Journal of Food Engineering 109 (2012) 701–711

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Journal of Food Engineering

journal homepage: www.elsevier .com/ locate / j foodeng

Drying kinetics of skim milk with 50 wt.% initial solids

Nan Fu a, Meng Wai Woo a, Cordelia Selomulya a, Xiao Dong Chen a,b,⇑, Kamlesh Patel a, Pierre Schuck c,Romain Jeantet c

a Department of Chemical Engineering, Monash University, Clayton, Victoria 3800, Australiab Department of Chemical and Biochemical Engineering, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen City, Fujian 361005, PR Chinac UMR1253, INRA, Agrocampus Ouest, F-35000 Rennes, France

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 May 2011Received in revised form 21 August 2011Accepted 16 November 2011Available online 29 November 2011

Keywords:Single droplet dryingDrying kineticsSkim milkReaction Engineering ApproachHigh initial solids contentGlass filament method

0260-8774/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.jfoodeng.2011.11.018

⇑ Corresponding author at: Department of Chemicaing, College of Chemistry and Chemical Engineering, XSouth Road, Xiamen, Fujian 361005, PR China. Tel.: +82188855.

E-mail addresses: nan.fu@monash.edu (N. Fu), mWoo), cordelia.selomulya@monash.edu (C. SelDong.Chen@monash.edu (X.D. Chen), kamlesh.papierre.schuck@rennes.inra.fr (P. Schuck), romain.jeanJeantet).

Drying kinetics data are of paramount importance for simulating industrial spray drying operations. Thisstudy reports for the first time the drying kinetics of skim milk droplets with 50 wt.% initial solids, as typ-ically encountered in practice. The changes in droplet temperature, moisture content, and diameter wereexperimentally determined using glass-filament single droplet drying technique. Enhanced effects of dry-ing temperature on droplet shrinkage were observed. Experimental data were correlated using the Reac-tion Engineering Approach (REA) with the master activation-energy curve providing a good description tothe drying histories. Activation energy curves obtained here were compared with previous data fromlower initial concentrations, as well as the plot obtained using a preliminary desorption method. The out-comes support the suitability of REA to interpret the drying behavior of skim milk with high initial solidslevel, which is the norm for practical spray drying of milk with feed concentration of around 50 wt.%.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Dry powders in food and pharmaceutical industries are oftenproduced by spray drying to achieve a rapid and convenient dehy-dration process leading to high quality products. Simulation ofsuch spray drying processes requires accurate drying kinetics datafor individual droplets inside the dryer. Single droplet dryingexperiment is capable of providing such kinetics data by dryingan isolated droplet under controlled conditions analogous to spraydrying (Charlesworth and Marshall, 1960; Walton and Mumford,1999). In either process, the moisture is being removed by convec-tion at an elevated air temperature. Although the air temperaturein single droplet drying (70–110 �C) is usually below that appliedin spray dryers, the resultant wet-bulb temperatures are relativelysimilar (Lievense and van’t Riet, 1993). Currently there are threemajor approaches in the single droplet experiment, categorizedby the different means of supporting the droplet during drying.These are free falling droplets inside a tall tower (Kinzer and Gunn,

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l and Biochemical Engineer-iamen University, 422 Siming6 592 2189911; fax: +86 592

eng.woo@monash.edu (M.W.omulya), xdc@xmu.edu.cn,tel@monash.edu (K. Patel),tet@agrocampus-ouest.fr (R.

1951), droplets levitated by acoustic or aero-dynamic fields (Schiff-ter and Lee, 2007a,b), and droplets suspended on the tip of a glassfilament/glass capillary tube (Charlesworth and Marshall, 1960;Cheong et al., 1986; Lin and Chen, 2002). Amongst these ap-proaches, the glass-filament single droplet experiment has beenthe method of choice in many studies (Sano and Keey, 1982;Yamamoto and Sano, 1992; Walton and Mumford, 1999; Che andChen, 2010). A major advantage of this technique is the ease inmonitoring the droplet mass and temperature changes during dry-ing (Adhikari et al., 2000). Recent improvement in the glass fila-ment method utilized three different droplet suspension modulesfor accurate measurements of droplet temperature, diameter, andmass, respectively (Lin and Chen, 2002, 2004; Fu et al., 2011).The kinetics data of dairy materials generated using this techniquehave been used to verify a number of drying models (Chen and Lin,2005; Lin and Chen, 2007; Mezhericher et al., 2007, 2008).

