Thin-layer modelling of the convective, microwave, microwave-convective and microwave-vacuum drying of lactose powder.pdf

Journal of Food Engineering 72 (2006) 113–123

www.elsevier.com/locate/jfoodeng

Thin-layer modelling of the convective, microwave,

microwave-convective and microwave-vacuum

drying of lactose powder

W.A.M. McMinn *

Food Process Engineering Research Group, School of Chemical Engineering, Queens University Belfast,

David Keir Building, Stranmillis Road, Belfast BT9 5AG, UK

Received 5 August 2004; accepted 11 November 2004

Available online 22 December 2004

Abstract

Lactose-water samples were dried under selected convective, microwave, microwave-convective and microwave-vacuum condi-

tions in an experimental system (2.45 GHz, 90W). Irrespective of the drying technique, a typical drying proﬁle, with a constant dry-

ing rate stage followed by two falling rate periods, was exhibited. The magnitude of the drying rate, however, was dependent on the

convective air temperature and velocity, and system pressure. The experimental moisture loss data were ﬁtted to selected semi-

theoretical and empirical thin-layer drying equations. The mathematical models were compared according to three statistical param-

eters, i.e. reduced chi-square, root mean square error and residual sum of squares. The drying characteristics were satisfactorily

described by the Page, Logarithmic, Chavez-Mendez et al. and Midilli et al. models, with the latter providing the best representation

of the experimental data.

Keywords: Convective; Drying; Lactose; Powder; Thin-layer models; Microwave; Vacuum

1. Introduction

correlations and models, veriﬁed by experimental data,

will enable engineers and operators to provide optimum

solutions to aspects of drying operations such as energy

use, operating conditions, process control, without

undertaking experimental trials on the system ( Dincer,

1998 ). In particular, thin-layer equations contribute to

the understanding of the heat and mass transfer phe-

nomena, and computer simulations, for designing new

processes and improving existing commercial operations

( Kardum, Sander, & Skansi, 2001 ).

Thin-layer drying models can be categorised as theo-

retical, semi-theoretical and empirical ( Parti, 1990 ).

Models within the latter two categories consider only

external resistance to moisture transfer ( Panchariya,

Popovic, & Sharma, 2002 ) and neglect the eﬀect of a

variation in sample temperature on the drying process

( Parti, 1993 ).

Quantitative understanding of drying operations is of

great practical and economic importance. An under-

standing of the fundamental mechanisms, and knowl-

edge of the moisture and temperature distributions

within the product, is crucial for process design, quality

control, product handling and energy savings. A number

of complex theoretical models to describe the heat and

mass transfer phenomena during drying are available.

However, both design and process engineers involved

in industrial drying operations clearly need simple, but

accurate, analytical tools, in order to conduct design

analysis and relevant calculations. Availability of such

* Tel.: +44 28 9027 4065; fax: +44 28 9038 1753.

E-mail address: w.mcminn@qub.ac.uk

doi:10.1016/j.jfoodeng.2004.11.025

114

W.A.M. McMinn / Journal of Food Engineering 72 (2006) 113–123

Nomenclature

a, b, c, g, h, L 1 , L 2 , n constants

k, k 1 , k 2 drying rate constants (min 1 )

MR moisture ratio

MR exp,i experimental moisture ratio

MR pre,i predicted moisture ratio

N number of experimental data points

n p number of parameters in model

R residual error

R c maximum drying rate (kg m 2 s 1 )

RMSE root mean square error

RSS residual sum of squares

t time (min)

t total total drying time (min)

X moisture content at time t (kg kg 1 , dry solid)

X e equilibrium moisture content (kg kg 1 , dry

solid)

X 0 initial moisture content (kg kg 1 , dry solid)

v 2

Semi-theoretical models oﬀer a compromise between

theory and ease of use. The models are generally derived

by simplifying general series solutions of Ficks second

law and are only valid within the drying conditions for

which they have been developed ( Fortes & Okos,

1980 ). However, they require short time, as compared

with theoretical thin-layer equations, and do not require

assumptions regarding sample geometry, mass diﬀusiv-

ity and conductivity. Such models include the Lewis

(1921) , Page (1949) , Henderson and Pabis (1961) ,

Two-Term ( Sharaf-Eldeen, Blaisdell, & Hamdy, 1980 ),

Approximation of Diﬀusion ( Yaldiz & Ertekin, 2001 ),

and Midilli, Kucuk, and Yapar (2002) equations.

Empirical models, which derive a direct relationship

between moisture content and drying time, neglect the

fundamentals of the drying process and have parameters

with no physical meaning ( Ozdemir & Devres, 1999 ).

