Journal of Food Engineering xxx (2012) xxx–xxx

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Journal of Food Engineering

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

Modeling deep-fat frying for control of acrylamide reaction in plantain

Joseph Bassama a, Pierre Brat a, Renaud Boulanger a, Ziya Günata b, Philippe Bohuon c,⇑a CIRAD, UMR QualiSud 40/15, 73 rue J.-F. Breton, 34398 Montpellier Cedex 5, Franceb Université Montpellier II, UMR Qualisud, place E. Bataillon, 34095 Montpellier Cedex 5, Francec Montpellier SupAgro, UMR QualiSud, 1101 avenue Agropolis, CS 24501, 34093 Montpellier Cedex 5, France

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

Article history:Received 22 July 2011Received in revised form 6 April 2012Accepted 17 April 2012Available online xxxx

Keywords:FryingHeat and mass transferMaillard reactionModelingProcess optimization

0260-8774/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.jfoodeng.2012.04.004

⇑ Corresponding author. Tel.: +33 4 67 615726; faxE-mail address: philippe.bohuon@supagro.inra.fr (

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This paper discusses the possibility of controlling acrylamide formation/elimination reactions in plantainduring frying. A 2D model including heat and vapor transfer and acrylamide reactions was developed. Themodel was validated against experimental data, consisting of the plantain core temperature and averagewater and acrylamide contents. Validations were made on two different typical plantain-based foods, i.e.‘‘tajadas’’ (thick product) and ‘‘tostones’’ (thin product), in which the acrylamide contents were found tobe 0.24 and 0.44 mg kg�1 (fat-free dry basis), respectively. The simulations highlighted that non-isother-mal heat treatment is a good strategy to reduce the acrylamide content (up to 50% reduction). However,controlling the asparagine content in the raw material through maturity stage selection or by implement-ing immersion pretreatments is an easier way to mitigate the acrylamide net amount in plantainproducts.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Acrylamide, a potential human carcinogen, is formed in foodthrough Maillard reactions (Elmore et al., 2005). Since 2002, manystudies have focused on acrylamide contents in frequentlyconsumed heat treated food products (Brunton et al., 2007; Pedreschiet al., 2007a; Tareke et al., 2002). However, the presence ofacrylamide in typical tropical foods remains poorly investigated.Acrylamide contents in different tropical foods were estimatedthrough correlations with non-enzymatic browning values andranged from 0.02 to 1.04 mg kg�1 (Quayson and Ayernor, 2007).To our knowledge, no studies have focused on the analytical quan-tification of acrylamide in plantain-based food. Plantain is a sub-group of cooking bananas and widely consumed in tropicalcountries. In 2006, world plantain production represented 18% ofthe world banana production with 18 million tons (Lescot, 2008).Due to the high native starch content in plantain (close to that ofpotato), the foodstuff must be cooked (gelatinized) before it is edi-ble. Plantain-based products are mainly prepared by deep-fat fry-ing and plantain crisps are more consumed, in terms of volume,than potato or banana crisps (Vitrac and Raoult-Wack, 2002).

Deep-fat frying is defined as the process of cooking foods bysoaking them in edible fat or oil at a temperature above the boilingpoint of water, usually 120–180 �C (Farkas et al., 1996a). Frying isoften chosen because of its ability to create unique flavors andtextures in processed foods. It is also a very fast food processing

ll rights reserved.

: +33 4 67 615728.P. Bohuon).

t al. Modeling deep-fat frying2.04.004

method among conventional heat transfer methods. A properunderstanding of the mechanisms of deep-fat frying is importantfor the development of predictive models, which save experimen-tation time and cost. Since the studies of Farkas et al. (1996a),during the frying process the material is often described as beinga two-region model with a sharp boundary separating the coreand the crust region. Frying is considered as a moving boundaryproblem where the interface between crust and core moves. Thisformulation is also called a front-tracking model.

Farkas et al. (1996a,b) provided a detailed model of heat andwater transport in deep-fat frying of potato slices. Separate equa-tions were used for each region (crust and core), while pressure-driven flow was included in the crust for the vapor phase.However, diffusion flow in the crust region and pressure-drivenflow of liquid and vapor in the core region were overlooked. More-over, the model did not include the oil phase or the effect of chang-ing porosity on heat and mass transfer. Moving boundary modelsthat just solve the heat transfer equation have also been reported(Bouchon and Pyle, 2005; Farid and Chen, 1998). In contrast tosharp boundary models, distributed evaporation models weredeveloped which consider evaporation to be distributed over azone (Ni and Datta, 1999; Yamsaengsung and Moreira, 2002). Fora given frying situation, it is possible that the real evaporation zoneis very narrow, closer to the sharp interface, and the distributedevaporation formulation would actually predict such narrow evap-oration zone. At high internal evaporation rates, significant pres-sure-driven flows can be present for all phases and throughoutthe material. Therefore, a set of empirical equations describingthe water–vapor equilibrium relation for specific food materials

for control of acrylamide reaction in plantain. Journal of Food Engineering

Nomenclature

aw water activitycpi

specific heat of component i (J kg�1 K�1)ci concentration of component i (M or mg kg�1)DM dry matterEaX activation energy (J mol�1)H smooth approximation of the Heaviside functionh heat transfer coefficient (W m�2 K �1)_I evaporation rate (kg m�3 s�1)Keff thermal conductivity (W m�1 K�1)krv relative permeability of the material to vaporKv intrinsic pseudo-permeability of vapor (m2)kX formation (X = F) or elimination (X = E) rate constants

