Drying kinetics of skimmilk solution is investigated in thiswork. Dry oven method used to determine the characteristic drying curves. The experiments are carried out at two temperatures of 45Cand 60C and three different initial solid contents. The
ull Paper
Experimental study of drying kinetics of skim milk
M.S.Hatamipour*, A.Rahimi, M.Sadripour
Department of Chemical Engineering, Faculty of Engineering, University of Isfahan,P.O. Box 8174673441, Isfahan, (IRAN)Email : hatami@eng.ui.ac.ir
Received: 15
th
August, 2010 ; Accepted: 25
th
August, 2010
CTAIJ 6(1) 2011 [15]
An Indian Journal
Trade Science Inc.
Volume 6 Issue 1
chemical technologychemical technology
ISSN : 0974  7443
KEYWORDS
Drying kinetics;Skim milk;Characteristic moisturecontent.
ABSTRACT
Drying kinetics of skim milk solution is investigated in this work. Dry ovenmethod used to determine the characteristic drying curves. The experiments are carried out at two temperatures of 45
!
C and 60
!
C and three different initial solid contents. The obtained characteristic curves for drying rateare normalized, based on a simple mass transfer model in which the dryingrate is considered as a first order reaction. These normalized curves areindependent of temperature and initial concentration and coincide together.The obtained experimental data are applied to identify a simple mass transfer model parameter. Finally a relative humidity factor f, is obtained as afunction of
"
, characteristic moisture content. This model can be used inCFD modeling of spray dryers for simple and efficient calculations.
#
2011 Trade Science Inc.  INDIA
INTRODUCTION
Dehydration operations are important steps inchemical and food processing industries. Regarding thisfact, drying technologies along with better control andoperational strategies have contributed to a better quality dried products. Spray drying is a wellknown methodfor drying that nowadays covers large number of applications for products ranging from food to mineral oresand chemicals. It is the core component of a milk powder production plant. The moisture content of milk powder is one of the predominant factors for preserving thequality of the product
[5]
. There is a great need for drying models to describe the drying process which helpsin its optimization and can be useful in effective designof dryers or improve existing drying systems
[7]
. A drying process can be described completely by using anappropriate drying model, which usually includes differential equations of heat and mass transfer in the interior of the product and at its interphase with the dryingagent
[9]
. Having mixed a mass transfer model with theknowledge of the drying kinetics, the calculation mightbe simple and efficient.
Drying kinetics of the productsare the most important required data for design andsimulation of air dryers
[3]
. Also these models can beused in CFD software to reduce calculations andachieve more realistic performance.In fact characteristic drying curve which expressesthe time history of temperaturemoisture content couldbe used to propose a mass transfer model
[6]
. In therecent years, several investigations have been conductedon the drying kinetics of different food and chemicalmaterials. There have been more than 200 drying kinetics models offered for various foods in the literature, which are formally characterized by two differentphysical and empirical approaches
[7]
. But the existing
Experimental study of drying kinetics of skim milk
2
ull
Paper
CTAIJ, 6(1) 2011
An Indian Journal
chemic l technologyhemic l technology
differences among the model formulations can be considerable. Chen & Lin
[2]
have studied air drying of milk droplet under constant and timedependent conditions.An attempt has been made to examine two significantmodels in a more comprehensive manner. One modelis the characteristic drying rate curve approach and theother (new) model is the reaction engineering approach.The model predictions are compared against a very widerange of experimental results including isothermal andtimevarying temperature conditions
.
Both models predict and cover the experimental results reasonably well.Besides, the results indicated that the reaction engineering approach model is better than the others. The characteristic drying rate curve approach assumes beforehand the falling rate in all kinds of conditions for milk droplet drying, whereas the reaction engineering modelsimply reflects the experimental results closely. Zbicinskiet al.
[8]
have developed a method for measuring dryingkinetics of different products in a dispersed system. Theyused phase doppler anemometry (PDA) technique todetermine initial spray atomization parameters, the structure of spray during drying, particle size distribution,velocity of the particles and mass concentration of theliquid phase, etc.The main objective of this research is to formulatean accurate model for analyzing the simulated dryingkinetics of skim milk samples based on a good fit onthe corresponding moisture content. This kinetics modelis to be used in CFD modeling of a spray dryer usedfor skim milk drying to reduce computational time andaccurate calculations. For determination of drying kinetics, the dry oven method is much easier and its duration may vary considerably depending on the dryingtemperature. The range of the studied parameters wasnear to those used in industrial spray dryers.