There are several types of drying models to describe the evapo-ration process in droplets and thin slabs, such as the Reaction Engi-neering Approach (REA) modeling (Chen and Xie, 1997; Chen et al.,2001; Chen and Lin, 2005), mathematical models describing com-prehensive transport phenomena (Cheong et al., 1986; Dalmazet al., 2007; Mezhericher et al., 2007, 2008), and the characteristicsdrying rate curve approach (Langrish and Kockel, 2001). REA em-ploys comparatively simpler calculations without involving com-plex partial differential equations, yet still provides accuratedescriptions of drying history (Chen and Xie, 1997; Chen and Lin,2005; Woo et al., 2008). More importantly, regardless of the types

Nomenclature

DEv apparent activation energy of evaporation (J/mol)DHl latent heat of water vaporization (J/kg)A droplet surface area (m2)Cp specific heat capacity at constant pressure (J/(kg K))D droplet diameter (m)h external heat transfer coefficient (W/(m2 K))hm external mass transfer coefficient (m/s)m mass (kg)ms solid mass in one droplet/particle (kg)Nu Nusselt numberPr Prandtl numberR gas constant, 8.314 (J/(mol K))Re Reynolds numberSc Schmidt numberSh Sherwood numbert time (s)

T temperature (K)X average moisture content on dry basis (kg/kg)

Greek lettersw fractionality coefficient, which is in effect the relative

humidity at the interface of the dropletqv vapor density (kg/m3)

Subscripts0 initial valueb bulk aird droplets droplet surface/solid fractionsat saturationv vaporization

702 N. Fu et al. / Journal of Food Engineering 109 (2012) 701–711

of mathematical models used, the behavior of moisture removalfrom different feed materials or different concentrations of thesame material needs to be understood. In this regard, REA consid-ers drying as an activation-energy-based process and establishes amaster relative-activation-energy curve for each material to de-scribe its specific drying behavior. Previous studies have shownthat this material-specific activation energy curve is irrespectiveof the drying air temperature, humidity, velocity, and is minimallyaffected by the initial droplet size in the cases investigated (Chenand Lin, 2005; Lin and Chen, 2005; Fu et al., 2011). This featuremakes REA particularly suitable for modeling the industrial spraydrying processes, during which droplets with varied initial sizesare dried in continuously changing ambient conditions.

Previous experimental studies on the drying kinetics of singlemilk droplet have used lower initial solids concentrations such as20 and 30 wt.% (Chen and Lin, 2005). In actual industrial applica-tions, higher initial concentration, typically 50 wt.%, is oftenadopted (Lin and Chen, 2009). To date, there is no published liter-ature that systematically studies the drying kinetics of milk withsuch a high initial concentration. Drying behavior of higher solidsfeed might be somewhat different from those of the lower initialsolids, due to the possible advanced crust formation during drying.In addition, different surface composition of the milk componentsmay result from the multi-component mass transfer while dryingoccurs. It has been shown that the master activation-energy curveof the REA is sensitive to the initial solids concentration of a givenmaterial (Chen, 2008; Patel et al., 2009). Thus the suitability of REAto interpret drying of milk with high initial solids needs experi-mental verification. In the present study, drying kinetics experi-ments were conducted for skim milk droplets with 50 wt.% initialsolids using the glass-filament method. The obtained dryingbehavior is correlated under the framework of REA. The new acti-vation energy curve obtained here is compared to those reportedfor air-drying of milk with lower initial concentrations.

2. A brief review of the Reaction Engineering Approach (REA)

The Reaction Engineering Approach is a semi-empirical modelthat assumes an ‘‘activation energy barrier’’ between solid andgas phase, which needs to be overcome for drying to occur (Chenand Xie, 1997; Chen et al., 2001). The increasing normalized (or rel-ative) activation energy during drying in effect represents theincreasing difficulty for moisture removal from the material beingdried.