(s�1)kXref formation (X = F) or elimination (X = E) rate constants at

the reference temperature (s�1)Mi molar mass of component i (kg mol�1)~n normal vectorp pressure of the gaseous phase (Pa)qv vapor flux (kg m�2 s�1)R universal gas constant (J mol�1 K�1)S saturation stateT temperature (K)Tsat saturated temperature of pure water (K)Tref reference temperature (K)t time (s)~v vapor velocity (m s�1)W water content (in wet basis) (kg kg�1)

x, y coordinates (m)

Greek symbolsd smooth approximation of the Dirac delta functionei volume fraction of phase ik latent heat vaporization of water (J kg�1)l viscosity (Pa s)qi density of phase i (kg m�3)q�i intrinsic density of phase i (kg m�3)1 ambient

Superscripts and subscriptsAA acrylamideAsn asparaginecb close boundariesDP molecules coming from acrylamide degradationeff effective propertyi component or phase i‘ liquid phaseob open boundariess solid phasesat saturated state(t) at time t(0) at time t = 0v vapor⁄ intrinsic property

2 J. Bassama et al. / Journal of Food Engineering xxx (2012) xxx–xxx

was used to describe the evaporation rate as function of time(Halder et al., 2007a). Recently, the Heaviside function was usedto represent the evaporation rate as function of temperature inthe wood fry-drying process (Grenier et al., 2010). The studyshowed that intense water vaporization involved in the woodfry-drying process generated pressure as the sample core pressureincreased to over 250 kPa. The authors suggested that, under suchpressure conditions, vapor transport driven by Darcy’s law shouldbe considered as the prevailing phenomenon in a simplified heatand mass transport model. Achir et al. (2008) represented arealistic desorption isobar with the parametric function.

The kinetics of acrylamide formation and degradation has beendescribed by several mathematical models of varying complexityusing a simple kinetic model, multiple response kinetic model orlogistic kinetic model (Claeys et al., 2005b; Corradini and Peleg,2006; Knol et al., 2005). Corradini and Peleg (2006) combined afrying model with a Fermi model of acrylamide formation and deg-radation. The model was validated with different published datahaving high variability in terms of acrylamide content. Moreover,the heat and mass transfer associated with the kinetic model didnot account for the impact of water content (or water activity)on the rate constants of acrylamide formation and elimination.Recently, Bassama et al. (2011) investigated acrylamide kineticsin plantain paste at different water activities. The study showedthat the free asparagine content in plantain was 1000-fold lowerthan free sugar content. The authors also observed a 75% reductionin asparagine content during plantain ripening, showing thatasparagine was the limiting factor in acrylamide formation. Thekinetic experiments were performed in a closed reactor and thestudy revealed a significant increase in acrylamide formation andelimination reaction rates with increasing temperature anddecreasing water activity.

The aim of this study was, first, to develop a frying model to de-scribe combined transfer (water and heat) and the reaction of

Please cite this article in press as: Bassama, J., et al. Modeling deep-fat frying(2012), http://dx.doi.org/10.1016/j.jfoodeng.2012.04.004

acrylamide within two kinds of plantain-based products. A thickproduct (‘‘tajadas’’) characterized by an intermediate final watercontent (30% w.b.), and a thin product (‘‘tostones’’) with a verylow residual water content (5%). The kinetic parameters used forthe acrylamide kinetics were those identified by Bassama et al.(2011). The second aim was to use simulations to identify and testdifferent strategies to control acrylamide formation during deep-fat frying: isothermal and non-isothermal heat treatment, pre-treatment of plantain products, and effects of the maturity stage.

2. Materials and methods

2.1. Plantain sampling

The raw material was prepared as shown by Rojas-Gonzalezet al. (2006). Plantains (Musa AAB ‘‘barraganete’’) at level two ofcommercial maturity (peel still completely green) from Colombiawere purchased from a retail shop in Montpellier (France). Theraw material was characterized (asparagine and free sugarcontent) and processed the day of their reception. Before frying,the raw plantains were peeled and cut into disks (30.0 ± 0.2 mm)with a cork borer in the longitudinal direction of the plantain.The disks were then trimmed to a thickness of 10.0 ± 0.2 mm usingparallel blades.

2.2. Frying equipments

A large insulated household deep-fat fryer (model KPB 50,Kenwood, France) was filled with 4.5 kg of palm oil and heatedwith an electric element (effective power 1.6 kW) submerged3 cm above the bottom of the tank. This heating configurationgenerated a ‘‘cold’’ region below the electrical resistance. The oilbath was not stirred and the bulk temperature, T1, was controlled

for control of acrylamide reaction in plantain. Journal of Food Engineering

J. Bassama et al. / Journal of Food Engineering xxx (2012) xxx–xxx 3

by a numerical PID controller based on the median of five temper-ature measurements. Six plantain disks (approximately 40 g) werefried at 180 �C at atmospheric pressure. When the disks were firstplunged into the oil, the maximum local temperature variation wasT1 — 3 �C. Plantain cylinders were maintained submerged in awire basket.