Among them, the Wang and Singh (1978) and Chavez-

Mendez, Salgado-Cervantes, Garcia-Galindo, De La

Cruz-Medina, and Garcia-Alvarado (1995) have found

application in literature.

Although thin-layer equations have been widely used

to describe experimental convective drying data, appli-

cation to microwave-assisted drying operations is more

limited. Prabhanjan, Ramaswamy, and Raghavan

(1995) assessed the ability of the Lewis and Page equa-

tions to characterise the experimental drying curves for

microwave-assisted convective air drying of carrots,

and reported that only the Page model adequately de-

scribed the data. Kiranoudis, Tsami, and Maroulis

(1997) represented the microwave-vacuum drying kinet-

ics of fruits using an one-parameter empirical mass

transfer model of exponential form, and further indi-

cated that the magnitude of the drying constant was

dependent on the vacuum pressure and microwave

power of the system. Drouzas, Tsami, and Saravacos

(1999) modelled the microwave-vacuum drying kinetics

of model fruit gels using the Lewis thin-layer drying

equation, and further proposed an empirical correlation

to estimate the drying rate constant as a function of the

absolute pressure and microwave power of the system.

Kardum et al. (2001) reported that the microwave dry-

ing kinetics of a pharmaceutical product was adequately

described by the Lewis and Page models, with the latter

providing a better correlation with the experimental

data. Abdelghani-Idrissi (2001) approximated the tran-

sient behaviour of normalised moisture during the

microwave heating of cement powder by an exponential

evolution with a time constant.

Previous work by McLoughlin, McMinn, and Magee

(2003a, 2003b) , and McMinn, McLoughlin, and Magee

(in press) involved extensive experimental examination

of the convective, microwave, and combined micro-

wave-convective and microwave-vacuum drying behav-

iour of lactose powder. Using the acquired data, the

aim of this work is to assess the ability of selected

thin-layer based drying models to quantify the moisture

removal behaviour.

2. Materials and methods

2.1. Equipment

The atmospheric microwave drying system used in

this work is a standard microwave oven (Brother, Hi-

speed cooker, Model No. MF 3200 d13) of variable

power output settings (650, 500, 250, 90 and 30 W)

and a rated capacity of 650W at 2.45 GHz. The equip-

ment was modiﬁed to facilitate microwave-convective

processing. A precisely dimensioned duct, ﬁtted with a

fan and a heater, was attached to the side of the oven.

The air velocity (0–1.0 ± 0.05 m s 1 ) and temperature

(20–100 ± 5 C) are controlled by means of analogue

controllers. The system was also modiﬁed to allow for

microwave-vacuum drying. A glass dessicator was posi-

tioned inside the microwave cavity, to which a vacuum

pump was attached. The vacuum level is controlled

(0–101 kPa (absolute)) by means of an actuator valve

and released using a vent valve. Further details on the

equipment are outlined in McLoughlin et al. (2003a,

2003b) and McMinn et al. (in press) .

reduced chi-square

W.A.M. McMinn / Journal of Food Engineering 72 (2006) 113–123

115

2.2. Experimental method

2.3. Data analysis

The drying characteristics of lactose powder during

convective, microwave (90W), microwave-convective

and microwave-vacuum processing were examined.

Before each experimental run, the microwave oven was

preheated at full power (650W) for 5 min using a

500 ml water load ( Lu, Tang, & Ran, 1999 ) and the con-

vective system allowed to stabilise, at the selected condi-

tion, for 10min. A water load (approximately 75 g) was

placed in the microwave cavity to provide a heating load

suNcient to protect the magnetron from overheating,

especially during the latter stages of drying. For each

experiment, a water-wetted lactose sample of 1.0kg

kg 1 db (dry basis, water) was prepared, and placed in

a glass dish in the oven. At 5-min intervals throughout

the drying process (until material had attained at least

95% moisture loss) the sample was removed, weighed,

and then agitated for 15 ± 1 s. This procedure was

adopted to investigate the eﬀect of product and process-

ing characteristics on the drying behaviour, as summa-

rized in Table 1 . Each experiment was performed in

triplicate. Further information on the experimental

procedures is detailed in McLoughlin et al. (2003a,

2003b) and McMinn et al. (in press) .

The experimental moisture content data were non-

dimensionlized using the equation:

MR ¼ X X e

X 0 X e

ð 1 Þ

where MR is the moisture ratio; X 0 is the initial moisture

content (kg kg 1 , dry solid); X e is the equilibrium mois-

ture content (kg kg 1 , dry solid), and X is the moisture

content at time t (kg kg 1 , dry solid).

For the analysis it was assumed that the equilibrium

moisture content, X e , was equal to zero.

Selected thin-layer drying models, detailed in Table 2 ,

were ﬁtted to the drying curves (MR versus time), and

the equation parameters determined using non-linear

least squares regression analysis.

