Diffusion Coefficient Relationships during Drying of Soya Bean Cultivars

ARTICLE IN PRESS Biosystems Engineering (2007) 96 (2), 213–222 doi:10.1016/j.biosystemseng.2006.10.015 PH—Postharvest Technology

Diffusion Coefficient Relationships during Drying of Soya Bean Cultivars M.C. Gely1; S.A. Giner2,3 1

Laboratorio de Tecnologı´ a de Semillas (TECSE), Departamento de Ingenierı´ a Quı´ mica, Facultad de Ingenierı´ a, Universidad Nacional del Centro de la Provincia de Buenos Aires, Avda del Valle 5737 (7400) Olavarrı´ a, Prov. Bs As, Argentina; e-mail: cgely@fio.unicen.edu.ar 2 Investigador CICPBA, at Centro de Investigacio´n y Desarrollo en Criotecnologı´ a de Alimentos (CIDCA), Universidad Nacional de La Plata-CONICET, Calle 47 y 116 (B1900AJJ) La Plata, Argentina 3 Area Departamental Quı´ mica, Facultad de Ingenierı´ a-UNLP; e-mail of corresponding author: [email protected] (Received 25 January 2006; accepted in revised form 26 October 2006; published online 19 December 2006)

A drying kinetics equation, the diffusive analytical solution for short times previously developed for wheat, was utilised to explore its applicability for a larger grain as soya bean, in order to determine diffusion coefficients and their dependence with temperature. Thin-layer drying of cv. Nidera A6381 was measured for air temperatures between 19 and 75 1C. The diffusive solution accurately described the experimental drying curves thus allowing the calculation of the diffusion coefficients, which varied from 178  1011 m2 s1 at 19 1C to 728  1011 m2 s1 at 75 1C. The temperature dependence was evaluated first by the Arrhenius equation, to find activation energies of 166 kJ mol1 below 50 1C, and of 288 kJ mol1 above that threshold. The relationship between diffusion coefficient and temperature was also accurately predicted above 50 1C by the Williams–Landel–Ferry (WLF) model. Drying curves were also recorded for cultivar Nidera A5409 in its conventional and genetically modified variants. Soya beans were dried from moisture contents of 015 and 030 dec., d.b., at 25 and 70 1C, and the activation energy was found to be 27 kJ mol1. The Arrhenius pre-exponential factor increased linearly with the initial moisture content, unlike the activation energy, which remained substantially constant. Reliable correlations between the diffusion coefficients and temperature are required to confidently simulate energy expenditure in dryers. r 2006 IAgrE. All rights reserved Published by Elsevier Ltd

1. Introduction Soya bean, as most other grains, is harvested with an excess of moisture with respect to the safe value for storage. This is removed by near ambient or hot air drying, which are complex, heat and mass transfer phenomena between air and grain. Modern methods of dryer design and optimisation include simulation as an decision-support stage so as to find energy-efficient drying leading to high-quality grain. The deep bed drying models used in simulators evaluate air temperature and humidity, and grain moisture and temperature as a function of time and bed depth. In this regard, a proper drying kinetics equation, the so-called, thin-layer equation is essential in deep bed models (Brooker et al., 1992; Giner & Mascheroni, 2002). 1537-5110/$32.00

The internal moisture movement during the grain drying process has been correctly predicted by assuming a diffusion mechanism (Becker & Sallans, 1955; Parry, 1985). Grain drying can be described using the solution of the microscopic mass balance in unsteady state (second Fick’s law). Becker (1959) has deduced a simplified analytical solution for short times to study isothermal drying of wheat under strict internal control of the mass transfer rate. In another study on wheat, Giner and Mascheroni (2002) demonstrated, on the basis of the mass transfer Biot number, that the isothermal drying assumption could be used for a small grain as wheat, and developed further the solution for short times by proposing the equilibrium moisture content as a prescribed surface condition, while the diffusion coefficient was found to be dependent on 213

r 2006 IAgrE. All rights reserved Published by Elsevier Ltd

ARTICLE IN PRESS 214

M.C. GELY; S.A. GINER

Notation A, B, C, C1, C2 aw Bic Bim Cpd Cpw D Ea G hr hT J kp kT Lb

coefficients specific to individual equations water activity in soya beans, dec. heat transfer Biot number, dimensionless mass transfer Biot number, dimensionless specific heat of dry matter, J kg1 1C1 specific heat of adsorbed water, J kg1 1C1 water Diffusion coefficient in soya beans, m2 s1 activation energy, kJ mol1 air mass flow rate, kg m2 s1 relative humidity, dec. heat transfer coefficient, W m2 K1 Colburn factor mass transfer coefficient, kg m2 s1 Pa1 thermal conductivity, W m1 K1 heat of desorption of water in the grain, J kg1

