Prediction of Thermohydric History of Whey Protein Concentrate Droplets during Spray Drying

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http://dx.doi.org/10.1007/s11947-012-0963-x

http://dx.doi.org/10.1007/s11947-012-0963-x

AUTHOR'S PROOF

Metadata of the article that will be visualized in OnlineFirst

1 Article Title Prediction of Thermohydric History of Whey Protein Concentrate

Droplets during Spray Drying2 Article Sub- Title

3 Article Copyright -Year

Springer Science+Business Media, LLC 2012(This will be the copyright line in the final PDF)

4 Journal Name Food and Bioprocess Technology

5

CorrespondingAuthor

Family Name Bernard6 Particle

7 Given Name Clémence8 Suffix

9 Organization AgroParisTech, UMR 1145-Ingénierie-Procédés-Aliments

10 Division

11 Address 1 Avenue des olympiades, Massy 91300, France

12 Organization Ecole de Biologie Industrielle (EBI)

13 Division

14 Address 32 Boulevard du port, Cergy-Pontoise 95000,France

15 e-mail [email protected]

16

Author

Family Name Broyart17 Particle

18 Given Name Bertrand19 Suffix


21 Division



24

Author

Family Name Absi25 Particle

26 Given Name Rafik27 Suffix

28 Organization Ecole de Biologie Industrielle (EBI)

AUTHOR'S PROOF

29 Division

30 Address 32 Boulevard du port, Cergy-Pontoise 95000,France


32

Author

Family Name Granda33 Particle

34 Given Name Pablo35 Suffix


37 Division


39 e-mail

40

Author

Family Name Relkin41 Particle

42 Given Name Perla43 Suffix


45 Division



48

Schedule

Received 27 April 2012

49 Revised

50 Accepted 11 September 2012

51 Abstract In this study, we analyzed heat and mass transfer phenomenaoccurring during spray drying of a whey protein concentrate at pilotscale. Conservation equations were written for both liquid dropletsand humid air. Predicted results were then compared withexperimental data: particle final moisture content, outlet airtemperature, and humidity. The good adequacy found betweenexperimental and predicted data allowed us to use the predictedvalues as a good indicator of thermohydric history followed by adroplet during drying. These results can also be used to help to findoptimal process settings during production of spray-dried powderswith specific properties.

52 Keywordsseparated by ' - '

Spray drying - Modeling - Whey protein

53 Foot noteinformation

AUTHOR'S PROOF

UNCORRECTEDPROOF

1

23 ORIGINAL PAPER

4 Prediction of Thermohydric History of Whey Protein

5 Concentrate Droplets during Spray Drying

7 Clémence Bernard & Bertrand Broyart & Rafik Absi &

8 Pablo Granda & Perla Relkin

9

10

11 Received: 27 April 2012 /Accepted: 11 September 2012

12 # Springer Science+Business Media, LLC 2012

13

14 Abstract In this study, we analyzed heat and mass transfer

15 phenomena occurring during spray drying of a whey protein

16 concentrate at pilot scale. Conservation equations were writ-

17 ten for both liquid droplets and humid air. Predicted results

18 were then compared with experimental data: particle final

19 moisture content, outlet air temperature, and humidity. The

20 good adequacy found between experimental and predicted

21 data allowed us to use the predicted values as a good

22 indicator of thermohydric history followed by a droplet

23 during drying. These results can also be used to help to find

24 optimal process settings during production of spray-dried

25 powders with specific properties.

26 Keywords Spray drying . Modeling .Whey protein

27 Abbreviation

29 DA30 dry air

31 DM32 dry matter

33 WPC34 whey protein concentrate

35

36Introduction

37Nowadays, the main challenges in the production of spray-

38dried products are the development of speciality powders

39(having a high added value) and the reduction of the process-

40ing costs (Verdurmen et al. 2002). Mathematical modeling of

41spray-drying unit operation are very helpful in order to reduce

42the time needed to find optimal settings for a given product in

43a given drying equipment and in order to ensure a better

44control of end-product properties. It is a well-known fact that

45the thermohydric history followed by a liquid droplet during

46spray-drying influences directly the degradation rates of bio-

47chemical components of the product and hence the final

48properties of the powder. Nevertheless, few studies have

49clearly expressed causal and quantitative relationships be-

50tween the particles’ temperature rise and moisture loss profiles

51in the spray dryer and the final quality of product.

52For this purpose, different types of models have been devel-

53oped in the past decades. Earlier, a number of semi-empirical

54models were suggested to understand drying. However, these

55simplified models were for specific product in a specific spray

56dryer (Paris et al. 1971). Latter, mathematical models have been

57used for drying process in order to predict heat and mass

58transfer. The complexity of drying involves different levels

59and scales in mathematical modeling of spray drying

60(Langrish 2009). Each model presents advantages and limita-

61tions in the design and optimisation of spray dryers.

62Computational fluid dynamics (CFD) is a useful tool in food

63industry (Sun 2007). CFD was largely used in the area of spray

64drying (Zbicinski and Li 2006;Woo et al. 2008; Mezhericher et

65al. 2009; Chen and Jin 2009; Anandharamakrishnan et al.