2.3. Preparation of ‘‘tajadas’’ and ‘‘tostones’’

‘‘Tajadas’’ were obtained after these disks were fried at 180 �Cat times ranging from 4 to 7 min (Fig 1), as described by Rojas-Gonzalez et al. (2006). Six plantain disks were kept submerged ina wire basket with a separate compartment for each disk(70 � 100 � 15 mm). ‘‘Tostones’’ are made of plantain disks thatwere first fried (similar to ‘‘tajadas’’), crushed, and fried again, asdescribed by Avallone et al. (2009). The time interval betweenthe first and second frying did not exceed 90 s. For each time, sixdisks were sampled, wiped, and frozen at �20 �C.

2.4. Water content

Because of the high lipid and starch content of the samples, thewater content was determined in two steps by the gravimetricmethod. Raw and fried plantains were first pre-dried at 50 �C for12 h and then dried at 70 �C at low pressure for 12 h. The values

Fig. 1. Processing of ‘‘tajadas’’ and ‘‘tostones’’ (a) first frying, (b) second fryi

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correspond to the mean of three plantain disks fried at the sametime.

2.5. Fat content

The fat content was determined with an Accelerated SolventExtractor, DIONEX (ASE-200, Sunnyvale, CA, USA). Lipids wereextracted from the dried samples (approximately 2 g) with petro-leum ether at 70 �C for 35 min. The solvent was then evaporatedand the lipids weighed. The values correspond to the mean of threeplantain disks fried at the same time.

2.6. Analysis of acrylamide and asparagine

Finely ground samples (1 g) were weighed in a 35-mL glass cen-trifuge tube with a cap. The targeted compound was quantifiedthrough isotope dilution analysis. Samples were spiked at thisstage with 1 lg of labeled acrylamide (3H2-acrylamide). Thesample was suspended in 10 mL of water with 0.2% formic acidand homogenized for 2 min using an Ultraturax (IKA, Staufen,Germany), followed by 2 h extraction on a shaker (Heidolph, MultiReax, Schwabach, Germany). The extract was centrifuged at10,000 rpm for 10 min (Allegra 21 centrifuge, Beckman Coulter,Brea, CA, USA). The clear supernatant was transferred into a centri-fuge tube and treated with Carrez I and II solutions (100 lL of each)to precipitate the co-extractives. Carrez I and II solutions were

ng from Rojas-Gonzalez (2007) and Avallone et al. (2009), respectively.

for control of acrylamide reaction in plantain. Journal of Food Engineering

4 J. Bassama et al. / Journal of Food Engineering xxx (2012) xxx–xxx

prepared by dissolving 15 g of potassium hexacyanoferrate and30 g of zinc sulfate in 100 mL of water, respectively. This was fol-lowed by centrifugation at 10,000 rpm for 10 min, all clear super-natant (8 mL) was transferred into a conical bottomed test tube.Purification and concentration were performed as described byRosén et al. (2007). After filtration through a 0.45-lm syringe filter,the sample was analyzed by HPLC–ESI-MS/MS, as described byBassama et al. (2011). The asparagine analysis was performed asdescribed by Bassama et al. (2011).

2.7. Measurement of the core temperature

The plantain core temperatures were monitored using 0.5-mm-thick K-type microthermocouples (Model 12MK 0.25, TC, Dardilly,France). Temperature data were acquired using dedicated software(Labview version 5.1, Natl. Instrument).

2.8. Repeatability of the results

At least three batches were carried out for each test and thestandard deviation is presented in the figures or mentioned inthe captions for clarity.

3. Mathematical formulation

3.1. Major assumptions

A global model, which combines heat and water transfer withthe formation/elimination of acrylamide in Maillard reaction kinet-ics, was developed to predict the acrylamide content in plantainproducts (‘‘tostones’’ and ‘‘tajadas’’) under different frying condi-tions (isothermal and non-isothermal conditions). A schematicdescription of the problem (a 2D axial-symmetric domain) isshown in Fig 2. The external heat convection flux was assumedon the top and lateral sides (open boundary). The vapor flux wasmodeled using an adjusted pseudo-permeability. The bottom andaxial sides (closed boundary symmetry plane) were insulated andthe heat and vapor fluxes were zero. Five other major assumptionsare used in this work: (1) the solid, liquid, and gas phases werecontinuous; (2) the geometry did not change; (3) a local thermalequilibrium existed between the phases; (4) the initial air in thematrix was considered as vapor; and (5) oil penetration is ignoredbecause it essentially takes place at the end of the fry-drying pro-cess (Moreira et al., 1997).

3.2. Equilibrium state variables

The three different phases constituted a continuous medium:solid matrix (s), liquid (l) and vapor (v). The studied state variableswere asparagine concentration (cAsn), acrylamide concentration

Fig. 2. Schematic representati

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(cAA), temperature (T), pressure (p) and equivalent saturation ofthe liquid water (S‘), defined as:

S‘ ¼e‘

e‘ þ evð1Þ

where ei is defined as the volume fraction occupied by component i.Liquid saturation describes the bulk densities of the liquid and thevapor phases:q‘ ¼ S‘q�‘ 1� esð Þ ð2Þ

qv ¼ 1� S‘ð Þq�v 1� esð Þ ð3Þwhere q�i is the intrinsic density of phase i. The intrinsic density ofvapor is given by

q�v ¼MvpRT

ð4Þ

where Mv is the water molar mass, R the universal gas constant and Tthe temperature. The water content (noted W and expressed in drybasis) is related to the liquid (q‘) and solid matrix (q�ses) density by

W ¼ q‘

q�sesð5Þ

Liquid saturation at time t (noted S‘) was calculated using theHeaviside function, which is an interpolation polynomial of an ex-plicit Boolean function, as proposed by Grenier et al. (2010):

S‘Sð0Þ‘¼ 1� H ð6Þ

where H is a smooth Heaviside function of ðT � TsatÞ=DT in a 2DTtransition interval around the saturated temperature of pure water(Tsat). This function is a of a polynomial of degree 5 which is C2 con-tinuous at ðTsat � DTÞ and ðTsat þ DTÞ. H was used to represent thatS‘=Sð0Þ‘ switched from 1 to 0 when T increased from Tsat � DT toTsat þ DT .