temperature as well as on the initial moisture content. However, as no test has been carried out on the appropriateness of the ‘isothermal drying assumption’ to allow the use of the short times solution for this oilseed, isothermal and non-isothermal drying models should be compared. Although diffusion coefficients would depend on the geometry assigned to the grain, as shown by Gasto´n et al. (2004) this complexity does not apply to the almost spherical soya beans. The diffusion coefficient is obtained by fitting a drying model to the experimental drying curves measured at various temperatures and, sometimes, starting from several initial moisture contents (Jayas et al., 1991). There are relatively few studies devoted to soya bean drying kinetics where the experimental data is analysed using well-founded theory. Misra and Young (1980) analysed the kinetics of soya bean drying by numerically solving the diffusion equation. They found an Arrhenius activation energy for diffusion of 285 kJ mol1. Their model, however, is still time-consuming for using within interactive dryer simulators aimed at equipment design. Suarez et al. (1980) have used another slow model, the analytical infinite series solution of the diffusion equation for soya bean drying to optimise diffusion coefficients. These were related to temperature by an activation energy of 364 kJ mol1. In turn, to predict data of Overhults et al. (1973), Irudayaraj et al. (1992) have used the finite element method (FEM), thus solving the partial differential equation of diffusion plus

M pvs ps R Rg t t r

moisture content, dec., dry basis vapour pressure of water in grain surface, Pa saturation vapour pressure of pure water, Pa radius, m gas constant, J mol1 temperature, 1C time, s dry matter concentration, kg m3

Subscripts 0 a d e R s

initial air dimensionless equilibrium reference grain surface

conduction in only one operating condition. A sharp increase of soya bean temperature towards the air asymptote was predicted, while the drying curve was correctly described. These authors used diffusion coefficients from the bibliography, so they did not determine their own diffusion coefficients. The problem with the FEM method for design is that their calculations are still slow on the computer, particularly within dryer simulation programs. In most other works on soya bean drying, empirical thin-layer equations were utilised to determine drying coefficients by fitting (White et al., 1981). These equations are useful for quick drying time estimations, but lack physical meaning and, therefore, are unable to identify the prevailing mass transfer mechanism. However, soya bean drying kinetics can be predicted with well-founded analytical models that, at the same time, do not demand long computing times. These models shall be useful for process design by simulation and automatic control, yet their meaningful parameters can be used in more rigorous numerical models (Gasto´n et al., 2004). Of particular interest is the relationship between the diffusion coefficient and temperature, represented by the activation energy Ea, which is currently considered a grain structural parameter. Concerning grain structure, concepts from the polymer science are now being applied to evaluate the effects of moisture and temperature during food conservation processes (Roos, 1995). For instance, in amorphous materials as grain biopolymers (starch, proteins, fibre),

ARTICLE IN PRESS DIFFUSION COEFFICIENT RELATIONSHIPS DURING DRYING OF SOYA BEAN CULTIVARS

phase transitions from the rubbery to the glassy state may occur drying drying, especially near the grain surface where changes in moisture and temperature are more manifest. For example, the soya bean seedcoat may begin drying in the rubbery state, soft and elastic, but, after substantial dehydration in hot air followed by cooling, may convert into a glassy, brittle material leading to split grains (Cnossen & Siebenmorgen, 2000). In the glassy state, there is less room for molecules to translate, affecting diffusion-limited properties as water diffusivity, and its temperature dependence, represented by the Arrhenius activation energy. The William– Landel–Ferry (WLF) model relates diffusion-limited properties at a temperature T with respect to a reference temperature. The WLF equation can be used alternatively to the Arrhenius equation in the rubbery state but, to date, it was seldom tested in the drying literature. The general objective of this work was to deepen the understanding of soya bean drying kinetics. The specific objectives were (1) to test the validity of the isothermal drying assumption in soya beans, to enable the use of the analytical diffusive solution for short times in spheres in order to determine diffusion coefficients for two soya bean cultivars, one of them in its conventional and genetically modified (GM) version; and (2) to carry out a specific study on the relationship between diffusion coefficient and temperature, especially to compare the classical Arrhenius expression with an equation utilised in studies of the rubbery and glassy state of amorphous materials—the WLF model.

2. Materials and methods 2.1. Soya bean seeds The soya bean varieties used were Nidera A6381 (moisture content, 0115 dec., d.b.), and one of the latest soya bean cultivars, the conventional (C) Nidera A5409 (moisture content, 01044 dec., d.b.), and its GM version, Nidera A5409RG (moisture content, 01069 dec., d.b.). For those moisture contents, the equivalent diameter (of a sphere with the same volume as the grain) were determined by pycnometry with toluene, and the results were 600 mm for A6381, 602 mm for A5409 (C) and 597 mm in A5409RG. To conduct the thin-layer drying experiments, soya bean samples of 200 g were conditioned with calculated amounts of distilled water to bring moisture contents to predetermined values, following the procedure described by Giner and Gely (2005). Moistened seeds were stored at 5 1C for at least 96 h until using.

