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Modelling dehydration and quality degradation of maize during fluidized-bed drying
Journal of Food Engineering 100 (2010) 527–534
Contents lists available at ScienceDirect
Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Modelling dehydration and quality degradation of maize during fluidized-bed drying Sébastien Janas a,*, Sébastien Boutry b, Paul Malumba c, Luce Vander Elst b, François Béra a a
University of Liege, Gembloux Agro-Bio Tech, Food Technology Department, Process and Quality Engineering Laboratory, Passage des déportés 2, B-5030 Gembloux, Belgium Department of General, Organic and Biomedical Chemistry, NMR and Molecular Imaging Laboratory, University of Mons, Avenue Maistriau 19, B-7000 Mons, Belgium c Kinshasa University, Faculty of Agricultural Sciences, BP 1471 Kinshasa 1, Congo b
a r t i c l e
i n f o
Article history: Received 15 December 2009 Received in revised form 27 April 2010 Accepted 2 May 2010 Available online 10 May 2010 Keywords: Drying FEM Heat and mass transfer Maize MRI Quality Salt-soluble proteins
a b s t r a c t At harvest time, maize (Zea mays L.) has a moisture content too high to be stored, and has to be dried. To control the drying impact on maize characteristics, it is necessary to accurately know the spatial distribution of temperature and moisture content in the kernel, and the kinetics of quality loss in relation to these two factors. To this end, a physical model of heat and mass transfer in a maize kernel was designed. The Fick and Fourier equations were solved by the finite element method (FEM). The real 3D geometry of maize was obtained by NMR imaging and then used to build the mesh needed for the FEM computations. The model correctly describes the evolutions of maize moisture and salt-soluble protein content during fluidized-bed drying with a constant drying air temperature between 50 °C and 100 °C. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction In 2007, Maize (Zea mays L.) was the first crop in the world, before rice and wheat (FAOSTAT, 2010). At the time of harvest, maize has a moisture content too high to be stored (between 30% and 40% w.b.), and has to be dried. During drying, the maize kernel is submitted to cracks (Gustafson et al., 1979; Davidson et al., 2000; Prachayawarakorn et al., 2004), protein denaturation (Lupano and Anon, 1987; Malumba et al., 2008), changes of functional properties of wet-milled starch granules (Malumba et al., 2009b) and loss of wet-milling properties (Lasseran, 1973). To control the drying impact on food characteristics, it is necessary to follow accurately the spatial distribution of temperature and moisture content, and the kinetics of quality loss in relation to these two factors. The spatial evolution of temperature and moisture content in the product during drying can only be assessed by modelling heat and mass transfer. To this end, several models based on a simplified geometry of a maize kernel were used (Hatamipour and Mowla, 2003, 2006; Mourad et al., 1995; Nemenyi et al., 2000). These models accurately gives the evolution of average moisture content and temperature of maize grains during drying. * Corresponding author. E-mail address: [email protected] (S. Janas). 0260-8774/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2010.05.001
To follow the evolution of maize quality during dehydration, the glutamic acid decarboxylase activity (Linko, 1961) and electrical properties (Holaday, 1964) were used as indicators of heat damages but were not correlated with any particular industrial use of maize. In addition, their measurement needs equipments not always available in a traditional laboratory. Recently, Malumba et al. (2009a) has shown that the salt-soluble protein content of maize presented a high correlation to the wet-milling properties of the maize kernel. A method for the determination of salt-soluble protein content has also been published to estimate maize quality for the starch industry (AFNOR, 2008). To the knowledge of the authors, the kinetics of salt-soluble protein denaturation in maize during drying as a function of moisture content and temperature are not known. These kinetics, in combination with a predictive model of heat and mass transfer in maize during drying, would be a very useful tool to study the impact of drying parameters on the final quality of the product. This article is an attempt to find an expression of the kinetics of salt-soluble protein denaturation in maize during drying. A simple model of heat and mass transfer was used to predict the evolution of temperature and moisture content in the grains. The model was solved by the finite element method. To find separately the evolution of moisture content in the germ and endosperm, the real 3D grain geometry was obtained by nuclear magnetic resonance imaging. This geometry permits the use of different initial values
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Nomenclature Cp Cpair D Deff Dw dg FT Hw h k L n ~ n Nu P Patm PE PG Pr Re RH
maize specific heat (J/kg °C) air specific heat (J/kg °C) decimal reduction time ðs1 Þ effective water diffusivity in maize (m2 /s) water vapor diffusivity in air (m2 /s) grain diameter (m) saturated vapor pressure (Pa) water latent heat of vaporization (J/kg) mass transfer coefficient (m/s) heat transfer coefficient (W/m2 °C) reaction rate ðs1 Þ number of experimental values (–) unit vector normal to the surface (–) Nusselt number (–) salt-soluble protein content (mg proteins/100 ml) atmospheric pressure (Pa) salt-soluble protein content in the endosperm (mg proteins/100 ml) salt-soluble protein content in the germ (mg proteins/ 100 ml) Prandtl number (–) Reynolds number (–) air relative humidity (–)
Sc Sh T t X Y
Schmidt number (–) Sherwood number (–) temperature (°C) time (s) grain moisture content (kg water/kg dry matter) air absolute humidity (kg water/kg air)
Greek symbols q maize grain density (kg/m3 ) qair air density (kg/m3 ) qdb dry matter density of maize grain (kg dry matter/m3 wet maize) k maize thermal conductivity (W/m °C) air thermal conductivity (W/m °C) kair lair air viscosity (Pa s) Subscripts a in the air calc calculated value exp experimental value s at the surface of the product 0 at the initial time
of salt-soluble protein content in the two parts of the grain. The evolution of maize salt-soluble protein content was followed during dryings between 50 °C and 100 °C, and described with a first order differential equation.
grams were used for the determination of maize moisture content, and 50 g were immediately immersed in iced water and then stored at 20 °C until the determination of salt-soluble protein content. All the dryings were made in triplicate.
2. Materials and methods
2.2. Determination of the initial moisture content of maize
2.1. Fluidized-bed drying of the maize kernel
To get the initial moisture content of the maize germ and endosperm, these two parts were separated by hand with the help of a scalpel. The moisture content was measured in triplicate on ±5 g of endosperm and ±0.5 g of germ by differential weighing after 48 h at 105 °C.