Three criteria were adopted to evaluate the goodness

of ﬁt of each model, the reduced chi-square (v 2 ), root

mean square error (RMSE) and residual sum of squares

(RSS). These parameters were calculated using ( Sun &

Byrne, 1998 ; Togrul & Pehlivan, 2003 ):

v 2 ¼ P i ¼ 1 ð MR exp ; i MR pred ; i Þ 2

N n p

ð 2 Þ

Table 1

Summary of experiments

Experimental

parameter

Dry mass

· 10 3 (kg)

Surface area

· 10 3 (m 2 )

Depth

· 10 3 (m)

Microwave

power (W)

Air velocity

(m/s)

Air temperature

(C)

Pressure

(kPa)

Convective

Air temperature

6.36

–

0.7

101

Microwave

Bed depth/surface area

6.36

–

101

100

6.36

15.4

100

57.3

Microwave–convective

Air velocity/temperature

0.4

0.7

6.36

0.7

101

0.7

Bed depth/surface area

6.36

15.4

0.7

101

100

57.3

Microwave-vacuum

Pressure

6.36

–

116

W.A.M. McMinn / Journal of Food Engineering 72 (2006) 113–123

Table 2

Thin-layer models ﬁtted to experimental data

Model

Mathematical expression

Lewis ( Lewis, 1921 )

MR = exp( kt)

Page ( Page, 1949 )

MR = exp( kt n )

Henderson and Pabis ( Henderson and Pabis, 1961 )

MR = aexp( kt)

Modiﬁed Henderson and Pabis ( Karathanos, 1999 )

MR = aexp( kt)+bexp( gt)+cexp( ht)

Logarithmic ( Yaldiz and Ertekin, 2001 )

MR = aexp( kt)+c

Two-Term ( Sharaf-Eldeen et al., 1980 )

MR = aexp( k 1 t)+bexp( k 2 t)

Wang and Singh ( Wang and Singh, 1978 )

MR=1+at + bt 2

Approximation of Diﬀusion ( Yaldiz and Ertekin, 2001 )

MR = aexp( kt)+(1 a)exp( kbt)

Chavez-Mendez et al. (Chavez-Mendez et al., 1995)

MR ¼½ 1 ð 1 L 2 Þ L 1 t ð 1 =ð 1 L 2 ÞÞ

Midilli ( Midilli et al., 2002 )

MR = aexp( kt n )+bt

# 0 : 5

1.4

ð MR exp ; i MR pred ; i Þ 2

RMSE ¼

ð 3 Þ

1.2

Mw Mw-V (80kPa)

Mw-C (60°C) C (60°C)

Mw-C (20°C) C (20°C)

i ¼ 1

1.0

RSS ¼ X

ð MR exp ; i MR pred ; i Þ 2

ð 4 Þ

0.8

i ¼ 1

0.6

where MR exp,i is the experimental moisture ratio;

MR pred,i is the predicted moisture ratio; N is the number

of experimental data points, and n p is the number of

parameters in model.

The lower the calculated values of reduced chi-square

and root mean square error, the better the ability of the

model to represent the experimental data. The reduced

chi-square accounts for the number of constants in the

model, with the magnitude of this parameter giving a

measure of the reliability of the model to describe the

experimental data, irrespective of the number of param-

eters ( Panchariya et al., 2002 ). These statistical parame-

ters have been widely used as the primary criterion to

select the best equation to account for variation in the

drying curves of dried samples ( Ertekin & Yaldiz,

2004 ; Ozdemir & Devres, 1999 ; Sarsavadia, Sawhney,

Pangavhane, & Singh, 1999 ). The residual sum of

squares value is an important parameter in the non-

linear regression process, with the ﬁtting procedure

being designed to achieve the minimum RSS ( Sun &

Byrne, 1998 ).

0.4

0.2

0.0

0.2

0.4

0.6

0.8

1.0

Moisture Content (kgkg -1 , dry basis)

Fig. 1. Drying characteristics of water wetted lactose dried under

selected processing conditions [Mw—microwave; Mw-C—microwave-

convective; Mw-V—microwave-vacuum].

dried using convective, microwave and microwave-

convective processing exhibiting a secondary moisture

content of 0.36 kg kg 1 db. This is reduced to 0.14 kg

kg 1 db during microwave-vacuum (80kPa) operation.

The observed decrease may be attributed to the corre-

sponding reduction in solvent boiling point, and the

pulling eﬀect of the vacuum, which draws the solvent

out of the material pores. The magnitude of the maxi-

mum drying rate, drying rate constants and drying time

are, however, speciﬁc to the method of moisture re-

moval. Table 3 provides a summary of the maximum

drying rate (R c ) and total drying time (t total ) for all con-

vective, microwave, microwave-convective and micro-

wave-vacuum conditions examined. It should be noted,

however, that during microwave-vacuum processing at

less than 80kPa, material loss occurred at low moisture

contents, so kinetic data is available for the initial stages

only.