215

2.2. Drying Grain containers were removed from refrigerated storage and allowed to equilibrate with room conditions for 24 h before using in the drying experiments. Thin-layer drying experiments were conducted in an experimental equipment composed of a cylindrical drying chamber with a removable, mesh-bottomed tray of 00232 m2 containing the thin layer of grains. Tray sides were covered with rubber stripping to avoid air leakages. An electrical blower was used to force the air through a 0043 m internal diameter pipe. Airflow rate was measured by an orifice plate connected to a U-tube manometer. Ambient air temperature and humidity was determined with a ventilated psychrometer (Gely & Santalla, 2000; Giner & Mascheroni, 2002). Air was heated by electric resistances in series up to the target temperature, then conducted to the drying chamber and, after passing through the tray, exhausted to the atmosphere. Once the dryer was warmed up, the grains were placed in the tray. This was removed periodically for weighing in a Ohaus digital balance (GT 410) with an accuracy of 0001 g to assess the moisture loss by drying. For the Nidera A6381 cultivar, drying kinetics was determined at air temperatures of 19, 30, 40, 50, 60, 70 and 75 1C for an initial moisture of 02615 dec., d.b. (2073% w.b.). The air velocity varied from 022 m s1 at 19 1C to 025 m s1 at 70 1C, a typical range in commercial soya bean dryers. (Table 1). With regard to cultivars Nidera A5409 in its GM and conventional (C) variants, drying experiments were carried out for two initial moisture levels: 015 and 030 dec., d.b. In each level, samples were dried at air temperatures of 25 and 70 1C. In each experiment, drying was maintained up to reaching an approximate dimensionless moisture content Md of 05, sufficiently low for practical purposes. This was called drying time. Differences between final moisture duplicates were always below 0006 dec., d.b. Drying times in these Table 1 Experimental conditions for thin layer drying of soya bean cv. Nidera A6381, initial moisture content M0 of 0.2615 dec., d.b. Air temperature (Ta),1C 19 30 40 50 60 70 75

Air relative Soya bean equilibrium moisture content (Me), dec., d.b humidity (hra), dec. 067 052 023 011 0065 005 003

0135 0091 0037 0018 0011 0009 0005

ARTICLE IN PRESS 216

M.C. GELY; S.A. GINER

cultivars ranged from 1 h (A5409 conventional, 70 1C, 030 dec., d.b.) to 692 h (A5409 conventional, 25 1C, 015 dec., d.b. An air velocity of 0237001 m s1 was used in all drying runs. (Table 2).

2.3. Calculation of thermophysical properties Film, air-grain, heat and mass transfer coefficients are important parameters for modelling the drying process. The heat transfer coefficient was calculated following the method used by Giner and Mascheroni (2001). These authors, in turn, have employed the Colburn factor J correlation provided by Sokhansanj and Bruce (1987). This factor may be considered equal in heat and mass transfer. In heat transfer, J depends on Nusselt, Reynolds, and Prandtl numbers whereas, for mass transfer, on the Sherwood, Reynolds and Schmidt numbers. The equilibrium moisture content of soya bean for the drying conditions was calculated by the Modified Henderson equation, with parameters provided by Brooker et al. (1992). The particle thermal conductivity was calculated using the method of Saravacos and Maroulis (2001). This method states that thermal conductivity kT in W m1 K1 be obtained from the corresponding values of the pure components, knowing their proportion in the grain. As the only variable component is water, the model for soya bean can be expressed in the following fashion: kT ¼ 012 þ 058M

Table 2 Average operating conditions for drying two variants of Nidera A5409 soya bean: conventional (C) and genetically modified (GM) Initial Air Soya bean Variant Air moisture temperature relative equilibrium of content (Ta), 1C humidity moisture content Nidera A5409 (M0), dec., (hra), dec. (Me), dec., d.b d.b 015 015 030 030 015 015 030 030

25 70 25 70 25 70 25 70

039 006 044 006 038 008 038 006

rs0 ¼

0072 0009 0077 0010 0066 0013 0066 0010

12304 1 þ M0

(2)

where M0 is the initial moisture content For the calculation of the mass transfer Biot number, the diffusion coefficient D in m2 s1 was calculated from an Arrhenius equation developed from data by Suarez et al. (1980), valid for air temperatures between 415 and 708 1C, where the value for Ea is 364 kJ mol1, and for the gas constant Rg is 8314 J mol1. The expression is:   36 400 5 D ¼ 339  10 exp (3) Rg ðT þ 27316Þ

3. Results and discussion 3.1. Determination of the controlling mechanisms for heat and mass transfer Being drying a coupled heat and mass transfer process, the determination of the controlling mechanism requires the calculation of Biot numbers for heat Bic [Eqn (4)] and mass transfer Bim [Eqn (5)] (Giner & Mascheroni, 2001). Both depend on drying and grain properties. Bic ¼

(1)

where M is the moisture content on a decimal, dry basis (d.b.). Soya bean seed density was taken to be 12304 kg m3 for Biot calculations, an average value reported by Giner et al. (1994). The initial dry matter