The maize kernel used was a flint maize, of the Baltimore variety. The moisture content at harvesting was about 40% w.b. In order to get a biological material as close as possible to its initial state for a very long time, the maize was received in the laboratory directly after harvesting and stored at 20 °C in plastic bags until the drying was performed. Drying curves and initial protein content did not show any change from the day of harvesting to the end of trials. Before each drying, 1.5 kg of maize was equilibrated at laboratory temperature for one night. A schematic view of the laboratory fluidized-bed dryer used for the experiments is presented on Fig. 1. This dryer was composed of a polycarbonate tube from VINK (Belgium) (height = 1.6 m and diameter = 0.12 m), in which air was introduced by the bottom at 50 °C, 65 °C, 80 °C, and 100 °C with a superficial velocity of 5.8 m/s. During this process, air temperature, relative humidity and velocity were measured downstream of the drying chamber, and air temperature and relative humidity were measured upstream. Temperatures were measured with a thermocouple type T TT-T-30-SLE from OMEGA (England), air relative humidity with probes TR200 from NOVASINA (Switzerland) and air velocity with an anenometer TEST0 445 (Germany). Thermocouple and air humidity probe signals were measured with a 3595551H UNIVERSAL IMP from SOLARTRON (England), and recorded with a program written in LABVIEW 5.1. Air velocity data were recorded with the TESTO LOGICIEL-COMFORT ‘‘Light” interface. The accuracy of temperature, humidity and velocity measures were respectively of 0.1 °C, 0.1% and 0.2 m/s. Each drying was 3 h long. During these trials, maize samples of ±60 g were collected after 5, 10, 15, 30, 60, 120, and 180 min. Ten
2.3. Determination of maize density A 100 ml flask was weighed (P1 in g) and ±5 g of endosperm were added. The flask was then weighed (P2 in g) and filled with distilled water before being weighed again (P3 in g). The density of endosperm was then calculated with the equation
q ¼ 1000
P2 P1 V ðP3 P2 Þ
ð1Þ
where V is the exact volume of the flask (ml), measured by weighing of distilled water. The experiment was carried out six times. The same procedure was used for the determination of germ density but with flasks of 50 ml and ±0.5 g of germ. 2.4. Determination of maize salt-soluble protein content 2.4.1. Extraction solution The extraction solution was composed of 13.6 g KH2 PO4 , 4.2 g K2 HPO4 and 20 g NaCl for 2000 ml of distilled water. 2.4.2. Coomassie blue Six hundred milligrams of coomassie brilliant blue G250 from Merck (Germany) was added in a flask of 1000 ml with 500 ml of HCl 0.6 N. The solution was agitated for 24 h out of light before
S. Janas et al. / Journal of Food Engineering 100 (2010) 527–534
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Fig. 1. Schematic view of the fluidized-bed dryer.
2.4.3. Standard solutions Six standard solutions corresponding to 10, 20, 30, 40, 50, and 60 mg/100 ml of bovine serum albumin from VWR (Belgium) were used to calibrate the UV-2401 PC UV-VIS recording spectrometer from Shimadzu (China).
Fig. 2. 3D geometry of a maize grain obtained by reconstruction of the 2D MRI data. The germ is shown in red and the endosperm in white. (For interpretation of color mentioned in this figure the reader is referred to the web version of the article.)
the final 500 ml of HCl 0.6 N was added. The solution continued to be agitated as long as it was needed to get an optical density of 3.0 ± 0.1, filtered on Whatman 595 1/2 filters (Germany) and stored out of light for 6 weeks maximum.
2.4.4. Determination of salt-soluble protein content All the samples were freeze-dried in a HETO DRYWINNER, model DW8 (Denmark). The moisture content of maize was about 6% d.b. at the end of freeze drying. The determination of maize saltsoluble protein content was carried out with the official method AFNOR NF-V03-741 (AFNOR, 2008). The samples were milled in a IKA Universalmühle M20 (Germany). Flour (5.4 g ± 0.01 g) was then introduced in an ernelmeyer with 100 ml of extraction solution and agitated for 3 min. The samples were filtered on filters Whatman 595 1/2 (Germany), the first 10 ml was pulled of and the following 20 ml kept for analysis. Into macro cuvets PMMA of 4 ml from VWR (Belgium) were added 40 ll of standard, 40 ll of sample and 3 ml of coomassie blue. The cuvets were agitated slowly and then the optical density at 595 nm was measured. 2.5. Determination of the maize geometry The maize geometry was obtained using the magnetic resonance imaging (MRI) technique. This method relies on the
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magnetic properties of atoms exposed to an external magnetic field. Its main usefulness is that it allows for a cartography of the mobile hydrogen atoms of a sample in a non-invasive manner. Thus, the MR signal collected when analyzing maize arises from water molecules contained in the kernels. MR images were obtained at room temperature on an AVANCE-200 system (Bruker, Karlsruhe, Germany), equipped with a 4.7 T vertical super wide bore magnet, using the animal/object handling system (inner diameter: 56 mm) to maintain the analyzed sample, which was prepared as follows: wet maize kernels were placed in 15 ml tubes, individually separated by cotton wools. This tube was then placed in a 50 ml tube containing a mixture of H2O and deuterium oxide (D2O) in equal volumes. Using this preparation method, the MR signal of the whole sample was sufficient to allow a correct set up of the MRI system, which could not be achieved with maize kernels only (containing too low levels of water). Thanks to the use of a H2O/D2O mixture (D2O giving no MR signal), the weak maize MR signal was not obscured by a too strong signal of surrounding water. MRI experiments were conducted with the following acquisition parameters: spin echo sequence, TR/TE 1001.7/3.5 ms, FOV: 3 cm, 64 64 matrix, slice thickness: 1.2 mm, acquisition time: 80 3200 , number of acquisitions: 8. A linear smoothing was applied to MR images using the PARAVISION software.
kðT a T s Þ ¼ ~ n ðkrTÞ Hw hqair ðY a Y s Þ
ð4Þ
The air water content in equilibrium with the product’s surface is related to the water content of the product according to equation :
Ys RHs FT s ¼ 0:622 1 Ys Patm RHs FT s
ð5Þ
The balance between the water flux from the product core to its surface and the vapor removed by air can be written as
~ n qdb ðDeff rXÞ ¼ hqair ðY a Y s Þ
ð6Þ
The following formula is used to calculate the heat transfer coefficient (Kunii and Levenspiel, 1993)
Nu ¼
1 1 kdg ¼ 2 þ 0:6Re2 Pr3 kair
ð7Þ
The mass transfer coefficient was obtained with the following equation (Kunii and Levenspiel, 1993)
Sh ¼
1 1 hdg ¼ 2 þ 0:6Re2 Sc3 Dw
ð8Þ
The physical properties of air and maize were found in the literature or measured in the laboratory and are summarized in Table 1.
2.6. Mathematical modelling of drying In order to know the evolution of moisture content and temperature in maize grains during drying, a simple heat and mass transfer model was used. The shrinkage was neglected because of the small magnitude of this phenomenon for flint maize like the Baltimore variety. Using Fourier’s law (Carslaw and Jaeger, 1986), the energy balance in the product leads to
qC p
At the boundary of the grain, heat provided by air is absorbed by the heating of the product and by water evaporation.
dT ¼ r ðkrTÞ dt
ð2Þ
Water diffusion in grain can be described by Fick’s second law (Cranck, 1979)
dX ¼ r ðDeff rXÞ dt
ð3Þ
Theoretically, the effective diffusivity of water in the grain should be correlated to local temperature. In the case of maize drying, it was observed that the grain temperature quite rapidly reached air temperature (Mourad et al., 1995). For this reason, it was assumed that the effective diffusivity was correlated to air temperature, and not to local temperature.
