mass transfer paper

1. Estimation of mass transfer coefficients of the extraction process of
essential oil from orange peel using microwave assisted extraction
Avelina Franco-Vega, Nelly Ramírez-Corona, Enrique Palou, Aurelio L
opez-Malo*
Departamento de Ingeniería Química, Alimentos y Ambiental, Universidad de las Am
ericas Puebla, Sta. Catarina M
artir, San Andr
es Cholula, Puebla 72810,
Mexico
a r t i c l e i n f o
Article history:
Received 15 May 2015
Received in revised form
18 September 2015
Accepted 23 September 2015
Available online 30 September 2015
Keywords:
Microwave assisted extraction
Essential oil
Mass transfer
Modeling
a b s t r a c t
Microwave assisted extraction (MAE) is an emerging technique of extraction that improve yields and
reduce process time and energy. The aim of this work was to evaluate the effect of different MAE process
parameters in the extraction yield of orange peel essential oil (EO), and the description and simulation of
this process with mathematical models based on mass transfer fundamentals. For the assessment of
process parameters effects on EO yield, different extractions were carried out following a two-level
factorial design varying orange peel particle shape (spheres or plaques) and moisture content (dry or
not), as well as microwave potency (360 or 540 W). Results demonstrated that particle size, moisture
content, and its interaction significantly affected (p 0.05) the yield obtained and had an influence on
the extraction mechanism. Model parameter values associated to mass transfer coefficients (k1 and k2)
indicated that diffusion was the process that defined extraction velocity.
© 2015 Elsevier Ltd. All rights reserved.
1. Introduction
Citrus are the most cultivated fruits in the world, being oranges
60% of the world fruit production. The orange peel, depending on
the orange variety, may represent 45% of the total bulk. Orange peel
includes the epidermis covering the exocarp that consists of
irregular parenchymatous cells, which encloses numerous glands
or oil sacs (Farhat et al., 2011; Vel
azquez-Nu~
nez et al., 2013). The oil
in these sacs represents the citrus essential oil (EO) that is obtained
as by-product of citrus processing (Bousbia et al., 2009). Besides its
use as a flavoring agent, citrus EO has gained relevance in the food
industry due to its antimicrobial effect against both bacteria and
fungi (Rezzoug and Louka, 2009; Vel
azquez-Nu~
nez et al., 2013;
Lago et al., 2014). Typical processes for obtaining essential oils
from citrus include cold pressing, solvent extraction, and different
distillation techniques (Bica et al., 2011; Lago et al., 2014). However,
these procedures involve several disadvantages, such as the use of
volatile and hazardous solvents, low yields, long extraction times,
and high energy consumption (Zu et al., 2012).
The extraction method is one of the prime factors that deter-
mine the quality of EOs (Tongnuanchan and Benjakul, 2014); thus
the use of new extraction techniques for natural substances, which
typically use less solvent and energy, such as supercritical fluid
extraction, ultrasound extraction, microwave assisted extraction,
and sub-critical water extraction are being evaluated (Bousbia et al.,
2009; P
erino-Issartier et al., 2010). Among these emergent tech-
nologies, microwave assisted extraction (MAE) has showed many
advantages such as convenience, less processing times, and high
efficiency (Zhai et al., 2009; Flamini et al., 2007).
MAE uses microwave radiation as the source of heating for the
solventesample mixture. Due to the particular effects of micro-
waves on matter (namely dipole rotation and ionic conductance),
heating with microwaves is instantaneous and occurs in the inte-
rior of the sample, leading to rapid extractions (Camel, 2001). The
main advantage of MAE resides in its heating mechanism (P
erino-
Issartier et al., 2010); acceleration of the extraction can be partly
explained by the specific effect of microwaves on plant material
(Camel, 2001).
Mathematical modeling of extraction processing must be
considered as a fundamental step during operation of an efficient
industrial process (Xavier et al., 2011; Reyes-Jurado et al., 2014).
Mathematical models are used to simulate different process sce-
narios without the need to run a large number of experimental
trials and identify the best conditions for the process (Cassel et al.,
2009; Rezzoug and Louka, 2009). Different mathematical ap-
proaches have been reported that explain the process involved
* Corresponding author.
E-mail address: aurelio.lopezm@udlap.mx (A. L
opez-Malo).
Contents lists available at ScienceDirect
Journal of Food Engineering
journal homepage: www.elsevier.com/locate/jfoodeng
http://dx.doi.org/10.1016/j.jfoodeng.2015.09.025
0260-8774/© 2015 Elsevier Ltd. All rights reserved.