3.3. Mass balances

The conservation equation for liquid water and vapor, are writ-ten respectively as:

@q‘

@t¼ �_I ð7Þ

@qv@tþ r!� qv~vv

� �¼ _I ð8Þ

where ~vv , is the vapor velocity. When adding Eq. (7) with Eq. (8),the evaporation term I is eliminated, such that Eq. (9) for the watercomponent is obtained.

@ q‘ þ qv� �

@tþ r! � qv~vv

� �¼ 0 ð9Þ

on of the physical model.

for control of acrylamide reaction in plantain. Journal of Food Engineering

J. Bassama et al. / Journal of Food Engineering xxx (2012) xxx–xxx 5

3.4. Vapor transport equation

The total flux of vapor (qv~vv ) consists of Darcy’s flow in termsof total pressure

qv~vv ¼ �qvkrvKv

lv

~rp ð10Þ

where lv is the viscosity of vapor, Kv is the intrinsic pseudo-perme-ability of vapor and krv is the relative permeability of the material tovapor given by Bear (1972):

krv ¼1� 1:1S‘ S‘ < 1=1:10 S‘ > 1=1:1

�ð11Þ

3.5. Energy balances

The temperature (T) distribution in the computational domaincan be obtained from the energy conservation equation. Energytransport by convection is neglected ð~r � ðPqicpi

T~v iÞÞ. Grenieret al. (2010) showed that the magnitude of its contribution was20-fold lower than the energy transported by conduction duringthe wood fry-drying process. Therefore, in this study only heatconduction is considered and Fourier’s law is applied:

qcp� � @T

@tþ r! � �Keffr

!T

� �¼ �_Ik ð12Þ

where q is the bulk density, cp is the bulk specific heat and k is thelatent heat vaporization of water. Keff is the effective thermalconductivity given by

Keff ¼ KDMeDM þ S‘K‘ 1� eDMð Þ þ 1� S‘ð ÞKv 1� eDMð Þ ð13Þ

By using the mass conservation Eq. (7) and replacing (@q‘=@t) byð@q‘=@TÞð@T=@tÞ in Eq. (12), Eq. (14) may be:

qcp �@q‘

@T

� �k

|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

qcpð Þeff

@T@tþ r!� �Keffr

!T

� �¼ 0 ð14Þ

Eq. (14) may be written in terms of an effective heat ðqcpÞeff asfollows:

qcp� �

eff

@T@tþ r! � �Keffr

!T

� �¼ 0 ð15Þ

with

qcp� �

eff ¼ esq�s cpsg dry matrix term

þ 1� esð Þq�‘ S‘cp‘ þ Sð0Þ‘ dkh i

g liquid water term

þ 1� esð Þq�v 1� S‘ð Þcpv g vapor term

ð16Þ

where cpiis the specific heat of component i. The smooth Heaviside

function (H) is the integral of the smooth approximation of theDirac delta function d

HðTÞ ¼Z T

�1dds ð17Þ

which is also constrained to satisfy the identityZ þ1

�1dds ¼ 1 ð18Þ

This impulsion function is frequently used to represent anabrupt change in one or more physical properties (in particularhere the heat capacity) with a small change in a thermodynamicvariable such as the temperature during phase change (Grenieret al., 2010).

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3.6. Reaction kinetics modeling

According to Bassama et al. (2011), acrylamide formation/elim-ination can be described Asnþ Glu !kF AA !kE DP as a first-order for-mation (kF) and a first-order elimination (kE), where Asn isasparagine, Glu the sum of the glucose, fructose and sucrosecontent, AA for acrylamide and DP for molecules coming fromacrylamide degradation. The scheme is translated mathematicallyby an differential equations system (Eq. (19)):

@cAsn@t ¼ �kF cAsn ðaÞ

@cAA@t ¼ kF cAsn � kEcAA ðbÞ@cDP@t ¼ kEcAA ðcÞ

9>>=>>; ð19Þ

cDP is the degradation/elimination product concentration. Therate constant, kX (s�1 for formation and elimination), varied withthe system’s absolute temperature, T (K), according to the Arrhe-nius law, as follows:

kX ¼ kXrefexp

�EaX

R1T� 1

Tref

� � ð20Þ

where kXref , EaX and R are, respectively, the rate constant at the ref-erence temperature (Tref ¼ 443 K) for formation (X ¼ F) or elimina-tion (X ¼ E), the apparent activation energy (J mol�1) for the rateconstant and the gas constant (8.314 J mol�1 K�1). kXref is also linkedto the water activity (aw) using a non-linear regression on the reac-tion constant values as a function of the water activity proposed byBassama et al. (2011).

kFref¼ exp �9:40þ 0:0531

ln awð Þ

� �kEref¼ exp �3:80þ 0:0882

ln awð Þ

� �9>=>; ð21Þ

The water activity was computed by smoothing the moisturesorption isotherm of freeze–dried plantain at 25 �C using a non-lin-ear regression on the values of aw as a function of the water content(W) from previously published data (Bassama et al. 2011).

aw ¼0:099þ 20:97W

1þ 20:01W

� �2

ð22Þ

The regressions (Eqs. (21) and (22)) were performed (Table-Curve 2D software) with an assigned correlation coefficient valueof R2 � 0:98.

