Innovative Food Science and Emerging Technologies 4

(2003) 203–209

1466-8564/03/$ - see front matter

䊚 2003 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S1466-8564(03)00016-X

Modelling of dehydration-rehydration of orange slices in combined

microwave

yair drying

G. Ruız Dıaz, J. Martınez-Monzo, P. Fito, A. Chiralt*

´

´

´

´

Department of Food Technology, Universidad Politecnica de Valencia, Camino de Vera, syn, 46022, Valencia, Spain

´

Received 12 December 2002; accepted 24 January 2003

Abstract

The development of new citrus products, such as dry products for direct use or for rehydration, is interesting to promote their

consumption. Combined microwaves

(MW)–air (2 mys, 60 8C) drying of orange slices has been studied in terms of process

kinetics and of the rehydration capability as affected by the applied MW power

(0, 0.17, 0.36, 0.69 and 0.88 Wyg). Drying

curves were modelled considering two periods, with different kinetic constants, related with the effective water diffusivity. These
constants increased linearly with the applied MW power and, despite the low levels of MW power used, a sharp reduction in
drying time of orange slices was obtained. Rehydration behaviour of orange slices was modelled through Peleg’s and Weibull’s
equations. No differences in rehydrating behaviour were observed as a function of the applied MW power. So, the highest level,
which was limited to avoid sample browning, will be recommended to reduce the drying time.

䊚 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Orange; Drying; Microwaves; Rehydration

Industrial relevance: A combined microwave

(power levels 0 to 0.88 Wys) proved effective in increasing drying rates. However, lack of

steadiness of the drying rate in the first drying period suggests a diffusion controlled water transport in the sample interface with the process
driving force progressively being reduced in linear with the water activity reduction of the external cells for all samples. Also of interest is that
the rehydration properties were not influenced by the drying conditions tested. Close fit of both models

(Weibull’s, Peleg’s equations) was

observed.

1. Introduction

Citrus fruit occupy an important place in world fruit

production. They have a great nutritional potential due
to their high content in vitamins and fibber as well as
in flavonoids and terpenes

(Ting & Attaway, 1971;

Monselise, 1986

). Most of the citrus production is

destined for the direct consumption or processed to
produce juice, the fresh consumption having decreased
in the last few years. The demand for healthy, natural
and tasty is continuously increasing, not only for fin-
ished products, but also for ingredients to be included
in complex foods such as ice-creams, cereals, dairy,
confectionery and bakery products. In this sense, orange
is dehydrated for different products such as powders,
flakes and slices

(Samson, 1986). The development of

*Corresponding author. Tel.: q34-96-387-7341; fax: q34-96-387-

7369.

E-mail address: [e-mail]

(A. Chiralt).

new citrus products

(such as dry products for direct use

or for rehydration

) is interesting to promote their con-

sumption according to the current tendencies.

High temperatures or long drying times in conven-

tional air drying, may cause serious damage to product
flavour, colour and nutrients, reducing bulk density and
rehydration capacity of the dried product

(Lin, Durance

& Scaman, 1998; Drouzas, Tsami & Saravacos, 1999

).

The desire to avoid these problems to some extent,
prevent significant quality loss, and achieve fast and
effective thermal processing has resulted in the increased
use of microwaves for food drying. The use of micro-
wave power in some food processes such as baking,
tempering, pasteurisation, cooking, and heating results
in a substantially reduced processing time leading to
increased production capacity, as well as improved
quality and shelf life of final products

(Shiffman, 1985).

Studies on drying applying a combined microwave

y

convection has been tackled by several authors

(Deca-

204

G.R. Dıaz et al. / Innovative Food Science and Emerging Technologies 4 (2003) 203–209

´

Fig. 1. Scheme of combined MW-hot air equipment.

reau, 1985; Rosenberg & Boegl, 1987; Mudgett, 1989;
Tulasidas, Raghavan & Norrish, 1992, 1993; Maskan,
2000, 2001

). The combination of microwaveyhot air

was successfully used for the final drying of onions by
conducting experiments using various combinations of
hot air and microwave energy for drying materials with
high higroscopicity