The mathematical expression of REA was derived from a basicconvection drying principle, which used a vapor density differenceto characterize the driving force for the removal of moisture at theinterface between air (the medium of convective drying) and thedroplet being dried:

dmdt¼ �hmAðqv;s � qv;bÞ ð1Þ

where dm/dt is the rate of moisture removal (i.e., drying rate, kg/s),hm is the mass transfer coefficient (m/s), A is the surface area of thedroplet (m2), and qv,s and qv,b represent the vapor density (kg/m3) atthe droplet surface and of the bulk air respectively. During drying,the surface vapor density qv,s will continuously change as dryingprogresses. The surface vapor density qv,s and the saturated surfacevapor density qv,sat can be correlated using the equation below:

qv;s ¼ wqv;satðTsÞ ð2Þ

where w is a fractionality coefficient related to the moisture contentof the droplet being dried, and Ts is the temperature at the interface(K). When the modified Biot number (Chen–Biot number) (Chenand Peng, 2005) is sufficiently small, Ts would be similar to the aver-age droplet temperature Td (K). The fractionality coefficient w, in ef-fect, is the relative humidity at the interface of the droplet beingdried and the bulk air.

The REA model contains a term of ‘‘apparent activation energyof evaporation’’, symbolized as DEv (J/mol), to describe the changesof w during drying using the correlation below (Chen and Xie,1997; Chen and Lin, 2005; Chen, 2008):

w ¼ exp �DEv

RTs

� �ð3Þ

where R is the universal gas constant (8.314 J/(mol K)). Note againhere, Ts is similar to Td. From Eqs. (2) and (3), DEv can be expressedin the following form:

DEv ¼ �RTs lnqv;s

qv ;satðTsÞ

!ð4Þ

Eq. (4) indicates that DEv is actually a reflection of vapor con-centration depression at the interface of the droplet. CombiningEqs. (2) and (3) and substituting them into Eq. (1) leads to the fol-lowing equation:

dmdt¼ �hmA qv;sat exp �DEv

RTd

� �� qv;b

� �ð5Þ

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It can be seen that the apparent activation energy DEv during a dry-ing process can be experimentally determined with the equationbelow, provided that dm/dt, Td and A can be measured:

DEv ¼ �RTd ln�ðdm=dtÞð1=hmAÞ þ qv;b

qv ;sat

!ð6Þ

The apparent activation energy during a drying process can benormalized with the equilibrium or maximum activation energyDEv,b, in the form: DEv/DEv,b (0–1 scale). According to Eq. (1), whenthe surface vapor density qv,s achieves equilibrium with the bulkair vapor density qv,b, drying ceases because of no more drivingforce. At this stage, the dried particle would be heated to environ-mental temperature Tb and the apparent activation energy DEv

achieves maximum, i.e., DEv,b:

DEv;b ¼ �RTb lnqv;b

qv ;satðTbÞ

!ð7Þ

Previous studies have shown that for the drying of a givenmaterial with a given initial concentration, this normalized activa-tion energy DEv/DEv,b can be correlated to the reduced moisturecontent X�Xb in the material using an empirical function (Chenand Xie, 1997; Chen and Lin, 2005):

DEv

DEv;b¼ gðX � XbÞ ð8Þ

where X is the particle’s moisture content on a dry basis (kg/kg) andXb is the particle’s moisture content when the drying achieves equi-librium (kg/kg). This correlation is found to hold for all air dryingconditions tested and hence becomes approximately a characteris-tic correlation of a specific material with specific initial solids con-centration (Chen and Lin, 2005; Lin and Chen, 2005). This kind offunction may be treated as a ‘‘fingerprint’’ of the drying behaviorof the material (Chen and Xie, 1997).

To predict the droplet temperature and moisture content histo-ries, the following energy balance equation is used:

mCp;ddTd

dt¼ hAðTb � TdÞ þ DHlms

dXdt

ð9Þ

where m is the overall mass of the droplet (kg), Cp,d is the specificheat capacity of the droplet (J/(kg K)), h is the heat transfer coeffi-cient (W/(m2 K)), DHl is the latent heat of water evaporation (J/kg), and ms is the total solid mass of the droplet (kg). The masstransfer coefficient hm (m/s) and the heat transfer coefficient h(W/(m2 K)) used in the above equations can be obtained from themodified Ranz and Marshall correlations (Ranz and Marshall,1952a,b; Lin and Chen, 2002):