Journal of Food Engineering 170 (2016) 136e143

2. during traditional methods of extraction. Some authors have
described the extraction variables effects on essential oil yield
through statistical analysis of experimental data (Ghasemi et al.,
2011; Parikh and Desai, 2011; Zhang et al., 2012), being response
surface methodology (RSM) successfully applied for optimizing
extraction conditions. However, this type of analysis represents
parameter values for the optimization process within the experi-
mental values, thereby; it just can be used in the experimental
range tested and just represents the evaluated variables effect on
analyzed response (Almeida et al., 2008). For this reason, models
that try to explain the physical mechanism of the extraction process
based on mass transfer fundamentals have been developed (Sovov
a
and Aleksovski, 2006; Cassel et al., 2009; Moreno et al., 2010;
Xavier et al., 2011) with the aim of determining physical parame-
ters that make possible extrapolations.
Sovov
a and Aleksovski (2006) developed a model for the hydro-
distillation process; in their model two different kinds of particles
were considered: spherical particles or slabs, with different distri-
bution of the oil in each one. In their assumptions, the only mass
transfer process that had to be taken into account was the oil
diffusion from the particle core to the region of broken cells,
ignoring the initial rate of distillation from intact cells. Similar to
Sovov
a and Aleksovski, Xavier et al. (2011) proposed a model based
on mass transfer fundamentals, their model considers a fluidized
bed and is based on the concept of broken and intact cells, but it
considers the presence of two extraction periods (each one asso-
ciated with the velocity of EO extraction from cells) for the
description of the extraction curve based on mass balance of the
solute (EO).
Despite that MAE has proven to be a more effective extraction
process than traditional methods, to our knowledge, available ap-
proaches to describe this process are primarily based in statistical
analysis of process variables (Wang et al., 2007; Fang et al., 2010;
Farhat et al., 2011; Song et al., 2011), while the study in terms of
mass transfer is limited. Since MAE is based in a distillation process
with a different source of heating, it should be expected that MAE
can be properly modeled by describing the mass transfer mecha-
nisms during distillation, taking into account the microwave effect
on the diffusion coefficients. The aim of this work was to evaluate
the effect of different MAE process parameters in the extraction
yield of orange peel EO, to describe the process through statistical
analysis based on a factorial design, and as well as description of
this process with a mathematical model based on mass transfer
fundamentals.
2. Materials and methods
2.1. Plant material
The essential oil was extracted from orange (C. sinensis var.
Valencia) peel without bagasse obtained from a local juice producer
of San Andres Cholula, Puebla (Mexico) during AprileAugust 2014.
The peel was used at two moisture levels, high (50% of moisture)
and low (10% of moisture), and using two different shapes of par-
ticles, plaques (1 cm) and spheres (40 mm). To adjust orange peel
moisture content, the peel was dried in a tray dehydrator (Excal-
ibur, USA) for different times at 35 C according to the final target
moisture content, the final moisture was determined in a forced air
oven at 105 C for 24 h according to the official method reported by
A.O.A.C (2000). Peels were ground in a domestic mixer to obtain the
orange peel spheres and their particle size was determined with a
particle analyzer (Bluewave, Microtrac, USA), while the peel pla-
ques were obtained manually.
2.2. Microwave assisted extraction
MAE was carried out on a NEOS microwave extraction system
(800 W, 60 Hz) (Milestone, Italy), which is designed to utilize
different beakers for the extraction of different sample/solvent
volumes. The MAE system is equipped with a TFT multicolor liquid
crystal screen, a power sensor (power range 0e1000 W), an
infrared temperature sensor, a temperature controller, and a mag-
netic stirrer in the base of the reactor. Fig. 1 displays a schematic
description of the hydro-distillation system. During extraction, a
sample of 250 g of orange peel and 700 mL of distilled water were
placed into the beaker (A), which was introduced and fixed to the
MAE system. The sample was then subjected to the extraction
process for 50 min at two different irradiation powers (360 or
540 W). A condenser (B) was used to collect the extracted essential
oil in a graduated trap (C). Irradiation power and extraction time
were controlled from the equipment front panel (D). During the
process, system temperature rises until the sample starts to boil
and the extraction starts; since each sample was processed at
different conditions of moisture content, particle size and micro-
wave power, the time required to achieve the boiling temperature
(90e94 C) was also different depending on the characteristics of
the sample, such delay time was registered as tCUT.