C C C C GM GM GM GM

concentration (ratio of the dry matter to the initial grain volume) rs0 in kg m3 was calculated in Eqn (2):

Bim ¼ 

hT R kT

kp Rps  qM r D qaws T s0

(4)

(5)

where: hT is the heat transfer coefficient in W m2 K1, R the soya bean radius; and kp the mass transfer coefficient in kg m2 s1 Pa1. The vapour pressure at grain surface pvs was expressed in terms of the product aws ps, where aws is the water activity at grain surface and ps the saturation vapour pressure of pure water in Pa. 3.1.1. Heat transfer Biot number For an average air mass flow rate G of 026 kg m2 s1 and air temperatures varying from 19 to 75 1C, the value of the heat transfer coefficient was 594 W m2 K1 at 19 1C and 629 W m2 K1 for 75 1C. At the airflow used, the particle Reynolds number varied between 77 and 85, being included in the validity range of the Sokhansanj–Bruce correlation. In turn, the thermal conductivity of soya bean grains, as determined by Eqn (1) was, on average, 021 W m1 K1. Equation (4) was used to calculate the heat transfer Biot number as a function of the water activity aw within

ARTICLE IN PRESS DIFFUSION COEFFICIENT RELATIONSHIPS DURING DRYING OF SOYA BEAN CULTIVARS

the normal drying range at the grain surface (025oaw o095). Predictions were carried out at two temperatures, 25 and 70 1C (Fig. 1). The heat transfer Biot number Bic is the ratio of the internal resistance R/kT to the external, 1/hT. Values ranged between 073 and 123 depending on temperature and water activity, so internal and external resistances are comparable. The value of Bic is higher in soya bean than it is in wheat (Giner & Mascheroni, 2002) mostly because of the larger equivalent radius in the oilseed. Figure 1 shows that lower water activities lead to higher values of Bic because the lower thermal conductivity increases the internal resistance to heat conduction. Higher temperatures also increase the values of Bic because temperature gradients are steeper. The calculated Bic were below the threshold of 15 suggested by Parti (1993) as the maximum value permitting the use of models for externally controlled heat transfer in drying studies. 3.1.2. Mass transfer Biot number The mass transfer Biot number Bim calculated by Eqn (5), varies between 138 (25 1C, aw ¼ 095) and 4140 (70 1C, aw ¼ 025) thus showing strict internal control (Bim 450) (Giner & Mascheroni, 2001) (Fig. 2). This means that changes in air mass flow rates will not affect the thin-layer drying curve. As drying proceeds, the value of Bim increases by one order of magnitude, being the mathematical cause of this the decrease in the slope of the sorption isotherm qM/qaws for lower values of aws. More physically, the internal resistance increases as moisture gradients become steeper, i.e. as the grain periphery turns drier. Therefore, the path the diffusing water molecules have to traverse until being evaporated at the surface becomes longer. On the same grounds, higher air temperatures lead to higher values of Bim. The ratio of Bim to Bic varies from 189 (25 1C, aw ¼ 095) to 3536 (70 1C, aw ¼ 03). Therefore, heat

Heat transfer Biot Bic , dec.

1.33 1.23 1.13 1.03

217

transfer becomes instantaneous compared to mass transfer and the response of the coupled system would be considerably more sensitive to variations in the mass transfer equations than in those of heat transfer. Therefore, predictions of the model for isothermal drying would not differ considerably from those for non-isothermal drying, but this feature will be verified in the next section. 3.2. Thin-layer drying model In order to interpret the drying kinetics data, an analytical equation was used, which is the solution of the unsteady-state diffusion equation considering semiinfinite behaviour or short dimensionless times and isothermal drying. It was first proposed by Becker (1959) and further developed by Giner and Mascheroni (2001). For spheres, it is valid between 03pMdp1 [Eqn (6)].    2 M  Me 2 3 pffiffiffiffiffiffi 3 Dt þ 0331 Md ¼ ¼ 1  pffiffiffi Dt R M0  Me p R (6) where: Me is the equilibrium moisture content; and t is the time, in seconds. To compare predictions by Eqn (6) which, as such, considers isothermal drying, with a model that considers heat transfer, Eqn (6) was derived with respect to time, to obtain the drying rate rffiffiffiffiffi  2 3 D 3 D  0331 dM R pt R ¼ ðM  M e Þ  2 ! dt 2 3 pffiffiffiffiffiffi 3 Dt þ 0331 Dt 1  pffiffiffi R pR (7) which is solved simultaneously with the macroscopic energy balance [Eqn (7)], which predicts the variation of temperature, assuming absence of temperature gradients inside the grain.     3 dM hT ðT a  T Þ  rs0  Lb dT R dt   ¼ (8) dt rs0 C pd þ C pw M

where the specific heat of dry matter, Cpd is 1300 J kg1 1C1 and that for water, Cpw is 4187 J kg1 1C1. The soya bean heat of sorption Lb in 0.83 J kg1 was calculated from the Modified Henderson isotherm equation plus the Clapeyron equation, follow0.73 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 ing the method already developed by Gely and Giner Water activity aw , dec. (2000) for maize. In Eqns (7)–(8), the diffusion Fig. 1. Heat transfer Biot number (Bic ) as a function of water coefficient [Eqn (3)] is not calculated at the air activity (aw), at two temperatures: - - - - - - - - -, 25 1C; ———, temperature Ta, in 1C, as in Eqn (6), but at the 70 1C instantaneous grain temperature T. 0.93