2.7. Denaturation kinetic of maize salt-soluble proteins The thermal denaturation of salt-soluble proteins was described by a first order ODE
dP ¼ LP dt
ð9Þ
The time D (s) after which a content reduction of 90% occurs can be calculated with equation:
D¼
2:303 L
ð10Þ
were the 2.303 coefficient is used to convert from a logarithm to a decimal basis. In order to take into account the influence of the moisture content on the denaturation kinetics, the following equation was used: X ref X
D ¼ D0 10
ð11Þ
z
X ref was fixed to 0.388 d.b., the average moisture content of grain during the dryings.
Table 1 Air and maize physical properties used in the model. Property
Equation
Reference Perry (1984)
Air density
qair ¼
Air viscosity
0:756 lair ¼ 1:66 105 ðTþ273 273 Þ
Perry (1984)
Air thermal conductivity
kair ¼ 4 105 ðT þ 273Þ þ 0:0246
Perry (1984)
Air specific heat
Cpair ¼ 0:9774 þ 0:1124 103 ðT a þ 273Þ þ 1:19035 107 ðT a þ 273Þ2 T 1:81 Dw ¼ 273 0.57 0.98 q ¼ 966:9 q ¼ 552:8 X X þ 0:26 ð1 ð1þXÞ Þ k ¼ 0:55 ð1þXÞ
Perry (1984)
Moisture diffusivity in the air Endosperm initial moisture content (d.b.) Germ initial moisture content (d.b.) Endosperm density Germ density Maize thermal conductivity
341:25 ðTþ273Þ
X ð1þXÞ
X þ 840 ð1 ð1þXÞ Þ
Maize specific heat
Cp ¼ 4190
Maize moisture sorption isotherm
RH ¼ 1 expðaTX b Þ a ¼ 3:11 105 b ¼ 1:713 61.9% 38.1%
Germ salt-soluble protein content Endosperm salt-soluble protein content
Perry (1984) Measured Measured Measured Measured Earle (1983) Earle (1983) Samapundo et al. (2007) Landry and Moureaux (1980) Landry and Moureaux (1980)
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Two different methods were used to model the salt-soluble protein denaturation kinetics.
Table 2 Statistics of the mesh applied to the 3D maize kernel geometry. Number of degrees of freedom Number of mesh points Number of tetrahedral elements Number of triangular elements Number of edge elements Number of vertex elements Minimum element quality Element volume ratio
274,729 18,558 95,343 14,718 3718 466 0.2629
2.7.1. Method 1 The salt-soluble protein content was assumed to remain homogeneous in the whole grain. In Eq. (11), X is the average moisture content of the grain kernel after each time increment.
5:45 107
2.7.2. Method 2 The evolution of salt-soluble protein content is calculated separately for the germ and the endosperm, using Eq. (9). The initial protein contents were calculated with Eqs. (12) and (13).
Table 3 Effective moisture diffusivity and residual error for the four drying temperatures. T (°C)
Deff (m /s)
Residual error (kg water/kg d.b.)
50 °C
7:14 1011
9:4 103
65 °C
9:26 1011
1:1 102
80 °C
1:21 1010
1:0 102
100 °C
10
2
2
1:86 10
P0 V tot 0:381 VE P0 V tot 0:619 PG0 ¼ VG
PE0 ¼
ð12Þ ð13Þ
The salt-soluble protein content for the whole grain was then estimated with Eq. (14)
1:1 10
Exp 50 °C Exp 65°C Exp 80 °C Exp 100 °C Calc 50 °C Calc 65 °C Calc 80 °C Calc 100 °C
0.6
WATER CONTENT (d.b.)
0.5
0.4
0.3
0.2
0.1
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
TIME (s) Fig. 3. Experimental and calculated values of moisture content (d.b.) for dryings at 50 °C, 65 °C, 80 °C and 100 °C.
1 Endosperm Germ
WATER CONTENT (d.b.)
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
TIME (s) Fig. 4. Comparison of the moisture content evolution in the germ and in the endosperm for drying at 80 °C.
11000
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Table 4 D0 and z coefficients of Eq. (11) obtained for each drying temperature with the two different methods. Method
D0 (min)
z (d.b.)
Residual error (mg/100 ml)
50
Method 1 Method 2
732 1773
0.28 0.47
0.17 0.17
65
Method 1 Method 2
273 945
0.18 0.33
0.74 0.71
80
Method 1 Method 2
175 542
0.15 0.29
0.27 0.22
100
Method 1 Method 2
47 91
0.22 0.27
0.47 1.34
PEV E PGV G þ V tot V tot
ð14Þ
3. Results and discussion 3.1. Determination of the maize geometry The 3D geometry of the maize kernel (Fig. 2) was reconstructed from the 2D MRI data according to the procedure described in the COMSOL MULTIPHYSICS 3.5 manual. The volumes of the whole maize kernel, the germ and the endosperm were respectively 1:80 107 m3 ; 1:46 108 m3 and 1:65 107 m3 .
48 Experimental Method 1 Method 2
46
PROTEIN CONTENT ( mg / 100 ml )
44
42
40
38
36
34
32
30 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
TIME (s) Fig. 5. Experimental salt-soluble protein content and the values calculated with the two methods for the dryings at 50 °C.
50 Experimental Method 1 Method 2
45
PROTEIN CONTENT ( mg / 100 ml)
T (°C)
P¼
40
35
30
25
20
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
TIME (s) Fig. 6. Experimental salt-soluble protein content and the values calculated with the two methods for the dryings at 65 °C.
11000
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The mesh used was refined until no variation in the solution of the model was observed. The mesh statistics are presented in Table 2.
previously in the literature. Mujumdar (2006), for example, give a diffusivity between 1=1012 and 3=1010 m2 =s for maize. Fig. 3 compares the predicted and the experimental values of the maize kernel’s moisture content. It can be seen that the model correctly describes the experimental values of maize moisture content. The model is also able to predict specifically the evolution of moisture content in the germ and in the endosperm of the maize kernel. Fig. 4 shows these evolutions for drying at 80 °C. The two curves are quite different, which indicates the usefulness of the 3D geometric model to predict the denaturation phenomena occurring specifically in the germ and in the endosperm, or phenomena with initial values differing greatly between these two morphological parts of the product.
