Microwave and Ultrasound Assisted Rotary Drying of Carrot: Analysis of Process Kinetics and Energy Intensity

Abstract

Convective drying is one of the most commonly employed preservation techniques for food. However, the use of high temperatures and extended drying times often leads to a reduction in product quality and increased energy consumption. To address these issues, hybrid processes combining convective drying with more efficient methods are frequently employed. This study investigates the convective rotary drying of carrot (cv. Nantes), assisted by microwaves and ultrasound, using a hybrid rotary dryer. In total, four distinct drying programs—comprising one convective and three hybrid approaches—were evaluated. The study assessed drying kinetics, energy consumption, and product quality. The use of ultrasound increased the drying rate by 13%, microwaves by 112%, and microwaves and ultrasound together by 140%. The use of microwaves reduced energy consumption by 30%, whereas ultrasound resulted in a slight increase. All processes resulted in a significant reduction in water activity. Ultrasound decreased the color difference index, while microwaves increased it compared to convective drying.

Full text

Citation: Mierzwa, D.; Musielak, G.
Microwave and Ultrasound Assisted
Rotary Drying of Carrot: Analysis of
Process Kinetics and Energy Intensity.
Appl. Sci. 2024,14, 10676. https://
doi.org/10.3390/app142210676
Academic Editors: Sotirios
Oikonomou and Anastasia
Kyriakoudi
Received: 18 October 2024
Revised: 15 November 2024
Accepted: 16 November 2024
Published: 19 November 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Microwave and Ultrasound Assisted Rotary Drying of Carrot:
Analysis of Process Kinetics and Energy Intensity
Dominik Mierzwa and Grzegorz Musielak *
Division of Process Engineering, Institute of Chemical Technology and Engineering, Poznan University of
Technology, ul. Berdychowo 4, 60-965 Poznan, Poland; dominik.mierzwa@put.poznan.pl
*Correspondence: grzegorz.musielak@put.poznan.pl; Tel.: +48-61-665-3622
Abstract: Convective drying is one of the most commonly employed preservation techniques for food.
However, the use of high temperatures and extended drying times often leads to a reduction in prod-
uct quality and increased energy consumption. To address these issues, hybrid processes combining
convective drying with more efficient methods are frequently employed. This study investigates
the convective rotary drying of carrot (cv. Nantes), assisted by microwaves and ultrasound, using a
hybrid rotary dryer. In total, four distinct drying programs—comprising one convective and three
hybrid approaches—were evaluated. The study assessed drying kinetics, energy consumption, and
product quality. The use of ultrasound increased the drying rate by 13%, microwaves by 112%, and
microwaves and ultrasound together by 140%. The use of microwaves reduced energy consumption
by 30%, whereas ultrasound resulted in a slight increase. All processes resulted in a significant
reduction in water activity. Ultrasound decreased the color difference index, while microwaves
increased it compared to convective drying.
Keywords: color difference; drying constant; drying curves; drying rate; drying time; effective diffusion
coefficient; mass transfer coefficient; specific energy consumption; temperature; water activity
1. Introduction
One of the world’s greatest challenges is the preservation of food. Drying is among
the most common methods for preserving fruits and vegetables, effectively reducing mois-
ture content and water activity—key factors in limiting natural decomposition processes.
Drying foods limits bacterial and fungal decomposition, resulting in product stabiliza-
tion [
1
]. However, most drying techniques involve prolonged heat application, which
often compromises product quality and value. Factors like drying method, temperature,
humidity, air flow rate, and additional heat sources such as microwave (MW), infrared
(IF), or ultrasound (US) influence the extent of quality changes. Convective drying, a
widely used method involving hot air, often requires high temperatures and extended
durations, which trigger chemical and biochemical reactions that alter color, flavor, aroma,
and nutritional properties [
2
–
5
]. Drying can also cause excessive shrinkage and/or shape
deformation [6–8], making the product less appealing to consumers.
Another significant issue with drying is its high energy consumption. The energy
needed to provide sufficient heat for evaporation makes drying one of the most energy-
intensive unit operations. It is estimated that drying processes account for up to 25%
of total industrial energy consumption [
9
,
10
]. Given the environmental and energy con-
cerns, such as fossil fuel depletion and the need to reduce greenhouse gas emissions [
11
],
reducing energy consumption in all industrial sectors, including those utilizing drying
processes, is paramount. Therefore, ensuring good product quality while minimizing
energy consumption remains a key challenge in drying operations.
One possibility for improving drying processes is the use of pretreatment. Examples
of pretreatment methods include osmosis [
11
–
14
], ultrasound [
15
,
16
], or pulsed electric
Appl. Sci. 2024,14, 10676. https://doi.org/10.3390/app142210676 https://www.mdpi.com/journal/applsci