Sh ¼ 1:63þ 0:54Re1=2Sc1=3 ð10Þ

Nu ¼ 2:04þ 0:62Re1=2Pr1=3 ð11Þ

3. Materials and methods

3.1. Materials

Skim milk powder was purchased locally. According to theproduct specification, the composition was approximately as fol-lows: 37.97 wt.% of protein, 1.34 wt.% of fat, 58.96 wt.% of sugarand 1.73 wt.% of minerals. For reconstitution, 50.0 g of milk pow-der was mixed with 50.0 g of Milli-Q water (QGARD00R1, Milli-pore, Australia) to make a final concentration of 50 wt.%. Thereconstitution was processed in 50 �C water bath with continuousstirring for 3–5 min, and the resultant solution was subjected to 5-min homogenization (Wisemix™ Homogenizer HG-15D, Daihan

Scientific Co. Ltd., Korea) and 5-min ultrasonication (Ultrasoniccleaner DC-400H, MRC Ltd., Israel), to maximally remove airbubbles.

3.2. Single droplet drying system

The detailed equipment set-up and experimental procedure ofthe glass-filament single droplet experiment have been describedelsewhere (Lin and Chen, 2002; Che and Chen, 2010; Fu et al.,2011). For reference, the schematic illustrations of the rig andthe air supply system are shown in Fig. 1. Briefly, the air flowwas conditioned to provide a laminar flow with controlled humid-ity, temperature and velocity for the convective drying experiment.Single droplet was attached to the tip of a specially-made fine glassfilament. During drying, the changes in diameter, temperature andmass of the droplet were recorded in separate runs with identicalconditions.

Temperature measurement was carried out with a fine thermo-couple (Type K, Part #CHAL-001, Omega Engineering Inc., USA) in-serted inside the droplet during drying. The thermocouple wasconnected to a Picometer TC-08 (Pico Technology, UK) and temper-ature data were obtained from the data logger (Picolog R5.17, PicoTechnology, UK) at 1 s time interval.

For diameter and mass measurements, the drying process wascontinuously recorded using a video camera (Sony DCR-HC36Camcorder, Sony Corporation, Japan) equipped with five 4�close-up lenses. Post-drying image analysis of droplet diameterand mass data was carried out using ImageJ 1.40f (National Insti-tutes of Health, USA). For diameter measurement, the images wereextracted from the video using Adobe After Effects 7.0 (Adobe Sys-tems Incorporated, USA) at a frame rate of 1 frame/s. The projecteddroplet area on each figure was considered as a perfect circle andthe equivalent diameter was calculated, which was then comparedto the diameter of the knob at the tip of the glass filament to esti-mate the actual droplet size. The diameter of the knob is measuredusing a standard calibration slide under microscope.

The droplet mass was determined by the different degree ofdeflection of a glass filament specially made for the mass measure-ment, with detailed procedures described in a previous study (Fuet al., 2011). Images were extracted from the video at a frame rateof 5 frames/s and the results of 5 frames were averaged to give themass data at 1 s time interval.

3.3. Droplet generation and drying conditions

The single droplet was generated using a 2 lL micropipette(Pipetman P2, Gilson S.A.S., France), and transferred using a sepa-rate transferring glass filament to the drying chamber. The gener-ation and transfer of the droplet were completed in 10 s tominimize undesired water evaporation prior to drying. The dryingconditions used in the present study are shown in Table 1. The ac-tual tunnel temperature and the actual initial droplet size were asexperimentally determined.

Each of the three parameters was measured twice at both dry-ing temperatures and the results reported here were averages ofduplicate experiments. The experimental errors from temperaturemeasurement between the duplicate runs were less than 1%, ex-cept for the initial heating-up period with experimental errors ofless than 4%. The experimental errors of diameter measurementwere around 4%, which were reduced to less than 1% for the diam-eter reduction kinetics D/D0. The raw mass data showed relativelymore fluctuations due to the flexible glass filament exposed to theupwards air flow. The gradient of mass changes were calculated byfitting the raw data to trendlines. The experimental errors of thefitted moisture data between repeated runs were less than 4%.

