ± 0.01 200 ± 10 49.9 ± 0.92
1.8 3.12 ± 0.31 0.12 ± 0.01 190 ± 10 50.4 ± 0.84

parameters which must be controlled to obtain good m s–1 and 1.8 m s–1) and different control systems
quality products. According to Hansen et al. (1993), (automatic and manual). From the results observed
increasing the flow rate of the drying air exerts a in Figure 2 it may be concluded that the drying air
greater influence in reducing the drying time of velocities of 0.8 m s–1 and 1.3 m s–1 with manual
the temperature in places of low relative humidity. control system increased the essential oil extraction
There are wide variations in the values of​​ air velocity from lemon grass leaves compared to the automatic
recommended for medicinal plants. Some authors control; however, when compared to fresh plants
such as Hansen et al. (1993) used a speed of 0.039 (control) there was no significant difference. All
m s–1 in a fixed bed dryer working with thin layers dried samples from the automatic control system
of shaved Taxus x media Hicksii. In the drying of at all drying air velocities decreased the essential
basil (Ocimum basilicum L.), the speed used by oil content compared to fresh plants. There was no
Baritaux et al. (1992) was 0.4 m s–1. The highest significant difference in the drying air velocity of
value found was 3.3 m s–1, used by Venskutonis et 1.8 m s–1 with automatic and manual compared to
al. (1996) drying thyme (Thymus vulgarius L.) and the fresh plant reductions of 32 and 33% in essential
sage (Salvia L. officinales). Figure 2 shows the results oil content, respectively. Akpinar (2006) studied
obtained in the statistical analysis of the essential oil the influence of 4 drying air temperatures (40, 50,
content extracted from the fresh plant (control) and 60 and 70 °C), in thin layers and 2 air velocities
from the samples submitted to the drying process (0.9 and 1.9 m s–1) on the essential oil content
with different drying air velocities (0.8 m s–1, 1.3 of Ocimum basilicum. The highest essential oil

Figure 2. Essential oil content from fresh and dried plant in different control systems (automatic
and manual) and air velocities.
48 IDESIA (Chile) Volumen 32, Nº 4, Septiembre-Noviembre, 2014

content was obtained in the drying process with from the leaves. Table 2 shows the adjustment of
an air temperature of 40 °C and air velocity of 1.9 experimental data to thirteen drying mathematical
m s–1. The essential oil of Ocimum basilicum was models using non-linear regression, taking into
affected by both temperature and air velocity during account the different drying temperatures. In all
drying. Martins et al. (1998) in an experiment with drying conditions the coefficient of determination
lemon grass leaves found no statistically significant (R2) was greater than 0.99, signaling according
difference in essential oil content between the drying Madamba et al. (1996) a satisfactory drying
air velocities used: 0.5 and 1.0 m s–1. To evaluate process (Table 2). The Two Terms model gave the
air velocity effects in the drying of lemon grass, smallest estimated standard error of the mean (SE)
Martins et al. (1998) dried lemon grass at 40, 50 and relative mean error magnitude (P) of less than
and 60 ºC with four conditions of air velocity (0.8, 10%, suitable for describing the process (Tables 3
0.6, 0.4 and 0.2 m s–1). The author observed that at and 4) according to Mohapatra & Rao (2005).
the same temperature, the increase in air velocity Regarding the distribution of the residues (Table 5),
promoted an increase in essential oil extraction. the two terms model was the most random when
The highest essential oil content was obtained at fitted to the data by drying at 40, 50, 60 and 70 °C,
60 ºC and at 0.8 m s–1. The air velocity of 0.2 m s–1 providing the best fits to experimental data. The
provided the lowest mass of essential oil extracted. Diffusion Eight Terms and Exponential models also
Figure 3 depicts the curves of thin layer drying leaves represented satisfactory drying temperatures of 50,
Cymbopogon citratus for different temperatures. 60 and 70 ºC. The values of​​ the adjusted parameters
obtained in each model are shown in Table 6 for
3.2. Mathematical modeling of drying lemon the different experimental conditions, especially
grass the model of two terms that best represented the fit
of the experimental data of drying. Figure 5 shows
The effects of drying temperature on the a chart that lists the observed and predicted values​​
moisture reduction from leaves of lemon grass of moisture due to the different conditions tested.
observed in Figure 3 indicate that the higher In this figure the adjustment of the humidity with
the drying temperature the faster water removal the two terms model to describe the kinetics of

Figure 3. Drying curves versus time for different temperatures of the drying air.
 Mathematical modeling of the drying kinetics of the leaves of lemon grass (Cymbopogon citratus Stapf)… 49

Table 2. Coefficient of determination (R2) of drying of lemon grass (Cymbopogon citratus Stapf) due to different temperatures.