Extracted essential oil was dried with anhydrous sodium sulfate
and stored at 4 C in dark vials until used. The amount of essential
oil was determined during extraction and gravimetrically after
collection; the extraction yield was expressed as the percent ratio
Fig. 1. Schematic description of the microwave assisted extraction system. Beaker (A),
condenser (B) graduated trap (C), and equipment front panel (D).
A. Franco-Vega et al. / Journal of Food Engineering 170 (2016) 136e143 137

3. of the mass of extracted essential oil to the mass of orange peel in
dry basis (Li et al., 2012).
2.3. Process parameters effect
Two-level factorial designs allow the simultaneous evaluation of
a number of factors' effects on a particular process; as well as
permit determining possible interactions between (or among)
tested factors (Montgomery, 2009). In our case, each MAE process
parameter (initial moisture content, particle size, and microwave
power) was evaluated at two levels: low (1) and high (þ1). The
coded and un-coded values of each factor and their respective
levels are presented in Table 1. The evaluated responses were EO
extraction yield, as well as other calculated model parameters
described in Section 3. Experiments were replicated three times;
extraction yields and other calculated responses are reported as
average ± standard deviation values (Table 1).
Each evaluated response was analyzed by two-level factorial
design to fit polynomial equations and determine significant
(p 0.05) individual and interactions effects:
R ¼ b0 þ
X
biXi þ
X
biiXiXj þ
X
biiiXiXjXk þ 2 (2.1)
where, R is the predicted response; X are the independent variables
in coded values; b0 is the constant; bi are linear effects; bii are
double interaction effects, and biii is the triple interaction effect. The
statistical analysis was performed using Minitab 16 (Minitab Inc.,
State College, PA, USA). The significance of each term in the poly-
nomial model (linear, double, and triple interactions) was tested by
the associated ANOVA in the factorial design analysis, as well as the
accuracy of the regression model (Montgomery, 2009).
2.4. Physical properties
The orange peel samples used for the extraction were consid-
ered as a particle bed; apparent density, bulk density, porosity, and
surface area were determined for each extraction particle-bed in
order to satisfy the mathematical model described in Section 3.
Particle density (rp) and bulk density (rS) were determined ac-
cording to Shrestha et al. (2008). Bulk density is defined as the ratio
of the mass of the sample-particle bed in a vessel to the volume of
the bed (including the voids among primary particles), for its
measurement 20 g of orange peel were weighed in a graduated
cylinder of 100 mL and the occupied volume was registered.
Apparent density was determined using a pycnometer and calcu-
lated as reported by Barbosa-C
anovas et al. (2006). With the values
of rS and rp, the bed void fraction (ε) was calculated (V
elez-Ruíz,
2013). The superficial area a0 (cm2
/g) of the particle-bed was rep-
resented by the surface area of the total particles contained in the
bed (Chikazawa and Takei, 2006), geometrically calculated
assuming that particle size is uniform for both systems, spherical
with a diameter of Di and cubic particles for the bed of plaques with
a length of li. The average particle diameter (Dm) was determined
with a particle analyzer (Bluewave, Microtrac, Montgomeryville,
PA).
3. Mathematical modeling
For the modeling of orange peel EO microwave assisted
extraction, a model that takes into account the influence of the
process parameters considered in the factorial design (Section 2.3)
was used. The model was proposed by Xavier et al. (2011), which is
based on the concept of broken and intact cells and considers two
extraction periods, the first one governed by phase-equilibrium,
while the second one is limited by internal diffusion in the parti-
cles. The first part of the extraction curve is associated to the
extraction of the free solute from broken cells. In this extraction
step (hypothetical case with negligible external mass transfer
resistance), the fluid phase is in equilibrium with solid phase
throughout the extractor. The second period is controlled by the
solute diffusion from inner cells of vegetal structure and corre-
sponds to the diffusion from intact cells. In Xavier et al. (2011)
model, mass transfer properties of recovered oil were considered
constant throughout the process. The general equations considered
in this model are the mass balances per unit volume extraction bed
consist of equations for the solute in fluid and solid-phases
described by (eqs. 3.1 and 3.2).
rf ε
vY
vt
þ rf u
vY
vt
¼ Jðx; YÞ (3.1)
rSð1 εÞ
vx
vt
¼ Jðx; YÞ (3.2)
Associated fluxes are:
Jðx; YÞ ¼ kf a0rf
Y*
Y
for x xk; first period (3.3)
Jðx; YÞ ¼ kSa0rSx for x xk; second period (3.4)
According to Xavier et al. (2011), the model solution can be
expressed in terms of the maximum value for the extracted oil
(M∞), considering the two extraction periods, described as:
Table 1
Two-level factorial design to evaluate the effect of selected microwave assisted extraction factors on orange peel essential oil yield, modeling parameters, and characteristic
times of the process.