Fig. 1. Schematic illustration of the single droplet drying system used in the current study (not to scale in mm). (a) Air supply system; (b) glass-filament single droplet dryingrig. 1 – Dehumidifier; 2 – pressure regulator; 3 – needle valve; 4 – flowmeter; 5 – heating column containing electric heating elements; 6 – heater; 7 – temperaturecontroller; 8 – column section placing steel meshes; 9 – temperature probe; 10 – drying chamber; 11 – video camera; 12 – a single droplet suspended on the knob of asuspending glass filament; 13 – a iron wire used to fix the diameter-measuring glass filament; 14 – removable holder; 15 – box for the mass-measuring glass filament; 16 –mass-measuring glass filament.

Table 1Drying conditions used in the present study.

Air flow condition Temperature 70 �C, 90 �CVelocity 0.75 m/sMoisture content 0.0001 kg/kg

Droplet parameters Material Reconstituted skim milkInitial concentration 50 wt.%Initial droplet diameter 1.21 ± 0.02 mm

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4. Results and discussion

4.1. Drying kinetics of skim milk droplet with 50 wt.% initialconcentration

The measured temperature, moisture content, and diameterreduction data of skim milk droplets with 50 wt.% initial concen-tration during air drying are shown in Figs. 2–4 respectively. Thetemperature curves showed a dramatic increase immediately fromthe commencement of drying and quickly reached the environ-mental temperature. There was no period of wet-bulb tempera-ture, in contrast to that observed during the drying of dropletswith lower initial concentrations such as 20 and 30 wt.% (Chen

and Lin, 2005; Fu et al., 2011). At high initial solids concentration,the evaporation rate from the droplet is low and the heat loss dueto evaporation is insufficient to balance the heat convection fromhot air, resulting in the rapid increase of droplet temperature(Adhikari et al., 2004). The low evaporation rate could be partiallydue to the limited amount of moisture at the interface of the drop-let. Furthermore, the high solids content might also benefit a rapidsurface formation as soon as drying began. This dry surface layercould form an additional hindrance for water transport withinthe semi-dried milk droplets (Hassan and Mumford, 1993; Kentishet al., 2005).

Fig. 3 shows that the decrease of moisture content was more ra-pid at 90 �C than at 70 �C as expected. After 100 s of drying, thetemperature of the semi-dried particles reached approximatelythe environmental temperature (Fig. 2). Despite the high droplettemperature, there was still moisture remaining in the semi-driedparticles at this stage of drying (Fig. 3). The removal of moisturereached the final stage at approximately 150–170 s of drying.

Fig. 4 shows that the diameter reduction of milk droplet duringair drying was less than 10% of the initial droplet at this high initialsolids concentration. In addition, the final diameter of dried milkparticles at different drying temperatures had relatively large

Fig. 2. Temperature histories for 50 wt.% skim milk droplets dried at air temperatures of 70 and 90 �C.

Fig. 3. Moisture content histories (dry basis) for 50 wt.% skim milk droplets dried at air temperatures of 70 and 90 �C.

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difference. The final diameter of the dried particle at 70 �C wasapproximately 92% of the initial droplet. When the drying air tem-perature was increased to 90 �C, this value increased to 96%. It wasreported that a higher drying air temperature would lead to aslightly larger dried particle (Lee and Chou, 1996). However, atlower initial concentrations such as 10 wt.%, the final particlediameter at different drying temperatures did not show any signif-icant differences (Fu et al., 2011). Thus the result obtained heremight be an indication that the effects of drying temperature onthe diameter reduction kinetics were enhanced when a high initialsolids concentration was used for milk drying. The different diam-eter reduction kinetics might be attributed to different surface for-mation histories (Jayanthi et al., 1993). As drying proceeded morerapidly at 90 �C, the formation of surface crust could take place ear-lier, preventing the semi-dried particle from further shrinkage.

4.2. Activation energies of skim milk droplet with 50 wt.% initialconcentration

Based on the three measured kinetics parameters, the apparentactivation energy for the drying of 50 wt.% skim milk droplets wascalculated using Eq. (6) for each drying temperature. Drying rate

dm/dt was determined by taking the gradient of the fitted mathe-matical expression of the mass change data. Results are shown inFig. 5. As drying progressed, the activation energy to overcomethe ‘‘energy barrier’’ for moisture removal showed a continuous in-crease, representing the increased difficulty. The apparent activa-tion energy at the later drying stage was higher at 90 �C thanthat at 70 �C. This trend was in accordance with that observed dur-ing drying of lower initial solids solutions (Fu et al., 2011).