THEORY
The drying kinetics is greatly affected by air temperatures, initial and instant moisture content and airhumidity. A masstransfer model can be introduced byusing a characteristic drying curve. This approach assumes that there is a corresponding specific drying raterelative to the unhindered drying rate in the first dryingperiod on each volumeaveraged free moisture contentthat is independent of the external drying conditions
[6]
.The mass transfer between the gas and droplet couldbe calculated according to the following first order reaction kinetics:
)YY(KfA
dtam
egpp
(1)
where in eq. (1) A
p
is the surface of mass transfer,
e
Y
and Y
$
are the equilibrium moisture and air humidityrespectively. Also K
g
is the mass transfer coefficientthat can be obtained from eq. (2) with suitable coefficient values for
%
,
&
,
'
and
'
and
f is the relative dryingrate and is defined as eq. (3).
$
&'(#
ScResh
(2)
RDDRf
!
(3)
where DR is the drying rate and defines in eq. (4), DRis the rate in the first drying period.
1212
ttxxDR
"
(4)
where x is the moisture content (kg
H2O
/kg dry solid)and
t
is drying time between two successive steps. Parameter f takes on the values in Eq. (5)
[4]
.Unhindered moisture
f = 1;
)*
1(5)
Hindered moisture
0 < f < 1; 0<
)
< 1<
"
, so called characteristic moisture content, and defined in terms of critical moisture content
[4]
.
ecre
xxxx
"
#
(6)
where, x
e
is the equilibrium moisture content and x
cr
isthe critical moisture content. A unique relationship between f and
"
can be found for any specific material.The drying curve is normalized and at critical point,there is a transition in drying behavior. By definition of correction factor f, a simple lumpedparameter expression for the drying rate can be obtained.
MATERIALS AND METHODS
Skim milk solutions with three different initial solidcontents of 0.05, 0.1 and 0.15 (w/w) were preparedby adding water to milk powder at 24
!
C for experiments. The concentrated milk samples then were pouredinto a glass plate with 6 cm diameter.The experimental setup was consisted of a dryingoven (Fan Azma Gastar) with On/Off control and digi
M.S.Hatamipour et al.
3
ull
Paper
chemical technology
CTAIJ, 6(1) 2011
An Indian Journal
chemic l technology
Figure 1 : Drying curves of skim milk solutionsFigure 2 : Effect of drying temperature on drying timeFigure 3 : Drying rate curve at different initial solid contentFigure 4 : Drying rate curve at different initial solid contentFigure 5 : Drying rate curve vs. x for different of initial solidcontentFigure 6 : Drying rate curve vs. x for different of initial solidcontent
tal indicator. For each experiment, changes in weight of sample were measured continuously using a digital balance (Sartorius BP 310s model) with an accuracy of
(
0.001 gr. The balance was kept outside the oven andthe sample was placed on a special sample holder whichwas hung from the balance. The drying oven was calibrated for temperature using a calibrated thermometer.In order to obtain an accurate and uniform temperatureinside the oven, intensive air ventilation was used. Allthe required data were recorded every 15 min. To determine the equilibrium weight at a specified temperature, the samples were kept in the oven until the difference between two successive mass measurements became less than 0.02 g.Before putting any sample into the oven the dryingair temperature was fixed. It was assumed that the thickness of the milk solution sample is quite thin, so that theconditions of the drying air (temperature and humidity)were kept constant throughout the drying process, whilethe relative humidity in the room condition was 16%.To consider the effect of temperature on the rate of drying the experiments were carried out at similar conditions and different temperatures including 45
ºC and
60
ºC.
RESULTS AND DISCUSSIONCharacteristic drying curve
The drying behavior of skim milk solution as a func
Experimental study of drying kinetics of skim milk
4
ull
Paper
CTAIJ, 6(1) 2011
An Indian Journal
chemic l technologyhemic l technology
tion of time is shown in figure 1. It could be seen thatthe drying curve is almost a straight line with a continuous decrease of mass by the passage of time for allconcentrations due to the fact of constant drying rateperiod. At final times, a deviation from the straight linecan be observed which may be explained as the fallingdrying rate period. It also becomes obvious that skimmilk solutions with lower initial concentrations have drying rate curves with higher intercepts.Variations of the moisture content with the dryingtime
at different air temperatures and initial concentrations are plotted also in figure 2. As a result, an increasein the temperature of the drying air decreases the totaldrying time as a result of increasing the rate of heattransfer. Besides, when the temperature increases from45
!
