drying kinetics of rose hip fruits (rosa eglanteria l.)

www.elsevier.com/locate/jfoodeng

Journal of Food Engineering 77 (2006) 566–574

Drying kinetics of rose hip fruits (Rosa eglanteria L.)

Carlos Alberto Marquez a, Antonio De Michelis b,*, Sergio Adrian Giner c,1

a Asentamiento Universitario Villa Regina, Facultad de Ingenierıa, Universidad Nacional del Comahue,

Calle Tucuman No. 116 (8336) Villa Regina, Rıo Negro, Argentinab Consejo Nacional de Investigaciones Cientıficas y Tecnologicas (CONICET), INTA AER El Bolson,

Calle Marmol No. 1950 (8430) El Bolson, Rıo Negro, Argentinac CIDCA, Departamento de Ingenierıa Quımica, Facultad de Ingenıerıa, Universidad Nacional de La Plata,

Comision de Investigaciones Cientıficas de la Provincia de Buenos Aires (CIC), Calle 47 y 116 (1900) La Plata, Argentina

Received 7 October 2004; accepted 18 June 2005Available online 24 August 2005

Abstract

Simulation of dehydration in beds for food particles demand long computing times. So, models for equipment design should beas simple as possible. An equipment with particulate material can be visualised as formed by a number of beds of given depth, inturn composed of thin layers. Therefore, thin layer dehydration studies become essential as a step for developing updated methodsfor equipment design. Such studies are especially needed in products such as rose hips for which scarce if any drying kinetic data isavailable. Drying curves were experimentally determined for rose hip fruits, using air at: 50, 60, 70, 80 �C; relative humidities: 5%,50% and velocities: 1, 2, 3, 5 m/s. A short time predictive model for diffusion inside solids was selected to interpret the data withsatisfactory accuracy. By this fitting procedure, diffusion coefficients of water in rose hips were determined to vary between7.501 · 10�11 (50 �C) and 3.367 · 10�10 (80 �C) m2/s, with an Ea = 46 kJ/mol.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Rose hip fruits; Dehydration kinetic, experimental, and model

1. Introduction

Modern methods of equipment design for food dry-ing are based on the mathematical description of dehy-dration in beds to estimate drying time as accuratelyas possible (Giner, 1999).

According to the literature, a complex process asdehydration can be analyzed by decomposing it in sim-pler systems (Giner, 1999; Himmelblau & Bischoff, 1976;Ratti, 1991). For instance, a drying equipment can be di-vided into beds of given thickness in turn formed by very

0260-8774/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.jfoodeng.2005.06.071

* Corresponding author. Tel./fax: +54 2944 492422.E-mail addresses: [email protected] (C.A. Marquez), inta@

patagonsat.com.ar (A. De Michelis), [email protected] (S.A.Giner).

1 Tel.: +54 21 4249287.

thin product layers, normally one particle size. There-fore, the determination of the intrinsic drying propertiessuch thin layers—kinetic parameters—becomes animportant issue as far as industrial dryer design isconcerned.

In the thin layer dryer analysis, the food particlewhose transport (drying) properties need to be evaluatedis exposed to constant drying air conditions for a givenlength of time so all variations occur within the productand so, the drying parameters thus measured can be re-lated to those constant air conditions. Logically, theconclusions obtained at thin layer level, which are inter-esting in themselves as drying knowledge, must be con-sistent enough to allow their application at deep bedlevel, for equipment simulation and design.

Concerning the thin layer-drying problem, numerousstudies are available in the literature, which follow

mailto:[email protected]

mailto:inta@ patagonsat.com.ar

mailto:inta@ patagonsat.com.ar

mailto:[email protected]

Notation

am surface area of particle per unit particle vol-ume (m2/m3)

D diffusion coefficient (m2/s)D1 pre-exponential factorEa activation energy (kJ/mol)m total sample mass at time t (kg)m0 initial sample mass (kg)md dry matter mass (kg)mw water mass (kg)R universal gas constant (kJ/mol K)

Rp particle radius (m)T absolute air temperature (K)X* dimensionless moistureX the mean moisture content of the particle at

time t (kg water/kg dry matter)X0 initial particle moisture (kg water/kg dry

matter)Xe equilibrium particle moisture (kg water/kg

dry matter)

C.A. Marquez et al. / Journal of Food Engineering 77 (2006) 566–574 567

diverse methods. They can be classified into three typesof solutions: numerical, analytical and approximate.In turn, within the last, semi-empirical and empiricalsolutions can be distinguished. Moreover, in each cate-gory, some contributions take into account productshrinkage.