Run Microwave
power
(Watts)
Moisture
content
(%)
Particle shape Yield (% dry basis) k1 (g/min) k2 (min1
) tc (min) tCUT (min) ks (g/min*cm2
)
C 540 þ1 50 þ1 Sphere 1 1.56 ± 0.13 0.20 ± 0.07 0.10 ± 0.01 12.00 ± 1.41 11.25 ± 0.35 2.64 ± 0.22
B 360 1 10 1 Sphere 1 2.47 ± 0.05 0.45 ± 0.28 0.09 ± 0.01 17.75 ± 2.10 15.75 ± 1.06 2.21 ± 0.15
H 360 1 10 1 Plaque þ1 0.92 ± 0.42 0.21 ± 0.13 0.33 ± 0.07 3.00 ± 1.41 13.50 ± 0.71 0.35 ± 0.05
G 540 þ1 10 1 Plaque þ1 0.99 ± 0.15 0.34 ± 0.12 0.29 ± 0.02 12.75 ± 1.06 6.50 ± 0.71 0.15 ± 0.05
D 360 1 50 þ1 Sphere 1 1.22 ± 0.26 0.22 ± 0.05 0.14 ± 0.05 1.50 ± 0.71 19.00 ± 0.01 2.93 ± 0.02
E 540 þ1 50 þ1 Plaque þ1 0.94 ± 0.12 0.43 ± 0.14 0.38 ± 0.12 2.25 ± 0.35 10.50 ± 0.71 0.12 ± 0.05
F 360 1 50 þ1 Plaque þ1 0.98 ± 0.10 0.14 ± 0.02 0.38 ± 0.09 2.50 ± 0.01 18.75 ± 0.35 0.05 ± 0.01
A 540 þ1 10 1 Sphere 1 2.73 ± 0.43 0.39 ± 0.14 0.12 ± 0.01 22.75 ± 3.47 8.50 ± 0.71 2.77 ± 0.17
k1 constant associated to the equilibrium period; k2 constant associated to the diffusion controlled period; tCUT process time to reach an adequate temperature to start sample
boiling and begin the oil extraction; tc time at which the change of phases is observed during the extraction process (related to the slope change); and ks solid-phase mass
transfer coefficient.
A. Franco-Vega et al. / Journal of Food Engineering 170 (2016) 136e143
138

4. Mt
M∞
¼
Z t
0
_
mYdt
M∞
8
:
k1t
M∞
for the first period
1 ek2t
for the second period
(3.5)
where k1 can be also expressed as eq. (3.6), and k2 is related to the
mass transfer coefficient as can be seen in eq. (3.7).
k1 ¼ _
mY*
(3.6)
k2 ¼
ksa0
ð1 εÞ
(3.7)
As can be noticed, the first period is a linear function of time,
while the second period follows an exponential expression.
Detailed methodology of model development can be found in
Xavier et al. (2011).
The normalized extraction curves were obtained by plotting the
mass fraction of recovered essential oil (Mt/M∞) versus the
extraction time. The mass fraction was calculated as the ratio of the
EO's mass obtained at time t (Mt) to the EO's mass obtained at the
end of the process (M∞). Data were fitted to expressions described
in eq. (3.5), and the associated parameters k1 and k2 were deter-
mined by means of nonlinear regression. The obtained values of k2
were then used to calculate the mass transfer coefficient ks (eq.
(3.7)). Additionally, the time at which the phase change occurs was
registered as the point in which the slope changes (tc).
Different operation conditions and particle characteristics were
evaluated in order to assess the effect of these conditions on the
mass transfer mechanisms.