662010). In general, CFD was used in spray drying of food

67ingredients to predict the flow patterns and temperature distri-

68butions of gas and droplets inside the drying chamber

69(Straatsma et al. 1999) in order to give an insight into the

70problem of wall deposition of particles> (Oakley et al. 1988;

C. Bernard : R. AbsiEcole de Biologie Industrielle (EBI),

32 Boulevard du port,

95000 Cergy-Pontoise, France

R. Absi

e-mail: [email protected]

C. Bernard (*) :B. Broyart : P. Granda : P. RelkinAgroParisTech, UMR 1145-Ingénierie-Procédés-Aliments,

1 Avenue des olympiades,

91300 Massy, France


B. Broyart


P. Relkin


Food Bioprocess Technol

DOI 10.1007/s11947-012-0963-x

JrnlID 11947_ArtID 963_Proof# 1 - 17/09/2012

AUTHOR'S PROOF

UNCORRECTEDPROOF

71 Langrish and Fletcher 2001, 2003; Langrish and Kockel 2001;

72 Fletcher et al. 2006; Lin and Chen 2007) or to design and find

73 optimal settings for the drying equipment (Langrish and

74 Fletcher 2001; Verdurmen et al. 2002; Fletcher et al. 2006).

75 Moreover, the weak side of the CFD methodology applied to

76 spray drying lies in the fact that very few precise and reliable

77 experimental measurements of fluid flow pattern, temperature,

78 and composition distribution in the drying chamber are avail-

79 able. The predicted values of the CFD model are hence very

80 rarely confronted to experimental data. However, particle his-

81 tories (temperature, velocity, residence time, and impact posi-

82 tions) were not investigated adequately in the previous studies.

83 Particle histories are important to design and operating spray

84 drying and are involved in final product quality. Therefore, the

85 aim of our study is to develop amathematical model relating the

86 particles’ thermohydric history and air temperature and humid-

87 ity variations along the length of the drying chamber.

88 Different physical models based on classical drying kinetics

89 can be found (Parti and Palancz 1974; Papadakis and King

90 1988a, b; Ferrari et al. 1989; Nesic 1989; Zaror and Pérez-

91 Correa 1991; Hassan and Mumford 1993; Straatsma et al.

92 1999; Farid 2003; Chen and Lin 2004, 2005; Birchal and

93 Passos 2004; Lin and Chen 2007). Langrish and Kockel

94 (2001) estimated that a re-evaluation of the experimental data

95 in these works is necessary. In fact, very few studies include

96 some confrontation of predicted data with experimental ones

97 obtained in industrial dryers. These studies include generally a

98 simple validation of the predicted results for large droplets in

99 water bath where heating and drying kinetics are radically

100 different from the ones observed in industrial dryers. For ex-

101 ample, Ferrari et al. (1989) reported the drying kinetics for 10-

102 mm diameter milk droplets immobilized in agar gel at temper-

103 atures varying from 50 to 90 °C. However, the effect of the gel

104 on the drying kinetics was not clarified. Moreover, in these

105 studies, the droplet diameters were circa 13 orders of magni-

106 tude larger (2–10 mm in diameter) than those normally found

107 during spray drying unit operation (80 μm; Masters 2002)

108 because of the practical need to perform experiments on drop-

109 lets with measurable mass losses. Chong and Chen (1999) also

110 noticed a lack of simulated data for drying at high air temper-

111 ature above 200 °C, a temperature range at which the product

112 transformation is expected to occur at a higher rate.

113 In a previous study (Bernard et al. 2006, 2008; Relkin et al.

114 2007), we observed some difference in powders quality pro-

115 duced with different drying operating conditions such as

116 different air or product flow rates. Thus, the aim of this work

117 is to analyze and predict heat and mass transfer phenomena

118 occurring during spray drying of whey protein concentrate

119 (WPC) in order to understand the influence of spray-drying

120 operating conditions on the final powder quality observed in

121 previous studies (Bernard et al. 2006, 2008; Relkin et al.

122 2007). In this study, we present a simple but realistic model

123 of spray drying process based on mass and energy

124conservation equations written for both drying air and droplets

125and taking into account external resistance to heat and mass

126transfer. This model is expected to be able to predict the

127kinetics of variation of the droplets average temperature,

128average moisture content, and diameter during its residence

129time inside the dryer (or at a given position from dryer

130entrance). This type of model seems to be well adapted to

131the final objective of our study which is to interrelate simulat-

132ed moisture and temperature profiles of droplets and the level

133of product transformation. The model assumptions are mainly

134related to unavailable experimental data related to the process.

135Materials and Methods

136Main Assumptions of the Model

137& All the droplets, at a given position z (meter) from the

138dryer entrance, are assumed to have a spherical shape

139and the same mean diameter. This mean diameter is

140assumed to vary during droplet residence time inside

141the dryer according to a simplified law described in the

142“Mean Particle Diameter” section.

143& The temperature and moisture content gradients within

144the droplet are assumed negligible. In the following part

145the paper, the average temperature and moisture content

146for a droplet will be denoted by Tp (Kelvin) and np147(kilograms per kilogram dry matter (DM)).

148& The sophisticated CFD models are able to provide more

149details about the flow and the evolution of the different

150parameters in the dryer. However, in order to develop a

151simpler model, the actual flow pattern in the spray-drying

152chamber is approximated for both phases (WPCdroplets and

153drying air) by co-current parallel plug flows with no recir-

154culation. At a given position z from the spray dryer entrance,

155drying air temperature Ta (Kelvin), velocity va (meters per

156second) and partial vapor pressure pva (Pascal) are assumed

157uniform over the entire section of the spray dryer.

158& The motion of a droplet is not impeded by the motion of

159the other droplets.

160& The velocity of the liquid droplet vp (meters per second)

161relative to the velocity of the drying air va (meters per second)

162is assumed equal to the terminal velocity y vl (meters per

163second) of a rigid sphere in a fluid of known properties as

164described by Stokes’ law (Rep<1) and calculated by:

vp ¼ va þ vl ¼m�da

ρdaAz

þρp � ρa

� �

g d2p

18ηað1Þ

165166wherem

�

dais the dry air mass flow rate (kilograms per second),

167ρda, ρa, and ρp are the dry air, air, and particle densities

168(kilograms per cubic meter), Az is the area of a section of



AUTHOR'S PROOF

UNCORRECTEDPROOF

169 the drier at a position z from the dryer entrance, ηa is the

170 dynamic viscosity of air (Pascal second), dp is the particle

171 diameter (meters) and g is the gravitational acceleration

172 (meters per square second). In the following part of the paper,

173 the subscripts (a), (da), and (p) will be referring to air, dry air,

174 and particle, respectively.