Within the contributions presenting numerical solu-tions, the following articles can be considered represen-tative: Masi and Riva (1988), Karathanos, Villalobos,and Saravacos (1990), Ratti (1991), Rovedo, Suarez,and Viollaz (1995), Wang and Brennan (1995), Simal,Mulet, Catala, Canellas, and Rosello (1996), Ghiaus,Margaris, and Papanikas (1997), Hawlader, Ho, andQing (1999), Sabarez and Price (1999), Kechaou andMaalej (2000), Lima De and Nebra (2000), Queirozand Nebra (2001) and Lima De et al. (2002). All theseauthors start using the differential diffusion equationwhich, besides allowing the determination of the diffu-sion coefficient, also enable transient moisture and tem-perature gradients in the food to be predicted.Furthermore, some of these mathematical formalismsconsider particle shrinkage.

In the following articles, analytical solutions wereused and shrinkage was not taken into account by Giner(1989, 1999), Medeiros and Sereno (1994), Giner,Mascheroni, and Nellist (1996), Simal, Deya, Frau,and Rosello (1997), Park, Yado, and Brod (2001),Maskan, Kaya, and Maskan (2002) and Togrul andPehlivan (2002, 2003). In turn, authors who consideredvolume decrease during drying were Berna, Rosello,Canellas, and Mulet (1991), Gekas and Lamberg(1991), Alvarez et al. (1995), Thakor, Sokhansanj,Sosulski, and Yannacopoulos (1999), Di Matteo,Cinquanta, Galiero, and Crescitelli (2000, 2002, 2003)Hernandez, Pavon, and Garcıa (2000).

Finally, among the articles dealing with the dryingproblem, using semi-empirical or empirical expressions,the following are typical: Bala and Woods (1992), Cha-vez-Mendez, Salgado-Cervantes, Garcıa-Galindo, DELA Cruz-Medina, and Garcıa-Alvarado (1995), Pan-gavhane, Sawhney, and Sarsavadia (1999, 2000) and

Tsami and Katsioti (2000). Quotations correspond onlyto recent or relatively recent papers, though there are aconsiderable number of older contributions within eachcategory.

As an outcome from this literature review, isothermaldrying appear as the most common model assumptionin kinetic studies to solve the variation of the dimension-less moisture as a function of time for different air oper-ating conditions: temperature, velocity and relativehumidity. However, in many contributions, only thedry bulb drying air temperature was varied.

It is evident that the complexity inherent to the anal-ysis of drying processes lies in the diversity of biologicalmaterials and their shrinkage, so it is very difficult tofind a general model.

There are several possibilities to model the thin layerdrying with many different degree of complexity. Asdemonstrated by some authors (Giner, 1999; Mulet,1994), kinetic parameters vary substantially accordingto the method used to evaluate them, and even those ob-tained by the same method are often dependent on theequilibrium moisture content used to express the exper-imental data in dimensionless form (Gelly & Giner,1999).

As the objective of this work was to provide the infor-mation necessary to simulate food particle beds, animportant issue is to find thin layer drying methods withgood physical background, yet fast to run on the com-puter to facilitate equipment design, an endeavourwhere interactivity is essential.

The thin layer drying equation constitutes the socalled ‘‘product model’’, or constitutive equation formass transfer in individual particles. This equation isuseful in two main respects: It permits a means to studythe way a theory (represented by the equation) canadapt to the drying data of a given food. Once thesoundness of a theory was verified, it can be used todetermine kinetic parameters in operating conditionsusual in the drying practice, and then applied withindeep bed models, where both product and air conditionsvary with space and time, to predict temperature and

568 C.A. Marquez et al. / Journal of Food Engineering 77 (2006) 566–574

moisture profiles and calculate drying times for equip-ment simulation, and design.

The objective of this work was therefore to experi-mentally determine drying curves as a function of dryingair-operating variables and to propose a dehydrationkinetics to deal with drying of rose hip fruits and todetermine its kinetic parameters for further use withindrying simulation software.