Mathematical R2 (%)
models 40 °C 50 °C 60 °C 70 °C
Exponential 98.15 99.29 99.76 99.99
Page 99.85 99.87 99.97 99.99
Page Modified 99.85 99.87 99.97 99.99
Thompson 93.99 99.29 97.91 98.21
Eight Diffusion Terms 96.70 95.68 94.25 93.57
Henderson and Pabis 98.16 99.29 99.76 99.99
Logarithmic 99.84 99.96 99.99 99.99
Two terms 99.99 99.99 99.99 99.99
Two exponential terms 98.44 99.39 99.82 99.99
Wang and Sing 53.62 70.82 91.37 99.99
Henderson and Modified Pabis 99.99 99.99 99.47 99.99
Midilli et al. 99.90 99.92 98.41 98.85
Diffusion approximation 99.56 99.72 99.99 99.99

Table 3. Values of mean relative error (P) drying of lemon grass (Cymbopogon citratus Stapf) due to different temperatures.

Mathematical P (%)
models 40 °C 50 °C 60 °C 70 °C
Exponential 2.0631 1.7956 1.3303 0.1048
Page 0.0652 0.1161 0.1155 0.4567
Page Modified 0.0652 1.8079 0.1155 1.6745
Thompson 3.5866 1.8079 3.9337 4.7050
Eight Diffusion Terms 2.1356 1.4567 2.1245 0.8123
Henderson and Pabis 5.6069 1.8079 1.3450 0.1076
Logarithmic 2.3456 1.8976 0.0221 0.0007
Two terms 0.0038 0.0019 0.0226 0.0076
Two exponential terms 1.8240 1.5943 1.0610 0.2146
Wang and Sing 3.0291 3.2652 2.0560 0.0090
Henderson and Modified Pabis 2.0853 0.0007 13.9571 0.1076
Midilli et al. 0.0188 0.0398 1.7369 1.4537
Diffusion approximation 0.9270 0.3038 0.0225 33.3333

Table 4. Estimated values of average error (SE) of drying of lemon grass (Cymbopogon citratus Stapf)
due to different temperatures.

Mathematical SE (decimal)
models 40 °C 50 °C 60 °C 70 °C
Exponential 0.0501 0.0357 0.0270 0.0237
Page 0.0149 0.0160 0.0096 0.0053
Page Modified 0.0149 0.0160 0.0096 0.0055
Thompson 0.0935 0.0379 0.0880 0.1416
Eight Diffusion Terms 0.0321 0.0125 0.1235 0.4528
Henderson and Pabis 0.0523 0.0379 0.0302 0.0053
Logarithmic 0.0161 0.0087 0.0067 0.0063
Two terms 0.0036 0.0038 0.0014 0.0028
Two exponential terms 0.0482 0.0351 0.0256 0.0187
Wang and Sing 0.2313 0.2256 0.1756 0.0348
Henderson and Modified Pabis 0.0656 0.0014 0.0887 0.0053
Midilli et al. 0.0131 0.0140 0.1085 0.0299
Diffusion approximation 0.0267 0.0251 0.0011 0.0007
50 IDESIA (Chile) Volumen 32, Nº 4, Septiembre-Noviembre, 2014

Figure 4. Experimental and estimated values ​​of the moisture ratio by estimating the parameters of the equation of Two Terms.