Appl. Sci. 2024,14, 10676 2 of 14
field [
12
,
17
]. Another way to enhance drying processes is to use hybrid drying, which
combines two or more techniques in a single process [
18
]. To accelerate the process, several
methods are used in conjunction to supply additional energy to the process during drying.
Such acceleration can result in reduced energy consumption and improved product quality.
Plant materials are often dried using convection with the addition of microwaves [
15
,
19
–
21
],
infrared [
15
,
22
,
23
], or ultrasound [
20
,
24
–
26
]. In most cases, the materials being dried in
these processes are stationary, with exceptions being rotary convection–microwave and
convection–infrared drying [15,19,22].
The aim of this work was to investigate the effect of the independent use of microwaves
and ultrasound, as well as the simultaneous use of both energy sources, on rotary con-
vective drying. Carrot root was chosen as the research material due to its high degree of
hardness and inhomogeneous structure, making it particularly challenging to dry [
27
]. In
total, four drying schedules were experimentally tested to determine the most effective
process: convective–hot air drying (CV), convective drying assisted by ultrasound (CVUS),
convective drying assisted by microwaves (CVMW), and convective drying assisted by
both microwaves and ultrasound (CVMWUS). Each schedule was assessed in terms of
drying kinetics, product quality, and energy consumption. The use of ultrasound increased
the drying rate by 13%, microwaves by 112%, and both sources combined by as much as
140%. All processes resulted in a significant reduction in water activity, with the greatest
reduction observed in the CVUS process. Ultrasound also led to a decrease in the color
difference index (dE), while microwaves significantly increased the value of this index.
Additionally, the use of microwaves significantly reduced energy consumption, while
ultrasound resulted in a slight increase in energy consumption.
2. Methodology of the Study
2.1. Material
Fresh carrots (Daucus carota cv. Nantes), bought at a local market, were used as the
experimental material. Before processing, the material was stored in a refrigerator at 4
◦
C
for at least 24 h. Next, three or four of the roots were washed, peeled, and cut into slices
(5 mm thick) with the use of an industrial cutter, Hällde RG100 (Kista, Sweden). The
prepared samples were divided into two parts. One part was used to measure moisture
content, water activity, and color; the other was subjected to drying. The prepared batch
of material, weighing approximately 200 g, was placed into the drum of the dryer and
subjected to the drying process. The dryer was not preheated prior to the beginning of the
drying process.
The initial moisture content of the material was determined using a Precisa XM120
moisture analyzer (Dietikon, Switzerland) and equaled 86.63 ±1.73% (wet basis).
2.2. Drying Procedure
The drying tests were conducted using a laboratory rotary hybrid dryer constructed
by PROMIS-TECH (Wrocław, Poland), as shown schematically in Figure 1.
The dryer has two different techniques for drying: hot air-convective (CV) and mi-
crowave (MW). Convective drying utilizes air drawn in by a blower (Figure 1(1)) from
the dryer’s environment, which, after passing through a heater (5), is forced directly into
the dryer drum (12). After passing through the drum, the moistened air leaves the dryer
through the outlet duct (7b). Microwave drying is implemented using electromagnetic
waves at 2.45 GHz, generated continuously by two water-cooled magnetrons (10), pro-
duced by Muegge (Reichelsheim, Germany). Additionally, each of the drying techniques
may be supported by high-power ultrasound (US) generated by a transducer mounted
on the side of the dryer (13) and delivered through the air directly to the material. In the
experiment, the frequency of the acoustic waves was 26 kHz, and the maximum acoustic in-
tensity reached 160 dB. The operation of the transducer is controlled by two of the airborne
ultrasound system’s (AUS) other units, specifically the controller (2) and the preamplifier
(3). The system was developed and manufactured by Pusonics (Madrid, Spain).

Appl. Sci. 2024,14, 10676 3 of 14
Appl. Sci. 2024, 14, x FOR PEER REVIEW 3 of 16
Figure 1. Scheme of the rotary hybrid dryer: 1—blower, 2—Airborne Ultrasound system (AUS) con-
troller, 3—AUS amplifier, 4—microwave feeders, 5—heater, 6—pneumatic valve, 7a and 7b—air
outlet, 8—pyrometer, 9—drum drive, 10—microwave generators, 11—balance, 12—rotating drum,
13—AUS transducer, 14—control unit, A—temperature and humidity sensor, B—temperature sen-
sor.
The dryer has two different techniques for drying: hot air-convective (CV) and mi-
crowave (MW). Convective drying utilizes air drawn in by a blower (Figure 1(1)) from the
dryer’s environment, which, after passing through a heater (5), is forced directly into the
dryer drum (12). After passing through the drum, the moistened air leaves the dryer
through the outlet duct (7b). Microwave drying is implemented using electromagnetic
waves at 2.45 GHz, generated continuously by two water-cooled magnetrons (10), pro-
duced by Muegge (Reichelsheim, Germany). Additionally, each of the drying techniques
may be supported by high-power ultrasound (US) generated by a transducer mounted on
the side of the dryer (13) and delivered through the air directly to the material. In the
experiment, the frequency of the acoustic waves was 26 kHz, and the maximum acoustic
intensity reached 160 dB. The operation of the transducer is controlled by two of the air-
borne ultrasound system’s (AUS) other units, specifically the controller (2) and the pre-
amplifier (3). The system was developed and manufactured by Pusonics (Madrid, Spain).
The research included four drying schemes. Each drying schedule was elaborated on
the basis of the convective process (CV) supported by microwaves (MW) and/or ultra-
sound (US). The temperature and the velocity of the drying agent (air) was constant dur-
ing the whole research process. The power of the microwave and ultrasonic enhancement
was selected in accordance with the results of preliminary experiments. Each drying pro-
cedure was carried out in triplicate. Details about the drying conditions for the specified
schedules of drying are given in Table 1.
Table 1. Drying procedures.
No. Acronym
Air Parameters Radiation Power (W)
T
(°C)
v
(m/s)
RH
(%) US MW
1 CV
60 0.2 7
0 0
2 CVUS 200 0
3 CVMW 0 100
4 CVMWUS 200 100
T—air temperature, v—air velocity, RH—air relative humidity, US—ultrasound, MW—microwave.
The weight loss of the samples being dried was measured automatically throughout
the whole operation at 5 min intervals using a laboratory balance (Figure 1(11)) model
APP/25c (precision 0.01 g), produced by Radwag (Radom, Poland). To prevent any poten-
tial interference that might affect the accuracy of the mass measurement, the drum of the
Figure 1. Scheme of the rotary hybrid dryer: 1—blower, 2—Airborne Ultrasound system (AUS)
controller, 3—AUS amplifier, 4—microwave feeders, 5—heater, 6—pneumatic valve, 7a and 7b—air
outlet, 8—pyrometer, 9—drum drive, 10—microwave generators, 11—balance, 12—rotating drum,
13—AUS transducer, 14—control unit, A—temperature and humidity sensor, B—temperature sensor.
The research included four drying schemes. Each drying schedule was elaborated on
the basis of the convective process (CV) supported by microwaves (MW) and/or ultrasound
(US). The temperature and the velocity of the drying agent (air) was constant during the
whole research process. The power of the microwave and ultrasonic enhancement was
selected in accordance with the results of preliminary experiments. Each drying procedure
was carried out in triplicate. Details about the drying conditions for the specified schedules
of drying are given in Table 1.
Table 1. Drying procedures.
No. Acronym
Air Parameters Radiation Power (W)
T
(◦C)
v
(m/s)
RH
(%) US MW
1 CV
60 0.2 7
0 0
2 CVUS 200 0
3 CVMW 0 100
4 CVMWUS 200 100
T—air temperature, v—air velocity, RH—air relative humidity, US—ultrasound, MW—microwave.
The weight loss of the samples being dried was measured automatically throughout
the whole operation at 5 min intervals using a laboratory balance (Figure 1(11)) model
APP/25c (precision 0.01 g), produced by Radwag (Radom, Poland). To prevent any poten-
tial interference that might affect the accuracy of the mass measurement, the drum of the
dryer was temporarily stopped, and the drying air was redirected through a pneumatic
valve (6) to the outlet (7a), thus bypassing the chamber. The drying agent’s parameters,
such as temperature, velocity, and humidity, were also measured throughout the process
using two sensors (A, B) models HD29371TC1.5 and HD4817ETC1.5 (precision 0.01 m/s,
0.1
◦
C, 0.01%), produced by DeltaOHM (Selvazzano Dentro, Italy). All measured data were
collected by data acquisition software running on a personal computer (PC).
The temperature of the samples during drying was measured using two methods,
depending on the process variant. In the convective and convective-ultrasound (CV,
CVUS) processes, the temperature (T) was measured using a standalone HTDL-20 recorder
produced by DWYER (Michigan City, IN, USA). Before the test, a single slice of carrot was
impaled on the rigid external probe of the device and the whole was placed in the dryer
with the other samples. After the drying process, the temperature recorded over time (at
one-minute intervals) was read from the device. For the convective-microwave processes
(CVMW, CVMWUS), the surface temperature (T*) was measured using a model B1 infrared
thermal camera made by FLIR (Wilsonville, OR, USA). At preset intervals (every 10 min),
the drying process was paused in order to take a thermal image—a thermogram—of the