2. Theory

Being dehydration a coupled phenomenon of heatand mass transfer, it would be necessary to simulta-neously solve mass and energy balances to evaluatedehydration kinetics of individual particles. However,the literature has shown that as the rate of relaxationof the heat transfer potential is thousands of times fasterthan that for mass transfer, the temperature profile in-side the food can be considered flat, especially if com-pared with the steep moisture content gradient (Giner& Mascheroni, 2001). In this regard, experiments werecarried out to follow temperature variations inside theparticle under a range of drying air operating condi-tions. Experimental conditions are presented in Section3, but Fig. 1 is exhibited in this section to show the tem-perature changes mentioned above.

As observed in Fig. 1, particle temperature rapidlyapproaches the drying air asymptote, and the transient,is short compared with the dehydration times, nevershorter than 6 h. Transient, is normally even faster be-cause conditions of Fig. 1 include a low air velocity.So, a possible assumption is to consider flat temperatureprofile inside the particles. In turn, in view of the heating

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100

Time (min)

Tem

pera

ture

evo

lutio

n in

side

indi

vidu

al p

artic

les

(ºC

)

Air at 70 ˚C Air at 50 ˚C

Fig. 1. Temperature evolution inside individual particles, as a functionof time, for the following drying air conditions: velocity, 1 m/s; relativehumidity, 5%; temperature, 50 and 70 �C.

rate of fruits, their average temperature becomes verysimilar to that for air, which may allow the isothermaldrying assumption to be considered apt for modellingpurposes.

Giner (1999) as well as other contributions (Parry,1985) has analysed the ratio of thermal to mass diffusiv-ities inside the solid as a criterion to guide drying mod-elling, indicating that a large ratio would suggest an‘‘instant’’ heat transport compared with mass transport.Thermal diffusivity of rose hip fruits vary between1.196 · 10�7 and 2.009 · 10�7 m2/s (Marquez, 2003),while mass diffusivities—the effective diffusion coeffi-cients in solids—according to Zogzas, Maroulis, andMarinos-Kouris (1996), range from 10�10 to 10�11

m2/s in most foods. By taking an average of the valuespublished by them, (more than 100 diffusion coefficientsfrom 61 foods with diverse moisture contents), a valueof 1.45 · 10�10 m2/s is found, with which the ratio ofthermal to mass diffusivity varies around 824 and1386, that is, heat transfer is some 1000 times faster thanmass transfer. According to Parry (1985) or Giner(1999), this guarantees heat transfer to be instantaneousagainst mass transfer, and reinforces the former conclu-sions of isothermal drying as a valid simplification tomass transfer alone as far as determination of kineticparameters is concerned.

On the other hand, and in order to know the type ofmodel most suitable to interpret drying curves of thefruits, in Fig. 2 the experimental drying rate were repre-sented as a function of moisture. As can be seen inFig. 2, that only one falling rate period is detected,therefore can be proposed to follow a strict internal con-trol for mass transfer.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.1 0.2 0.3 0.4 0.5

Moisture content (dec., d.b.)

Dry

ing

rate

(kg

/kg

h)

80-055 60-055 50-502

Lineal (80-055) Lineal (60-055) Lineal (50-502)

Fig. 2. Experimental drying rate for rose hip fruits. 80-055: R2 =0.985; 60-055: R2 = 0.988; 50-502: R2 = 0.971.


This allows the analytical solution for unsteady statediffusion with prescribed condition on the surface to beresorted to (Bird, Stewart, & Lightfoot, 1960; Crank,1975). The analytical solution, obtained after integratinglocal moisture contents in the particle volume, consid-ered to be spherical for this work, is (Crank, 1975; Gi-ner, 1999; Parry, 1985):

X � ¼ X � X e

X 0 � X e

¼ 6

p2

Xn¼1n¼1

1

n2Exp �n2p2 Dt

R2p

!" #ð1Þ

where X* is the dimensionless moisture; X, the meanmoisture content of the particle at time t, X0 and Xe

the initial and equilibrium particle moisture, while D isthe diffusion coefficient and Rp the particle radius. Theinfinite series of Eq. (1) could be reduced to only oneterm for long times, but such simplification is valid forX* < 0.3 and not in the practical range of drying of highmoisture foods. Then, the complete series would be re-quired for this work, but this includes numerous short-comings previously listed by Giner and Mascheroni(2001). Most commercial software for non-linear fittingoften does not allow the use of equations with numerousterms.