Figure 5. Experimental data and estimated the moisture ratio, calculated by the model of Two Terms.

drying the lemon grass plant may be seen. There and 7.04x10–12 m2 s–1 for mint (Mentha spp.),
was an overestimation of the moisture ratio for parsley (Petroselinum crispum) and basil (Ocimum
most of the experimental values; however, with basilicum). According to Zhang & Xu (2003),
reduced amounts of the moisture there was a major the values of
​​ D for food products lie in the range
discrepancy between the experimental data and those of 10–11 to 10-9 m2 s–1. According to equation
estimated by the model. The increased diffusivity 20, the activation energy for liquid diffusion of
values (D)
​​ with increasing drying temperature are lemon grass plant was 62.84 kJ mol–1. In drying
shown in Figure 6. Doymaz (2006), drying sheets processes the lower the activation energy, the
of dill (Anethum graveolens L.), found values of ​​ higher the diffusivity of water in the product. The
6.693x10–10, 9.205x10–10 and 1.434x10-9 m2 s–1 activation energy found in this study was similar
at temperatures of 50, 60 and 70 °C, respectively. to those obtained by Doymaz (2006) for leaves of
Akpinar (2006) gave values between
​​ 4.53 x 10–12 Mentha spicata L. (62.96 kJ mol–1).
 Mathematical modeling of the drying kinetics of the leaves of lemon grass (Cymbopogon citratus Stapf)… 51

Table 5. Evaluation of the distribution of residuals for citratus Stapf varied from 2232.795 kJ kg–1 to
models fitted to experimental data of drying of lemon grass 2144.423 kJ kg–1. Figure 8 shows that an increase
(Cymbopogon citratus Stapf).
of energy was required for the removal of product
water, represented by integral values ​​of isosteric
Mathematical Distribution of waste
heat of desorption (Qst), as observed for several
models 40 °C 50 °C 60 °C 70 °C agricultural products (Jayendra et al. 2005). Brooker
Exponential T A A A et al. (1992) and Khatchatourian (2012) stated that
Page A T A A in order to remove water from grains with low water
Page Modified A T T A
Thompson T T T A
content a greater amount of energy is required
Eight Diffusion Terms T A A A on average than that required for wet products.
Henderson and Pabis T T A A These results confirm the fact that in products with
Logarithmic T T A A higher water content the bonding force between
Two terms T T T T the molecules of water and dry matter decreases
Two exponential terms T T T A
Wang and Sing T T T A
significantly. Possible differences between the
Henderson and Modified Pabis T T A A observed values of integral isosteric heat of sorption
Midilli et al. T T T A for different products can be justified, and the factors
Diffusion approximation T T A T inherent in the products themselves; according to
Hemis et al. (2012) there are possible errors in the
determination of the values of
​​ water activity of each
6284.077 ⎞
D = 3.17 × 10 −5 exp ⎛⎜ − of equilibrium water content, since the values were​​
⎟ (20)
⎝ R.Ta ⎠ obtained from the mathematical model. Despite
these discrepancies, Zhang & Xu (2003), studying
The Arrhenius representation showed uniform water sorption isotherms of some vegetables at
variation of diffusivity with temperature; the temperatures of 30 to 60 ºC, concluded that the
description of ln D as a function of reciprocal isosteric heat of desorption can be used to estimate
temperature (1/T) is shown in Figure 7. According to the energy required in the process of dehydration
Figure 8, the heat isosteric integral of Cymbopogon of agricultural products.

​​ the effective diffusion coefficient (m2 s–1), due to different air temperatures in the drying of lemon grass
Figure 6. Mean values for
(Cymbopogon citratus Stapf).
52 IDESIA (Chile) Volumen 32, Nº 4, Septiembre-Noviembre, 2014

Table 6. Parameters obtained from models fitted to the data for drying of lemon grass (Cymbopogon citratus Stapf)*.