3.2. Solution of the mathematical model The mathematical model is solved by the finite element method using the commercial package COMSOL MULTIPHYSICS 3.5a. The GMRES linear solver with the SSOR preconditioner and the backward difference time integrating scheme were used. Computation took ±40 min on a MacBook Pro dualcore 2.93 Ghz. The effective moisture diffusivities (Table 3) were obtained by nonlinear regression of the mathematical model for the four drying temperatures. They are in good agreement with values published
50 Experimental Method 1 Method 2
PROTEIN CONTENT ( mg / 100 ml)
45
40
35
30
25
20
15
10
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
TIME (s) Fig. 7. Experimental salt-soluble protein content and the values calculated with the two methods for the dryings at 80 °C.
50 Experimental Method 1 Method 2
PROTEIN CONTENT ( mg / 100 ml)
45
40
35
30
25
20 15
10 5
0 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
TIME (s) Fig. 8. Experimental salt-soluble protein content and the values calculated with the two methods for the dryings at 100 °C.
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3.3. Modeling the denaturation kinetic of salt-soluble proteins Table 4 presents the D0 and the z coefficients for each drying temperature obtained with the two different models. The two methods describes the denaturation of maize salt-soluble proteins with more or less the same accuracy, as indicated by residual errors calculated according to Eq. (15).
Pn error ¼
i¼1 jP calc
P exp j
n
ð15Þ
The values of the decimal reduction time and the z coefficient depend on the method used for their calculation. The D0 and z coefficients predicted by the method 2 are greater than those obtained by method 1. These differences show the importance of the initial heterogeneity of the protein content and of the evolution of the spatial heterogeneity in water content during the process on the protein denaturation kinetics. Figs. 5–8 present the experimental salt-soluble protein content and the values calculated with the two methods for each drying temperature. The two methods gave similar curves for the drying at 50 °C, but differed greatly when the temperature was increased. The temperature and moisture content have a great influence on the salt-soluble denaturation kinetics. From these results, it seems that variable temperature drying would be a interesting way to improve the final quality of maize. Low temperature drying should be used at the beginning of the process, to reduced maize moisture content without denaturing too much salt-soluble protein, and it should then be followed by a raise in temperature. 4. Conclusions Magnetic resonance imaging is a useful tool to build realistic 3D meshes of food products with respect to their internal morphological parts. In this article, a mesh of a maize kernel distinguishing the germ and the endosperm was built and used for the modeling of heat and mass transfer during fluidized-bed drying. The model correctly describes the evolution of moisture content during fluidized-bed drying with constant drying air temperatures between 50 °C and 100 °C. The evolution of the maize salt-soluble protein content during drying is a first order kinetic, with a reaction rate function of the grain moisture content. The initial protein content heterogeneity and the evolution of moisture content spatial heterogeneity during the process significantly influence the salt-soluble protein denaturation. The model designed in this study appears to be a very suitable tool to optimize maize drying taking into account the salt-soluble protein content. Acknowledgements S. Janas acknowledges financial support from the Fonds pour la Recherche dans l’Industrie et l’Agriculture, Belgium. He acknowl-
edges also Florence Lefebvre and Guy Delimme for their help in the laboratory, and Prof. Robert N. Muller (NMR and Molecular Imaging Laboratory, University of Mons) for his interest to this work and the access to the MRI facility. The authors thank Mrs. Patricia DeFrancisco for her help in preparing the manuscript. References AFNOR, 2008. Méthode Promatest d’évaluation de la dénaturation des protéines thermosensibles NF-V03-741. AFNOR. Carslaw, H., Jaeger, J., 1986. Conduction of Heat in Solids. OUP Oxford. Cranck, J., 1979. The Mathematics of Diffusion. OUP Oxford. Davidson, V.J., Noble, S.D., Brown, R.B., 2000. Effects of drying air temperature and humidity on stress cracks and breakage of maize kernels. J. Agric. Eng. Res. 77, 303–308. Earle, R., 1983. Unit Operations in Food Processing. Pergamon Press. Gustafson, R.J., Thompson, D.R., Sokhansanj, S., 1979. Temperature and stress analysis of corn kernel-finite element analysis. Trans. ASAE 22, 955–960. Hatamipour, M.S., Mowla, D., 2003. Correlations for shrinkage, density and diffusivity for drying of maize and green peas in a fluidized bed with energy carrier. J. Food Eng. 59, 221–227. Hatamipour, M.S., Mowla, D., 2006. Drying behaviour of maize and green peas immersed in fluidized bed of inert energy carrier particles. Food Bioprod. Process. 84 (3), 220–226. Holaday, C., 1964. An electronic method for the measurement of heat-damage in artificially dried corn. Cereal Chem. 41, 533–542. Kunii, D., Levenspiel, O., 1993. Fluidisation Engineering, vol. 491. ButterworthHeinemann. Landry, J., Moureaux, T., 1980. Distribution and amino acid composition of proteins groups located in different histological parts of maize grain. J. Agric. Food Chem. 28 (6), 1186–1191. Lasseran, J.C., 1973. Incidence of drying and storing conditions of corn (maize) on its quality for starch industry. Starch 28 (8), 257–262. Linko, P., 1961. Simple and rapid manometric method for determining glutamic acid decarboxylase activity as quality index of wheat. J. Agric. Food Chem. 9 (4), 310–313 . Lupano, C., Anon, M., 1987. Denaturation of wheat endosperm proteins during drying. Cereal Chem. 64 (6), 437–442. Malumba, P., Janas, S., Masimango, T., Sindic, M., Deroanne, C., Béra, F., 2009a. Influence of drying temperature on the wet-milling performance and the proteins solubility indexes of corn kernels. J. Food Eng. 95 (3), 393–399. Malumba, P., Massaux, C., Deroanne, C., Masimango, T., Béra, F., 2009b. Influence of drying temperature on functional properties of wet-milled starch granules. Carbohydr. Polym. 75 (2), 299–306. Malumba, P., Vanderghem, C., Deroanne, C., Béra, F., 2008. Influence of drying temperature on the solubility, the purity of isolates and the electrophoretic patterns of corn proteins. Food Chem. 111 (3), 564–572. Mourad, M., Hemati, M., Laguerie, C., 1995. Drying of maize in a fluidized bed: II: a kinetic model of drying. Chem. Eng. J. Biochem. Eng. J. 60 (1–3), 39–47. Mujumdar, A.S., 2006. Handbook of Industrial Drying. Marcel Dekker. Nemenyi, M., Czaba, I., Kovbas, A., Jani, T., 2000. Investigation of simultaneous heat and mass transfer within the maize kernels during drying. Comput. Electron. Agric. 26, 123–135. Perry, H.S., 1984. Chemical Engineer’s Handbook. McGraw Hill. Prachayawarakorn, S., Soponronnarit, S., Wetchacama, S., Chinnabun, K., 2004. Methodology for enhancing drying rate and improving maize quality in a fluidised-bed dryer. J. Stored Prod. Res. 40, 379–393. Samapundo, S., Devlieghere, F., Meulenaer, B.D., Atukwase, A., Lamboni, Y., Debevere, J.M., 2007. Sorption isotherms and isosteric heats of sorption of whole yellow dent corn. J. Food Eng. 79 (1), 168–175.