The minimum number of terms to ensure conver-gence is unknown and varies with time. A specific com-puter program is required to minimize residuals betweenpredicted and experimental values, including an errortolerance to achieve convergence for each time. Oncethe parameters are fitted, drying curve predictions needagain a specific computer program.

Using the infinite series as component of a fixed bedof particles increase computing time considerably, sincea bed is often divided into 100 thin layers.

For this reason, a simpler, faster equation is requiredto reduce complexity and calculation times for fixed bedapplications, especially those equipment design-ori-ented, without sacrificing accuracy nor sound physicalbackground.

The diffusive equation developed first by Becker(1959), and further by Giner (1999) and Giner andMascheroni (2001) has been used successfully for graindrying. The expression coincide in practice with theinfinite series solution from the beginning of drying todimensionless moisture contents as low as X* = 0.2 inspherical geometry. Becker (1959) has proposed a pre-scribed moisture content of 0.103 dec., d.b. independentof temperature and relative humidity for vacuum dry-ing of wheat. In turn, Giner (1999) has used equilib-rium surface moistures obtained from the sorptionisotherm, dependent on air relative humidity andtemperature.

The equation mentioned above for spherical geome-try, predicts (Giner, 1999):

X � ¼ X � X e

X 0 � X e

¼ 1� 2ffiffiffipp am

ffiffiffiffiffiDtp

þ 0.331a2mDt ð2Þ

where am is the surface area of particle per unit particlevolume. In spheres, am = Rp/3. Analytical solutions, aswell as semi empirical and empirical expressions, havebeen used in most cases with constant particle radius.However, in recent works, they were used with variableradius (Di Matteo et al., 2000; Thakor et al., 1999) in anextended use of integral equations. In the work by DiMatteo et al. (2000), the radius of a sphere with the samevolume as the particle was used as a variable. To esti-mate a drying curve for different times, calculation be-gan with the initial radius. The moisture contentobtained at a given time t was used to estimate the vol-ume reduction and then a new radius. An average ofboth radii is taken and a final calculation of moistureloss for that interval is carried out with the average ra-dius kept constant.

In this work, Eq. (2) will be used, considering theequilibrium moisture content given by the five-parame-ter GAB model presented by Marquez (2003). Particleradius will be evaluated by the volumetric shrinkageequation presented by Ochoa, Kesseler, Pirone,Marquez, and De Michelis (2002).

3. Materials and methods

3.1. Materials

Rose hip fruits used in this research were harvested inEl Bolson, Province of Rıo Negro, Argentina. The fruitwas kept refrigerated at 4 �C until use. Moisture contentof the fresh fruit was within 48% and 49.0% expressedon wet basis.

3.2. Drying equipment

Experiments were carried out in a purpose-built lab-oratory dryer, consisting basically of a closed systemwith forced air circulation and adequate air temperatureand humidity controls, as presented by Ochoa et al.(2002).

3.3. Experimental data acquisition technique

Air temperature was measured with thermocouplesinserted in the drying chamber and connected to a digi-tal thermometer Digi-Sense (Cole-Parmer InstrumentCompany) with 0.5 �C readability. Air velocity and rel-ative humidity content were measured with a Mini VaneCFM Thermo Anemometer (EXTECH Instruments)and Hygro Palm hygrometer (Rotronic instruments),respectively. The dryer chamber contained a mesh-bot-tomed tray to hold the sample of particles. The traywas easily removed or replaced sideways for periodicweighing of the sample. Air leakage was prevented usingrubber stripping.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

Time (h)

Moi

stur

e co

nten

t (de

c., d

.b.)

50-501 50-051 50-502 50-055 60-501 60-503

60-055 70-501 70-053 70-505 80-501 80-055

Fig. 3. Experimental thin layer drying curves for rose hip fruits.Codes: first two digits indicate air temperature in �C, the succeedingtwo digits stand for air relative humidity, %, while last digit indicatesair velocity in m/s.