Mathematical models T (°C) K

Exponencial 40 0.021782
50 0.026669
60 0.029555
70 0.032668
T (°C) K n
Page 40 0.397076 0.337252
50 0.394883 0.370576
60 0.247741 0.495543
70 0.048303 0.905750
T (°C) k n
Page Modified 40 0.064655 0.337252
50 0.081484 0.370575
60 0.059855 0.495541
70 0.035238 0.905797
T (°C) a b
Thompson 40 -0.951500 1.826723
50 0.002040 0.163197
60 -0.951470 1.826728
70 -0.095140 1.826729
T (°C) D
Eight Diffusion Terms 40 2.33 x 10-5
50 2.76 x 10-5
60 3.44 x 10-5
70 4.15 x 10-5
T (°C) a k
Henderson and Pabis 40 0.993407 0.021664
50 0.997958 0.026633
60 0.998785 0.029534
70 0.999899 0.326660
T (°C) a k c
Logarithmic 40 0.945515 0.026973 0.053409
50 0.960554 0.031267 0.039281
60 0.967522 0.033893 0.032334
70 0.992633 0.033620 0.073670
T (°C) a K0 b k1
Two Terms 40 0.106667 0.001632 0.893344 0.031594
50 0.065669 0.001516 0.934423 0.033776
60 0.067312 0.003302 0.932686 0.499392
70 0.499950 0.032666 0.499950 0.032666
T (°C) a k
Two exponential terms 40 0.353422 0.045071
50 0.387352 0.051502
60 0.395577 0.056767
70 0.221456 0.129494
T (°C) a b
Wang and Sing 40 -0.048360 0.000050
50 -0.006482 0.000090
60 -0.010902 0.000027
70 0.020561 0.000104
T (°C) a k b k0 c k1
Henderson and Pabis 40 0.457726 0.031585 0.435517 0.031626 0.106769 0.001635
Modified 50 3.162981 0.024216 0.098649 -0.00247 -2.26162 -0.02103
60 0.320483 0.035132 0.320483 0.35132 0.320483 0.035132
70 0.333300 0.032666 0.333300 0.032666 0.333300 0.032666
 Mathematical modeling of the drying kinetics of the leaves of lemon grass (Cymbopogon citratus Stapf)… 53

Mathematical models T (°C) K

T (°C) a k n B
Midilli et al. 40 1.000234 0.253595 0.439597 0.000043
50 1.006629 0.279694 0.454165 0.000042
60 1.000000 7.169768 1.496796 0.000192
70 1.000000 2.314524 0.817317 0.000631
T (°C) a k b
Diffusion 40 0.827413 0.033031 0.141289
approximation 50 0.776262 0.515767 0.011981
60 0.932745 0.036945 0.089254
70 0.220519 0.173700 0.165152
* All estimated coefficients were significant at 5% probability by t test.

Figure 7. Representation of the Arrhenius relationship for the effective diffusivity and air temperature drying of lemon grass
(Cymbopogon citratus Stapf).

3.3. Essential oil content the treatment at 30 °C (1.34%) showed significant

difference with 50 °C it is not indicated, because it
Figure 9 shows that there were reductions in favored fungus growth. Treatment at 70 and 90 ºC
levels of essential oils (p > 0.05) in dry plants for (1.19 and 1.06% respectively) showed significant
different temperatures of the drying air. It was also reduction in the essential oil content compared to
observed that increasing the drying temperature the other treatments. The worst results were obtained
influenced negatively the amount of essential oil. In at the drying temperature of 70 °C (Figure 9) which
the fresh plant oil content was 1.12% (d.b.); however, reduced the amount of oil to 0.34% (d.b.). Radünz
when the drying plant has a temperature of 40 °C, et al. (2010) used 5 temperatures (ambient air and
the oil content was reduced to 0.89% (db). Buggle heated air at 40, 50, 60 and 70 ºC) for the drying of
et al. (1999) carried out the drying of lemon grass in Lippia sidoides Cham, compared to the fresh plant,
an oven heated to 30, 50, 70 and 90 °C to constant to evaluate essential oil content. For the sample dried
weight to evaluate the quantity and quality of essential with environmental air a significant reduction of
oil. The best results were obtained for the essential 8% in the essential oil content was observed, while
oil content by drying at 50 °C (1.43%); although drying at 40, 50, 60 and 70 °C showed no significant
54 IDESIA (Chile) Volumen 32, Nº 4, Septiembre-Noviembre, 2014

Figure 8. Experimental values ​​and estimated integral isosteric heat of sorption as a function of moisture content equilibrium.