C to 60
!
C, the total drying time decreases to about40% of that for the solution with drying temperature of 45
!
C.
Drying rate curve as a function of time
The drying rate (DR) of the solutions during thedrying process could be obtained by using eq. (4). Figure 3 and 4 show the variation of DR, with time for twodifferent operating temperatures. As a result of the moisture transfer, the drying rate decreases, with elapse of time. Approximately entire drying process took placein the constant rate period. These figures illustrate thatfor a higher air temperature, the drying rate will be increased and drying will take placed at lower times.
Drying rate curve as a function of X
The drying rate curve for skim milk can be obtainedalso by plotting drying rate vs. moisture content (x).Figure 5 and 6 illustrate drying rate curve vs. x for twotemperature of 45
!
C and 65
!
C and initial solid contents of 0.05, 0.1, 0.015 (w/w). These figures showdrying rate curves of the samples at the selected temperatures, where about 8387% of water content wasevaporated at the end of constant rate period of drying,a linear falling rate can be observed at the end of process which is due to very low thickness of sample layers. It may indicate that the resistance to moisture transport is related to the thickness of solution.
Prediction of f
Figure 5 and 6 represent drying rate as a functionof X, according to eq. (1). When the characteristic drying curve became normalized, these curves are independent from the temperature and initial solid content.Figure 7 shows the relative drying rate as a function of
"
. In this figure f
is only a function of
"
. These six curvesat temperature 45
°C and 60°C and initial solid content
of 0.05, 0.1 and 0.15 (w/w) approximately coincidetogether.It is possible to find a relation between relative drying rate f vs characteristic moisture content (
"
). According to the best fitting of six data series of figure 5and 6, eq. (7) can be obtained with R
2
in the range of (9994%).
f = 0.325
)
4
+ 1.83
)
3
–
3.752
)
2
+ 3.27
)
–
0.031
(7)
CONCLUSION
Dry oven method applied for determination of char
Figure 7 : The relative drying rate vs.
)
A particle surface area (m
2
)
DR drying rate (s
1
) f relative drying rate (

) K mass transfer coefficient (kg s
1
) Sh Sherwood number (

) t time (s) T temperature (
!
C) X moisture content (kg moisture kg
1
dry solid) Y' gas humidity (kg kg
1
)
"
characteristic moisture content (

)
Â
,
ç
,
æ
,
î
constant in eq. (3) (

)
Subscripts
cr Critical e Equilibrium G dry bulb, bulk gas
Nomenclature
M.S.Hatamipour et al.
5
ull
Paper
chemical technology
CTAIJ, 6(1) 2011
An Indian Journal
chemic l technology
acteristic drying curve of skim milk solution. Dryingcurves have in general two stages after an initial warmup: constant drying and falling rate periods. Dryingmodels for constant and falling rate period of skim milk solution based on the concept of characteristic dryingrate are proposed, and found a unique relationship between relative drying rate f and characteristic moisturecontent for specific material. This model can be used inCFD software for simple and efficient calculations. Inparticular, the concept of a characteristic drying curvestates that the shape of the dryingrate curve for a givenmaterial is unique and independent of gas temperature,humidity and velocity.Convective drying of skim milk solutions was dependent on temperature, and the drying curve showeda constant rate period; only a short falling rate periodwas observed at the end of process.
REFERENCES
[1]
R.B.Bird, W.E.Stewart, E.Lightfoot; Transport Phenomena
.
New York, John Wiley & Sons,
(1960)
.
[2]
X.D.Chen, S.Lin, X.Q.i; AIChE J.,
51(6)
, 17901799
(2005)
.
[3]
J.Fontaine, C.Ratti; J.Food Proc.Eng.,
22
, 287305
(1999)
.
[4]
R.B.Keey, M.Suzuki; Int.J.Heat and Mass Trans,
17
, 14551464
(1974)
.
[5]
R.J.Knget, H.V.Brink; Int.Dairy J.,
8
, 733738
(1998)
.
[6]
T.A.G.Langrish, T.K.Kockel; Chem.Eng.J.,
84
, 6974
(2001)
.
[7]
B.Yesilata, M.A.Aktacir; Appl.Thermal Eng.,
29
,748752
(2009)
.
[8]
I.Zbicinski, A.Delag, C.Strumillo, J.Adamiec;Chem.Eng.J.,
86
, 207216
(2002)
.
[9]
V.T.Karathanos; J.Food Eng.,
39
, 337344
(1999)
.