Table 1Statistical analysis of experimental results from drying curves

Data Mean Variance N

One-way ANOVA on air velocity

50R051 0.32029 0.00465 1350R055 0.34939 0.00397 16F = 1.42221; p = 0.24342


Except the initial moisture content, determined by anoven procedure, all other experimental points of the dry-ing curve were determined by sample weighing. Thismethod is based on the constancy of sample dry matterduring drying. If the total sample mass m at time t is thesum of that for dry matter md plus the water mass mw.

m ¼ mw þ md

and it is considered that, by definition of moisture con-tent dry basis X = mw/md then

m ¼ mdX þ md ¼ mdð1þ X ÞThe same equation applied to the initial sample takesthe form

m0 ¼ mdð1þ X 0ÞBy dividing the equation for m and m0 for constant drymatter content, and solving for X, we arrive at the calcu-lation equation

X ¼ mm0

ð1þ X 0Þ � 1

Each weighing to determine m involved some 20–30 s ina digital balance, its readability being 0.001 g.

To measure only temperatures inside the fruits(Fig. 1), thermocouples were inserted in the center of fivefruits to record data as a function of time.

The operating variables, used in the drying air, were:temperature: 50, 60, 70 and 80 �C; velocity, 1, 2, 3 and5 m/s; relative humidity: 5% and 50%.

At the 0.05 level, the means are NOT significantly different

One-way ANOVA on air relative humidity

50R051 0.32029 0.00465 1350R501 0.34078 0.00472 16F = 0.64173; p = 0.43008At the 0.05 level, the means are NOT significantly different

One-way ANOVA on temperature

50R502 0.76566 0.01043 960R502 0.6618 0.01703 1070R502 0.34991 0.06531 14F = 15.22648; p = 2.72619E�5At the 0.01 level, the means are significantly different

4. Results and discussion

Fig. 3 presents the experimental results of dryingcurves for different air conditions.

As it can be observed in Fig. 3, the effect of temper-ature on drying curves is considerable, unlike those forvelocity or air relative humidity. By statistical analysisof results using ANOVA (Microcal Origin vs. 4.10),the influence of temperature is, in effect found to behighly significant, (significance level of 1%), while thosefor velocity or relative humidity are non significant(significance level 5%), as shown in Table 1. However,after close inspection of the data, air velocity influenceis, in effect, not detected, but there is some consistent,as can be expected, effect of relative humidity inFig. 4, though evidently not strong enough to be de-tected by statistical analysis. The same trend is observedfor other drying temperatures. When the moisture con-tent X is expressed dimensionless as in Eq. (2), no differ-ences between treatments at the same temperature canbe found, as is normally, in Fig. 5, for example, for50 �C.

These results allow diffusion coefficients to be ob-tained by fitting the Eq. (2) to all experimental dryingdata collected at the same temperature expressed as

X*. Table 2 presents effective diffusivities and statisticalparameters

As observed in Table 2, the drying kinetic model givesan accurate description of the experimental data, cor-roborated by the statistical indices as coefficient of deter-mination and standard error of the estimate. These closepredictions also imply that the assumption of internaltransport by liquid diffusion satisfactorily interpretsthe results for rose hip drying.

4.1. Correlation of the diffusion coefficients obtained as a

function of temperature

To evaluate the dependency of diffusion coefficients,an Arrhenius-type equation was used:

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

Time (h)

Moi

stur

e co

nten

t (de

c., d

.b.)

50-055 50-501 50-051

Fig. 4. Effect of air velocity and relative humidity on drying curves.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

Time (h)

Dim

ensi

onle

ss m

oist

ure

cont

ent

50-501 50-051 50-502 50-055

60-501 60-503 60-055 70-501

70-053 70-505 80-501 80-055

Estimated 50 ˚C Estimated 60 ˚C Estimated 70 ˚C Estimated 80 ˚C

Fig. 5. Experimental dimensionless moisture contents as function oftime and corresponding predictions in solid lines by the diffusivemodel, Eq. (2).

Table 2Effective diffusion coefficients (D) obtained using Eq. (2) and statisticalparameters for goodness of fit

Temperature (�C) D · 1011 (m2/s) R2 Standard error of theestimate (in units of X*)

50 7.501 0.991 0.00960 15.622 0.989 0.01270 22.639 0.986 0.06680 33.674 0.995 0.012

-23.4

-23.2

-23

-22.8

-22.6

-22.4

-22.2

-22

-21.8

-21.6

0.0028 0.00285 0.0029 0.00295 0.003 0.00305 0.0031 0.00315

1/T (k-1

)

Ln

D

Fig. 6. Dependency of diffusion coefficient D with temperature,arranged according to the Arrhenius correlation.