175 & The sticking of the droplets to the wall is not described by

176 our model. It was in fact not observed during our trials.

177 Taking into account these assumptions, we expect that our

178 model will be usable in all applications related to simple stage

179 spray drying process and no-stickingmaterial as dairy products.

180 Constitutive Balance Equations of the Model

181 Assuming that the net quantity of water lost by the product

182 is equal to the net quantity of water gained by the air (no

183 leak in the drying system), the mass balance equations

184 written for both particles and drying air at a given position

185 z from dryer entrance takes the form:

�mdp

dnp

dz

� �

¼ � �mda

dna

dz

� �

¼ �kp Sap y pvsat � pvað Þ ð2Þ

186187where m

�

dpand m

�

daare respectively the dry product and the dry

188 air flow rates (kilograms per second), np and na are respec-

189 tively the product moisture content and air specific humidity

190 (kilograms per kilogram DM and kilograms per kilogram

191 dry air (DA)), pvsat (Pascal) and pva (Pascal) are respectively

192 the saturated vapor pressure of pure water and the partial

193 vapor pressure of water in drying air.

194 In the previous equation, the net quantity of water ex-

195 changed by convective drying between air and particles is

196 proportional to:

197 – the mass transfer coefficient kp (kilograms square meter

198 per second per Pascal)

199 – the exchange surface between air and particle per unit

200 length of dryer Sap (meters)

201 – the difference between the partial vapor pressure in

202 equilibrium with the product ψ pvsat (Pascal) and the

203 partial vapor pressure pva (Pascal) of drying air

204 Note that in the mass balance equations, the vapor pressure

205 in equilibrium with the droplets (assumed at uniform temper-

206 ature and moisture content) is calculated using a dedicated

207 function so calledψ function. This function is characteristic of

208 the product and will be calculated from values of product

209 average temperature and moisture content. It is not explicitly

210 a value of water activity at the surface of the product since the

211 model does not allow us to calculate surface temperature and

212 moisture content. This ψ function is hence used as a calcula-

213 tion step (with strong physical signification) in order to inter-

214 relate product average temperature and moisture content

215and surface product vapor pressure. It is expected to

216decrease when product temperature increases and mois-

217ture content decreases during drying. This function

218includes the effects of decreasing mass diffusion rate

219inside the droplet and decreasing of water activity at

220the surface of the product, both effects getting more and

221more drastic during drying. The formalism chosen for

222the ψ function is close to an Oswin-type equation used

223to predict sorption isotherms (Andrieu et al. 1985). It

224takes the form:

Ψ ¼

npk0þk1Tp

� �k2þk3Tp

1þnp

k0þk1Tp

� �k2þk3Tpð3Þ

225226where k0, k1, k2, and k3 are four unknown parameters to

227be identified by comparing experimental and calculated

228values.

229The variation of droplets temperature inside the dryer is

230influenced by two phenomena: heat exchanged by convec-

231tion with drying air and heat lost by the product due to water

232vaporization (respectively first and second terms in the right

233hand side of Eq. 4):

m�

dpCpdm þ npCplw� � dTp

dz

� �

¼ h Sap Ta � Tp� �

þ m�

dp

dnp

dz

� �

ΔHvap ð4Þ

234235where Cpdm and Cplw are respectively the product dry

236matter and pure water specific heat (Joules per kilogram

237per Kelvin), h is the convective heat transfer coefficient

238(Watts per square meter per Kelvin), and ΔHvap is the latent

239heat of vaporization of pure water (Joules per kilogram).

240For the drying air, the temperature variation at a given

241position from dryer entrance is influenced by three phenomena:

242heat exchanged by convective heating, heat gained from vapor

243emitted by the product, and dryer heat loss (overall exchange

244between drying air and surrounding air outside of the dryer).

245These three phenomena are respectively described in the first,

246second and third terms in the right hand side of Eq. 5:

m�da Cpda þ na Cpvap

� � dTa

dz

� �

¼ h Sap Tp � Ta� �

þ m�da dna dz=ð Þ

Cpvap Tp � Ta� �

þ � � � . . . 2przU T1 � Tað Þ

ð5Þ247248where Cpda and Cpvap are respectively the dry air and pure

249vapor specific heat (Joules per kilogram per Kelvin), U is a

250global heat transfer coefficient estimated to be equal to 5Wm−2

251K−1 (J. Vasseur, personal communication) used to quantify heat

252loss between drying air at Ta (Kelvin) and the air outside of the

253dryer at T∞(Kelvin) and rz is the dryer radius (meter) at a

254position z from the dryer entrance.



AUTHOR'S PROOF

UNCORRECTEDPROOF

255 Mean Particle Diameter

256 The mechanism of particle shrinkage during drying was

257 simplified (Parti and Palancz 1974; Farid 2003) and as-

258 sumed to follow a two-stage procedure:

259 & A first stage called shrinkage period where the water

260 inside the droplet is evaporated at a significant rate and

261 during which the volume decrease of the droplet corre-

262 sponds to the volume of water evaporated.

263 & A second stage during which a rigid cover crust is

264 formed at the outer surface of the droplet. In this stage,

265 the mean particle diameter is assumed to remain con-

266 stant and equal to the measured mean particle diameter

267 of final powder d50 (meter).