Figure 9. Performance of essential oils according to the temperature of the drying air.

differences with fresh plants. In a study carried out and 3 sizes of dried leaves fragments (pulverized, 1
to determine the drying type and fragmentation cm fragments and 20 cm fragments). The authors
of lemon grass leaves to optimize the essential concluded that the highest essential oil content was
oil content, 6 drying treatments were established, obtained with the samples dried at room temperature
including 2 drying types (oven with forced ventilation with dehumidifiers, with no significant differences for
at 40 °C and room temperature with dehumidifiers) the leaf sizes (Martinazzo et al. (2010). Evaluating the
 Mathematical modeling of the drying kinetics of the leaves of lemon grass (Cymbopogon citratus Stapf)… 55

influence of the drying air temperature on Ocimum Conclusion

selloi Benth essential oil content, Martinazzo et
al. (2010) observed that the essential oil content The essential oil content extracted from dried
did not show significant variation. Radünz et al. plants at 0.8 m s–1 and 1.3 m s–1 with manual control
(2010) used common mint (Mentha x villosa Huds), system was not affected by the drying process.
drying it on a fixed-bed dryer with ambient air and The temperature of the drying air had a negative
air heated to 40, 50, 60, 70 and 80 °C and evaluated influence on the levels of the essential oil of the plant.
the essential oil content extracted after drying with Drying with automatic control caused reduction in
that extracted from fresh plants. They concluded the essential oil content for all velocities studied
that the highest content was obtained when the compared to the fresh plant. Increments in the
drying process was done with drying air at 50 °C. temperature of drying air significantly reduced the
The highest value of drying air velocity found in the drying time. The mathematical model of two terms
literature for drying medicinal plants was 3.3 m s–1, is adequate to describe the drying process of lemon
used by Venskutonis et al. (1996) in drying Thymus grass plants (Cymbopogon citratus Stapf). Diffusion
vulgaris and Salvia officinalis. Radünz et al. (2010) values increased with increasing temperature of the
observed that the essential oil of Ocimum basilicum drying air, while the value of activation energy was
L was affected by both temperature and air velocity 62.84 kJ mol–1.
during drying. Muller et al. (1992) used 0.2 m s–1
in drying leaves of Salvia officinalis. Martins et al. Acknowledgment
(1998) observed, in an experiment with lemon grass
leaves, no statistically significant difference in final The authors express their thanks to CNPq,
product quality for both drying air velocities used: CAPES and FAPEMIG for the financial support
0.5 and 1.0 m s–1. essential for conducting the project.

Literature Cited
Akpinar, E.K. Demir, V.; Gunhan, T.; Yagcioglu, A.K.; Degirmencioglu, A.
2006. Mathematical modelling of thin layer drying process 2004. Mathematical modelling and the determination of
under open sun of some aromatic plants. Journal of Food some quality parameters of air-dried bay leaves. Biosystems
Engineering, London, 77 (4): 864-870. Engineering, Edinburgh, 88 (3): 325-335.
ASAE Standards Doymaz, I.
2000. Standards Engineering Practices Data: Moisture 2006.Thin-layer drying behaviour of mint leaves. Journal of
measurement-forages, Adopted and published by: American Food Engineering, Davis, 74 (3): 370-375.
Society of Agricultural Engineers, 565-72. Hansen, J.A.; Nelssen, J.L.; Goodband, R.D.
Baritaux, O.; Richard, H.; Touche, J.; Derbesy, M. 1993. Evaluation of animal protein supplements of early-
1992. Effects of drying and storage of herbs and spices on weaned pigs. J. Anim. Sci., (71): 1853-1862.
the essential oil. Part I. Basil, ocimum basilicum L. Flavour Hemis, M.; Choudhary, R.; Watson, D.G.
2012. A coupled mathematical model for simultaneous
Fragr. J., (7): 267-271.
microwave and convective drying of wheat seeds, Biosystems
Buggle, V.; Ming, L.C.; Furtado, E.L.; Rocha, S.F.R.; Marques,
Engineering, 112 (3): 202-209.
M.O.M.
Jayendra, K.A.; Singh, R.R.B.; Patil, G.R.; Patel, A.A.
1999. Influence of different drying temperatures on the
2005. Effect of temperature on moisture desorption isotherms
amount of essential oils and citral content in cymbopogon of kheer. LWT-Food Science and Technology, 38: 303-310.
citratus (dc) stapf-poaceae. Acta Hort. (ISHS), (500): Khatchatourian, O.A.
71-74. 2012. Experimental study and mathematical model for soya
Brooker, D.B.; Baker-Arkema, F.W.; Hall, C.W. bean drying in thin layer, Biosystems Engineering, 113 (1):
1992. Drying and storage of grains and oilseeds. New York: 54-64.
AVI Book, 450 p. Madamba, P.S.; Driscoll, R.H.; Buckle, K.A.
Castro, H.G.; Ferreira, F.A. 1996. Thin layer drying characteristics of garlic slices. Journal
2001. Contribuição ao estudo das Plantas Medicinais: carqueja of Food Engineering, Davis, 29 (1): 75-97.
(Baccharis genistelloides). Viçosa, 102 p. Martinazzo, A.P.; Melo, E.C.; Corrêa, P.C.; Santos, R.H.S.
Corrêa, P.C.; Afonso Junior, P.C.; Martins, P.M.; Melo, E.C.; 2010. Modelagem matemática e parâmetros qualitativos da
Radunz, L.L. secagem de folhas de capim-limão Cymbopogon citratus
2002. Modelo matemático para representação da D. C. Stapf. Rev. bras. plantas med., 12: 488-498.
higroscopicidade de plantas medicinais. Revista Brasileira Martins, E.R.; Castro, D.M.; Castellani, D.M.; Dias, J.E.
de Armazenamento, 27 (1): 10-16. 1998. Plantas Medicinais. Viçosa: Editora UFV, 220 p.
56 IDESIA (Chile) Volumen 32, Nº 4, Septiembre-Noviembre, 2014