3.7. Initial conditions

Plantain was assumed to be at uniform temperature T ð0Þ, uni-form total pressure equal to the ambient pressure pð0Þ, uniformliquid saturation Sð0Þ‘ , uniform asparagine cð0ÞAsn, and acrylamide cð0ÞAA

contents. Thus, the initial conditions can be expressed as:

Tðr; zÞ ¼ Tð0Þ; pðr; zÞ ¼ pð0Þ; S‘ðr; zÞ ¼ Sð0Þ‘

cAsnðr; zÞ ¼ cð0ÞAsn; cAsnðr; zÞ ¼ cð0ÞAA ;

)t ¼ 0 ð23Þ

3.8. Boundary conditions

At the closed boundaries (symmetry lines), no vapor and energyexchanges took place.

n!� r!p���cb¼ 0 ð24Þ

n!� r!T���cb¼ 0 ð25Þ

for control of acrylamide reaction in plantain. Journal of Food Engineering

6 J. Bassama et al. / Journal of Food Engineering xxx (2012) xxx–xxx

n!� r!cAsn

���cb¼ 0 ð26Þ

n!� r!cAA

���cb¼ 0 ð27Þ

At the open boundaries (top and lateral sides) there was vaporand energy exchange. The vapor flux reaching the boundaries fromthe inner part was fully evaporated and drained away into theambient environment. The vapor pressure at the surface equaledthe ambient pressure p1.pob ¼ p1 ð28Þ

n!� Keffr!

T���

ob¼ h T1 � Tobð Þ ð29Þ

n!� r!cAsn

���ob¼ 0 ð30Þ

n!� r!cAsn

���ob¼ 0 ð31Þ

where h is the heat transfer coefficient.

3.9. Input parameters

Some of the input data are given in Table 1. The characteristicdimensions of plantain used are displayed in Fig. 3. The saturatedtemperature of pure water (Tsat) is an explicit function of thepressure (psat) given by Perré (1995):

Tsat ¼5204:9

25:5058� ln psatð Þ ð32Þ

The latent heat vaporization of water k is a function of temperature(Perré, 1995):

k ¼ 103 � ð3174:95� 2:46TÞ ð33Þ

The heat transfer coefficient (h) is taken as a decreasing func-tion of the vapor flux leaving the open boundaries qv job in orderto mimic the convection effect of the vapor bubbles. This functionis given by Costa et al. (1999):

h ¼ 28;820� qv job þ h0 ð34Þ

where h0 is the natural heat convection, h0 ¼ 271 W m�2 K�1 for allsimulations.

Table 1Input parameters used for simulations.

Input parameter

Specific heat of water, cp‘ (J kg�1 K�1)Specific heat of vapor, cpv (J kg�1 K�1)Specific heat of dry matrix, cps

(J kg�1 K�1)

Intrinsic permeability, Kv (m2) ‘‘Tajadas’’

‘‘Tostones’’

Water molar mass, Mv (kg mol�1)

Universal gas constant, R (J mol�1 K�1)Initial volume fraction of gas, e0

v ‘‘Tajadas’’‘‘Tostones’’

Initial volume fraction of solid matrix, es ‘‘Tajadas’’‘‘Tostones’’

Initial moisture saturation, S‘Initial natural heat convection, h0 (W m�2K�1)

Initial asparagine content, cð0ÞAsn (M)

Initial acrylamide content, cð0ÞAA (M) ‘‘Tajadas’’

‘‘Tostones’’

Oil temperature T1 (�C)Half transition interval (Heaviside function) DT (K)Viscosity of vapor, lv (kg m�1 s�1)

Intrinsic density of the solid matrix q�s (kg m�3)Intrinsic density of water q�‘ (kg m�3)

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3.10. Numerical solution

The system consists of four independent state variables:TðtÞðr; zÞ, pðtÞðr; zÞ, cðtÞAsnðr; zÞ and cðtÞAAðr; zÞ. The governing equationsfor TðtÞðr; zÞ and pðtÞðr; zÞ are the two coupled non-linear and time-dependent partial differential Eqs. (9) and (15). The governingequations for cðtÞAsnðr; zÞ and cðtÞAAðr; zÞ are the two coupled differentialequations. The system was solved using the FEM-based commer-cial code COMSOL Multiphysics™ package (version 3.1, COMSOLInc., Stockholm, Sweden) with a time step of 5 s. The geometryand mesh were created in COMSOL. The finite element mesh con-sisted of squares with four nodes per element. The total numbers ofelements used were 2078 for ‘‘tajadas’’ and 2008 for ‘‘tostones’’. Amesh convergence study was performed to verify that the resultswere not dependent on the mesh. Lagrange polynomials (second-order function) were the interpolation function. The linearizedproblem was solved at each time step by the UMFPACK method(unsymmetric multifrontal method and direct sparse LU factoriza-tion). The typical simulation time was 60 min using a 3-GB freememory (RAM) and 2670 Hz Xeon 4 core CPU computer (32 bits).