Appl. Sci. 2024,14, 10676 4 of 14
samples inside the dryer. The images were further analyzed using software provided by the
camera manufacturer. The point with the highest temperature was marked on the images
and its value was read.
2.3. Drying Kinetics and Energy Intensity
Drying kinetics were evaluated on the basis of drying curves, that is, changes in
dimensionless moisture content over time, and changes in drying rate as a function of
dimensionless moisture content. In addition, the average drying rate was also determined
for each process.
By defining the dry basis moisture content as the ratio of the mass of moisture (m
w
)
contained in the material to the mass of the dry phase (md) [28]:
X=mw/md, (1)
the drying kinetics of samples could be assessed in terms of dimensionless moisture content
(Y) and drying rate (DR) in accordance with the following equations [29]:
Yi=X(ti)/X0, (2)
DRi=−md(dX/dt)=−(dmw/dt)=−(m(ti)−m(ti−1))/(ti−ti−1), (3)
where
X(ti)
is the spatial average of the moisture content determined at time t
i
,X
0
is the
initial moisture content, dm
w
is the weight loss of the sample, and dt is the time at which
the weight loss dmwoccurred.
The mass of moisture m
w
can be defined as the difference between the mass of the
moist material mand the mass of the dry phase m
d
. After substituting this difference into
(1) the spatial average moisture content
X(ti)
(dry basis) at any i-th time of the process was
calculated using the following formula [30]:
X(ti)=(m(ti)−md)/md, (4)
where m(t
i
) is the sample mass measured at time t
i
, and m
d
is the dry matter determined
using a Precisa XM120 moisture analyzer (Dietikon, Switzerland) with an accuracy of 0.01%.
The average drying rate for a given drying process was calculated using the following
equation [30]:
DRav =∆m/DT, (5)
where
∆
mis the mass of moisture removed from the sample by drying, and DT is the total
drying time.
The experimental data was also used to determine the drying constant, k; mass
transfer coefficient,
α
; and effective diffusion coefficient, D
eff
. All these parameters could be
determined from the drying rate curves [
30
]. Based on the experimental results, the values
of the average moisture content
Xi
and the rate of moisture content change
−dX/dti
were calculated in accordance with the following equations [30]:
Xi=X(ti)+X(ti−1)/2, (6)
−dX/dti=X(ti−1)−X(ti)/(ti−ti−1), (7)
The rate of moisture content change
−dX/dti
(7) was calculated as an average value for
the time period
(ti−ti−1)
. For consistency in kinetics modeling, material moisture content
Xi
(6) was also averaged over the same time period
(ti−ti−1)
. Based on the linear
approximation of the moisture content change over average moisture content, the drying
constant, k, was determined to be the slope of approximation lines. The mass transfer,
α
, and the effective diffusion coefficient, D
eff
, were then calculated using the following
formula [30]:
α=kl, (8)