ARTICLE IN PRESS 218

M.C. GELY; S.A. GINER

tions by the two methods can be considered equal. Therefore, Eqn (6) will be used here as kinetic drying equation.

Mass transfer Biot Bim , dec.

10000

3.3. Fitting the kinetic model to drying kinetics data of soya bean cv. Nidera A6381

1000

Fig. 3. Comparison of drying rate curves predicted by solving the non-isothermal ordinary differential equation (EDO) system (upper curve) and by the analytical solution for isothermal drying and short times (lower curve); differences are below the error of oven-moisture determinations

Figure 4 shows the experimental results of soya bean drying in thin layers, at air temperatures of 19, 30, 40, 50, 60 70 and 75 1C. The diffusion coefficient was the only fitting parameter in applying Eqn (6) to the experimental data of Fig. 4. Values ranged from 178  1011 m2 s1 at 19 1C to 728  1011 m2 s1 at 75 1C (Fig. 5). The coefficient of determination r2 was in all temperatures above 0999, so the agreement of predictions and experimental data was excellent. In turn, Fig. 5 shows an Arrhenius plot of the relationship between the diffusion coefficient an air temperature (Jayas et al., 1991, Muthukumarappan & Gunasekaran, 1994). By applying the Arrhenius model to the whole temperature range, an average activation energy Ea of 193 kJ mol1 was found (line not shown). However, the trend of ln D versus 1/T (Fig. 5) exhibited two, rather than one, straight lines, with the change of slope being placed at about 50 1C. Therefore, the Arrhenius equation was applied below 50 1C to find an activation energy of 166 kJ mol1. Above that threshold, the value of Ea was 288 kJ mol1, almost equal to the value fitted by Misra and Young (1980).   Ea D ¼ A exp  (9) Rg ðT a þ 27316Þ

The two predicted drying curves [i.e. by Eqn (6) and by Eqns (7)–(8)] will be compared. While Eqn (6) is an integral model for isothermal drying, the pair of Eqns (7)–(8) constitute a coupled, ordinary differential equation (ODE) system, in an initial value problem (t ¼ 0, M ¼ M0; T ¼ T0) for a non-isothermal system. Both calculation methods were compared using the following conditions: drying air temperature, 60 1C; initial grain moisture content, 0205 (dec., d.b.); initial grain temperature, 20 1C. Results are plotted in Fig. 3. While the ODE system, integrated using the Matlab function ODE 45, predicted a drying time of 497 min to reach the final moisture content of 015 dec., d.b., the analytical solution [Eqn (6)] calculated a final moisture content of 01482 dec., d.b., after the same drying time, i.e., a moisture difference of 00018 dec., d.b. As this deviation is lower than the accepted error for oven moisture determinations (0003 dec., d.b.) the predic-

Sun and Woods (1994) have found an activation energy of 233 kJ mol1 for wheat drying in the low temperature range (4–50 1C), while Giner and Mascheroni (2002) have encountered a value of 272 kJ mol1, between 40 and 70 1C, close to the value found here for Nidera A6381 soya bean. This change of slope in the Arrhenius plot may be explained by the glass transition theory (Roos, 1995; Yang et al., 2003). In the lower temperature range (the data plotted in the right hand side of the Arrhenius plot), the temperature dependence, represented by the activation energy, is weaker, and this may be caused by the material being more rigid, with lower free volume available for translational movement of water molecules. At higher temperatures, the material turns softer, more rubbery, and the opposite occurs, i.e. the activation energy is higher. The temperature dependence of diffusion-limited processes can be predicted for rubbery polymer-based materials by the Williams, Landel and Ferry (WLF) expression (Roos, 1995) (Appendix A).

100

0.25

0.35

0.45 0.55 0.65 0.75 0.85 Water activity aw, decimal

0.95

1.05

Moisture content, dec. (d.b.)

Fig. 2. Mass transfer Biot number (Bim) as a function of water activity, at two temperatures: - - - - - - - - - - - -, 25 1C; ———, 70 1C

0.21 0.2 0.19 0.18 0.17 0.16 0.15 0.14 0

5

10

15

20

25 30 Time, min

35

40

45

50

ARTICLE IN PRESS DIFFUSION COEFFICIENT RELATIONSHIPS DURING DRYING OF SOYA BEAN CULTIVARS

219

0.26

Moisture content, dec. (d.b.)