4. Results and discussion

Two intrinsic pseudo-permeabilities of vapor were first adjusted(Section 4.1), while validating the water loss kinetics. This was fol-lowed by validation of the model on acrylamide kinetics and tem-perature variations in the core region. The pressure, temperature,water content and acrylamide concentration profiles were thenexamined (Section 4.2) in order to describe the combined effectsbetween transfer and reaction phenomena. The effectiveness ofnon-isothermal heating on acrylamide reduction during fryingwas also investigated (Section 4.3). Finally, the impact of the matu-rity stage and pretreatment of the raw material on final acrylamidecontents in ‘‘tajadas’’ and ‘‘tostones’’ were simulated (Section 4.4).

4.1. Model validation from water and acrylamide kinetics

Fig. 4 presents a comparison between the experimental andsimulated water and acrylamide contents in ‘‘tajadas’’ and ‘‘tos-tones’’. ‘‘Tajadas’’ were prepared in a single frying operation(180 �C), while ‘‘tostones’’ were obtained through a two-step fryingprocess, with a crushing step inserted between the heating steps

Value Reference

4182 Perré (1995)2010 Perré (1995)1419 Ni and Datta (1999)

7:0 � 10�16 Adjusted

1:6 � 10�16 Adjusted

0.018

8.314

0.09 Estimated0.13 Estimated0.260.320.86 Estimated271 Costa et al. (1999)

9:1 � 10�3

0

1:16 � 10�6

140–1802

1:2 � 10�5 Perré (1995)

1528 Farkas et al. (1996b)1000

for control of acrylamide reaction in plantain. Journal of Food Engineering

Fig. 3. Representation of the computational domain and boundary conditions in 2D.

J. Bassama et al. / Journal of Food Engineering xxx (2012) xxx–xxx 7

(final thickness, 3 mm). After 7 min of frying, 39% water loss and0.24 mg kg�1 acrylamide content were observed in ‘‘tajadas’’. For‘‘tostones’’ the corresponding water loss was 83% of the initialwater content and the acrylamide level was twofold higher(0.44 mg/kg). The water loss values were close to those obtainedin the previous studies (Avallone et al., 2009; Rojas-Gonzalezet al., 2006). The simulated water loss values were adjusted tothe experimental values and the corresponding apparent vaporintrinsic pseudo-permeabilities were 7.0 � 10�16 and 1.5 �10�16 m2 for ‘‘tajadas’’ and ‘‘tostones’’, respectively. The valuesare within the same range as those obtained in other studies

Fig. 4. Experimental (d) and simulated (solid lines) acrylamide (a and b) and water (c an‘‘tostones’’ (3 mm in thickness). The dashed lines representing an estimated confidenceinterval (p = 0.05).

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(Datta, 2006). The lower permeability identified in ‘‘tostones’’could be the consequence of crushing the plantain cylinder. Indeed,this step could induce changes in the structure of the food matrix,leading to a more compact and also less permeable product (Ni andDatta, 1999). Acrylamide contents in the two products were closeto those estimated in fried plantain-based food (Quayson andAyernor, 2007), and in the same magnitude as those measured inFrench fries (0.315 mg kg�1) and potato crisps (0.619 mg kg�1)(EFSA, 2010). The higher acrylamide level in ‘‘tostones’’ could beexplained by its thickness, with the thinner product being moredehydrated and submitted to a higher temperature. The

d d) kinetics during deep-fat frying at 180 �C, for ‘‘tajadas’’ (10 mm in thickness) andinterval calculated using the rate constants values plus or minus their confidence

for control of acrylamide reaction in plantain. Journal of Food Engineering

Fig. 5. Experimental (dashed lines) and simulated (solid lines) temperature in theplantain disk core during deep-fat frying at 180 �C for ‘‘tajadas’’ (10 mm inthickness).

Fig. 6. Simulated temperature profiles (a), pressure profiles (b), acrylamide contentand water content profiles (c) during deep-fat frying at 180 �C, for ‘‘tajadas’’ (10 mmin thickness).

8 J. Bassama et al. / Journal of Food Engineering xxx (2012) xxx–xxx

acrylamide kinetic simulations were close to experimental resultsfor ‘‘tajadas’’ and ‘‘tostones’’, thus highlighting the effect of thecrushing step (reducing thickness) on acrylamide formation inthe product. Fig. 4b shows an acceleration in the acrylamide forma-tion rate after the crushing of ‘‘tostones’’ (t P 3 min). However, theacrylamide content was consistently overestimated for both prod-ucts. This could be the consequence of a ‘‘matrix effect’’ on the ki-netic parameters. Indeed, the kinetic parameters were estimated inan unstructured plantain-based food (rehydrated plantain flour).The experimental and simulated temperature patterns in the coreregion are compared in Fig. 5. The experimental data were ob-tained from three cylinders of ‘‘tajadas’’ fried simultaneously. Thecore temperature (Tsat) was almost 110 �C for the three cylinders,suggesting overpressurization in the product (between 60 and40 kPa). This phenomena has been observed in gels (Vitrac et al.,2000) and wood (Grenier et al., 2010), but seldom in starchy food(Avallone et al., 2009; Costa et al., 1999; Rojas-Gonzalez et al.,2006). Despite simulating Tsat well, the temperature growth ratein the product was underestimated by the model. Indeed, Tsat

was experimentally reached in the core region after 50 s insteadof 200 s for the model. These differences could mainly be explainedby the transfer phenomenon assumptions. In fact, 5–8% of oil wasabsorbed by the product during frying of ‘‘tajadas’’ (data notshown). This oil could participate in heating the product by estab-lishing a higher temperature gradient between the core and thecrust region. Moreover, neglecting the internal liquid water trans-port could also lead to underestimation of the temperature growthrate (Vitrac and Bohuon, 2004).