Appl. Sci. 2024,14, 10676 5 of 14
De f f =4l2k/π2, (9)
where lis half of the sample’s thickness.
Each drying schedule was also assessed in terms of energy intensity. The total electric
energy consumed by the experimental setup during the drying tests was measured using an
electricity meter. The resulting electricity consumption, EC, was then transformed through
recalculation into specific energy consumption, SEC, that is, the amount of energy used to
evaporate one kilogram of moisture according to the relationship:
SEC =(3.6 ·EC)/∆m, (10)
The value thus determined enabled the energy consumption of each process to be compared.
2.4. Quality of Products
The quality of the obtained products was evaluated on the basis of water activity
and the color of the samples. Water activity (a
w
) was measured at room temperature
(~23
◦
C) before and after drying experiments with a TESTO 650 multimeter (Testo, Titisee-
Neustadt, Germany), equipped with a water activity measuring chamber. Prior to the
measurement, approximately 5 g of ground sample was placed in a polystyrene container
and subsequently inserted into a steel airtight measuring chamber. The measurement was
conducted until a constant a
w
value was reached, indicating no change at a value of 0.001
for a period of five minutes.
The color of the samples was measured using a CR400 colorimeter produced by
Konica Minolta (Tokyo, Japan) and quantified in terms of the three-dimensional color space,
CIELAB, where L* represents brightness, a* denotes the chromatic component of colors
ranging from red to green, and b* signifies the chromatic component of colors ranging from
yellow to blue. Based on the measured values for the raw material (index
0
) and the dried
sample (index
d
), the color difference index, dE, was determined according to the following
equation [31]:
dE =qL∗
0−L∗
d2+a∗
0−a∗
d2+b∗
0−b∗
d2(11)
The experimental data were processed using OriginPro 2024b [
32
]. The data presented
in Section 3, Results and Discussion, are means ±standard deviations.
3. Results and Discussion
3.1. The Kinetics and Energy Intensity of Drying
Figure 2a shows a graph demonstrating the dependence of dimensionless moisture
content (Y) on time (t). Despite the variations in drying methods, the curve paths are very
similar. The characteristic drying periods such as the constant drying-rate period and the
falling drying-rate period cannot easily be distinguished, which is typical for biomaterials
drying processes [
9
,
33
]. As expected, convective drying alone was the slowest among
the methods tested. However, the application of microwaves (MW) or ultrasound (US)
significantly reduced the drying time by increasing the rate of drying. Figure 2b illustrates
the relationship between the drying rate (DR) and dimensionless moisture content (Y)
during the process.
A comparative analysis of the drying rate curves reveals that the application of mi-
crowaves had a significantly greater impact than ultrasound (Figure 2b). The maximum
drying rate for the microwave processes (CVMW and CVMWUS) reached a value above
0.03 g/s, while for the convective–ultrasound process (CVUS), the highest observed value
was 0.02 g/s. The lowest drying rate was observed for the convection process (CV), with a
maximum of approximately 0.015 g/s, which resulted in a prolonged drying time.

Appl. Sci. 2024,14, 10676 6 of 14
Appl. Sci. 2024, 14, x FOR PEER REVIEW 6 of 16
from yellow to blue. Based on the measured values for the raw material (index 0) and the
dried sample (index d), the color difference index, dE, was determined according to the
following equation [31]:
()()()
=−+−+−
222
** ** **
000ddd
dE L L a a b b , (11)
The experimental data were processed using OriginPro 2024b [32]. The data pre-
sented in Section 3, Results and Discussion, are means ± standard deviations.
3. Results and Discussion
3.1. The Kinetics and Energy Intensity of Drying
Figure 2a shows a graph demonstrating the dependence of dimensionless moisture con-
tent (Y) on time (t). Despite the variations in drying methods, the curve paths are very similar.
The characteristic drying periods such as the constant drying-rate period and the falling dry-
ing-rate period cannot easily be distinguished, which is typical for biomaterials drying pro-
cesses [9,33]. As expected, convective drying alone was the slowest among the methods tested.
However, the application of microwaves (MW) or ultrasound (US) significantly reduced the
drying time by increasing the rate of drying. Figure 2b illustrates the relationship between the
drying rate (DR) and dimensionless moisture content (Y) during the process.
(a) (b)
(c)
0 3,600 7,200 10,800 14,400 18,000 21,600
0.0
0.2
0.4
0.6
0.8
1.0
CV
CVUS
CVMW
CVMWUS
Y
i
(-)
t
i
(s)
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.01
0.02
0.03
0.04 CV
CVUS
CVMW
CVMWUS
DR
i
(g/s)
Y
i
(-)
0 3,600 7,200 10,800 14,400 18,000 21,600
20
40
60
80
100
CV (T)
CVUS (T)
CVMW (T*)
CVMWUS (T*)
Ti (°C)/T*i (°C)
ti (s)
Figure 2. Evolution of dimensionless moisture content, Y
i
(a); drying rate, DR
i
(b); and temperature
of the samples, T/T* (c), for each process.
The shape of the drying rate curves exhibits a similar pattern across the different
processes, which enables the essential drying periods to be identified. These include the
initial stage, the constant drying rate period, and the falling drying rate period. The values
of Y
i
at which the transition between the drying periods occurs are slightly different for
each process; however, some similarities can be observed between the CV and CVUS
processes, as well as between the CVMW and CVMWUS processes.
The initial stage of the process lasts from the beginning until a constant drying rate
is reached. For the CV-CVUS pair of processes, this period lasted until the dimensionless
moisture content reached Y
i≈
0.89, while for the CVMW-CVMWUS pair, it lasted until
Yi≈0.87.
In both instances, this occurred after approximately 1200 s of the process’ dura-
tion. The relatively prolonged heating period observed in this study may be attributed to
two factors: the larger sample batch size compared to other studies on hybrid drying and
the initiation of drying on the cold dryer. In this approach, a portion of the heat energy
supplied with the hot air was utilized for the heating of the dryer components. The process
subsequently entered the constant drying rate period. In the case of the CV-CVUS pair of
processes, this period lasted until the material reached a dimensionless moisture content
of approximately 0.57, which occurred after 5400 s of the convection (CV) process and
3900 s of the ultrasound-assisted process (CVUS). In the microwave-assisted processes