The calculated apparent activation energy DEv was normalizedusing the equilibrium activation energy (or the maximum activa-tion energy) DEv,b and then correlated to the reduced moisturecontent X�Xb to establish a ‘‘master’’ activation energy curve aspresented in Fig. 6(a). The droplet moisture content X was obtainedfrom the fitted mass change expression and the equilibrium mois-ture content Xb was estimated with the previously established GAB(Guggenheim–Anderson–de Boer) desorption isotherm (Chen andLin, 2005; Lin et al., 2005). From the isotherm, at the temperatureand the low air humidity used in the current study, Xb would beapproximately less than 0.02 kg/kg, approaching zero moisture.For simplicity, in subsequent analysis Xb was taken as zero whencollapsing the individual activation energy curves to form the mas-ter curve.

Fig. 4. Diameter reduction histories for 50% skim milk droplets dried at air temperatures of 70 and 90 �C.

Fig. 5. Apparent activation energy curves obtained during drying of 50 wt.% skim milk droplets.

706 N. Fu et al. / Journal of Food Engineering 109 (2012) 701–711

As expected, the normalized activation energy curves at the twodrying temperatures were very close, despite the largely differentdrying histories as shown in Figs. 2–4. By grouping the two curvesin Fig. 6(a) together and fitting the resultant curve to a polynomialequation, a model for drying of 50 wt.% skim milk droplet wasestablished:

y ¼ ax3 þ bx2 þ cxþ 1 ð12Þ

where a ¼ �1:485, b ¼ 2:728, c ¼ �2:186, x is the reduced moisturecontent in the material being dried X�Xb (kg/kg), and y is the nor-malized activity energy DEv/DEv,b. The master curve and the fittedmodel are presented in Fig. 6(b).

4.3. Shrinkage models for drying of 50 wt.% skim milk droplet

To predict the drying histories using the REA, a model describ-ing the droplet shrinkage (diameter reduction) during drying isnecessary. In Fig. 7, the measured D/D0 curves are plotted againstX�Xb for both drying temperatures to establish such a model. Forsolutions with lower initial solids, a ‘‘master’’ diameter reductionmodel was commonly adopted to describe droplet shrinkage at

various drying temperatures (Lin and Chen, 2007) and with variousinitial droplet sizes (Fu et al., 2011). In the current study however,the discrepancy between the two diameter reduction curves wasconsiderably large as shown in Fig. 7. Hence a reasonable descrip-tion of both trends could not be achieved using a single linearequation. The two diameter reduction curves in Fig. 7 showednot only the different reduction per unit water removal, but possi-bly also the different stages of drying. At 90 �C the diameter reduc-tion could be linearly correlated to the moisture content, whereasat 70 �C a transition was observed at the moisture content around0.3 (kg/kg, on dry basis). This transition indicated that at the initialstage of drying, the semi-dried particle had an approximate con-stant rate of shrinkage. When the moisture content reachedapproximately 0.3 kg/kg, the shrinkage slowed down despite thecontinuous removal of moisture. The transition phenomenon couldbe due to that of the formed crust becoming sufficiently strong toresist further shrinkage at the later stage of drying. The effects ofdifferent drying temperatures on the shrinkage kinetics of highconcentration solutions still require further systematic experimen-tal investigation and careful interpretation, before the mecha-nism(s) could be clarified. In the present study, the two D/D0

curves in Fig. 7 were separately correlated to implement REA, so

Fig. 6. Normalized activation energy curves plotted against the fitted moisture content data for the air drying of 50 wt.% skim milk droplets. (a) Normalized activation curves;(b) master activation-energy curve obtained by fitting the experimental data to a polynomial model (Eq. (12)).

Fig. 7. Diameter reduction curves plotted against the droplet’s moisture content for the air drying of 50% skim milk droplets.

N. Fu et al. / Journal of Food Engineering 109 (2012) 701–711 707

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as to verify the performance of the overall concept for dropletswith high initial solids:

70 �C :D=D0¼0:0866ðX�XbÞþ0:9061 0:3<X�Xb<1 ð13aÞD=D0¼0:0301ðX�XbÞþ0:9238 0<X�Xb<0:3 ð13bÞ

�

90 �C : D=D0 ¼ 0:0447ðX � XbÞ þ 0:959 ð14Þ

4.4. Description of drying histories of 50 wt.% skim milk droplet usingthe REA

Under the REA framework, the prediction of drying history uti-lizes the Euler method to solve mass and energy transfer equationswith known initial values of droplet diameter, temperature, andmass. The detailed procedure has been described in previous re-ports (Chen and Lin, 2005; Fu et al., 2011). During the calculationfor the drying air temperature of 70 �C, Eq. (13a) was firstly usedto describe the diameter reduction. When the calculated moisturecontent reached below 0.3 kg/kg, Eq. (13b) was used to replace Eq.(13a).