268 The transition from the first to the second stage is as-

269 sumed to occur at a so-called critical moisture content npc270 (kilogram per kilogram DM) where the volume of the drop-

271 let during the first stage becomes equal to the volume of the

272 final powder with a mean diameter of d50. This two-stage

273 procedure used to describe particle shrinkage during drying

274 is presented in Fig. 1. The volume of particle Vp during these

275 two stages is hence calculated according to:

If np > npc; Vp ¼ Vpi �Vpi�V50

npi�npcnpi � np� �

ð6Þ

276277278

If np � npc; Vp ¼ V50 ¼43p d50

2

� �3ð7Þ

279280 where Vpi and V50 are the volumes (cubic meter) of the

281 droplet at initial diameter dpi (meter) and at the median final

282 powder diameter d50 obtained experimentally; npi is the

283 initial droplet moisture content. As no reliable data were

284 available for the initial diameter of the droplets, it was, as a

285 first approximation, assumed equal to a value 20 % higher

286 than mean powder diameter taking into account the indus-

287 trial experience and the value of 15 % found by Lin and

288 Chen (2007) for whey protein concentrate (30 wt%) dried at

289 a temperature equal to 67–106 °C. The corresponding crit-

290 ical moisture content npc was hence calculated from this

291estimated value of particle initial diameter and from the

292value of d50.

293Lineic Exchange Area between Air and Droplets

294Further calculations need the use of the number of particles

295Np for a unit length of dryer so-called lineic number of

296particles at a given position z from the dryer entrance. This

297variable takes into account the reduction of the area of the

298drying chamber section due to the conical part of the dryer.

299Np (in number of particles per meter of dryer) is calculated

300as:

Np ¼ q�

dp

� �

i�1

Vpi

�1

vpð8Þ

301302where q

�

dp

� �

iis the dry product volumic flow rate at the

303initial time of drying process (cubic meter per second) and

304vp the particle velocity (meter per second). The dry product

305volumic flow rate q

�

dp

� �

iis calculated as:

q�

dp

� �

i¼

m�dp

� �

i

ρdp

� �

i

ð9Þ

306307where m

�dp

� �

iis the dry product mass flow rate (kilograms

308of DM per second) and ρdp

� �

iis the dry product density

309(kilograms of DM per cubic meter) at the initial time of

310drying process (dryer entrance). Using the same definition,

311the lineic exchange area Sap (square meter per meter) be-

312tween air and droplets is then calculated as:

Sap ¼ Sp:Np ð10Þ

313314where Sp stands for the area of outer surface of the droplets

315at the position z from dryer entrance calculated using mean

316particle diameter (estimated itself using procedure described

317in the “Mean Particle Diameter” section).

318Estimation of External Heat and Mass Transfer Coefficients

319Classical correlation using Nusselt (Nu), Reynolds (Re), and

320Prandtl (Pr) numbers is used in the estimation of the external

321convective heat transfer coefficient hp as given by Perry et

322al. (1984) and using a formalism adapted from Dittus

323Boetler for Re<1:

Nu ¼hp dp

la¼ bNu Re

0:5p Pr0:33 ð11Þ

324325326

with Rep ¼vl dp

vaand Pr ¼

va

aa

ð12Þ

dpi=1,2 d50

d

z

d50

Shrinkage

Increase of internal

porosity

Position at which n = npc

Fig. 1 Change of droplet size (dpi initial droplet diameter, d50 final

mean particle diameter, npc critical moisture content, z dryer length)



AUTHOR'S PROOF

UNCORRECTEDPROOF

327328 where νa and αa stand respectively for drying air kinematic

329 viscosity (square meter per second) and thermal diffusivity

330 (square meter per second) and βNu is an empirical coeffi-

331 cient which must be identified by comparison with experi-

332 mental data and quantifies the efficiency of convective

333 transfers around the droplets. The external mass transfer

334 coefficient kp is related to the external heat transfer coeffi-

335 cient hp. As indicated in Loncin and Bimbenet (1995) for

336 industrial dryer conditions, kp is approximated by :

kp ¼hp

65ΔHvap;Tp

ð13Þ

337338

339 Solving Differential Equations and Parameters

340 Identification

341 To solve the system of ordinary differential equations de-

342 fined by Eqs. 2, 4, and 5, a specific algorithm so called

343 ode15s and developed in Matlab® environment is used. This

344 algorithm is specifically designed to deal with stiff systems

345 of ordinary differential equations.

346 The inputs of our model are inlet air temperature Tai347 (Kelvin) and specific humidity nai (kilograms per kilogram

348 DA) and inlet particle temperature Tpi (Kelvin) and moisture

349 content npi (kilograms per kilogram DM).

350The values of the five unknown parameters of the model

351k0, k1, k2, and k3 in Eq. 3 and βNu in Eq. 11 were fixed by

352comparison with the whole experimental dataset. These

353values were found by minimizing a root mean square error

354(RMSE) function between the experimental and calculated

355data measured at the end of the dryer: outlet air temperature

356Tao (Kelvin) and specific humidity nao (kilograms per kilo-

357gram DA) and outlet particle moisture content npo (kilo-

358grams per kilogram DM). This minimization procedure

359was realized using a Matlab® dedicated algorithm called

360lsqnonlin. Outlet particle temperature was not used to iden-

361tify the values of unknown parameters since it was not

362available from the experimental measurements. The RMSE

363function is calculated for each of the variable used for

364identification procedure according to:

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

X

Xið Þcalc� Xið ÞexpXið Þexp

ni

0

@

1

A

v

u

u

u

t ð14Þ

365366where Xi stands successively for outlet air temperature Tao,

367outlet air specific humidity nao, and final (outlet) product

368moisture content npo. ni is the number of experimental

369measurements available.