Appl. Sci. 2024,14, 10676 7 of 14
(CVMW, CVMWUS), the constant drying rate period ended at a dimensionless moisture
content of 0.47, which was reached after approximately 3600 s, despite the variations in the
types of processes. The condition for the end of the period of constant drying rate is the
slowing down of the transport of moisture from the inside of the sample to its surface. In
all the processes studied, the transport of moisture to the surface of the sample is caused by
diffusion. When microwaves are used (CVMW, CVMWUS), the temperature of the samples
is higher than in the other processes (CV, CVUS). This facilitates diffusion at lower moisture
contents. In addition, internal heating of the material with microwaves causes an increase
in moisture pressure, which in turn causes easier transport of moisture to the surface
(pressure flow). For these two reasons, the period of constant drying rate is longer in the
processes with microwaves (CVMW, CVMWUS) than in the processes without microwaves
(CV, CVUS). Once the aforementioned moisture content—frequently designated as the
critical moisture content—is surpassed, a falling drying rate period ensues, persisting until
the end of the process.
By analyzing the temperature curves (Figure 2c), it can be seen that in the microwave-
assisted processes (CVMW, CVMWUS) the temperature of the material increased much
faster and reached a significantly higher value than for the convection (CV) or ultrasonic-
assisted (CVUS) processes. This phenomenon is due to the effective interaction between
the microwaves and the moist material being dried, and results in high drying rates and
short processing times. The temperature curves also demonstrate the beneficial impact
of ultrasound on heat transfer. The application of acoustic waves in the CVUS process
resulted in a significantly enhanced heating rate when compared to the convection process
(CV). This phenomenon may be attributed to ultrasound-induced effects at the material’s
surface, which result in a reduction of the boundary layer’s thickness and thus enhances
heat transfer efficiency and the absorption of ultrasonic energy [26].
An analysis of the shape of the temperature curves (Figure 2c) also reveals the similarity
between the CV and CVUS processes, and between the CVMW and CVMWUS processes. In
the case of convective (CV) and ultrasound-assisted convective (CVUS) drying, there are no
evident characteristic periods, and the curves move asymptotically towards the temperature
of the drying agent. For the microwave processes (CVMW and CVMWUS), three stages
can be distinguished. During the first, there was intensive heating to a temperature of
about 60
◦
C. This stage lasted about 1200 s and corresponds to the initial stage on the
drying rate curves (Figure 2b). During the next stage, the temperature of the material
was approximately constant (about 60
◦
C) and lasted up to 3600 s; this coincides with the
constant drying rate period (Figure 2b). During the last stage, the temperature increased
again to reach a value of about 100
◦
C at the end of the process. This period corresponds to
a falling drying rate period.
Concerning the microwave processes, the intense heating during the initial stage was
the result of effective absorption of microwave radiation by the very moist material. In
this stage, intense moisture evaporation also began, leading to an increase in the drying
rate (Figure 2b). The constant temperature of the material during the constant drying
rate period (from 1200 s to 3600 s of the process) was due to the very intensive evapora-
tion of moisture from the sample’s surface. Because of this, convectively supplied and
microwave–generated
heat is used to evaporate moisture and does not heat up the material
being dried. This phenomenon occurs only when there is enough moisture in the material,
so that it can be transported efficiently to the surface/evaporation front, and that transport
within the material does not limit the process rate. Given the constant value of the heat of
vaporization, the rate of drying (evaporation) is thus primarily determined by the amount
of energy applied per unit time. If drying is conducted under constant process conditions
(i.e., constant air temperature and radiation power), it can be assumed that the amount of
energy supplied to the surface of the material being dried is also constant. Consequently,
the evaporation rate remains constant, resulting in a constant drying rate (Figure 2b) and
also in almost constant temperature of material [
34
]. Once the moisture content of the
material has decreased below a critical value, the effectiveness of the moisture transport

Appl. Sci. 2024,14, 10676 8 of 14
to the surface/evaporation front drops. The energy applied to the material is then used
not only to evaporate the moisture but also to heat the material, resulting in a temperature
increase (Figure 2c). As the drying rate during this period is determined primarily by the
internal transport of moisture, the value of this parameter continues to decrease (Figure 2b)
and falling drying rate period occurs.
The notable occurrence of a constant drying rate period may be somewhat unexpected.
A review of the literature reveals numerous reports concerning materials of plant origin for
which a constant drying rate period is not observed, and the entire drying process occurs
during the period of falling drying rate [
9
]. However, some researchers have reported the
presence of a constant drying rate period. Arslan et al. reported similar drying curves for
carrot [
35
] and red pepper [
36
]. On the other hand, Abbaspour-Gilandeh et al. [
15
] did not
observe a constant drying rate period during the drying of carrot using multiple techniques.
The underlying reason behind this discrepancy remains unclear. May and Perré[
33
]
hypothesized that this phenomenon may be linked to a variation in the mass exchange
area resulting from material shrinkage during the drying process. However, determining
exchange surface area is extremely difficult and requires advanced experimental techniques.
In Figure 3, the average drying rate, DR
av
; time, DT
av
; and specific energy consumption,
SECav, for each particular drying process are presented.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 9 of 16
(a) (b)
Figure 3. Average drying rate, DRav and time, DTav (a); and specific energy consumption, SECav (b)
for each process.
The average drying rate obtained during the hybrid processes was visibly higher
compared to the convective process (Figure 3a). In the case of the fastest drying procedure
(CVMWUS) the average drying rate increased by 140% compared to CV, while for other
hybrid programs, namely ultrasound–assisted (CVUS) and microwave–assisted (CVMW)
convective drying, the increase equaled 13% and 112%, respectively. These changes were
reflected in the value of the average drying time, which exhibited reductions of 10%, 53%,
and 59% for CVUS, CVMW, and CVMWUS, respectively (Table 2). A strong positive cor-
relation (Pearson’s r = 0.99) was identified between the DRav and DTav values; a finding that
is also evident in the graphical representation (Figure 3a).
Table 2. Relative change in average drying rates and specific energy consumption.
Process Relative Change
DRav DTav SECav
CV – – –
CVUS 13% −10% 59%
CVMW 112% −53% −30%
CVMWUS 140% −59% −28%
On the basis of the obtained results, microwaves were found to be a more efficient
enhancement agent compared to ultrasound; this follows from the different mechanisms
of interaction they have with the material being dried. Microwaves heat the entire volume
of the sample, thereby significantly intensifying the transport of moisture within the body
(through the intensification of diffusion and evaporation). Furthermore, the application of
MW radiation typically results in a reduction in the temperature gradient within the ma-
terial, which additionally enhances the drying process (through the reduction of thermod-
iffusion) [34]. The obtained results are in good agreement with the reports of other au-
thors. Abbaspour-Gilandeh et al. [15] also observed a 50% reduction in drying time for
microwave-assisted hot air drying of carrot. Kroehnke et al. [37] noted a fivefold decrease
in drying time during the microwave-assisted convective processing of this vegetable.
The influence of ultrasound on the material being dried is very limited and depends
strictly on the acoustic impedance mismatch between the sample material and the sur-
rounding air. Several authors have proposed different mechanisms for ultrasound inter-
action, for example, cavitation, the “sponge effect”, microstreaming, the formation of
CV CVUS CVMW CVMWUS
0.006
0.009
0.012
0.015
0.018
0.021
DR
av
DT
av
DR
av
(g/s)
7,200
10,800
14,400
18,000
21,600
25,200
DT
av
(s)
CV CVUS CVMW CVMWUS
80
100
120
140
160
180
200
SEC
av
(MJ/kg)
Figure 3. Average drying rate, DR
av
and time, DT
av
(a); and specific energy consumption, SEC
av
(b) for each process.
The average drying rate obtained during the hybrid processes was visibly higher
compared to the convective process (Figure 3a). In the case of the fastest drying procedure
(CVMWUS) the average drying rate increased by 140% compared to CV, while for other
hybrid programs, namely ultrasound–assisted (CVUS) and microwave–assisted (CVMW)
convective drying, the increase equaled 13% and 112%, respectively. These changes were
reflected in the value of the average drying time, which exhibited reductions of 10%, 53%,
and 59% for CVUS, CVMW, and CVMWUS, respectively (Table 2). A strong positive
correlation (Pearson’s r= 0.99) was identified between the DR
av
and DT
av
values; a finding
that is also evident in the graphical representation (Figure 3a).