Fig. 8 compares the calculated drying histories of 50 wt.% skimmilk droplets with experimental results. The prediction closely

Fig. 8. Comparison of the drying history of 50 wt.% reconstituted skim milk droplets be70 �C; (b) drying air temperature of 90 �C.

followed experimental data for the two drying temperatures. Theresults indicated the capability of REA to describe the air dryingbehavior of high concentration milk droplets, as generally encoun-tered in the industrial spray drying operations. The agreement fur-ther provides confidence in the suitability of REA to combine withother simulation approaches, such as 1-D plug flow spray dryersimulations (based on an Excel sheet modeling) (Patel et al.,2010) or more detailed CFD simulations (Woo et al., 2008; Jinand Chen, 2009), to predict the spray drying behavior of milk par-ticles via dryer-wide simulations.

4.5. On the correlation between initial droplet concentration and theREA ‘‘master’’ activation-energy curve for skim milk

One of the main advantages of the REA model is the material-specific master activation-energy curve, which is expected to holdfor different drying air conditions and initial droplet sizes, but var-ies upon different initial concentrations. It is therefore worthwhileto study the different activation energy curves obtained with var-ied initial concentrations of the same material. Based on the re-ported REA models of 20 and 30 wt.% skim milk (Chen and Lin,2005), Patel et al. (2010) developed mathematical models for high-er initial concentrations, including 40 and 50 wt.%, using an upper

tween the experimental data and the REA prediction. (a) Drying air temperature of

N. Fu et al. / Journal of Food Engineering 109 (2012) 701–711 709

and lower bound approach. The correlation for 50 wt.% reconsti-tuted skim milk was given by the following equation (Patel et al.,2010):

DEv

DEv;b¼ 1:0063� 1:5828ðX � XbÞ þ 3:3561ðX � XbÞ2

� 9:389ðX � XbÞ3 þ 12:22ðX � XbÞ4 � 5:5924ðX � XbÞ5 ð15Þ

So far there were no experimental data to test the accuracy ofthe extended approach. Here, to provide better understandingson the fundamental aspects of REA, the activation energy data ob-tained in the present study were compared with previously re-ported results or predictions (Chen and Lin, 2005; Patel et al.,2010; Zhu et al., 2011). The results used for comparison includethe activation energy data obtained with 20 and 30 wt.% initialconcentrations (Chen and Lin, 2005), the estimated parametersfor 50 wt.% initial concentration (Eq. (15)) (Patel et al., 2010) andthe activation energy data obtained for drying of 50 wt.% skim milkusing a desorption method (a liquid layer dried in a desiccant-filledbox) (Zhu et al., 2011). The comparison is presented in Fig. 9(a),while, the moisture content ranging from 0 to 1 is magnified togive a clearer illustration in Fig. 9(b).

Fig. 9. Comparison of the normalized activation energy curves between 50 wt.% skim m(Chen and Lin, 2005), 30 wt.% (Chen and Lin, 2005), an extrapolated model for 50 wt.% iniobtained with 50 wt.% initial concentration using desorption method (Zhu et al., 2011). (comparison.

It can be seen from Fig. 9(a) and (b) that the activation energydata obtained with the single droplet experiment (i.e., the twocurves reported in the present study, the 20 and 30 wt.% data re-ported by Chen and Lin (2005) and the 50 wt.% model developedbased on these data (Patel et al., 2010)) were in agreement witheach other, whereas the 50 wt.% model obtained with the desorp-tion method tended towards the lower moisture content range.The desorption method was novel but was somewhat preliminary(Schuck et al., 2009). The activation energy curve went below zeroat high water content, indicating that at least the heat transfer con-ditions might not yet be accurately and fully characterized. Thedesorption method utilized a small cup filled with a large amountof milk solution, which was then dehydrated in an incubator withcontrolled air conditions. Thus the heat transfer occurred both atthe surface of the milk, and from the wall and the bottom of thecup filled with milk. This kind of experimental set-up might resultin two phenomena, both of which are negligible in the single drop-let experiment, but could play a significant role for the data ob-tained using the desorption method. Firstly, the crust formationon the surface may affect the evaporation process more signifi-cantly than that observed during the single droplet drying. Thethick crust on the surface may hinder water evaporation at the