Websites FAOSTAT: http://faostat.fao.org.
Contents lists available at ScienceDirect
Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Modelling dehydration and quality degradation of maize during fluidized-bed drying Sébastien Janas a,*, Sébastien Boutry b, Paul Malumba c, Luce Vander Elst b, François Béra a a
University of Liege, Gembloux Agro-Bio Tech, Food Technology Department, Process and Quality Engineering Laboratory, Passage des déportés 2, B-5030 Gembloux, Belgium Department of General, Organic and Biomedical Chemistry, NMR and Molecular Imaging Laboratory, University of Mons, Avenue Maistriau 19, B-7000 Mons, Belgium c Kinshasa University, Faculty of Agricultural Sciences, BP 1471 Kinshasa 1, Congo b
a r t i c l e
i n f o
Article history: Received 15 December 2009 Received in revised form 27 April 2010 Accepted 2 May 2010 Available online 10 May 2010 Keywords: Drying FEM Heat and mass transfer Maize MRI Quality Salt-soluble proteins
a b s t r a c t At harvest time, maize (Zea mays L.) has a moisture content too high to be stored, and has to be dried. To control the drying impact on maize characteristics, it is necessary to accurately know the spatial distribution of temperature and moisture content in the kernel, and the kinetics of quality loss in relation to these two factors. To this end, a physical model of heat and mass transfer in a maize kernel was designed. The Fick and Fourier equations were solved by the finite element method (FEM). The real 3D geometry of maize was obtained by NMR imaging and then used to build the mesh needed for the FEM computations. The model correctly describes the evolutions of maize moisture and salt-soluble protein content during fluidized-bed drying with a constant drying air temperature between 50 °C and 100 °C. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction In 2007, Maize (Zea mays L.) was the first crop in the world, before rice and wheat (FAOSTAT, 2010). At the time of harvest, maize has a moisture content too high to be stored (between 30% and 40% w.b.), and has to be dried. During drying, the maize kernel is submitted to cracks (Gustafson et al., 1979; Davidson et al., 2000; Prachayawarakorn et al., 2004), protein denaturation (Lupano and Anon, 1987; Malumba et al., 2008), changes of functional properties of wet-milled starch granules (Malumba et al., 2009b) and loss of wet-milling properties (Lasseran, 1973). To control the drying impact on food characteristics, it is necessary to follow accurately the spatial distribution of temperature and moisture content, and the kinetics of quality loss in relation to these two factors. The spatial evolution of temperature and moisture content in the product during drying can only be assessed by modelling heat and mass transfer. To this end, several models based on a simplified geometry of a maize kernel were used (Hatamipour and Mowla, 2003, 2006; Mourad et al., 1995; Nemenyi et al., 2000). These models accurately gives the evolution of average moisture content and temperature of maize grains during drying. * Corresponding author. E-mail address: [email protected] (S. Janas). 0260-8774/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2010.05.001
To follow the evolution of maize quality during dehydration, the glutamic acid decarboxylase activity (Linko, 1961) and electrical properties (Holaday, 1964) were used as indicators of heat damages but were not correlated with any particular industrial use of maize. In addition, their measurement needs equipments not always available in a traditional laboratory. Recently, Malumba et al. (2009a) has shown that the salt-soluble protein content of maize presented a high correlation to the wet-milling properties of the maize kernel. A method for the determination of salt-soluble protein content has also been published to estimate maize quality for the starch industry (AFNOR, 2008). To the knowledge of the authors, the kinetics of salt-soluble protein denaturation in maize during drying as a function of moisture content and temperature are not known. These kinetics, in combination with a predictive model of heat and mass transfer in maize during drying, would be a very useful tool to study the impact of drying parameters on the final quality of the product. This article is an attempt to find an expression of the kinetics of salt-soluble protein denaturation in maize during drying. A simple model of heat and mass transfer was used to predict the evolution of temperature and moisture content in the grains. The model was solved by the finite element method. To find separately the evolution of moisture content in the germ and endosperm, the real 3D grain geometry was obtained by nuclear magnetic resonance imaging. This geometry permits the use of different initial values
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Nomenclature Cp Cpair D Deff Dw dg FT Hw h k L n ~ n Nu P Patm PE PG Pr Re RH
maize specific heat (J/kg °C) air specific heat (J/kg °C) decimal reduction time ðs1 Þ effective water diffusivity in maize (m2 /s) water vapor diffusivity in air (m2 /s) grain diameter (m) saturated vapor pressure (Pa) water latent heat of vaporization (J/kg) mass transfer coefficient (m/s) heat transfer coefficient (W/m2 °C) reaction rate ðs1 Þ number of experimental values (–) unit vector normal to the surface (–) Nusselt number (–) salt-soluble protein content (mg proteins/100 ml) atmospheric pressure (Pa) salt-soluble protein content in the endosperm (mg proteins/100 ml) salt-soluble protein content in the germ (mg proteins/ 100 ml) Prandtl number (–) Reynolds number (–) air relative humidity (–)
Sc Sh T t X Y
Schmidt number (–) Sherwood number (–) temperature (°C) time (s) grain moisture content (kg water/kg dry matter) air absolute humidity (kg water/kg air)
Greek symbols q maize grain density (kg/m3 ) qair air density (kg/m3 ) qdb dry matter density of maize grain (kg dry matter/m3 wet maize) k maize thermal conductivity (W/m °C) air thermal conductivity (W/m °C) kair lair air viscosity (Pa s) Subscripts a in the air calc calculated value exp experimental value s at the surface of the product 0 at the initial time
of salt-soluble protein content in the two parts of the grain. The evolution of maize salt-soluble protein content was followed during dryings between 50 °C and 100 °C, and described with a first order differential equation.
grams were used for the determination of maize moisture content, and 50 g were immediately immersed in iced water and then stored at 20 °C until the determination of salt-soluble protein content. All the dryings were made in triplicate.
2. Materials and methods
2.2. Determination of the initial moisture content of maize
2.1. Fluidized-bed drying of the maize kernel
To get the initial moisture content of the maize germ and endosperm, these two parts were separated by hand with the help of a scalpel. The moisture content was measured in triplicate on ±5 g of endosperm and ±0.5 g of germ by differential weighing after 48 h at 105 °C.