Appl. Sci. 2024,14, 10676 9 of 14
Table 2. Relative change in average drying rates and specific energy consumption.
Process
Relative Change
DRav DTav SECav
CV – – –
CVUS 13% −10% 59%
CVMW 112% −53% −30%
CVMWUS 140% −59% −28%
On the basis of the obtained results, microwaves were found to be a more efficient
enhancement agent compared to ultrasound; this follows from the different mechanisms of
interaction they have with the material being dried. Microwaves heat the entire volume of
the sample, thereby significantly intensifying the transport of moisture within the body
(through the intensification of diffusion and evaporation). Furthermore, the application
of MW radiation typically results in a reduction in the temperature gradient within the
material, which additionally enhances the drying process (through the reduction of ther-
modiffusion) [
34
]. The obtained results are in good agreement with the reports of other
authors. Abbaspour-Gilandeh et al. [
15
] also observed a 50% reduction in drying time for
microwave-assisted hot air drying of carrot. Kroehnke et al. [
37
] noted a fivefold decrease
in drying time during the microwave-assisted convective processing of this vegetable.
The influence of ultrasound on the material being dried is very limited and depends
strictly on the acoustic impedance mismatch between the sample material and the surround-
ing air. Several authors have proposed different mechanisms for ultrasound interaction, for
example, cavitation, the “sponge effect”, microstreaming, the formation of microchannels,
disturbance in the boundary layer, etc. [26]. The proposed phenomena may accelerate the
drying operation by reducing both the internal and external resistances. On the basis of
the results obtained during the authors’ previous research [
38
,
39
], it can be stated that in
the case of the presented drying system, ultrasound influences the kinetics of the process
rather by reducing external resistance factors such as the laminar boundary layer. Due
to the significant losses in ultrasound power/intensity that occur during the transfer of
energy between the radiator plate and the material, only a small proportion of the acoustic
energy is involved in accelerating the drying process. Nevertheless, the positive effect of
the ultrasound assistance could be easily distinguished and is in agreement with the results
presented by other researchers. Kroehnke et al. [
37
] noted a 20% reduction in processing
time during the ultrasound-assisted convective drying of carrot.
An analysis of the specific energy consumption (SEC) (Figure 3b) reveals that the
application of additional energy-consuming devices, in the form of microwave generators
or ultrasound transducer, affects the energy intensity of the process in a different manner.
In the case of the microwave processes (CVMW, CVMWUS), a notable enhancement of
the drying rate—which also resulted in a considerable reduction in drying time—led to a
reduction in the amount of energy required to evaporate a given mass of moisture. The
SEC
av
values for these processes were the lowest for all the schemes studied: 87 MJ/kg and
90 MJ/kg for CVMW and CVMWUS, respectively. This represents a respective 30% and
28% reduction compared to the convection CV process (Table 2). The ultrasound-assisted
convective process (CVUS), despite an observable increase in drying rate and reduction
in drying time, did not prove to be more energy efficient than the reference process. A
notable increase (59%) in the value of specific energy consumption was observed for CVUS,
reaching an approximate value of 190 MJ/kg.
The considerable increase in SEC for CVUS can be attributed to the higher instan-
taneous energy consumption (in comparison to CV) necessitated by the requirement to
power the AUS ultrasound generation system. Despite the beneficial effects of acoustic
waves on the drying rate and time, their effectiveness was insufficient to compensate for
additional energy expenditure, leading to an increase in total energy consumption. This