370The boundary conditions for the four parameters using in

371the model between z00 and z01.15 m are:

372

373

374

Ta 50� 260�C½ �; na 0:005� 0:05kg kg DA= ; Tp

18� 140�C ; np

0:02� 5kg:kg DM

:

375376

377

378 Experimental Measurements

379 AWPC in liquid form provided by Ingredia (Arras, France)

380 has been submitted to different operating conditions by

381 combining the following drying control variables (Table 1):

382 – air inlet temperature Tai fixed between 170 and 260 °C in

383 order to observe the effect of temperature on product quality,

384 being awell known that this variable affects the denaturation

385 of proteins (Donovan and Mulvihill 1987; Relkin 1996;

386 Galani and Apenten 1999; Livney et al. 2003)

387– air flow rate m�

afixed between 0.021 and 0.029 kgs−1 in

388order to observe the effect of the level of convection

389drying and of the residence time in the spray dryer on

390product quality

391– product flow rate m�

pfixed between 4.7 10−4 and 18.9

39210−4kgs−1

393– initial concentrate moisture content npi fixed to 0.8 or

3940.9 kg of water per kilogram of concentrate. The experi-

395ments at varying product flow rate and initial moisture

396content were carried out to study the effect of increasing

t1:1 Table 1 Processing conditions for spray drying experiments

t1:2 Processing conditions 1 2 3 4 5 6 7 8 9 10 11 12 13 14

t1:3 Tai (°C) 170 190 212 217 234 247 260 170 217 260 217 234 260 260

t1:4 npi (kgkg−1) 0.8 0.8 0.8 0.9

m�

p(10−4kgs−1) 9.4 9.4 11.1 18.9 4.7 4.7

m�

a(kgs−1) 0.029 0.021 0.029 0.029 0.021 0.021

t1:7 Varying Tai Varying m�

aVarying m

�

pVarying np0



AUTHOR'S PROOF

UNCORRECTEDPROOF

397 moisture flow rate at the entrance of the dryer on product

398quality by using two different means (changing m

�

por npi)

399 Experimental trials have been performed on a pilot scale

400 dryer (NIRO Minor pilot, GEA, Niro Atomizer, Denmark)

401 equipped with a rotary disk (Fig. 2). Liquid WPC (with initial

402 dry matter mass fraction circa 0.2, 85 % of which being

403 proteins) was introduced at 20 °C. Air temperature and mois-

404 ture content are measured using a psychrometer and air flow

405 rate is measured with Pitot tube within the outlet pipe.

406 Final product moisture content npowasmeasured on a sample

407 of 1 g of dried powder heated in a ventilated oven at 105 ±2 °C

408 during the period needed to reach a constant weight. The meas-

409 urements were realized in triplicate on various powder samples.

410 Particle size distribution of the different exiting powders

411 from the dryer chamber was measured by laser diffraction

412 using the Malvern Mastersizer with powder feeder unit

413 (Scirrocco 2000, Malvern Instruments SA, Orsay, France),

414 and used by the Malvern software for determination of

415 particle median diameter values (d50).

416 Results and Discussion

417 The identified values of the fivemodel parameters (k0, k1, k2, k3,

418 and βNu) using the procedure described in the “Solving differ-

419 ential equations and parameters identification” section are:

k0 ¼ 6:29 10�2; k1 ¼ �2:72 10�8K�1; k2 ¼ �8:37 10�2 and

k3 ¼ 1:78 10�4K�1

bNu ¼ 11:1 10�2

420421

422These values are pseudo-empirical and related to the

423particular process and product used in this study. They are

424used in order to estimate the product vapor pressure as a

425function of average temperature and moisture content (k0,

426k1, k2, and k3 parameters for the ψ function given in Eq. 3) or

427to calculate the external heat transfer coefficient (βNu pa-

428rameter in Eq. 11).

429A comparison between data obtained from the model and

430measured experimentally is presented in Figs. 3 and 4. For

431the whole experimental dataset, the RMSE value is equal to:

432– 10 % for outlet air temperature Tao433– 18 % for outlet air specific humidity nao434– 26 % for final (outlet) product moisture content npo

435A relatively good adequacy is observed between pre-

436dicted and experimental data taking into account the exper-

437imental accuracy for final product moisture content

438measurements realized in triplicate on various powder sam-

439ples. Nevertheless, we can notice that the predicted values

440for experiments giving particle with high final moisture

441content are underestimated by the model. Experiments

4428 and 9, for low levels of air flow rate and low air inlet

443temperature (Table 1) are concerned. A sensitivity study of

444the model to the experimental uncertainties on process op-

445erating conditions have shown that a little variation of air

446inlet temperature or air flow rate value have an important

447incidence on the final product moisture content especially

448when this product is not completely dried. For example, for

449tests carried out with air inlet temperature Tai between 150

450and 220 °C and m

�

da00.02 kgs−1, a variation of 10 % on the

451value of Tai causes a great variability from 55 % up to 115 %

452on the value of product final moisture content.