Mohapatra, D.; Rao, P.S. Radünz, L.L.; Melo, E.C.; Rocha, P.P.; Berbert, P.A.; Gracia,
2005. A thin layer drying model of parboiled wheat. Journal L.M.N.
of Food Engineering, Davis, 66 (4): 513-518. 2010. Study of essential oil from guaco leaves submitted to
Muller, J.; Koll-Weber, M.; Kraus, W. different drying air temperature. Engenharia na Agricultura,
1992. Effect of drying on the essential oil of Salvia officinalis. 18: 241-247.
In Annual Congress on Medicinal Plant Research, 40, 1992, Thompson, T.L.; Peart, R.M.; Foster, G.H.
New York. Proceedings… New York: Thieme, p. 104. 1968. Mathematical simulation of corn drying: A new model.
Panchariya, P.C.; Popovic, D.; Sharma, A.L. Transactions of ASAE, St. Joseph, 11 (4): 582-586.
2002. Thin-layer modeling of black tea drying process. Journal Venskutonis, R.; Poll, L.; Larsen, M.
of Food Engineering, Davis, 52 (4): 349-357.
1996. Influence of drying and irradiation on the composition
Park, K.J.; Vohnikova, Z.; Brod, F.P.R.
of volatile compounds of thyme (Thymus vulgaris L.).
2002. Evaluation of drying parameters and desorption isotherms
Flavour and Fragance Journal, 11: 123-8.
of garden mint leaves (Mentha crispa L.). Journal of Food
Engineering, 51: 15-25. Zhang, M.; Xu, Y.Y.
Prates, M.O.; Pizziolo, T.A.; Melo, E.C.; Rocha, R.P.; Nicácio, J.V. 2003. Research developments of combination drying
2011. Controle da temperatura e velocidade do ar de secagem technology for fruits and vegetables at home and abroad.
em um secador de plantas medicinais. Revista Engenharia Journal of Wuxi University of Light Industry, 22 (6):
na Agricultura, 19: 101-111. 103-106.

Nomenclature

RU moisture ratio, dimensionless

t drying time, h;
k, ko, k1 drying constant, h–1;
a, b, c, n model coefficients;
n number of terms of the equation;
D diffusion coefficient, m2 s–1;
L product thickness, m
U* water content of product (d.b.), %
Ui* initial water content of the product (d.b.), %
Ue* equilibrium water content of the product (d.b.), %
A constant, m2 s–1
E activation energy, kJ kmol–1
R universal gas constant, 8,314 kJ kmol–1 K–1
Tabs absolute temperature, K
Y experimentally observed value
Ŷ : value calculated by the model
n number of experimental observations