ilk droplet and previously reported results with initial concentrations of 20 wt.%tial concentration (Eq. (15)) (Patel et al., 2010), and a master activation-energy curvea) X axis ranging from 0 to 4, and (b) X axis ranging from 0 to 1 for a more effective

710 N. Fu et al. / Journal of Food Engineering 109 (2012) 701–711

surface; in the meantime, the heat transfer from the bottom andthe wall of the cup maintains the heating of the bulk milk to theenvironmental temperature. The combination of both could resultin a situation where the bulk milk is heated to the environmentaltemperature with significant moisture content remaining. Thedesorption method also uses much larger volume of milk thanthe single droplet drying. In the case of more viscous skim milkat high solids content, this could induce a complex heat transferphenomenon leading to a non-identical temperature profile ofthe milk layer being dried. Considering that the REA is applicableto thin layers and small droplets where the modified Biot numberis sufficiently small and the temperature gradient within the mate-rial is negligible (Chen and Xie, 1997), a complex spatial tempera-ture pattern would certainly affect the ease in applying the REAmodel. To this end, the desorption method could be further im-proved by simplifying the heating conditions and the quantitativeinterpretations.

In comparison to the desorption method, the four single dropletdata sets together with the ‘‘extrapolated’’ mathematical model(Eq. (15)) were in close agreement in Fig. 9. Since Eq. (15) (Patelet al., 2010) was extrapolated based on the 20 and 30 wt.% exper-imental data (Chen and Lin, 2005), only the trends of the fourexperimental activation energy data are to be discussed here. Ascan be seen from Fig. 9(a), along with the increase in the initialconcentration from 20 wt.% to 30 wt.% and 50 wt.%, the startingpoint of the normalized activation energy curve recedes from themoisture content of 4 to 2.33 and 1 (kg/kg) on dry basis. The trendsof the activation energy data at the moisture range of 0–0.8 kg/kgare very similar for all tested initial concentrations, with the50 wt.% data reported in the present study having an approxi-mately 0.05 (kg/kg) lower deviation towards the lower moisturecontent end. This finding suggested that the drying behavior ofskim milk might deviate slightly when the initial concentrationwas increased from 20 to 50 wt.%. In a previous study (Patelet al., 2010), Eq. (15) was developed for 50 wt.% initial skim milksolids assuming the behavior at the lower moisture portion be-tween 0 and 0.8 kg/kg was similar across all concentrations. Thecurrent experimental analysis indicated that there could be a slightdeviation even at the lower moisture end. Nevertheless, it is note-worthy that such slight deviation would not translate to significantchanges in the drying kinetics, as the evaporation rate and mois-ture content should already be very low at the later stage of drying.

5. Conclusions

In this study, the drying kinetics for single skim milk dropletswith a high initial concentration of 50 wt.% was experimentallyinvestigated and correlated using the REA approach. The establish-ment of the master activation energy model for the drying of50 wt.% skim milk droplets is shown to be feasible. The REA ap-proach was further exploited by comparing the obtained mastercurve with previously reported data, obtained using the same ap-proach at lower initial concentrations and by desorption method.The master activation energy curve reported here is in agreementwith that obtained by single droplet drying of lower initial solidsmilk. However, a small deviation of 0.05 kg/kg was observed forthe normalized activation energy curves between 20 and 50 wt.%initial concentration, which could possibly suggest a slightly devi-ated drying behavior at higher initial concentration. These findingsverified the reliability and robustness of REA to describe the dryingbehavior of single droplets. Although the activation energy curveobtained with the desorption method was different from others,this desorption method is in progress which already gave satisfyingprediction of product and drying air parameters when combinedwith the REA. The parameters reported in this study will

strengthen the dryer-wide ‘‘1-D’’ to ‘‘3-D’’ simulation of industrialspray drying of milk.

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