(Witt, 1980; Bhartia, Stuchly &

Hamid, 1973

). The quick energy absorption by water

molecules causes rapid evaporation of water

(resulting

in higher drying rates of the food

), creating an outward

flux of rapidly escaping vapour

(Lyons, Hatcher &

Sunderland, 1972

). In addition to improving the drying

rate, this outward flux can help to prevent the shrinkage
of tissue structure, which prevails in most conventional
air drying techniques. Hence better rehydration charac-
teristics may be expected in microwave dried products
(Prabhanjan, Ramaswamy & Raghavan, 1995; Tsami,
Krokida & Drouzas, 1999; Krokida, Kiranoudis & Mar-
oulis, 1999

). Microwave application has been reported

to improve product quality such as better aroma, faster
and better rehydration, considerable savings in energy
and much shorter drying times compared with hot air
drying alone

(Rosenberg & Boegl, 1987; Decareau,

1985

).

The objective of this study is to analyse and model

drying kinetics of orange slices using combined micro-
wave

yhot air-drying and to determine rehydration kinet-

ics and properties of the obtained products in the
different conditions.

2. Materials and methods

Oranges

(variety Navel Late) were obtained from a

local supermarket and stored at 5"0.5 8C for a maxi-

mum of two days until the experiments were carried
out. Prior to drying, they were cut with peel in 5 mm
thick slices taken from the equatorial zone of the fruit.
The samples were characterised as for their moisture
content and soluble solid content before and after the
drying.

Water content was analysed by vacuum drying at 60

8C until constant weight was achieved

(AOAC, 1980).

Soluble solid contents were measured in a refractometer
(ABBE ATAGO 89553 of Zeiss) at 20 8C.

Drying experiments were carried out in a modified

microwave oven

(Fig. 1), with two parallel connected

lines, one for the application of hot air and another for
the generation and application of the microwaves
(Martın, Andres, Martınez-Navarrete, Chiralt & Fito,

´

´

´

1999

). The temperature and velocity of the air were 60

8C and 2 m

ys, respectively. The incident and reflected

power of MW were controlled by using a directional
coupler in the power measure system to estimate the
power absorbed by sample. Five levels of supplied MW
power were applied 0, 20, 40, 60 and 100 W

(0, 0.17,

0.36, 0.69 and 0.88 W

yg of sample, respectively

). In

each experiment, 5 slices were put in the oven. One of
these was suspended in the centre of the cavity by
means of a nylon thread from a balance in order to
monitor the sample weight loss. The other samples were
suspended from a Teflon cylinder also parallel to the
airflow.

The dried slices

(until approx. 0.12 d.b.), previously

characterised in 8Brix and moisture content were rehy-
drated in distilled water at 25 8C, using a ratio dry
sample

ywater of 1:25. At the different rehydration times

(between 0 and 1560 min), the weight of the samples

205

G.R. Dıaz et al. / Innovative Food Science and Emerging Technologies 4 (2003) 203–209

´

Fig. 2. Drying curves and drying rate curves at different drying conditions

(or MW power applied).

was determined as well as the weight and 8Brix of the
rehydrating solution.

3. Results and discussion

The drying rate was significantly increased for micro-

wave-heated samples compared to only air-dried as can
be seen in Fig. 2, that shows drying curves and drying
rate curves for all the applied power levels. The higher
the power level, the greater the increase in drying rates.
Nevertheless, a limit for power application was estab-
lished on the basis of the colour stability of the product,
since for the maximum level applied incipient browning
was detected probably due to sugar caramelisation by
excessive local heating

(Ruız Dıaz, Martınez-Monzo,

´

´

´

´

Barat, Chiralt & Fito, 2000

). Drying rate showed a fast

increase at the beginning of the process due to MW
sample heating and a subsequent decrease, showing two
differentiated periods: the first, where drying rate
decreases slowly to reach a plateau with a practically
constant value, and the second with a rapidly decreasing
drying rate from a given critical moisture content. So,
drying rate curves showed a sigmoid shape, where the
influence of MW power can be observed in practically
the entire range of sample moisture content. Neverthe-
less, at a higher power level, the initial rates are more
greatly enhanced.

The lack of steadiness in the drying rate in the first

period, even in the air drying experiment, points out the
diffusion controlled water transport in the sample inter-
face where the process driving force is progressively
reduced in line with the water activity reduction of the
external cells. From a specific moisture content, when a
great number of cell layers in the tissue have lost a
considerable amount of moisture, dried cell layers offer

a much greater resistance to water diffusion through the
interface and the drying rate slows down rapidly.