0.24 0.22 0.2 0.18 0.16 0.14 0.12 0

100

200

300 Time, min

400

500

600

Fig 4. Experimental thin-layer drying curves of soya bean cv. Nidera A6381, at seven air temperatures; initial moisture content ¼ 02615 dec., d.b.; n, 19 1C; m, 30 1C; &, 40 1C; ’, 50 1C; B, 60 1C; K, 70 1C; J, 75 1C

−23.2 −23.4 −23.6

ln (D)

−23.8 −24 −24.2 −24.4 −24.6 −24.8 −25 0.0028 0.0029 0.003 0.0031 0.0032 0.0033 0.0034 0.0035 1/T, K−1

Fig. 5. Two-slope Arrhenius plot for the temperature (T) dependence of the diffusion coefficient (D) in m2 s1 in soya bean cv. Nidera A6381. ——, T o 50 1C; - - - - - - -, T 450 1C; K, values fitted by the thin layer drying equation

3.4. Dependence of the diffusion coefficient with moisture content and temperature Further thin-layer drying experiments were carried out on two variants of a more recent soya bean variety, Nidera A5409, the conventional (C) and GMO forms. These were done to corroborate the behaviour of the kinetics drying model [Eqn (6)], and to assess the effects of the cultivar, air

temperature and initial moisture content on the diffusion coefficient and Arrhenius parameters. Figure 6 shows the experimental results of dimensionless moisture versus time in four drying experiments conducted at 70 1C for different conditions. The period required to reach a dimensionless moisture of 05, determined with the data of Fig. 6, was defined as the drying time. For an initial moisture of 015 dec., d.b. and drying air temperature of 70 1C, the drying time was of 73 min for C seeds, whereas, for an initial moisture content of 030 dec., d.b., it reduced to 55 min. A similar effect was assessed for GM seeds. Soya beans of higher initial moisture content take less time to reach the same final dimensionless moisture content. According to Eqn (6), this may only occur if the diffusion coefficient is higher . The drying kinetics model [Eqn (6)] was utilised to determine the effective diffusivities of soya bean Nidera 5409 C and GM. The coefficients of determination r2, listed in Table 3 indicate accurate prediction for this cultivars as well. As mentioned above, in some conditions the diffusion coefficients for A 5409 C soya bean are slightly higher than in the GM variant, though not enough to be demonstrated on a statistical basis (probability a ¼ 005). With respect to the possible combined effect between temperature and seed cultivar, the Analysis of variance (ANOVA) test indicates no interaction (F ¼ 154) for a significance level of 5%. Therefore, the effect of temperature on the diffusion coefficient is similar in both cultivars (Fig. 7).

ARTICLE IN PRESS 220

M.C. GELY; S.A. GINER

Moisture content, Md , dec. (d.b.)

0.95

0.85

0.75

0.65

0.55

0.45 0

10

20

30

40

50 60 Time, min

70

80

90

100

Fig. 6. Dimensionless moisture content as a function of time for thin-layer drying of Nidera A 5409 in its conventional (C )and genetically- modified (GM) variants. ’, C 70 1C 030 dec., d.b.; &, GM 70 1C 030 dec, d.b.; K, C 70 1C 015 dec., d.b.; J, GM 70 1C 015 dec, d.b.

Ea 1 ln D ¼ ln A  Rg ðT þ 27316Þ

(10)

whose parameters are shown in Table 4. As both lines are parallel and different, the initial moisture does not affect activation energy but increases the pre-exponential factor A of Eqn (10). For this purpose, the activation energy was considered constant at Ea ¼ 270 kJ mol1. The Arrhenius line for Nidera A 5409 was proposed to be:   Ea D ¼ ðB þ CM 0 Þ exp  (11) Rg ðT þ 27316Þ Figure 7 shows a suitable prediction of Eqn (11) with values for coefficient B of 451  107 m2 s1 (55  108) and for coefficient C of 19  108 m2 s1 kg[dry matters] kg1 [H2O] (2  109), the standard error of the parameters being indicated in parenthesis. The value of r2 was 0992. The value of Ea found for Nidera A 5409 soya beans was similar to that found for Nidera A6381 in the range of 50–75 1C (288 kJ mol1), close to the average activation energy (272 kJ mol1) found for various wheat cultivars by Giner and

-23 −23.5 ln (D)

Given that differences of drying rates between Nidera A 5409 C and GM are not statistically significant, all diffusion coefficients of Table 3 were pooled in two files of different initial moisture, to fit corresponding Arrhenius lines

−24 −24.5 −25 −25.5 0.0029

0.003

0.0031

0.0032

0.0033

0.0034

1/T, K−1

Fig. 7. Graphical representation of the Arrhenius-type functionality of the effective diffusion coefficient of moisture D in soya bean seeds for both conventional (C) and genetically modified (GM) variants considering both temperature and initial moisture dependences. &, 015 dec., d.b. C; ’, 030 dec., d.b. C; n, 015 dec., d.b. GM m 030 dec., d.b. GM; ——, Eqn (11) 015 dec., d.b.; - - - - - -, Eqn (11) 030 dec., d.b.