4. Results and discussion
4.1. Effect of process parameters on the efficiency of EO extraction
The obtained orange peel EO yields resulting after the pro-
posed MAE process following the two-level factorial design at two
microwave powers (360 or 540 W), two initial orange peel
moisture content (10 or 50%), and two particle shapes (plaques or
spheres) are presented in Table 1, these data are expressed in
terms of the oil yield (expressed in dry basis) obtained at the end
of each process. In general, extraction yield was higher than 0.9%,
achieving in some conditions more than 2.5%. The yields obtained
in our study were higher than those reported in the literature;
lower yields (0.13%e0.74%) were reported for orange maltaise
(Citrus sinensis) by Bourgou et al. (2012) obtained by hydro-
distillation and by Strano et al. (2014) for Tarocco orange after
three hours of hydrodistillation (2.1% of yield). Rezzoug and Louka
(2009) obtained a maximum yield of 2% for orange peel EO by
steam distillation but in a process with double the time (100 min)
that in our case. Besides the increase in yields achieved by mi-
crowave assisted extraction, another of the advantages is its ability
to reduce processing times. The greatest yields were obtained
when extraction was carried out with spheres of dry orange peel
(experiments A and B); at these conditions, no influence of the
microwave power was observed with regards to the extraction
efficiency (p 0.05, Table 2). Lower yields were obtained for other
evaluated processing conditions.
Table 2 presents the obtained coefficients and their probability
of being significant after analyzing the two-level factorial design.
Good adjustments of eq. (2.1) to the experimental data were veri-
fied through the determination coefficients obtained (R2
0.85 for
the majority of the analyzed responses, except for k1 where R2
was
0.50), representing the proportion of variation in the response
explained by the terms in the model. The results demonstrate the
significant effect (p 0.05) of initial moisture content and particle
size on essential oil yield. In the case of particle size, the decrease of
it in the sample (spheres) improved extraction (Fig. 2) and this can
be related to an increase in the superficial area which promotes a
better contact of the sample with the solvent and penetration of
microwaves (Veggi et al., 2012). Different to our results, Sovov
a and
Aleksovski (2006) reported that for extraction of thyme oil from the
herb Thymus serpyllum by steam distillation, yields for the smallest
particles (0.18 mm) were lower than those for large particles; they
assumed that part of T. serpyllum oil, easily accessible, was lost from
their surface during gridding.
Letellier and Budzinski (1999) affirm that a wet matrix (high
moisture) improves the extraction recovery in most cases, due to
microwaves interacting selectively with the free water molecules
present in the gland and vascular systems, leading to rapid heating
and temperature increase, followed by rupture of the walls and
release of the essential oils into the solvent. Camel (2001) reported
that in some cases, drying the matrix before the extraction or
adding a drying agent has favored the MAE process. Similar to our
results, Moreno et al. (2010) obtained higher yields of extraction
using dry samples for the extraction of eucalyptus EO by steam
distillation; these authors reported a decrease in yield when the
moisture content in the eucalyptus leaf increase from 16.1 to 35.9%.
However, these results are associated with a process of higher costs
due to the previous processing (drying) step needed before
extraction. In our experiments the cost of the process using a try-
dryer increases, approximately, 10 times the price of using sam-
ples with the high moisture content. Microwave power did not
affected in EO extraction yield, Farhat et al. (2009) during lavender
flowers EO extraction by microwave steam diffusion did not find
difference in oil yield when they tested five different microwave
powers between 50 and 400 W, observing that the only effect in the
process was the time needed for EO extraction.
The effect of the interaction between particle size and moisture
content observed (Table 2) in the statistical analysis was significant
(p 0.05), but this is not the only interaction that affects the effi-
cacy of EO extraction, since the interaction between particle size
and microwave power was also significant (p 0.05) on EO yield, as
can be observed in Fig. 2. Orange peel EO extraction by MAE is
favored by the use of samples with low moisture content and with a
sphere particle shape. However, these affirmations are only true for
a range of levels within the ones tested in this work. Therefore, with
the aim to understand the physical mechanism of extraction, a
model based on mass transfer was also studied. Due to the rele-
vance that particle size and moisture content have in the process,
the model proposed by Xavier et al. (2011) was selected, since the
model takes into account both variables.
4.2. Extraction kinetics
Fig. 3 presents the evolution of the orange peel EO extraction
yield during MAE at selected conditions. Results are presented in
terms of the mass fraction of obtained EO at different process times
(Mt/M∞). As can be seen in Fig. 3, the extraction process clearly
displays an exponential behavior with the presence of two phases.
The first phase that corresponds to a rapid increase in the yield,
which other authors have associated with an easy accessibility of
solvent to the EO (Reverchon et al., 1999; Farhat et al., 2009), and a
second phase, almost asymptotic, that defines the end of the pro-
cess and it is limited by the mass transfer. This kind of behavior in
the extraction of EO from plants have been observed not only for
microwave extraction, it was found that the presence of the two
phases is due to changes in the mass transfer mechanisms and the
changes in the surface area from which essential oils evaporates
A. Franco-Vega et al. / Journal of Food Engineering 170 (2016) 136e143 139

5. (Reis-Vasco et al., 2000). Hence, the mechanism of the extraction is
related to the physical properties of the sample while the energy
source utilized for the EO extraction determines the velocity at
which each phase appears. Different to our results, Haj Ammar et al.