At the first step of the process, sample MW power

absorption provokes internal water heating and evapo-
ration, greatly increasing the effective water diffusion.
This can also provoke cell rupture and debonding since
solubility of pectic material of middle lamellae increases.
In this sense, the less structured material will offer lower
resistance to water transport and drying rate becomes
much higher. Nevertheless, the loss factor of the sample
decreases in the course of drying, thus inhibiting the
MW effect and limiting drying rate at lower moisture
content.

On the basis of these considerations, drying of orange

slices was modelled through a simple empiric model
with two steps, also considered by other authors for
microwave drying of fruits

(Tulasidas, Raghavan &

Mujumdar, 1995; Kiranoudis, Tsami & Maroulis, 1997;
Maskan, 2000, 2001

) In each step, a kinetic coefficient

(k ) related with the water effective diffusion was

i

obtained. To obtain kinetic coefficients, the logarithm of
reduced moisture content

(ratio between the moisture

content at time

t

(x ) and the initial value (x ), both

w

wo

on d.b.x was plotted as a function of the drying time. In
this way, two linear ranges for experimental points were
observed at each MW power. The slopes of each fitted
straight-lines are

k and k coefficients, respectively, for

1

2

the first and second periods, according to kinetic Eqs.
(1) and (2). Critical values of moisture (x ) and time

wc

(t ) that separate these periods were obtained from the

c

straight-line intersection. Table 1 shows the kinetic
parameters obtained for all drying conditions. In all
linear regressions

r was greater than 0.96.

2

For

tGt :

c

y

k Øt

(

)

1

x

x Øe

(1)

s

w

wo

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G.R. Dıaz et al. / Innovative Food Science and Emerging Technologies 4 (2003) 203–209

´

Table 1
Values of kinetic constants and critical times and moisture contents obtained for each drying condition

Microwave power

(Wyg)

k

(min )

y

1

1

k

(min )

y

1

2

x

(d.b.)

wc

t

(min)

c

x

(d.b.)

wf

S.E.

0

y

0.0031

y

0.014

0.605

653

0.14

2.85

0.17

y

0.0120

y

0.033

0.888

127

0.13

0.38

0.36

y

0.0209

y

0.038

0.876

72

0.10

0.20

0.69

y

0.0324

y

0.076

1.005

44

0.11

0.21

0.88

y

0.0453

y

0.085

1.038

29

0.14

0.21

2

8

x yx calc.

Ž

.

i

i

S.E.

y

N

For

tFt :

c

y

k tyt

(

(

))

2

c

x sx Øe

(2)

w

wc

Values of kinetic constants and critical time were

correlated with the applied MW power, expressed per
mass unit of product. The following Eqs.

(3) and (4)

obtained by linear regression, allow us to explain a high
percentage of the total variance. In Eqs.

(3) and (4),

k

and

k

were the

k and k values obtained in air

01

02

1

2

drying, without applying MW. Although the standard
deviation of

k

and

k

are higher than those of other

01

02

k , this fact does not imply a great error in predictions

i

due to their very small values when compared with the
other

k . Model predicts a linear increase in kinetic

i

constants in line with the MW power level, whereas an
inversely proportional

(hyperbolic) relationship was

deduced between critical time, from which moment
forwards the drying rate falls sharply, and the applied
MW power.

k yk sbØ

(P ym )

(3)

1

01

i

o

k yk sgØ

(P ym )

(4)

2

02

i

o

a

t s

(5)

c

P ym

Ž

.

i

o

where

P is the applied MW power

(W), m the sample

i

o

initial weight

(g),

a

s

23.584 W min

yg,

b

s

0.047 g

y

Wmin,

g

s

0.082 g

yWmin, and critical time

(t ) and k

c

i

are, respectively, in min and min

.

y

1

In Fig. 2a, lines represent the predicted drying curves,

by applying Eqs.

(1)–(5) at each MW power level. A

close fit can be observed which was quantified through
standard error

(S.E.) of the model shown in Table 1 for

each drying condition. The higher the power level, the
closer the fit of the model.

Rehydration experiments were performed to obtain

the sample moisture uptake and also the decrease of
soluble solids. In this sense, the solute concentration in

the rehydrating solution

(RS) was followed through

refractometry, as well as the solution weight losses
during sample manipulation at each control. Applying
mass balances for water and solutes

(Eqs. (6) and (7))

the water gain

(DM ) (Eq. (8)) and solute loss (DM )

w

s

(Eq. (9)) of the samples were deduced at each time, as
well as the moisture and solute contents. At the end,
sample analysis was carried out to check balances. In
Eq.