The maize kernel used was a flint maize, of the Baltimore variety. The moisture content at harvesting was about 40% w.b. In order to get a biological material as close as possible to its initial state for a very long time, the maize was received in the laboratory directly after harvesting and stored at 20 °C in plastic bags until the drying was performed. Drying curves and initial protein content did not show any change from the day of harvesting to the end of trials. Before each drying, 1.5 kg of maize was equilibrated at laboratory temperature for one night. A schematic view of the laboratory fluidized-bed dryer used for the experiments is presented on Fig. 1. This dryer was composed of a polycarbonate tube from VINK (Belgium) (height = 1.6 m and diameter = 0.12 m), in which air was introduced by the bottom at 50 °C, 65 °C, 80 °C, and 100 °C with a superficial velocity of 5.8 m/s. During this process, air temperature, relative humidity and velocity were measured downstream of the drying chamber, and air temperature and relative humidity were measured upstream. Temperatures were measured with a thermocouple type T TT-T-30-SLE from OMEGA (England), air relative humidity with probes TR200 from NOVASINA (Switzerland) and air velocity with an anenometer TEST0 445 (Germany). Thermocouple and air humidity probe signals were measured with a 3595551H UNIVERSAL IMP from SOLARTRON (England), and recorded with a program written in LABVIEW 5.1. Air velocity data were recorded with the TESTO LOGICIEL-COMFORT ‘‘Light” interface. The accuracy of temperature, humidity and velocity measures were respectively of 0.1 °C, 0.1% and 0.2 m/s. Each drying was 3 h long. During these trials, maize samples of ±60 g were collected after 5, 10, 15, 30, 60, 120, and 180 min. Ten
2.3. Determination of maize density A 100 ml flask was weighed (P1 in g) and ±5 g of endosperm were added. The flask was then weighed (P2 in g) and filled with distilled water before being weighed again (P3 in g). The density of endosperm was then calculated with the equation
q ¼ 1000
P2 P1 V ðP3 P2 Þ
ð1Þ
where V is the exact volume of the flask (ml), measured by weighing of distilled water. The experiment was carried out six times. The same procedure was used for the determination of germ density but with flasks of 50 ml and ±0.5 g of germ. 2.4. Determination of maize salt-soluble protein content 2.4.1. Extraction solution The extraction solution was composed of 13.6 g KH2 PO4 , 4.2 g K2 HPO4 and 20 g NaCl for 2000 ml of distilled water. 2.4.2. Coomassie blue Six hundred milligrams of coomassie brilliant blue G250 from Merck (Germany) was added in a flask of 1000 ml with 500 ml of HCl 0.6 N. The solution was agitated for 24 h out of light before
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Fig. 1. Schematic view of the fluidized-bed dryer.
2.4.3. Standard solutions Six standard solutions corresponding to 10, 20, 30, 40, 50, and 60 mg/100 ml of bovine serum albumin from VWR (Belgium) were used to calibrate the UV-2401 PC UV-VIS recording spectrometer from Shimadzu (China).
Fig. 2. 3D geometry of a maize grain obtained by reconstruction of the 2D MRI data. The germ is shown in red and the endosperm in white. (For interpretation of color mentioned in this figure the reader is referred to the web version of the article.)
the final 500 ml of HCl 0.6 N was added. The solution continued to be agitated as long as it was needed to get an optical density of 3.0 ± 0.1, filtered on Whatman 595 1/2 filters (Germany) and stored out of light for 6 weeks maximum.
2.4.4. Determination of salt-soluble protein content All the samples were freeze-dried in a HETO DRYWINNER, model DW8 (Denmark). The moisture content of maize was about 6% d.b. at the end of freeze drying. The determination of maize saltsoluble protein content was carried out with the official method AFNOR NF-V03-741 (AFNOR, 2008). The samples were milled in a IKA Universalmühle M20 (Germany). Flour (5.4 g ± 0.01 g) was then introduced in an ernelmeyer with 100 ml of extraction solution and agitated for 3 min. The samples were filtered on filters Whatman 595 1/2 (Germany), the first 10 ml was pulled of and the following 20 ml kept for analysis. Into macro cuvets PMMA of 4 ml from VWR (Belgium) were added 40 ll of standard, 40 ll of sample and 3 ml of coomassie blue. The cuvets were agitated slowly and then the optical density at 595 nm was measured. 2.5. Determination of the maize geometry The maize geometry was obtained using the magnetic resonance imaging (MRI) technique. This method relies on the
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magnetic properties of atoms exposed to an external magnetic field. Its main usefulness is that it allows for a cartography of the mobile hydrogen atoms of a sample in a non-invasive manner. Thus, the MR signal collected when analyzing maize arises from water molecules contained in the kernels. MR images were obtained at room temperature on an AVANCE-200 system (Bruker, Karlsruhe, Germany), equipped with a 4.7 T vertical super wide bore magnet, using the animal/object handling system (inner diameter: 56 mm) to maintain the analyzed sample, which was prepared as follows: wet maize kernels were placed in 15 ml tubes, individually separated by cotton wools. This tube was then placed in a 50 ml tube containing a mixture of H2O and deuterium oxide (D2O) in equal volumes. Using this preparation method, the MR signal of the whole sample was sufficient to allow a correct set up of the MRI system, which could not be achieved with maize kernels only (containing too low levels of water). Thanks to the use of a H2O/D2O mixture (D2O giving no MR signal), the weak maize MR signal was not obscured by a too strong signal of surrounding water. MRI experiments were conducted with the following acquisition parameters: spin echo sequence, TR/TE 1001.7/3.5 ms, FOV: 3 cm, 64 64 matrix, slice thickness: 1.2 mm, acquisition time: 80 3200 , number of acquisitions: 8. A linear smoothing was applied to MR images using the PARAVISION software.
kðT a T s Þ ¼ ~ n ðkrTÞ Hw hqair ðY a Y s Þ
ð4Þ
The air water content in equilibrium with the product’s surface is related to the water content of the product according to equation :
Ys RHs FT s ¼ 0:622 1 Ys Patm RHs FT s
ð5Þ
The balance between the water flux from the product core to its surface and the vapor removed by air can be written as
~ n qdb ðDeff rXÞ ¼ hqair ðY a Y s Þ
ð6Þ
The following formula is used to calculate the heat transfer coefficient (Kunii and Levenspiel, 1993)
Nu ¼
1 1 kdg ¼ 2 þ 0:6Re2 Pr3 kair
ð7Þ
The mass transfer coefficient was obtained with the following equation (Kunii and Levenspiel, 1993)
Sh ¼
1 1 hdg ¼ 2 þ 0:6Re2 Sc3 Dw
ð8Þ
The physical properties of air and maize were found in the literature or measured in the laboratory and are summarized in Table 1.
2.6. Mathematical modelling of drying In order to know the evolution of moisture content and temperature in maize grains during drying, a simple heat and mass transfer model was used. The shrinkage was neglected because of the small magnitude of this phenomenon for flint maize like the Baltimore variety. Using Fourier’s law (Carslaw and Jaeger, 1986), the energy balance in the product leads to
qC p
At the boundary of the grain, heat provided by air is absorbed by the heating of the product and by water evaporation.
dT ¼ r ðkrTÞ dt
ð2Þ
Water diffusion in grain can be described by Fick’s second law (Cranck, 1979)
dX ¼ r ðDeff rXÞ dt
ð3Þ
Theoretically, the effective diffusivity of water in the grain should be correlated to local temperature. In the case of maize drying, it was observed that the grain temperature quite rapidly reached air temperature (Mourad et al., 1995). For this reason, it was assumed that the effective diffusivity was correlated to air temperature, and not to local temperature.