453In industrial conditions, the air outlet temperature is

454assumed equal to the final product temperature and hence,

455is often used as a rough indicator of the product final

Product

Air

a, amb

nai

T

Tao* npo *

nao*

am

Tpi npi pim

2

1 3

Fig. 2 Schematic representation of spray dryer at pilot scale: 1 drying

chamber, 2 atomizer, and 3 cyclone collector. Tpi, npi, and mpi are the

initial product temperature, moisture content and flow rate, respective-

ly; npo is the final product moisture content; Ta,amb, Tao, nai, and nao are

the ambient and final air temperature and initial and final air specific

humidity, respectively, andm�

ais the air flow rate. Asterisks corresponds

to the measured variables used to identify the unknown parameters of

the model

89

0

0,02

0,04

0,06

0,08

0,1

0,12

0 0,02 0,04 0,06 0,08 0,1 0,12

exp

erim

enta

l v

alu

es

simulated values

Fig. 3 Comparison between experimental and simulated values for air

outlet specific humidity nao (gray diamond) in kilograms per kilogram

DA and final particle moisture content npo (black square) in kilograms

per kilogram DM for different drying experiments



AUTHOR'S PROOF

UNCORRECTEDPROOF

456 moisture content. The model confirms the fact that, in the

457 experimental range covered here, the product final temper-

458 ature may be assumed equal to air outlet temperature

459 (Table 2), except for experiments 1 and 8. These trials

460 produce powders whose final moisture content is most im-

461 portant (circa 6 and 10 % for trials 1 and 8, respectively). In

462 this case, the product is not completely dried and its tem-

463 perature does not reach the air temperature. Hence, the

464 model developed above enables us to physically and pre-

465 cisely correlate the air outlet temperature, the final product

466 temperature and moisture content. Moreover, the online

467 measured outlet air temperature coupled with the model

468 can be used for better understanding of transfer phenomena

469 during drying and further automatic control of spray drying

470 in order to produce a product with specified level of mois-

471 ture content.

472 Analysis of Thermohydric Histories Experienced by Liquid

473 Droplets during Drying

474 In this paragraph, the thermohydric histories followed by the

475 liquid droplets and the air during drying are simulated by the

476 model and analyzed.

477 Figure 5 shows for the trial 4 (Table 1), the evolution

478 during drying of (A) air temperature Ta, product temperature

479 Tp and wet bulb temperature of the air Twb (B) product

480 moisture content np, air specific humidity na, and drying

481 rate of the product—dnp/dt and (C) the value of the ψ

482 function and the drying rate of the product—dnp/dt accord-

483 ing to the product moisture content, np.

484By analyzing the kinetics of evolution of these variables,

485four drying periods can be distinguished.

486– Period 1 which corresponds to an increase of the product

487temperature (Fig. 5a), a fast increase of the drying rate of

488the product (Fig. 5b and c). This period is extremely short

489(<0.5 s) and is generally observed in the case of finely

490divided products (Bimbenet et al. 2002).

491– Period 2 during which the product temperature remains

492constant and equal to the wet bulb temperature of hot air

493(circa 48 °C for this trial) as shown in Fig. 5a. It is noted

494that the wet bulb temperature decreases by 1–2 °C,

495probably due to the thermal losses and to the variations

496of air temperature and moisture content. During this

497period, a large amount of the water contained in the

498product is evaporated (Fig. 5b) while the air humidity

499increases and the air temperature decreases (Fig. 5b). It

500is important to notice that, in this case, the phase of

501drying at constant rate is not observed. Results pre-

502sented here show that the product drying rate is always

503decreasing (Fig. 5b and c). The calculation of product

504drying rate can be made according to:

�dnp

dt¼

kp Sap�mdp

pvsat � pvað Þ ð15Þ

505506

507By analyzing Eq. 15, the monotically decrease of product

508drying rate is explained by:

509– the decrease of the mass transfer coefficient kp due to

510the decrease of droplet terminal velocity vl (itself due to

511product shrinkage during drying)

512– the decrease in the lineic exchange area between air and

513particles Sap due to particle diameter dp decrease

514– the increase of air partial vapor pva due to drying of

515droplets

516517An inflection is also noted in the drying rate of the

518product after 2 s of treatment (Fig. 5b) for a product mois-

519ture content of 2 kgkg−1 DM (Fig. 5c). This inflection can

520be related to the profile of variation of the particle diameter

521dp which starts to remain constant at this moment. Thus,

522after 2 s of drying, the decrease of the drying rate of the

523product does not depend anymore on the variations of the

524variable Sap.

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160

exp

erim

enta

l v

alu

es

simulated values

Fig. 4 Comparison between experimental and simulated values for air

outlet temperature, Tao (degree Celcius)

t2:1 Table 2 Simulated values of air

outlet temperature and particles

outlet temperature

t2:2 Processing conditions

t2:3 1 2 3 4 5 6 7 8 9 10 11 12 13 14

t2:4 Tao (°C) 72 87 101 96 117 124 132 51 74 97 86 92 129 124

t2:5 Tpo (°C) 59 88 102 97 118 125 133 46 75 98 87 93 130 125



AUTHOR'S PROOF

UNCORRECTEDPROOF

525 – Period 3 during which the residual water is evaporated

526 (Fig. 5b) and the drying rate of the product decreases

527 brutally and tends towards a zero value (Fig. 5b and c).

528 This phenomenon is explained by the development of a

529resistance to the evaporation of water when a moisture

530content circa 1 kgkg−1 DM is reached for the product.

531This resistance can also be seen on the rapid decrease of

532the value of ψ function (Fig. 5c). It is also noted that the

533temperature of the product increases quickly and becomes

534close to air temperature. The total energy received by the

535product is not mainly used to evaporate residual water but

536also to increase its internal energy. Fast increase in the

537product temperature leads to a fast increase in pvsat which

538allows, in spite of the reduction of the value ofψ function,

539to maintain the drying rate of the product to a value

540relatively high in the field of product moisture content

541between 0.1 and 0.4 kgkg−1 DM.