(6) and Eq. (7), weight changes were always

referred per initial sample dry matter, according to Eq.
(8) to Eq. (11).

D

M

s

D

M qDM

(6)

w,RS

w

w,L

D

M

s

D

M qDM

(7)

s,RS

s

s,L

being,

t

t

o

o

m Øx ym Øx

w

w

D

M s

(8)

w

o

o

m Ø 1yx

Ž

.

w

t

t

o

o

m Øx ym Øx

s

s

D

M s

(9)

s

o

o

m Ø 1yx

Ž

.

w

t

t

o

o

m Ø 1yy ym Ø 1yy

Ž

.

Ž

.

RS

s

RS

s

D

M

s

(10)

w,RS

o

o

m Ø 1yx

Ž

.

w

t

t

o

o

M Øy ym Øy

RS

s

RS

s

D

M

s

(11)

s,RS

o

o

m Ø 1yx

Ž

.

w

t

t

t

D

m Ø 1yy

Ž

.

s

8

ts0

D

M

s

(12)

w,L

o

o

m Ø 1yx

Ž

.

w

t

t

t

D

m Øy

s

8

ts0

D

M s

(13)

s,L

o

o

m Ø 1yx

Ž

.

w

Where:

207

G.R. Dıaz et al. / Innovative Food Science and Emerging Technologies 4 (2003) 203–209

´

Fig. 3. Water gain and soluble solid loss in rehydration experiments for the different MW power applied in drying.

m:

mass

(g)

x:

mass fraction of component

i

(water or solutes) in

sample

y:

mass fraction of component

i

(water or solutes) in

rehydrating solution.

Subscripts:

s:

soluble solids,

w: water, RS: rehydrating solution,

L: rehydrating liquid losses during sample handling.

Superscripts:

t: at time t, 0: at initial time

D

m :

t

difference between the total mass

(sample plus solu-

tion

) at the time t and the total mass at the previous

control time, which corresponds to the liquid lost be-
tween two successive controls.

Fig. 3 shows the water gain and solute loss of the

samples dried by different treatments as a function of
the rehydration time. No clear tendencies concerning
rehydration rate or asymptotic values were observed as
a function of the MW power, although samples treated
with 0.36 W

yg seem to show lesser water gains and

solute losses at long rehydration times. Nevertheless,
this result might not be significant since it corresponds
to an isolated result at intermediate MW power level.
On the other hand, the two experimental series carried
out at 0.69 W

yg show experimental values that cover

practically the complete range of variation at a deter-
mined time. The water absorption capacity

(g of gained

water per g of water lost during drying

) range between

0.62 and 0.77 without clear tendencies as a function of
the MW power applied. In the same sense the soluble
solid retention

(g of soluble solids in dehydrated sample

per g of soluble solids in dried sample

) was 0.6"0.2.

In Fig. 4, the development of water and soluble solid

contents

(d.b.) as a function of rehydration time can be

observed. Experimental values at long dehydration cover
a wide range but, as commented on above, no clear
tendencies as a function of applied MW power were

observed. Treatment at the highest power level showed
the highest values of soluble solid loss, whereas the
samples dried by hot air seems to show the highest
values of water uptake.

Table 2 shows the initial moisture content of dried

samples as well as the parameters obtained from fitting
the Peleg’s (Eq.

(14) and Eq. (15)) and Weibull’s (Eq.

(16)) models (Hahn & Shapiro, 1967; Peleg, 1988;
Cunha, Oliveira & Oliveira, 1998

) to rehydration data,

in terms of water and soluble solid contents, for the
different drying conditions and for all data obtained in
different conditions grouped. Both models were fitted
by a non-linear procedure

(using SOLVER from

EXCEL97

) and the standard error (S.E.) estimated

either in the individual fittings or in the fitting or
grouped data are shown in Table 2. The close fit of both
models can be seen through the low values of S.E.,
even when considering data from all treatments together.

t

o

x t sx q

(14)

Ž .

w

w

k qk Øt

1

2

where,

1

o

x sx q

(15)

we

w

k

2

a

B

B

B

E EE

t

o

o

C

C C F FF

x t sx q x yx Ø 1yexp y

(16)

Ž .