4.2. Analysis of temperature, pressure and concentration profiles

4.2.1. Temperature profilesThe temperature profile simulations (Fig. 6a) showed a differ-

ence in pattern between the core and the crust. The temperaturedifference between the core and surface was very high (almost150 �C) at the beginning of frying and was reduced graduallyduring the process (40 �C). After 60 s, the temperature at 1 mmfrom the surface was 95 �C but only 65 �C at the core of the prod-uct. These temperatures increased to 125 and 110 �C, respectively,after 7 min of frying. The results are close to those of Halder et al.(2007b), who found at the same position (1 mm from the surface)in French fry temperatures of 70 and 130 �C at 1 and 7 min, respec-tively. Temperatures at the core were not comparable, with theproduct thickness in the study being substantially higher(12 mm). The temperature profiles showed variations in crustthickness, corresponding to the region where T > Tsat. The crust

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thickness reached 24% of the half-thickness (1.2 mm) for ‘‘Tajada’’as compared to 73% (1.1 mm) for ‘‘tostones’’ (data not shown) after7 min of frying. The same crust thickness (1.2 mm) was observed at4, 6 and 7 min, respectively, in other studies (Farkas et al., 1996b;Halder et al., 2007a; Ni and Datta, 1999).

4.2.2. Pressure profilesFig. 6b presents the pressure profiles generated in the product

during the frying process. The model indicated 60 kPa overpressur-ization in ‘‘tajadas’’ after 7 min of frying. This result is consistentwith the Tsat value in the product (110 �C). For ‘‘tostones’’, higheroverpressurization (150 kPa) was simulated after 4 min of the sec-ond frying process (180 �C). The same result was reported byYamsaengsung and Moreira (2002b) (overpressure of 185 kPa after60 s) in tortilla chips. This overpressurization may seem unrealistichowever significant expansion was observed in ‘‘tostones’’.

4.2.3. Water and acrylamide profiles and combined effectsFig. 6 presents variations in the water and acrylamide profiles

during the frying process. The growth of the crust closely

for control of acrylamide reaction in plantain. Journal of Food Engineering

Fig. 7. Experimental (d) and simulated acrylamide (solid line) content kineticsduring deep-fat frying at 180 �C for ‘‘tajadas’’ (10 mm in thickness). The dashedlines are simulated with rate constants (kFref

; kEref) calculated at constant water

activity (aw).

J. Bassama et al. / Journal of Food Engineering xxx (2012) xxx–xxx 9

corresponded to the results obtained with the temperature profiles(Section 4.2.1). This is consistent because the vaporization ratesimulation depends only on the temperature (Eq. (6)). The decreasein water content in the crust region led to changes in the thermo-physical properties of the product, corresponding to a decrease inthermal conductivity. These phenomena together with the de-crease in the temperature gradient resulted in gradual loweringof the vaporization rate.

The region with an high acrylamide content was localized at theextreme periphery of the product (0.5 mm from the surface after7 min). The temperatures were higher than 140 �C (Fig. 6a), whichshows the major effect of temperature on acrylamide formation(Claeys et al., 2005a; de Vleeschouwer et al., 2007). The acrylamidecontent was negligible in the water-rich part of the product, but itwas high at the surface of the product. Halder et al. (2007b) found100-fold higher acrylamide contents in the same region for Frenchfries. These results seem unrealistic because the model neglectedacrylamide elimination during the process.

As shown above, temperature and water activity were linkedduring the frying process. Energy and water transfers were com-bined, and it was shown in a previous study (Bassama et al.,2011) that acrylamide rate formation/elimination constantsincrease with increasing temperature and decreasing water activ-ity. In the model, the coupling between transfer and reaction wasexpressed by an Arrhenius equation (Eq. (20)) and an empiricalregression for the reaction rate dependency on water activity (Eq.(21)). Fig. 7 compares acrylamide kinetics in the case of varyingor constant water activity assumptions. The results showed thatthe kinetics at varying water activity were close to that at the low-est water activity (aw ¼ 0:40). These results could be explained byfact that acrylamide was formed exclusively in the hygroscopic andperipheral regions (Fig. 6c), which were characterized by the high-est reaction rates for acrylamide formation/elimination. Thereaction rates were maximal and almost constant throughoutthe heat treatment, which explains the trend observed betweenthe kinetics in both cases. In short, because of the peripheralformation of acrylamide in the product, the coupling effect oftemperature and water activity could be overlooked, while consid-ering the reaction rates in the crust region as being constant andmaximal throughout the frying process.

4.2.4. Limits of the model assumptions(i) Isotropy of the system. The isotropy of the water and precur-

sors’ concentration in the plantain is not certain. Indeed, the distri-bution of chemical species in plant products is seldom uniform.