542– Period 4 which follows period 3 when the difference

543between product and air temperature becomes lower

544than 2 °C (Fig. 5a). It is noted that, during this period,

545the product temperature decreases, due to the dryer

546thermal losses and consequent decrease of air tempera-

547ture. The product and the drying air are in equilibrium

548with respect to the mass and heat transfers. In this trial,

549the duration of the period 4 (5 s) is about half of the total

550duration of drying (12 s). This period corresponds to an

551additional time of drying, since the product drying rate

552is nearly equal to 0. Moreover, we can assume that

553during this, period when the product temperature rea-

554ches values higher than 100 °C, the product can be more

555subjected to physicochemical transformations. This hy-

556pothesis is based on previous studies on protein dena-

557turation which was found to occur for WPC at a

558temperature higher than 60 °C [ Q137–40].

559So, these thermohydric histories seem to be in agree-

560ments with kinetics of liquid droplet evaporation obtained

561by Nesic and Vodnik (1991) from individual droplets sus-

562pended in a controlled air stream.

563Analysis of the Influence of Processing Conditions upon

564Thermohydric History of Droplets

565After analyzing the patterns of variation of various variables

566relative to product and air during drying, the influence of a

567variation of Tai, m

�

a, and m

�

pon the thermohydric history of the

568droplets is discussed in this paragraph using simulated data.

569Case study 1: Effect of increasing air inlet temperature Tai570upon thermohydric history of droplets.

571In Fig. 6a–c, the thermohydric histories of droplets (Tp,

572np) and the product drying rate (−dnp/dt) variation are pre-

573sented for different air inlet temperature. Three sets of

574simulated data are presented for air inlet temperatures of

575170, 217, and 260 °C, corresponding to experiments 1, 4,

576and 7, respectively (Table 1).

Fig. 5 Simulated thermohydric histories for drying air and product

(trial 4, Table 1). a Air temperature (Ta), product temperature (Tp), and

wet bulb temperature (Twb), function of drying time (t); b product

moisture content (np) and air moisture content (na) function of drying

time (t); c drying rate of the product (−dnp/dt) and ψ function values,

function of product moisture content (np). The values 1, 2, 3, and 4

correspond to different drying periods



AUTHOR'S PROOF

UNCORRECTEDPROOF

577 The four periods of drying defined in the preceding part are

578 observed for two of the three drying conditions. In fact, period

579 4 cannot be distinguished for the trial carried out at an air inlet

580 temperature of 170 °C. For all drying conditions, the product

581 temperature during the second period of drying is equal to the

582 wet bulb temperature of the drying air and thus is increased

583 when the air inlet temperature is increased. Indeed, the wet

584 bulb temperature is circa 42 °C for the trial with Tai0170 °C,

585 48 °C for Tai0217 °C, and 54 °C for Tai0260 °C (Fig. 6a). The

586 product temperature during the period 4 of drying is also

587 found higher for higher air inlet temperature. This result was

588 expected since the air outlet temperature is higher. Moreover,

589 the product reaches its final moisture content more quickly

590 when the air inlet temperature is increased. This is due to an

591 increase of the product drying rate at the beginning of the

592 period 2 (Fig. 6c). Increasing Tai increases the drying rate and

593 reduces consequently the duration of the second period of

594 drying (Fig. 6a and b). This duration is close to 4 s for Tai0

595 260 °C and 10 s for Tai0170 °C. It is noted that, for the three

596 experiments, the product moisture content is always lower

597 than 5 %. The powders obtained with Tai0217 and 260 °C

598 reach more quickly their final moisture content and the dura-

599 tion of the period 4 of drying is hence increased.

600 Case study 2: Effect of decreasing air flow rate valuem�

aupon

601 thermohydric history of droplets.

602 Fig. 7a and b present two sets of simulated data for air

603 flow rates of 0.029 and 0.021 kgs−1 corresponding to the

604 experiments 4 and 9, respectively (Table 1).

605As expected, the particles residence time increases slight-

606ly with a decrease of the air flow rate (12 s for 0.029 kgair

607secs−1 and 17 s for 0.021 kgairsecs−1). This result seems

608logical since the velocity of the liquid droplet in the drier vp609is the sum of the velocity of the drying air va and of the

610terminal velocity of the particle in the air vl (see Eq. 1).

611However, the variations of vl are very small compared to the

612variations of va when the air flow rate is modified (vl varies

6130.003 to 0.0004 ms−1 and va from 0.07 to 1.9 ms−1 when the

614air flow rate is increased from 0.021 to 0.029 kgkg−1 DA).

615The increase of air flow rate increases slightly the product

616drying rate and hence increases the duration of period 4 of

617drying. The product reaches hence a higher final tempera-

618ture for a higher air flow rate (97 °C for 0.029 kgdryairs−1

619and 75 °C for 0.021 kgdryairs−1).

620Case study 3: Effect of decreasing WPC flow rate m�

pupon

621thermo-hydric history of droplets.

622On Fig. 8a and b, two sets of simulated data are presented

623for product flow rate of 9.4 10−4 and 4.7 10−4kgs−1

624corresponding to the experiments 10 and 13, respectively

625(Table 1).

626An increase in WPC flow rate induces an increased of the

627load of liquid water in the spray drying chamber. Air final

628specific humidity is more hence important for high level of

629product flow rates (0.046 kgkg−1 DA for a WPC flow rate of

6309.4 10−4kgs−1 and 0.024 kgkg−1 DA for a WPC flow rate of

6314.7 10−4kgs−1). In the range investigated in our trials, the

632time needed for water evaporation (duration of the second

np

(g.g

-1D

M)

a) b) c)

Fig. 6 Simulated moisture (a) and temperature (b) profiles for droplets and product drying rate (c) for three different air inlet temperatures Tai:

170 °C (broken line), 217 °C (dashed line), and 260 °C (straight line)

a) b)

np

(g.g

-1D

M)

Fig. 7 Simulated moisture (a)

and temperature profiles (b) for

air and droplets at different air

flow rates m�

a: 0.029 kgs−1

(broken line) and 0.021 kgs−1

(straight line)



AUTHOR'S PROOF

UNCORRECTEDPROOF

633 period of drying) is slightly longer when WPC is increased

634 (4.6 s for a WPC flow rate of 9.4 10−4kgs−1 and 3.3 s for a

635 WPC flow rate of 4.7 10−4kgs−1) as shown in Fig. 8a and b.

636 For period 4 of drying, the product reaches higher temper-

637 atures when product flow rate is decreased (93 °C for 9.4

638 10−4kgs−1 and 118 °C for 4.7 10−4kgs−1). This is due to the

639 air outlet temperature which is lower when the product flow

640 rate is increased.