2.7. Denaturation kinetic of maize salt-soluble proteins The thermal denaturation of salt-soluble proteins was described by a first order ODE
dP ¼ LP dt
ð9Þ
The time D (s) after which a content reduction of 90% occurs can be calculated with equation:
D¼
2:303 L
ð10Þ
were the 2.303 coefficient is used to convert from a logarithm to a decimal basis. In order to take into account the influence of the moisture content on the denaturation kinetics, the following equation was used: X ref X
D ¼ D0 10
ð11Þ
z
X ref was fixed to 0.388 d.b., the average moisture content of grain during the dryings.
Table 1 Air and maize physical properties used in the model. Property
Equation
Reference Perry (1984)
Air density
qair ¼
Air viscosity
0:756 lair ¼ 1:66 105 ðTþ273 273 Þ
Perry (1984)
Air thermal conductivity
kair ¼ 4 105 ðT þ 273Þ þ 0:0246
Perry (1984)
Air specific heat
Cpair ¼ 0:9774 þ 0:1124 103 ðT a þ 273Þ þ 1:19035 107 ðT a þ 273Þ2 T 1:81 Dw ¼ 273 0.57 0.98 q ¼ 966:9 q ¼ 552:8 X X þ 0:26 ð1 ð1þXÞ Þ k ¼ 0:55 ð1þXÞ
Perry (1984)
Moisture diffusivity in the air Endosperm initial moisture content (d.b.) Germ initial moisture content (d.b.) Endosperm density Germ density Maize thermal conductivity
341:25 ðTþ273Þ
X ð1þXÞ
X þ 840 ð1 ð1þXÞ Þ
Maize specific heat
Cp ¼ 4190
Maize moisture sorption isotherm
RH ¼ 1 expðaTX b Þ a ¼ 3:11 105 b ¼ 1:713 61.9% 38.1%
Germ salt-soluble protein content Endosperm salt-soluble protein content
Perry (1984) Measured Measured Measured Measured Earle (1983) Earle (1983) Samapundo et al. (2007) Landry and Moureaux (1980) Landry and Moureaux (1980)
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Two different methods were used to model the salt-soluble protein denaturation kinetics.
Table 2 Statistics of the mesh applied to the 3D maize kernel geometry. Number of degrees of freedom Number of mesh points Number of tetrahedral elements Number of triangular elements Number of edge elements Number of vertex elements Minimum element quality Element volume ratio
274,729 18,558 95,343 14,718 3718 466 0.2629
2.7.1. Method 1 The salt-soluble protein content was assumed to remain homogeneous in the whole grain. In Eq. (11), X is the average moisture content of the grain kernel after each time increment.
5:45 107
2.7.2. Method 2 The evolution of salt-soluble protein content is calculated separately for the germ and the endosperm, using Eq. (9). The initial protein contents were calculated with Eqs. (12) and (13).
Table 3 Effective moisture diffusivity and residual error for the four drying temperatures. T (°C)
Deff (m /s)
Residual error (kg water/kg d.b.)
50 °C
7:14 1011
9:4 103
65 °C
9:26 1011
1:1 102
80 °C
1:21 1010
1:0 102
100 °C
10
2
2
1:86 10
P0 V tot 0:381 VE P0 V tot 0:619 PG0 ¼ VG
PE0 ¼
ð12Þ ð13Þ
The salt-soluble protein content for the whole grain was then estimated with Eq. (14)
1:1 10
Exp 50 °C Exp 65°C Exp 80 °C Exp 100 °C Calc 50 °C Calc 65 °C Calc 80 °C Calc 100 °C
0.6
WATER CONTENT (d.b.)
0.5
0.4
0.3
0.2
0.1
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
TIME (s) Fig. 3. Experimental and calculated values of moisture content (d.b.) for dryings at 50 °C, 65 °C, 80 °C and 100 °C.
1 Endosperm Germ
WATER CONTENT (d.b.)
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
TIME (s) Fig. 4. Comparison of the moisture content evolution in the germ and in the endosperm for drying at 80 °C.
11000
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Table 4 D0 and z coefficients of Eq. (11) obtained for each drying temperature with the two different methods. Method
D0 (min)
z (d.b.)
Residual error (mg/100 ml)
50
Method 1 Method 2
732 1773
0.28 0.47
0.17 0.17
65
Method 1 Method 2
273 945
0.18 0.33
0.74 0.71
80
Method 1 Method 2
175 542
0.15 0.29
0.27 0.22
100
Method 1 Method 2
47 91
0.22 0.27
0.47 1.34
PEV E PGV G þ V tot V tot
ð14Þ
3. Results and discussion 3.1. Determination of the maize geometry The 3D geometry of the maize kernel (Fig. 2) was reconstructed from the 2D MRI data according to the procedure described in the COMSOL MULTIPHYSICS 3.5 manual. The volumes of the whole maize kernel, the germ and the endosperm were respectively 1:80 107 m3 ; 1:46 108 m3 and 1:65 107 m3 .
48 Experimental Method 1 Method 2
46
PROTEIN CONTENT ( mg / 100 ml )
44
42
40
38
36
34
32
30 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
TIME (s) Fig. 5. Experimental salt-soluble protein content and the values calculated with the two methods for the dryings at 50 °C.
50 Experimental Method 1 Method 2
45
PROTEIN CONTENT ( mg / 100 ml)
T (°C)
P¼
40
35
30
25
20
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
TIME (s) Fig. 6. Experimental salt-soluble protein content and the values calculated with the two methods for the dryings at 65 °C.
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The mesh used was refined until no variation in the solution of the model was observed. The mesh statistics are presented in Table 2.
previously in the literature. Mujumdar (2006), for example, give a diffusivity between 1=1012 and 3=1010 m2 =s for maize. Fig. 3 compares the predicted and the experimental values of the maize kernel’s moisture content. It can be seen that the model correctly describes the experimental values of maize moisture content. The model is also able to predict specifically the evolution of moisture content in the germ and in the endosperm of the maize kernel. Fig. 4 shows these evolutions for drying at 80 °C. The two curves are quite different, which indicates the usefulness of the 3D geometric model to predict the denaturation phenomena occurring specifically in the germ and in the endosperm, or phenomena with initial values differing greatly between these two morphological parts of the product.
3.2. Solution of the mathematical model The mathematical model is solved by the finite element method using the commercial package COMSOL MULTIPHYSICS 3.5a. The GMRES linear solver with the SSOR preconditioner and the backward difference time integrating scheme were used. Computation took ±40 min on a MacBook Pro dualcore 2.93 Ghz. The effective moisture diffusivities (Table 3) were obtained by nonlinear regression of the mathematical model for the four drying temperatures. They are in good agreement with values published
50 Experimental Method 1 Method 2
PROTEIN CONTENT ( mg / 100 ml)
45
40
35
30
25
20
15
10
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
TIME (s) Fig. 7. Experimental salt-soluble protein content and the values calculated with the two methods for the dryings at 80 °C.