(2013) tested a mathematical model based only in diffusion during
extraction of EOs of myrtle (Myrtus communis L.), rosemary (Ros-
marinus officinalis L.), or sour orange (Citrus aurantium L.),
observing that the calculated values by their model showed de-
viations with regards to the experimental ones during the first
minutes of the process, these deviations are related to the omission
of the first phase of the process (the equilibrium) that in Xavier
et al. (2011) model, utilized in our work is taken into account.
Comparison among the experimental data and the results of the
mathematical modeling of MAE EO yield by the model proposed by
Xavier et al. (2011) are presented in Fig. 3. Data are plotted without
taking into account the time that the process need to reach an
adequate temperature to start the sample boiling and begin the oil
extraction (tCUT), since such time only affects the total processing
time but not parameters estimation. The analysis of the results
indicated that, in general, tested mathematical model adequately
fitted the experimental data (R2
0.90); the model goodness of fit
to experimental data is presented in Fig. 4. The poorest fit for the
second phase was observed for case E (Table 1), presented in
Fig. 2d; this sample has the largest moisture content and largest
particle size, and as described in Table 2 it also corresponds to the
larger variability data for k2. In the different curves displayed in
Fig. 2, it can be seen that the maximum oil extracted was reached
after a time varying between 18 and 40 min, being faster extrac-
tions realized at 540 W of microwave power (Fig. 2). Microwave
power did not have a significant effect (p 0.05) on yield (Table 2).
However, the effect observed (Fig. 3) in the time needed to reach
the maximum yield, it would seem that the use of high power can
reduce process time and probably costs; yet, it is necessary to take
into account that microwave power is important to ensure the
essential oil is extracted quickly; but, the power should not be too
high, since higher powers promote a faster temperature rise, such
that in some cases the cooling system is not able to condensate all
vapor at the same rate and it may result in loss of volatile com-
pounds (Camel, 2001).
In Table 1, obtained values for the parameters k1 and k2 (asso-
ciated with extraction phases) are presented, as well as the values
for the time that the processes need to reach an adequate tem-
perature to start the sample boiling and begin the oil extraction
(tCUT), the time in which the change of phases is observed during
the extraction process, related to the slope change (tc) and the
solid-phase mass transfer coefficient for each experiment (ks).
Reverchon et al. (1999) suggested that in the first phase of the
extraction curve, the oil is freely available for extraction; this linear
part of the extraction process (also called the equilibrium phase) is
represented by k1. Observing the curves of extraction; we expected
that the equilibrium phase vary according to the physical properties
of the sample, experiments E and F (which have the same initial
moisture content and particle shape) the slope of this first part of
the curve seemed to be higher than in other conditions and this
could be related with a higher process velocity in the equilibrium
phase; however, particle size and initial moisture content of the
sample did not affect (p 0.05) k1 (Table 2), but the interaction
(Fig. 2) of particle size with microwave power had a significant
effect (p 0.05) on k1. These results indicate that the amount of
easily accessible EO in orange peel is the same at any condition of
the sample, although the interaction between particle size with
microwave may enhance the velocity at which the process begins
(Fig. 2), and that the only mass transfer process that affects the oil
extraction rate is the EO diffusion from the particle core to the re-
gion of broken cells (Sovov
a and Aleksovski, 2006; Wang and
Weller, 2006), which is promoted at higher microwave power
levels.