641 Thus, when the operating conditions of the drier are

642 changed, the thermohydric histories followed by the product

643 can be very different and differences in quality of the pow-

644 ders can be expected. We noted no significant effect of

645 increasing WPC initial concentrate moisture content npi646 (between 0.8 and 0.9 kgkg−1) on drying kinetics. Thus, very

647 few differences are expected for product quality changes

648 when the WPC initial moisture content is varied from 0.8

649 to 0.9 as investigated in this study.

650 Conclusion

651 Spray drying is a unit operation with a very short residence

652 time (less than 20 s for a pilot height of 1.15 m). The model

653 detailed in this study allows us to assess to the liquid

654 droplets and drying air thermohydric histories during the

655 drying process.

656 The influence of drying operating conditions on the ther-

657 mohydric histories followed by the product during the pro-

658 cess has been detailed. For all the spray-drying experiments,

659 the drying kinetics presented a period with constant temper-

660 ature (equal to wet bulb temperature) and the product drying

661 rate was always found monotically decreasing with drying

662 time. During the last period, a rapid increase in particle

663 temperature is noted. At the end of drying, particles and

664 drying air are nearly in thermal equilibrium. In all cases, an

665 important increase in product final temperature is noted in

666 the last period of drying and the product can reach temper-

667 atures higher than 100 °C. The most significant variations in

668 product thermohydric history are noted when the inlet air

669 temperature is increased or when the air or the WPC flow

670 rate is decreased. However, when WPC initial moisture

671content is increased, very few variations are observed for

672particles thermohydric histories. Therefore, an important

673impact of the drying on product quality is expected when

674air inlet temperature, air flow rate, and product flow rate are

675modified.

676One of the main issues in spray drying is actually to

677establish causal relationships between the liquid droplet

678history in terms of temperature and moisture content fol-

679lowed during its residence in the spray dryer and the level of

680induced transformations. So, in our future work, the influ-

681ence of time and product temperature and moisture content

682variations upon product physicochemical changes will be

683investigated using the thermohydric profiles calculated by

684the model. The model will then be a helpful tool in order to

685adjust the drying operating conditions to obtain powders

686with desired qualities, rather than relying on trial and error

687methodology.

688In addition to this first step, there are several ways to

689improve the model such as the consideration of the droplets

690size distribution in the drying chamber. It is also important

691to be able to validate the model by using another set of

692experimental data, or by using other suspensions on another

693pilot scale or industrial dryer.

694Nome Q2nclature

696Az 697Area of dryer cross-section at position z (m2)

698d 699Diameter (m)

700Cp 701Specific heat (Jkg−1K−1)

702h 703Convective heat transfer coefficient (Wm−2K−1)

704ΔHvap 705Latent heat of vaporization (Jkg−1)

706k 707Mass transfer coefficient (kgm2s−1Pa−1)

708k0, k2 709Empirical coefficients in Eq. 2

710k1, k3 711Empirical coefficients in Eq. 2 (K−1)

712m 713Mass flow rate (kgs−1)

714n 715Moisture content (kgkg−1dm)

716Np 717Number of particles per unit length of dryer (m−1)

718Nu 719Nusselt number (SD)

720P 721Pressure (Pa)

722Pr 723Prandtl number (SD)

724pv 725Partial vapor pressure (Pa)

726Re 727Reynolds number (SD)

a) b)

np

(g.g

-1D

M)

Fig. 8 Simulated moisture (a)

and temperature (b) profiles for

air and droplet at different

product flow rates m�

p: 9.4 10−4

kgs−1 (broken line) and 4.7

10−4kgs−1 (straight line)



AUTHOR'S PROOF

UNCORRECTEDPROOF

728 rz729 Dryer radius (m)

730 Sap731 Lineic exchange area between air and particles (m)

732 T733 Temperature (K)

734 U735 Global heat transfer coefficient (Wm−2K−1)

736 v737 Velocitym (s−1)

738 V739 Volume (m3)

740 z741 Position from dryer entrance (m)742

743 Greek letters

745 α746 Thermal diffusivity (m2s−1)

747 βNu748 Empirical coefficient for heat transfer calculation in

749 Eq. 11

750 ν751 Kinematic viscosity (m2s−1)

752 ρ753 Density (kgm−3)754

755 Subscripts

757 a758 Air

759 c760 Critical

761 d762 Droplet

763 da764 Dry air

765 dm766 Dry matter

767 dp768 Dry product

769 i770 Inlet

771 l772 Terminal

773 lw774 Pure liquid water

775 o776 Outlet

777 p778 Particle

779 sat780 At the saturation

781 vap782 Vapor

783 wb784 Wet bulb

785 0786 Initial

787 50788 Mean

789790

791 Acknowledgments The authors acknowledge P. Schuck (INRA-

792 Rennes/STLO) and J.F. Boudier (Ingredia-France) for fruitful

793 discussions.

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920



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Prediction of Thermohydric History of Whey Protein Concentrate Droplets during Spray Drying

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