Mascheroni (2002) and Gasto´n et al. (2004), and also in agreement with the value of 285 kJ mol1 found for soya bean by Misra and Young (1980). The increase of diffusion coefficient for higher initial moistures M0 is also in agreement with the glass transition theory. The rubbery nature and molecular mobility in polymerbased materials increases with temperature and moisture content (Roos, 1995).

ARTICLE IN PRESS 221

DIFFUSION COEFFICIENT RELATIONSHIPS DURING DRYING OF SOYA BEAN CULTIVARS

Table 3 Average diffusion coefficients in m2 s1 between duplicates, for each experimental condition, for Nidera A5409 conventional (C) and genetically modified (GM) Experimental drying conditions Nidera A5409 variant

Air temperature (Ta), 1C

Soya bean initial moisture content (M0), dec., d.b.

25 25 70 70 25 25 70 70

015 030 015 030 015 030 015 030

C C C C GM GM GM GM

Diffusion coefficient (D) 1011, m2 s1

r2 average

1344 2208 5885 8466 1395 1723 5709 7645

0960 0987 0998 0997 0994 0989 0997 0998

 r2, coefficient of determination.

Table 4 Results from the fitting of Eqn (10) to Nidera A5409 diffusion coefficients, valid for both conventional (C) and geneticallymodified (GM) variants Initial Moisture Content (M0), dec. (d.b.) 015 030

A (SE) m2 s1

Activation Energy(Ea) (SE) kJ mol1

r2

820  107 (4.3  107) 920  107 (6.9  107)

273 (1048)

0993

26.7 (2.11)

0986

 Values in parenthesis indicate parameter standard errors.  r2, coefficient of determination.

4. Conclusions A Biot number analysis and the prediction of a heat and mass transfer model suggested that an isothermal model is sufficiently accurate to describe thin-layer drying of soya beans. The analytical solution of the diffusion equation for short times in spheres proved to be an excellent thinlayer drying model to predict soya bean drying curves. It demands short computing times and is well suited for using within interactive dryer simulation programs. For the soya bean cultivar Nidera A6381, the Arrhenius equation relating diffusion coefficients and temperatures showed an activation energy of 166 kJ mol1 below 50 1C and 288 kJ mol1 above that threshold. As representative of the dependence of diffusion coefficient with temperature, greater activation energies are expected at higher temperatures because of the increased molecular mobility. Above the critical temperature of 50 1C, predictions of the diffusion

coefficient by the Williams–Landel–Ferry relationship were almost exact. Further experiments carried out with two variants of the recent cultivar Nidera A 5409 soya bean in its conventional (C) and genetically modified (GM) variant confirmed the accuracy of the drying kinetic equation, the magnitude of the activation energy (27 kJ mol1) and the increase of the Arrhenius preexponential factor with the initial moisture content, in agreement with previous results for wheat and with the glass transition theory. Increasing evidence, supported by the glass transition theory, suggests that activation energies for low or ambient temperature drying are below those for heated air drying. The latter tend vary around 28 kJ mol1. The predicted effect of air temperature on dryer throughput or specific heat consumption is affected by the activation energy of drying, so accurate determination of this transport parameter, as well as its possible variation during drying is essential to devise reliable design methods based on mathematical simulation.

Acknowledgements This work was funded by the Agencia Nacional de Promocio´n Cientı´ fica y Tecnolo´gica (ANPCyT) of Argentina, Project PICT 2002 09-12196, by Facultad de Ingenierı´ a, Universidad Nacional de La Plata (UNLP), and by Comisio´n de Investigaciones Cientı´ ficas de la Provincia de Buenos Aires (CIC). References 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