D ¼ D1e�EaRT ð3Þ

where T is the absolute air temperature in K, D1 thepre-exponential factor, Ea the activation energy and R

the universal gas constant. In Fig. 6, results are pre-sented for the logarithmic form of Eq. (3), from whichwe found a corresponding activation energy ofEa = 46 kJ/mol with a coefficient of determinationr2 = 0.978, considered a satisfactory value for thisfitting.

4.2. Comparison of experimental moisture contents with

values predicted by Eq. (2) with values for D obtained

with the thin layer drying curves

Figs. 7–10 present some of the experimental curves ofdimensional moisture content (decimal, dry basis) as afunction of time and the prediction by Eq. (2) with thediffusion coefficients obtained.

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

Time (h)

Moi

stur

e co

nten

t (de

c., d

.b.)

50-501 Estimated 50-501 50-051 Estimated 50-051

Fig. 7. Comparison of experimental drying curves (symbols) andpredictions by Eq. (2), for a drying air temperature of 50 �C.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12 14

Time (h)

Moi

stur

e co

nten

t (de

c., d

.b.)



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10

Time (h)

Moi

stur

e co

nten

t (de

c., d

.b.)



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5

Time (h)

Moi

stur

e co

nten

t (de

c., d

.b.)

80-055 80-501 Estimated 80-055 Estimated 80-501

Fig. 10. Comparison of experimental drying curves (symbols) andpredictions by Eq. (2), drying air temperature, 80 �C.


According to the comparison in Figs. 7–10, the modelsatisfactorily interprets the experimental behaviour.However, for low moisture contents, below 0.1 (mois-ture content in wet basis), the model tends to overesti-mate the mean moisture content of fruits. This wasexpected because, the lower threshold of validity ofEq. (2)—dimensionless moisture content less than 0.2,as mentioned above—was evidently reached. In fact,this limit coincides for dimensional moisture contentdecimal wet basis of 0.15. However, this shortcominglacks practical importance because the safe storage

moisture content for rose hips, established as it is cus-tomary for a water activity of 0.7 is, according to thesorptional equilibrium curves measured by Marquez(2003) of 0.15, decimal wet basis, and the model fits cor-rectly up to about 0.1.

Therefore, the model chosen is adequate for the pur-poses of this work, that is, for further use in drying sim-ulation of thick layers of rose hips, such as thoseappearing in commercial scale batch and continuousdryers

5. Conclusions

Air dehydration curves of rose hip fruits were exper-imentally determined in a thin layer drying equipment.Drying runs were carried out for several values of therelevant air variables: air temperature, relative humidityand velocity.

As the objective of this work was to determine thedrying kinetics for further use in simulation of thick lay-ers of particles as those found in commercial dryingequipment, a simple, yet physically well founded modelwas selected to evaluate the drying curves. This diffusivemodel for short times—though valid in all the practicaldrying range was used in conjunction with a sorptionalequilibrium and a volumetric shrinkage correlation.When applied to the data, this kinetic model allowedthe determination of effective water diffusion coefficientinside rose hip fruits. These diffusivities were correlatedwith temperature using an Arrhenius type model, show-ing a satisfactory agreement, and their values are withinthose found for other foods.


The model presented a more than satisfactory behav-iour because, besides predicting moisture loss correctly,is fast to run on the computer which is an essential as-pect for interactive design of industrial dryer equipment.

Acknowledgements

Authors thank: Facultad de Ingenierıa, UniversidadNacional del Comahue (Project FAIN-I089), andANPCyT (Projet PICT 09-06427) for financial support.To CORFO-CHUBUT and INTA AER El Bolson forproviding the raw material.

Author De Michelis is a Member of CONICET.Author Giner is a Member of CIC.

References

Alvarez, C. A., Aguerre, R., Gomez, R., Vidales, S., Alzamora, S. M.,& Gerschenson, L. N. (1995). Air dehydration of strawberries:effect of blanching and osmotic pretreatments on the kinetics ofmoisture transfer. Journal of Food Engineering, 25, 167–178.

Bala, B. K., & Woods, J. L. (1992). Thin layer drying model for malt.Journal of Food Engineering, 16, 239–249.

Becker, H. A. (1959). A study of diffusion in solids of arbitrary shape,with application to the drying of the wheat kernel. Journal of

Applied Polymer Science, 1(2), 212–226.Berna, A., Rosello, C., Canellas, J., & Mulet, A. (1991). Drying

kinetics of a Majorcan seedless grape variety. Technology Today, 3,134–137.