50 Experimental Method 1 Method 2
PROTEIN CONTENT ( mg / 100 ml)
45
40
35
30
25
20 15
10 5
0 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
TIME (s) Fig. 8. Experimental salt-soluble protein content and the values calculated with the two methods for the dryings at 100 °C.
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3.3. Modeling the denaturation kinetic of salt-soluble proteins Table 4 presents the D0 and the z coefficients for each drying temperature obtained with the two different models. The two methods describes the denaturation of maize salt-soluble proteins with more or less the same accuracy, as indicated by residual errors calculated according to Eq. (15).
Pn error ¼
i¼1 jP calc
P exp j
n
ð15Þ
The values of the decimal reduction time and the z coefficient depend on the method used for their calculation. The D0 and z coefficients predicted by the method 2 are greater than those obtained by method 1. These differences show the importance of the initial heterogeneity of the protein content and of the evolution of the spatial heterogeneity in water content during the process on the protein denaturation kinetics. Figs. 5–8 present the experimental salt-soluble protein content and the values calculated with the two methods for each drying temperature. The two methods gave similar curves for the drying at 50 °C, but differed greatly when the temperature was increased. The temperature and moisture content have a great influence on the salt-soluble denaturation kinetics. From these results, it seems that variable temperature drying would be a interesting way to improve the final quality of maize. Low temperature drying should be used at the beginning of the process, to reduced maize moisture content without denaturing too much salt-soluble protein, and it should then be followed by a raise in temperature. 4. Conclusions Magnetic resonance imaging is a useful tool to build realistic 3D meshes of food products with respect to their internal morphological parts. In this article, a mesh of a maize kernel distinguishing the germ and the endosperm was built and used for the modeling of heat and mass transfer during fluidized-bed drying. The model correctly describes the evolution of moisture content during fluidized-bed drying with constant drying air temperatures between 50 °C and 100 °C. The evolution of the maize salt-soluble protein content during drying is a first order kinetic, with a reaction rate function of the grain moisture content. The initial protein content heterogeneity and the evolution of moisture content spatial heterogeneity during the process significantly influence the salt-soluble protein denaturation. The model designed in this study appears to be a very suitable tool to optimize maize drying taking into account the salt-soluble protein content. Acknowledgements S. Janas acknowledges financial support from the Fonds pour la Recherche dans l’Industrie et l’Agriculture, Belgium. He acknowl-
edges also Florence Lefebvre and Guy Delimme for their help in the laboratory, and Prof. Robert N. Muller (NMR and Molecular Imaging Laboratory, University of Mons) for his interest to this work and the access to the MRI facility. The authors thank Mrs. Patricia DeFrancisco for her help in preparing the manuscript. References AFNOR, 2008. Méthode Promatest d’évaluation de la dénaturation des protéines thermosensibles NF-V03-741. AFNOR. Carslaw, H., Jaeger, J., 1986. Conduction of Heat in Solids. OUP Oxford. Cranck, J., 1979. The Mathematics of Diffusion. OUP Oxford. Davidson, V.J., Noble, S.D., Brown, R.B., 2000. Effects of drying air temperature and humidity on stress cracks and breakage of maize kernels. J. Agric. Eng. Res. 77, 303–308. Earle, R., 1983. Unit Operations in Food Processing. Pergamon Press. Gustafson, R.J., Thompson, D.R., Sokhansanj, S., 1979. Temperature and stress analysis of corn kernel-finite element analysis. Trans. ASAE 22, 955–960. Hatamipour, M.S., Mowla, D., 2003. Correlations for shrinkage, density and diffusivity for drying of maize and green peas in a fluidized bed with energy carrier. J. Food Eng. 59, 221–227. Hatamipour, M.S., Mowla, D., 2006. Drying behaviour of maize and green peas immersed in fluidized bed of inert energy carrier particles. Food Bioprod. Process. 84 (3), 220–226. Holaday, C., 1964. An electronic method for the measurement of heat-damage in artificially dried corn. Cereal Chem. 41, 533–542. Kunii, D., Levenspiel, O., 1993. Fluidisation Engineering, vol. 491. ButterworthHeinemann. Landry, J., Moureaux, T., 1980. Distribution and amino acid composition of proteins groups located in different histological parts of maize grain. J. Agric. Food Chem. 28 (6), 1186–1191. Lasseran, J.C., 1973. Incidence of drying and storing conditions of corn (maize) on its quality for starch industry. Starch 28 (8), 257–262. Linko, P., 1961. Simple and rapid manometric method for determining glutamic acid decarboxylase activity as quality index of wheat. J. Agric. Food Chem. 9 (4), 310–313 . Lupano, C., Anon, M., 1987. Denaturation of wheat endosperm proteins during drying. Cereal Chem. 64 (6), 437–442. Malumba, P., Janas, S., Masimango, T., Sindic, M., Deroanne, C., Béra, F., 2009a. Influence of drying temperature on the wet-milling performance and the proteins solubility indexes of corn kernels. J. Food Eng. 95 (3), 393–399. Malumba, P., Massaux, C., Deroanne, C., Masimango, T., Béra, F., 2009b. Influence of drying temperature on functional properties of wet-milled starch granules. Carbohydr. Polym. 75 (2), 299–306. Malumba, P., Vanderghem, C., Deroanne, C., Béra, F., 2008. Influence of drying temperature on the solubility, the purity of isolates and the electrophoretic patterns of corn proteins. Food Chem. 111 (3), 564–572. Mourad, M., Hemati, M., Laguerie, C., 1995. Drying of maize in a fluidized bed: II: a kinetic model of drying. Chem. Eng. J. Biochem. Eng. J. 60 (1–3), 39–47. Mujumdar, A.S., 2006. Handbook of Industrial Drying. Marcel Dekker. Nemenyi, M., Czaba, I., Kovbas, A., Jani, T., 2000. Investigation of simultaneous heat and mass transfer within the maize kernels during drying. Comput. Electron. Agric. 26, 123–135. Perry, H.S., 1984. Chemical Engineer’s Handbook. McGraw Hill. Prachayawarakorn, S., Soponronnarit, S., Wetchacama, S., Chinnabun, K., 2004. Methodology for enhancing drying rate and improving maize quality in a fluidised-bed dryer. J. Stored Prod. Res. 40, 379–393. Samapundo, S., Devlieghere, F., Meulenaer, B.D., Atukwase, A., Lamboni, Y., Debevere, J.M., 2007. Sorption isotherms and isosteric heats of sorption of whole yellow dent corn. J. Food Eng. 79 (1), 168–175.
Websites FAOSTAT: http://faostat.fao.org.