Ambient temperature (20 C) convective drying

exhibits the slowest drying rate, with the reduction in

rate between the constant and falling stages being rela-

tively indistinguishable. As expected, the drying rate

can be enhanced, and hence drying time lowered, by

increasing the air temperature; an increase in constant

drying rate of approximately 150%, from 0.26 to

3. Results and discussion

3.1. Drying characteristics

Representative drying rate curves for lactose-water

samples dried under convective (C) (20and 60C air),

microwave (Mw), microwave-convective (Mw-C) (20

and 60 C air) and microwave-vacuum (Mw-V)

(80kPa) conditions are shown in Fig. 1 . In general, four

distinct periods are identiﬁable, namely a warming-up,

constant rate and two falling rate periods. Irrespective

of the drying technique, a critical moisture content of

0.54 kg kg 1 db (dry basis) is observed, with samples

W.A.M. McMinn / Journal of Food Engineering 72 (2006) 113–123

117

Table 3

Comparison of maximum drying rate (R c ) and drying time (t total ) for convective, microwave-convective and microwave-vacuum drying of lactose

powder

Dry mass · 10 3

(kg)

Surface area · 10 3

(m 2 )

Depth · 10 3

(m)

Microwave

power (W)

Air temperature

(C)

Air velocity

(ms 1 )

Pressure

(kPa)

R c (·10 3 kg m 2 s 1 ) t total (min)

Convective

101

0.26

270

6.36

–

0.7

101

0.46

140

101

0.66

Microwave

6.36

0.18

190

6.36

0.70

175

6.36

–

101

0.72

210

100

6.36

0.88

370

15.4

0.38

175

100

57.3

0.19

185

Microwave-convective

0.4

101

0.68

140

6.36

0.7

101

0.80

120

0.7

101

0.97

0.7

101

1.12

6.36

0.54

15.4

0.7

101

0.62

100

57.3

0.38

Microwave-vacuum

–

1.36

–

6.36

–

1.17

–

0.98

105

0.66 · 10 3 kg m 2 s 1 , is achieved by elevating the air

temperature from 20to 60C.

The use of microwave-only drying provides a slight

elevation in the maximum drying rate, as compared with

high temperature convective processing (0.66 · 10 3

kg m 2 s 1 for convective at 60 C and 0.70 · 10 3

kg m 2 s 1 for microwave). With the subsequent

introduction of air over the sample surface, i.e. micro-

wave-convective drying, the microwave drying rate is in-

creased. Again this can be further elevated by increasing

the air temperature (60 C). Air temperature, however,

has a less signiﬁcant aﬀect during microwave-convective

operation than convective-only. In the former process, a

reduction in drying time of approximately 17%, from 90

to 75 min, is achieved by increasing the air temperature

from 40to 60C. However, in convective drying, the

drying time is decreased by approximately 32%, with

the same temperature elevation. Thus, increasing air

temperature during microwave-convective drying is less

energy eNcient than during convective drying. During

microwave-convective operation, the velocity of the air

also has a relatively limited impact on the drying behav-

iour. Drying times of 140and 120min were observed

with the use of 0.4 and 0.7 m s 1 air, respectively.

Microwave-vacuum drying is found to provide drying

times comparable with those observed during high tem-

perature microwave-convective processing. The maxi-

mum drying rate increases signiﬁcantly as the system

pressure decreases from 101 to 30 kPa; lowering of sys-

tem pressure is accompanied by a decrease in water

evaporation temperature. Consequently, a reduction in

system pressure from 101 to 80 kPa oﬀers a reduction

in drying time of more than 38%, from 170to 105 min.

The drying characteristics are also observed to be

dependent on the bed dimensions, with an increase in

depth and decrease in surface area, in general, providing

enhanced drying rates. The extent of the rate elevation

is, however, dictated by the sample geometry and pro-

cessing technique (microwave, microwave-convective).

A more detailed characterisation of the drying behav-

iour of lactose-water samples subjected to convective,

microwave and combined microwave-convective and

microwave-vacuum drying is presented in McLoughlin

et al. (2003a, 2003b) and McMinn et al. (in press) .

3.2. Model application

Thin-layer models have found wide application due

to their ease of use and lack of required data, such as

phenomenological and coupling coeNcients, as in com-

plex theoretical models. Many correlations are avail-

able in the literature, with those included in this study

( Table 1 ) being selected as they represent some of the

more commonly adopted. Although other models were

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