ARTICLE IN PRESS 222

M.C. GELY; S.A. GINER

Becker H A; Sallans H R (1955). A study of internal moisture movement in the drying of the wheat kernel. Cereal Chemistry, 32, 212–226 Brooker D B; Bakker-Arkema F W; Hall C W (1992). Drying and Storage of Grains and Oilseeds. AVI Publishing Co., Westport, Connecticut Cnossen A G; Siebenmorgen T J (2000). The glass transition temperature concept in rice drying and tempering: effect on milling quality. Transactions of the ASAE, 43(6), 1661–1667 Erickson D R (1995). Practical Handbook of Soya bean Processing and Utilization. AOAC Press, Champaign, Illinois, and United Soya bean Board, St Louis, Missouri Gasto´n A; Abalone R; Giner S A; Bruce D M (2004). Effect of modelling assumptions on the effective water diffusivity in wheat. Biosystems Engineering, 88(2), 175–185 Gely M C; Santalla E M (2000). Effect of some physical and chemical properties of oilseeds on drying kinetics parameters. Drying Technology, 18(9), 2155–2166 Giner S A; Borra´s F; Robutti J L; An˜o´n M C (1994). Drying rates of 25 Argentinian varieties of soya bean: A comparative study. Lebensmittel-Wissenschaft und Technologie, 27, 308–313 Giner S A; Gely M C (2005). Sorptional parameters of sunflower seeds of use in drying and storage stability studies. Biosystems Engineering, 92(2), 217–227 Giner S A; Mascheroni R H (2001). Diffusive drying kinetics in wheat, part 1: potential for a simplified analytical solution. Journal of Agricultural Engineering Research, 80(4), 351–364 Giner S A; Mascheroni R H (2002). Diffusive drying kinetics in wheat, part 2: applying the simplified analytical solution to experimental data. Biosystems Engineering, 81(1), 85–97 Irudayaraj J; Haghighi K; Stroshine J L (1992). Finite element analysis of drying with application to cereal grains. Journal of Agricultural Engineering Research, 53(3), 209–230 Jayas D S; Cenkowski S; Pabis S; Muir W E (1991). Review of thin-layer drying and wetting equations. Drying Technology, 9(3), 551–588 Misra R N; Young J H (1980). Numerical solution of simultaneous moisture diffusion and shrinkage during soya bean drying. Transactions of the ASAE, 23(5), 1277–1282 Muthukumarappan K; Gunasekaran S (1994). Moisture diffusivity of corn kernel components during adsorption, part I: germ. Transactions of the ASAE, 37(4), 1263–1268 Overhults D G; White G M; Hamilton H E; Ross I J (1973). Drying of soya beans with heated air. Transactions of the ASAE, 16(1), 112–113 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, 1–29 Parti M (1993). Selection of mathematical models for drying grain in thin layers. Journal of Agricultural Engineering Research, 54(4), 339–352 Roos Y H (1995). Phase Transitions in Foods. Academic Press, New York Saravacos G D; Maroulis Z B (2001). Transport Properties of Foods. Marcel Dekker, Inc., New York

Siebenmorgen T J; Yang W; Sun Z (2004). Glass transition temperature of rice kernels determined by dynamic mechanical thermal analysis. Transactions of the ASAE, 47(3), 835–839 Sokhansanj S; Bruce D M (1987). A conduction model to predict grain tempertures in grain drying simulation. Transactions of the ASAE, 30(4), 1181–1184 Suarez C, Viollaz P, Chirife J (1980). Kinetics of soya bean drying. In Drying 80 (Mujumdar, A S, ed), 2, Hemisphere Publishing Corp. Washington DC, 251–255 Sun D W; Woods J L (1994). Low temperature moisture transfer characteristics of wheat in thin layers. Transactions of the ASAE, 37(6), 1919–1926 White G M; Bridges T C; Loewer O J; Ross I J (1981). Thin layer drying model for soya beans. Transactions of the ASAE, 24(6), 1643–1646 Yang W; Jia C C; Siebenmorgen T J; Pan Z; Cnossen A G (2003). Relationship of kernel moisture content gradients and glass transition temperatures to head rice yield. Biosystems Engineering, 85(4), 467–476

Appendix A The moisture gradients induced in the grain by the heated air drying process and the subsequent cooling may be analysed in the light of the glass transition principles (Siebenmorgen et al., 2004). This theory was borrowed from the synthetic polymer science, and can be applied to foods. In soya beans, the proportion of biopolymers as carbohydrates plus proteins may reach 70% of the grain weight (Erickson, 1995). After drying, the grain is hot and rubbery with internal moisture gradients: the grain periphery is very dry and the centre remains mostly undried. As the grain is cooled, the surface becomes dry and cool, and possibly undergoes a phase transition from the rubbery to the glassy state, thus becoming fragile; if the seedcoat breaks, the grain may split. The centre, being wet and cool, may possibly continue in the rubbery state. Before cooling, the dependence of the diffusion coefficient with temperature, during the rubbery state, can be modelled by the Williams–Landel–Ferry (WLF) Equation (Roos, 1995) [Eqn (12)], where TR is considered as the reference temperature, here 50 1C, value for which the Arrhenius slope exhibits a change. The WLF equation indicates that the ratio of the relaxation time of a diffusion-limited property at any temperature T to the relataxion time at a reference temperature TR (usually the glass transition temperature but not necessarily, as here) depends on the extent of the deviation from the reference state (T–TR) as indicated by Eqn (12). log

DðTÞ C 1 ðT  T R Þ ¼ DðT R Þ C 2 þ ðT  T R Þ

(12)

where C1 ¼ 465 (000011) and C2 ¼ 32315 (00083), the standard deviation of parameters being written in parenthesis. The coefficient of determination r2 was equal to 1. Considering its excellent agreement, the WLF equation becomes a valid alternative to the Arrhenius relationship in grains experiencing drying in the rubbery state.