The parameter k2 is related with the diffusion of the EO from the
inner part of the sample cells, hence with the internal diffusion in
the particles. In contrast to k1, k2 was significantly affected
(p 0.05) by particle size (Table 2); hence, the solid-phase mass
transfer coefficient (ks) was determined from k2 combined with
sample physical properties. The mass transfer coefficient can be
determined if the specific surface area is known. The values for ks
were determined and are also presented in Table 1; it can be seen
that the overall mass transfer coefficient obtained for experiments
with plaque shape were lower than the obtained in experiments
using a sphere shape (Fig. 2). These results confirm that reducing
the particle size of the sample facilitates diffusion (and extraction)
of the EO, because it permits increasing surface contact to occur
between the plant material and the solvent, therefore facilitating
essential oil extraction processes (Haj Ammar et al., 2013). How-
ever, the values of ks obtained are low compared with the values
obtained by Farhat et al. (2009) for the diffusion of lavender flowers
EO during microwave steam diffusion (MSD). In their work they
used different particle sizes, but the solvent was steam, thus they
assumed that the enhancement in the mass transfer observed
during MSD can be due that in MAE all the microwave energy is
mainly absorbed by water for heating and vaporization, and only a
fraction is absorbed by the essential oils inside the sample. Another
explanation for the effect of the initial moisture content observed in
the diffusion rates, that can be associated with the presence of
higher porosity in the bed of dry samples than in the bed of wet
samples, which also promotes the contact of the solvent with the
Table 2
Coefficient values of microwave assisted extraction process parameters (coded) and interactions on orange peel essential oil yield, modeling parameters, and characteristic
times of the process.
Term Yield (% dry basis) k1 (g/min) k2 (min1
) tc (min) tCUT (min) ks (g/min*cm2
)
Constant 1.096* 0.298* 0.229* 9.313* 12.969* 1.403*
Microwave power (p) 0.054 0.043 0.006 3.125* 3.781* 0.017
Initial moisture content (%M) 0.509* 0.050 0.021 4.750* 1.906* 0.033
Particle size (ps) 0.392* 0.018 0.116* 4.188* 0.656* 1.235*
p*%M 0.016 0.025 0.004 0.563 0.219 0.072*
p*ps 0.079* 0.063* 0.003 0.750* 0.031 0.050
%M*ps 0.344* 0.055 0.014 2.000* 0.406* 0.115*
p*%M*ps 0.029 0.015 0.013 1.937* 0.094 0.140*
R2
0.93 0.50 0.88 0.97 0.98 0.99
k1 constant associated to the equilibrium period; k2 constant associated to the diffusion controlled period; tCUT process time to reach an adequate temperature to start the
sample boiling and begin the oil extraction; tc time at which the change of phases is observed during the extraction process (related to the slope change); ks solid-phase mass
transfer coefficient; and R2
coefficient of determination.
*Coefficients with significant effect (p 0.05) in the evaluated response.
A. Franco-Vega et al. / Journal of Food Engineering 170 (2016) 136e143
140

6. particle surface (Eggers and Pliz, 2011).
As mentioned above, the microwave power utilized in the pro-
cess affected only the time of extraction, the time needed for the
start of EO extraction (tCUT) (Table 1) shows that the processes in
which the microwave power was 360 W needed more time for EO
extraction than that required at 540 W. In addition, microwave
power, particle size, initial moisture content, and the interaction
between moisture content and particle size also had a significant
effect (p 0.05) in tCUT (Table 2), being lower in samples with high
initial moisture contents (50%) than for dry samples (10%). Due to
tCUT can be associated with the cost of the process, the best con-
ditions to reduce this time were using a sample with low initial
0.0
0.5
1.0
1.5
2.0
0% 20% 40% 60%
Y
(%)
IniƟal moisture content
360 540
0.0
0.5
1.0
1.5
2.0
e
r
e
h
p
s
e
u
q
a
l
p
Y
(%)
ParƟcle size
360 540
0.0
0.1
0.2
0.3
0.4
0.5
0% 20% 40% 60%
k1
IniƟal moisture content
360 540
0.0
0.1
0.2
0.3
0.4
0.5
e
r
e
h
p
s
e
u
q
a
l
p
k1
ParƟcle size
360 540
0.0
0.1
0.2
0.3
0.4
0% 20% 40% 60%
k2
IniƟal moisture content
360 540
0.0
0.1
0.2
0.3
0.4
e
r
e
h
p
s
e
u
q
a
l
p
k2
ParƟcle size
360 540
0.0
0.5
1.0
1.5
2.0
2.5
0% 20% 40% 60%
ks
IniƟal moisture content
360 540
0.0
0.5
1.0
1.5
2.0
2.5
e
r
e
h
p
s
e
u
q
a
l
p
ks
ParƟcle size
360 540
Fig. 2. Interaction plots (each plot displays the interaction between initial moisture content or particle size and microwave power (360 or 540 W) during microwave assisted
extraction) on orange peel essential oil yield (Y, % dry basis), and selected modeling parameters: k1 (constant associated to the equilibrium period, g/min), k2 (constant associated to
the diffusion controlled period, min1
), and ks (solid-phase mass transfer coefficient, g/min*cm2
).