Appl. Sci. 2024,14, 10676 10 of 14
phenomenon was previously reported by Kowalski et al. [
38
], Kroehnke et al. [
37
], and
Kroehnke and Musielak [40].
In the case of the CVMW and CVMWUS processes, the instantaneous energy consump-
tion was also higher. However, the kinetic benefits resulting from the use of microwave
radiation (increased drying rate and reduced drying time) were substantial enough for com-
pensate this additional energy expenditure and reduce overall energy consumption. The
discrepancy between the SEC values for the ultrasound- and microwave-assisted processes
may also be attributed to the differing energy efficiency of the generators and the vary-
ing attenuation coefficient of the radiation along the path from the generator/transducer.
The energy efficiency of microwave-assisted processes was also confirmed in studies by
Abbaspour-Gilandeh et al. [
15
] and Kroehnke et al. [
37
]. In both cases, the microwave-
assisted drying of carrot was characterized by a lower energy consumption compared to
the reference convective drying.
The experimental data was also used to determine the drying constant, k; mass transfer
coefficient,
α
; and effective diffusion coefficient, D
eff
. Table 3presents the values obtained
for each process.
Table 3. Values for drying constant, k; mass transfer, α; and effective diffusion coefficient, Deff.
Process k(1/s) α(m/s) Deff (m2/s) adj. R2(–)
CV 1.75 ×10−4±6.02 ×10−64.39 ×10−7±1.50 ×10−84.44 ×10−10 ±1.52 ×10−11 0.9612
CVUS 2.17 ×10−4±5.50 ×10−65.43 ×10−7±1.38 ×10−85.50 ×10−10 ±1.39 ×10−11 0.9619
CVMW 3.29 ×10−4±2.07 ×10−58.23 ×10−7±5.17 ×10−88.34 ×10−10 ±5.23 ×10−11 0.9243
CVMWUS 4.59 ×10−4±2.79 ×10−51.15 ×10−6±6.99 ×10−81.16 ×10−9±7.08 ×10−11 0.9520
The values for all determined parameters corroborate the hypothesis that ultrasonic
and microwave assistance has a favorable impact on convective drying kinetics. For the
hybrid processes, the drying constant, mass transfer, and effective diffusion coefficient are
markedly higher than for the convective process. There is also a clear distinction between
acoustic waves and microwave radiation. In the case of the latter, the observed values are
higher than in the case of ultrasound, which confirms the fact that it has a more effective
influence on mass transfer processes. Arslan et al. [
35
] and Abbaspour-Gilandeh et al. [
15
]
also observed significant increases in the effective diffusion coefficient for the microwave
drying of carrot. On the other hand, Kroehnke et al. [
37
] noted an increase in the convective
mass transfer coefficient with an increase in the power of the ultrasound enhancement.
It can therefore be stated that the intensification of mass exchange is less pronounced
for ultrasound than for microwaves, yet it is discernible and has a beneficial impact on
convective drying kinetics. In turn, the values of the adjusted coefficient of determination
(adj. R
2
) confirm that there is close convergence between the experimental curve and the
linear approximation (Table 3).
3.2. Assessment of Product Quality
The water activity (a
w
) of a food product is a crucial factor in determining its shelf
life. A low a
w
inhibits the growth of pathogenic microorganisms, such as fungi, yeasts,
and molds, and prevents unfavorable biochemical reactions, including enzymatic and
non–enzymatic processes, and oxidation. It is generally accepted that microbial activity
ceases below an a
w
value of 0.6, while the most unfavorable biochemical reactions are
maximally inhibited for an a
w
below 0.4 [
41
]. Figure 4depicts the mean water activity
values for each dried sample and the raw material.