Bird, R. B., Stewart, W. E., & Lightfoot, E. N. (1960). Transport

phenomena. New York: Willey Publishers, Inc.Chavez-Mendez, C., Salgado-Cervantes, M. A., Garcıa-Galindo, H.

S., DE LA Cruz-Medina, J., & Garcıa-Alvarado, M. A. (1995).Modelling of drying curves for some foodstuffs using a kineticequation of high order. Drying Technology, 13(8&9), 2113–2122.

Crank, J. (1975). The mathematics of diffusion (2nd ed.). Oxforduniversity Press.

Di Matteo, M., Cinquanta, L., Galiero, G., & Crescitelli, S. (2000).Effect of a novel physical pre-treatment process on the dryingkinetics of seedless grapes. Journal of Food Engineering, 46(1),83–89.

Di Matteo, M., Cinquanta, L., Galiero, G., & Crescitelli, S. (2002).Physical pre-treatment of plums (Prunus domestica). Part 1.Modelling the kinetics of drying. Journal of Food Engineering,

79(1), 227–232.Di Matteo, M., Cinquanta, L., Galiero, G., & Crescitelli, S. (2003). A

mathematical model of mass transfer in spherical geometry: plum(Prunus domestica) drying. Journal of Food Engineering, 58(1),183–192.

Gekas, V., & Lamberg, I. (1991). Determination of diffusion coeffi-cients in volume-changing systems. application in the case ofpotato drying. Journal of Food Engineering, 14, 317–326.

Gelly, M. C., & Giner, S. A. (1999). Dependencia de los ParametrosCineticos de Secado de Trigo con la Isoterma de Equilibrio.Personal communication.

Ghiaus, A. G., Margaris, D. P., & Papanikas, D. G. (1997).Mathematical modelling of the convective drying of fruits andvegetables. Journal of Food Science, 62(6), 1154–1157.

Giner, S. A. (1989). Rough rice properties: grain density versusmoisture, bed resistance to airflow and kinetic parameters of dryingat ambient temperature. Latin American Research, 19, 75–82.

Giner, S. A. (1999). Diseno de Secadoras Continuas de Trigo.Simulacion de la Transferencia de Calor y Materia y de Perdidasde Calidad. Tesis Doctoral. Departamento de Quımica e IngenierıaQuımica, Facultad de Ingenierıa, Universidad Nacional de LaPlata.

Giner, S. A., & Mascheroni, R. H. (2001). Diffusive drying kinetics inwheat. Part.1. Potential for a simplified analytical solution. Journal

of Agricultural Engineering Research, 80, 351–362.Giner, S. A., Mascheroni, R. H., & Nellist, M. E. (1996). Cross-flow

drying of wheat. A simulation program with a diffusion-baseddeep-bed model and a kinetic equation for viability loss estima-tions. Drying Technology, 14(7&8), 1625–1671.

Hawlader, M. N. A., Ho, J. C., & Qing, Z. (1999). A mathematicalmodel for drying of shrinking materials. Drying Technology,

17(1&2), 27–47.Hernandez, J. A., Pavon, G., & Garcıa, M. A. (2000). Analytical

solution of mass transfer equation considering shrinkage formodelling food drying kinetics. Journal of Food Engineering, 45,1–10.

Himmelblau, D. M., & Bischoff, K. B. (1976). Process analysis and

simulation. New York: John Wiley & Sons, Inc.Karathanos, V. T., Villalobos, G., & Saravacos, G. D. (1990).

Comparison of two methods of estimation of the effective moisturediffusivity from drying data. Journal of Food Science, 55(1),218–231.

Kechaou, N., & Maalej, M. (2000). A simplified model for determi-nation of moisture diffusivity of date from experimental dryingcurves. Drying Technology, 18(4&5), 1109–1125.

Lima De, A. G. B., & Nebra, S. A. (2000). Theoretical analysis of thediffusion process inside prolate spheroidal solids. Drying Technol-

ogy, 18(1&2), 21–48.Lima De, A. G. B., Queiroz, M. R., & Nebra, S. A. (2002).

Simultaneous moisture transport and shrinkage during drying ofsolids with ellipsoidal configuration. Chemical Engineering Journal,

86, 85–93.Marquez, C. A. (2003). Deshidratacion de Rosa Mosqueta (Rose Hip).