Ž

.

w

w

we

w

D

D

D

G GG

b

Where

x smoisture content initial

(d.b)

o

w

x

(t)smoisture content (d.b.)

w

x smoisture equilibrium

(d.b)

we

208

G.R. Dıaz et al. / Innovative Food Science and Emerging Technologies 4 (2003) 203–209

´

Fig. 4. Moisture contents and soluble solid contents reached during rehydration experiments for different MW power applied in drying

(experi-

mental points and fitted models

). Horizontal lines show the equilibrium moisture content predicted by the models.

Table 2
Parameter of rehydration obtained from fitting of Peleg and Weibull equations for moisture and soluble solid content date

W

yg

D

M

wmax

x

(d.b.)

wo

x

(d.b.)

1

we

k

1
1

k

1
2

S.E.

a

2

b

2

x

(d.b)

2

we

S.E.

Water
0

3.1

0.18

7.4

1408

0.13

0.22

0.62

193.5

7.4

0.11

0.17

2.9

0.12

6.5

1060

0.15

0.18

0.64

116.9

6.3

0.02

0.36

2.5

0.07

4.8

1721

0.20

0.11

0.72

102.1

4.4

0.12

0.66

3.0

0.15

7.2

2163

0.14

0.29

0.60

341.9

7.6

0.04

0.66*

2.9

0.15

5.9

1336

0.17

0.34

0.50

235.6

6.5

0.18

0.88

3.0

0.07

6.2

1709

0.16

0.18

0.62

205.3

6.2

0.01

Group

2.9

0.16

6.9

1761

0.14

0.47

0.59

183.3

6.6

0.40

W

yg

D

M

smax.

x

(d.b.)

so

x

(d.b.)

1

se

k

1
1

k

1
2

S.E.

a

2

b

2

x

(d.b)

2

se

S.E.

Soluble solid content
0

y

0.53

0.58

0.09

y

20918

y

2.03

0.02

0.65

180.4

0.11

0.01

0.17

y

0.48

0.57

0.12

y

14278

y

2.22

0.022

0.83

89.24

0.17

0.02

0.36

y

0.41

0.52

0.15

y

18464

y

2.68

0.012

0.81

98.0

0.19

0.01

0.66

y

0.52

0.57

0.04

y

26478

y

1.91

0.03

0.64

252.5

0.05

0.02

0.66

*

y

0.44

0.57

0.19

y

21223

y

2.66

0.03

0.51

212.4

0.17

0.03

0.88

y

0.45

0.62

0.29

y

19297

y

3.02

0.01

0.59

122.6

0.30

0.004

Group

y

0.55

0.58

0.12

y

16993

y

2.10

0.04

0.48

230.0

0.18

0.03

Replicate.

*

k sconstant

(s )

y

1

1

k sconstant

2

a

s

shape parameter

b

s

rate parameter

tstime

(s)

From the obtained data it can be concluded that drying
conditions tested did not influence the rehydration
capacity of orange slices and so, this index did not
indicate notable differences in sample quality. Water and
soluble content predictions could be made with a similar
error by using Peleg’s or Weibull’s models and the
parameters obtained from the respective fitting of data
from all experimental conditions together. Similar results

were reported by Funebo and Ohlsson

(1998) and

Maskan

(2000) for microwave assisted drying of apple,

mushrooms and banana slices. Nevertheless, Drouzas
and Schubert

(1996) observed that microwave–vacuum

dried banana slices absorbed twice as much as moisture
than the one conventionally dried.

4. Conclusion

Despite the low levels of MW power used, a sharp

reduction in drying time of orange slices was obtained
when these were applied in combination with air drying
at 60 8C. Kinetic constants increase linearly with the
applied MW power, whereas time required to reach

209

G.R. Dıaz et al. / Innovative Food Science and Emerging Technologies 4 (2003) 203–209

´

critical moisture content decreases inversely proportional
to MW power. Additionally, no differences in rehydrat-
ing behaviour were observed as a function of the applied
MW power. So, the highest level, which was limited to
avoid sample browning, will be recommended to reduce
the drying time.

Acknowledgments

Authors thank the Commission Interministerial de

Ciencia y Tecnologıa

(Spain) and CYTED program for

´

the financial support.

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