Appl. Sci. 2024,14, 10676 11 of 14
Appl. Sci. 2024, 14, x FOR PEER REVIEW 11 of 16
The values for all determined parameters corroborate the hypothesis that ultrasonic
and microwave assistance has a favorable impact on convective drying kinetics. For the
hybrid processes, the drying constant, mass transfer, and effective diffusion coefficient are
markedly higher than for the convective process. There is also a clear distinction between
acoustic waves and microwave radiation. In the case of the laer, the observed values are
higher than in the case of ultrasound, which confirms the fact that it has a more effective
influence on mass transfer processes. Arslan et al. [35] and Abbaspour-Gilandeh et al. [15]
also observed significant increases in the effective diffusion coefficient for the microwave
drying of carrot. On the other hand, Kroehnke et al. [37] noted an increase in the convec-
tive mass transfer coefficient with an increase in the power of the ultrasound enhance-
ment. It can therefore be stated that the intensification of mass exchange is less pro-
nounced for ultrasound than for microwaves, yet it is discernible and has a beneficial im-
pact on convective drying kinetics. In turn, the values of the adjusted coefficient of deter-
mination (adj. R2) confirm that there is close convergence between the experimental curve
and the linear approximation (Table 3).
3.2. Assessment of Product Quality
The water activity (aw) of a food product is a crucial factor in determining its shelf
life. A low aw inhibits the growth of pathogenic microorganisms, such as fungi, yeasts, and
molds, and prevents unfavorable biochemical reactions, including enzymatic and non–
enzymatic processes, and oxidation. It is generally accepted that microbial activity ceases
below an aw value of 0.6, while the most unfavorable biochemical reactions are maximally
inhibited for an aw below 0.4 [41]. Figure 4 depicts the mean water activity values for each
dried sample and the raw material.
Figure 4. Average water activity, aw, and color difference index, dE, for each process.
From an analysis of the results, we can conclude that the safety and microbiological
stability of the material were ensured, as the results for the obtained (dried) products were
characterized by a water activity (aw) value below 0.4. Differences between the particular
drying procedures were negligible and did not affect the shelf-life of the material.
The color of the samples is also a significant quality parameter. It is primarily respon-
sible for determining the sensory properties of the product and indicating the so-called
palatability. Additionally, color can indirectly indicate the safety of a product or the
changes that occur in it, such as the color change in fruit during the ripening process. It
must be acknowledged, however, that color perception is highly subjective, and the
CV CVUS CVMW CVMWUS raw
0.0
0.2
0.4
0.6
0.8
1.0
aw dE
a
w
(-)
0
5
10
15
20
25
dE (-)
Figure 4. Average water activity, aw, and color difference index, dE, for each process.
From an analysis of the results, we can conclude that the safety and microbiological
stability of the material were ensured, as the results for the obtained (dried) products were
characterized by a water activity (a
w
) value below 0.4. Differences between the particular
drying procedures were negligible and did not affect the shelf-life of the material.
The color of the samples is also a significant quality parameter. It is primarily respon-
sible for determining the sensory properties of the product and indicating the so-called
palatability. Additionally, color can indirectly indicate the safety of a product or the changes
that occur in it, such as the color change in fruit during the ripening process. It must be
acknowledged, however, that color perception is highly subjective, and the evaluation of
products will invariably depend on the observer’s preferences. Consequently, instrumen-
tal color measurement was introduced as a means of objectively determining changes in
color relative to the raw material. Figure 4illustrates the color differences (dE) for dried
samples in relation to the raw material. It is assumed that a value above 4 units represents
a perceptible difference in color as discerned by an average observer.
As can be observed in Figure 4, all the dried products exhibited a color that was
discernibly distinct from that of the raw material, as indicated by color difference index
values exceeding 4 units. The application of microwaves in microwave-assisted convective
drying (CVMW and CVMWUS) resulted in the most detrimental impact on product quality.
The color difference index (dE) was, for these processes, visibly greater in comparison to
the solely convective (CV) or ultrasound-assisted convective processes (CVUS) (Figure 4).
Thus it turned out that the very significant achievements made in the drying kinetics led to
the opposite results regarding the quality of the products. This is often observed in drying
processes, for example, as found by Mierzwa and Szadzi´nska [39].
The color loss that occurs during microwave drying is usually caused by the high
temperatures to which the products are exposed. Figure 5shows thermal images specifically
of samples taken at the 140th minute of the CVMW and CVMWUS drying processes. The
maximum material temperature recorded in the image is approximately 98
◦
C, indicating a
considerable degree of overheating in the material. Such elevated temperatures give rise to
a number of detrimental changes, which, among other parameters, impact the color. These
changes are attributed to both biochemical processes and thermal decomposition [
42
]. The
rapid increase in temperature of the material being microwave-dried can be attributed to
the inhomogeneity of the microwave field and changes occurring in the material. In the
former, localized overheating of the material, known as “hot spots”, results in substantial
qualitative alterations at these locations. To address this phenomenon, advanced microwave
chamber designs are employed, and the dried material’s movement is maintained through
the microwave field (transmission belt, rotating pan, drum, etc.) [43].

Appl. Sci. 2024,14, 10676 12 of 14
Figure 5. Exemplary thermograms of samples dried in microwave–assisted processes: (a) CVMW
and (b) CVMWUS at 140th minute of the processes.
Additionally, changes in moisture content can also result in the material overheating.
This is due to the fact that the moisture affects the dielectric properties of the material,
namely, its capacity to absorb and reflect microwaves. When the material contains a sub-
stantial amount of moisture and the radiation power is properly adjusted, microwaves
can effectively evaporate moisture without causing a sudden increase in the material’s
temperature. However, as the moisture content decreases during the drying process, the
ability of the material to absorb microwaves changes. This can lead to a significant increase
in the temperature of the material and unfavorable changes in its color. Therefore, it is very
important to regulate the microwave power and exposure time, especially towards the end
of the process. An alternative solution is the periodic application of microwaves (intermit-
tent microwave drying) and the introduction of a so-called “relaxation period”, during
which the temperature and humidity gradients will be equalized. This non-stationary
hybrid drying is a promising technology that allows operational time to be reduced while
maintaining high product quality, including color [35,39,44].
The beneficial impact of ultrasound on product color (Figure 4, CVUS) can be at-
tributed to its non-thermal nature. Although ultrasound application accelerated heating of
the material (compared to CV), unlike microwave radiation, it did not result in overheating
effects (Figure 2c). Consequently, the initial color of the samples was preserved more
effectively, and the majority of observed changes can be attributed to the temperature of
the drying agent (air) and the high oxygen content in the atmosphere. These findings align
well with those reported by Kroehnke et al. [37].
4. Conclusions
The application of microwaves and/or ultrasound during the convective drying of
carrots positively influenced the drying kinetics. The hybrid processes exhibited higher
drying rates, resulting in shorter drying times. Among these methods, microwaves were
more effective than ultrasound across all evaluated aspects, including drying rate, time,
effective diffusion coefficient, and drying constant.
Microwave-assisted drying significantly improved energy efficiency by reducing
drying time, leading to lower energy consumption per unit mass of moisture evaporated. In
contrast, ultrasound-assisted drying showed higher specific energy consumption compared
to conventional convective drying, attributed to its lower drying intensification efficiency
and higher instantaneous energy use.
A negative impact of constant microwave irradiation on the color of the product was
also observed. In contrast, non-thermal ultrasound waves were found to have minimal
impact on the color of the material, thus acting as a quality promoter. All dried products
exhibited low water activity, ensuring their safety and microbiological stability. Further

Appl. Sci. 2024,14, 10676 13 of 14
research is necessary to investigate the influence of MW and US enhancement as a function
of applied power.
Author Contributions: Conceptualization, D.M.; methodology, D.M. and G.M.; formal analysis, D.M.;
investigation, D.M.; writing—original draft preparation, D.M. and G.M.; writing—review and editing,
D.M. and G.M.; visualization, D.M. All authors have read and agreed to the published version of
the manuscript.
Funding: This research was financially supported by the Ministry of Science and Higher Education
in Poland.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The raw data supporting the conclusions of this article will be made
available by the authors on request.
Conflicts of Interest: The authors declare no conflicts of interest. The funders had no role in the design
of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or
in the decision to publish the results.
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