Tesis Doctoral. Departamento de Tecnologıa de Alimentos,Universidad Politecnica de Valencia.

Masi, P., & Riva, M. (1988). Modelling grape drying kinetics. In S.Bruin (Ed.), Preconcentration and drying of food materials.Amsterdan: Elsevier science Publishers.

Maskan, A., Kaya, S., & Maskan, M. (2002). Hot air and sun dryingof grape leather (pestil). Journal of Food Engineering, 54, 81–88.

Medeiros, G. L., & Sereno, A. M. (1994). Physical and transportproperties of peas during warm air drying. Journal of Food

Engineering, 21, 355–363.Mulet, A. (1994). Drying modelling and water diffusivity in carrots and

potatoes. Journal of Food Engineering, 22, 329–348.Ochoa, M. R., Kesseler, A. G., Pirone, B. N., Marquez, C. A., & De

Michelis, A. (2002). Shrinkage during convective drying of wholerose hip (Rosa Rubiginosa L.) Fruits. Lebensmittel-Wissenchaff und

Technologie, 35(5), 400–406.Pangavhane, D. R., Sawhney, R. L., & Sarsavadia, P. N. (1999).

Effect of various dipping pretreatment on drying kinetics ofThompson seedless grapes. Journal of Food Engineering, 39,211–216.

Pangavhane, D. R., Sawhney, R. L., & Sarsavadia, P. N. (2000).Drying kinetic studies on single layers Thompson seedless grapesunder controlled heated air conditions. Journal of Food Processing

and Preservation, 24, 335–352.Park, K. J., Yado, M. K. M., & Brod, F. P. R. (2001). Estudo da

Secagem de Pera Bartlett (Pyrus sp.) em Fatias. Ciencia e

Tecnologıa de. Alimentos. Campinas, 21(3), 288–292.Parry, J. L. (1985). Mathematical modelling and computer simulation

of heat and mass transfer in agricultural grain drying: a review.Journal of Agricultural Engineering Research, 32(1), 1–29.


Queiroz, M. R., & Nebra, S. A. (2001). Theoretical and experimentalanalysis of the drying kinetics of bananas. Journal of Food

Engineering, 47, 127–132.Ratti, C. (1991). Diseno de Secaderos de Productos Frutihortıcolas.

Tesis Doctoral. Departamento de Quımica e Ingenierıa Quımica,Planta Piloto de Ingenierıa Quımica, Universidad Nacional del Sur,Bahıa Blanca, Argentina.

Rovedo, C. O., Suarez, C., & Viollaz, P. (1995). Drying of foods:evaluation of a drying model. Journal of Food Engineering, 26,1–12.

Sabarez, H. T., & Price, W. E. (1999). A diffusion model for prunedehydration. Journal of Food Engineering, 42, 167–172.

Simal, S., Deya, E., Frau, M., & Rosello, C. (1997). Simple modellingof air drying curves of fresh and osmotically pre-dehydrated applecubes. Journal of Food Engineering, 33, 139–150.

Simal, S., Mulet, J., Catala, P. J., Canellas, J., & Rosello, C. (1996).Moving boundary model for simulation moisture movement ingrapes. Journal of Food Science, 61(1), 157–160.

Thakor, N. J., Sokhansanj, S., Sosulski, F. W., & Yannacopoulos, S.(1999). Mass and dimensional changes of single canolakernels during drying. Journal of Food Engineering, 40,153–160.

Togrul, I. T., & Pehlivan, D. (2002). Mathematical modelling of solardrying of apricots in thin layers. Journal of Food Engineering, 55,209–216.

Togrul, I. T., & Pehlivan, D. (2003). Modelling of drying kinetics ofsingle apricots. Journal of Food Engineering, 58, 23–32.

Tsami, E., & Katsioti, M. (2000). Drying kinetics for some fruits:predicting of porosity and color during dehydration. Drying

Technology, 18(7), 47–60.Wang, N., & Brennan, J. G. (1995). A mathematical model of

simulation heat and moisture transfer during drying of potato.Journal of Food Engineering, 24, 209–216.

Zogzas, N. P., Maroulis, Z. B., & Marinos-Kouris, D. (1996).Moisture diffusivity data compilation in foodstuffs. Drying Tech-

nology, 14(10), 2225–2253.

drying kinetics of rose hip fruits (rosa eglanteria l.)

Documents