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However, the local concentration values are not easily accessibleand it is common to refer to global amounts. This approximationcan lead to differences in simulations since the study showed thatacrylamide levels depended only on the precursor content in thecrust. (ii) No changes in geometry: As the changes in geometry ob-served in ‘‘tajadas’’ were less than 15% of the initial volume, theycould be assumed to be negligible. However, we noted substantialswelling in ‘‘tostones’’ due to the high pressures generated in theproduct. In that case, the assumption of an unchanged geometrycould not apply. (iii) Local thermal equilibrium: The assumption ofthermal equilibrium seems reasonable, although difficult to calcu-late. The vapor velocity calculation showed that the rates fell from16 � 10�3 to 4 � 10�3 ms�1 between the beginning and end of fry-ing (7 min). This confirms the assumption of thermal equilibrium.(iv) Initial air in the product was assimilated to vapor: Vapor and airare perfect gases with very similar thermophysical properties. (v)Oil penetration was negligible: As mentioned above, adding oil diffu-sion to the model would enable a better representation of localtemperature variations in the food during processing.

4.3. Effect of non-isothermal frying

The non-isothermal heat treatment simulations were per-formed for the same final water content in the product; the resultsare presented in Fig. 8. In industrial conditions, continuous fryersconvey the product through different regions in the frying baththat may be set at different temperatures. Our aim was to deter-mine which frying procedure was better: beginning the frying athigh temperature and pursuing it at a lower one (Fig 8a), or theopposite (Fig. 8b). In this study, the first procedure consisted offrying in two consecutive baths regulated at 180 and 140 �C,respectively, with the frying time for the first bath (180 �C) rangingfrom 0 to 4 min (Fig. 8a). The results showed a significant increasein acrylamide content when the duration of the first frying stepwas increased. However, the acrylamide content was always lowerthan noted for a 7-min heat treatment at 180 �C (constant). Indeed,almost 50% acrylamide reduction was observed when the productwas fried for 4 min at 180 �C and then at 140 �C until a final prod-uct water content of 0.9 g/kg (d.b.) was obtained. For the secondprocedure, the opposite heat treatment was performed: the firstfrying was at 140 �C and the second at 180 �C. No significant effectson the final acrylamide content were observed (Fig. 8b).

In short, the procedure consisting of beginning frying at hightemperature and finishing it a lower one was an efficient way ofreducing the acrylamide content in the food product. The sameresult was observed by Achir et al. (2008), who confirmed thatrapidly decreasing the temperature from 180 �C was an efficientway to reduce Maillard reaction products when frying a food inwhich liquid water transfer is negligible (50% reduction).

4.4. Impact of precursor mitigation on the acrylamide content inplantain

The impact of lowering the initial asparagine content on acryl-amide reduction in the final product was simulated (Fig. 9). Theaim was to assess whether implementing steps to induce a reduc-tion in the initial asparagine content in food could decrease the netacrylamide content in plantain. In the literature, immersion orblanching processes were reported to be efficient in reducing pre-cursor quantities (asparagine, sugars) in the raw material, leadingto mitigation of acrylamide in the final product (Pedreschi et al.,2009). Moreover, Bassama et al. (2011) showed that the asparaginecontent in plantain decreased with fruit ripening (75% reductionafter 11 days of ripening). The initial asparagine contents used inthe model accounted for two different plantain maturity stagesand the extraction of 50% asparagine molecules by pretreatment

for control of acrylamide reaction in plantain. Journal of Food Engineering

Fig. 8. Effect of a variable oil temperature (T1) control between 140 and 180 �C onacrylamide content as regard of residual water content (equivalent to time scale)during deep-fat frying of ‘‘tajadas’’ (10 mm in thickness). Dt (ranging from 0 to4 min) is the frying duration at 140 �C (a) or at 180 �C (b).

Fig. 9. Simulation of the impact of maturity stage of plantain and pretreatment(50% asparagine extraction) of raw plantain on acrylamide reduction in ‘‘tajadas’’(10 mm in thickness) and ‘‘tostones’’ (3 mm in thickness) after deep-fat frying at180 �C.

10 J. Bassama et al. / Journal of Food Engineering xxx (2012) xxx–xxx

(e.g. blanching). The results are summarized in Fig.. 9, showing asignificant reduction in acrylamide content in all the differentcases. These results are consistent with those of Quayson andAyernor (2007), showing that the acrylamide content was lowerin unripe plantain-based products than in ripe ones. Moreover,the efficacy of immersion pretreatment against acrylamideformation had already been shown (Pedreschi et al., 2007b).

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5. Conclusion

The frying process is an operation that involves complex phys-ical phenomena and closely linked reactions. Using a model thatsimulated the coupling between transfers (energy/water) and thereaction enabled us to identify and test ways to control the fryingprocess in order to reduce acrylamide formation. The fryingtemperature seems to be the only ‘‘degree of freedom’’ in orderto lower the acrylamide contents during the frying process. Indeed,rapidly lowering the frying temperature from 180 to 140 �Callowed us to significantly reduce the acrylamide content in plan-tain (by at least 50%). However, our study showed that controllingasparagine levels in the raw material by selecting plantains at asuitable ripeness stage or implementing a pretreatment before fry-ing are more flexible ways to control the acrylamide content inplantain-based fried food. The extent to which these acrylamidereduction methods are used should be determined according tothe limits of organoleptic acceptability of the final product. Indeed,variations in the product organoleptic properties when using theseacrylamide control methods could be studied to determine theirrelevance.

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