A. Franco-Vega et al. / Journal of Food Engineering 170 (2016) 136e143 141

7. moisture content (10%) in a MAE process at 540 W. This can be
explained by the fact that at the start of the extraction, rate is
effectively limited by the solubility of the oil into the fluid phase
and this situation continues until the depletion of oil from the
lower portion of the bed has reduced the effective bed height to the
point where the fluid is no longer saturated when it leaves the top
of the bed (Reverchon et al., 1999). Finally, the time of the process
for the change of the equilibrium phase to the mass transfer rep-
resented by tc was significantly affected (p 0.05) by microwave
power, moisture content, and particle size, by the interactions be-
tween moisture content and particle shape and microwave power
and particle size, as well as by the triple interaction of process
factors, presenting higher values of tc the processes where the
sample was dry and with a sphere shape (A and B), indicating that
in processes with samples at lower initial moisture content and
higher surface area the phase of mass transfer in solid phase takes
more time to start.
5. Conclusions
The evaluated parameters during microwave assisted extraction
of orange peel essential oil had a significant effect in the extraction
process, demonstrating that the conditions of the sample (particle
size and initial moisture content) determine the extraction yield,
while microwave power affects the time of extraction. The model
based on mass transfer process utilized to predict the physical
mechanism of extraction showed to be a satisfactory approach to
the mathematical representation of the extraction of orange peel
essential oil by microwave assisted extraction, being capable to
describe the two observed phases during the extraction processes.
According to the parameters of the model (k1 and k2, associated to
fluid-phase mass transfer coefficient and solid-phase mass transfer
coefficient, respectively) the mass transfer in solid phase was the
only phase significantly (p 0.05) affected by the characteristics of
the sample, indicating that in orange peel essential oil extraction by
microwave assisted extraction the solute diffusion from the inner
cells is the process that defines the extraction velocity.
Acknowledgments
Financial support for the project 180748 from the National
Council for Science and Technology (CONACyT) of Mexico and
Universidad de las Am
ericas Puebla (UDLAP) is gratefully
acknowledged. Author Franco-Vega acknowledges financial sup-
port for her PhD studies in Food Science from CONACyT and UDLAP.
(a) (b)
(c) (d)
0.0
0.2
0.4
0.6
0.8
1.0
0 10 20 30 40
Mt/M∞
me (min)
0.0
0.2
0.4
0.6
0.8
1.0
0 10 20 30 40
Mt/M∞
me (min)
0.0
0.2
0.4
0.6
0.8
1.0
0 10 20 30 40
Mt/M∞
me (min)
0.0
0.2
0.4
0.6
0.8
1.0
0 10 20 30 40
(Mt/M∞)
me (min)
Fig. 3. Extraction kinetics of orange peel essential oil during microwave assisted extraction at 540 W and selected moisture conditions and particle size: (a) sphere with 10%
moisture content, (b) sphere with 50% moisture content, (c) plaque with 10% moisture content, or (d) plaque with 50% moisture content. Experimental data (A) and mathematical
model fit (phase 1ee, phase 2 ).
Fig. 4. Experimental data vs predicted values for different operation conditions.
A. Franco-Vega et al. / Journal of Food Engineering 170 (2016) 136e143
142

8. Nomenclature
tCUT Time at which the essential oil extraction starts, min
rp Particle density, g/cm3
Ɛ Porosity (bed void fraction), dimensionless
a0 Superficial area, (cm2
/g) (specific surface area per unit
volume of extraction bed (m2
/m3
)
Di Diameter of sphere particles, cm
Li Length of plaque particles, cm
Dm Average particle diameter, cm
rf Solvent density, g/cm3
rs Solid density (bulk density), g/cm3
u Superficial fluid velocity, cm/s
J Flux of solute, g/cm3
s
kf Fluid phase mass transfer coefficient, m/s
ks Solid phase mass transfer coefficient, m/s
Y* Equilibrium fluid phase mass fraction, g/g
Y Mass fraction in fluid phase, g/g
x Mass fraction in solid phase, g/g
xk Easily accessible solute in solid phase, g/g
k1 Constant associated to the equilibrium period, g/min
k2 Constant associated to the diffusion controlled period, 1/
min
ṁ Solvent flow rate, g/s
t Extraction time, min
Mt Mass of extract at time t, g
M∞ Maximum value of the mass extracted, g
R Predicted response from the factorial design
bi Coefficients from the polynomial model from the factorial
design
Xi Independent factors in the factorial design
2 Error
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