Physical, mechanical, thermal and electrical properties of cooked red bean (Phaseolus vulgaris L.) for continuous ohmic heating process

Journal of Food Engineering 81 (2007) 447–458 www.elsevier.com/locate/jfoodeng

Physical, mechanical, thermal and electrical properties of cooked red bean (Phaseolus vulgaris L.) for continuous ohmic heating process A. Legrand a, J.-C. Leuliet a, S. Duquesne b, R. Kesteloot c, P. Winterton d, L. Fillaudeau e,* a

INRA (Institut National de la Recherche Agronomique), LGPTA (Laboratoire de Ge´nie des Proce´de´s et Technologie Alimentaires), 369, rue Jules Guesde, F-59650 Villeneuve D’Ascq cedex, France b ISA – 48, Boulevard Vauban, F-59046 Lille cedex, France c ENSCL (Ecole Nationale Supe´rieure de Chimie de Lille) – PERF (Laboratoire des Proce´de´s d’Elaboration de Reveˆtements Functionnels) CNRS UMR 8008-BP 90108F-59652 Villeneuve D’Ascq cedex, France d UPS – 118, route de Narbonne, Batiment 4A, 31062 Toulouse cedex, France e INSA – Laboratoire de Biotechnologie – Bioproce´de´s, CNRS UMR 5504, INRA UMR 792, 135, avenue de Rangueil, F-31077 Toulouse cedex 4, France Received 31 August 2006; received in revised form 21 November 2006; accepted 22 November 2006 Available online 12 January 2007

Abstract Due to their complex composition and properties, the continuous thermal processing of solid–liquid mixtures (e.g. suspension of fragile particle in viscous carrier fluids) remains an empirical and random operation as compared to canning. Alternative technologies (e.g. ohmic heating) may achieve high-temperature treatment in a short time (HTST) but requires a perfect knowledge of thermo-physical and electrical properties of both particles and carrier fluid. Food properties are needed and play a significant role to predict and define the quality and behaviour of solid–liquid mixture. The properties of red beans (Phaseolus vulgaris L.) and a model non-Newtonian carrier fluid were studied throughout the duration of the process. Physical (rheological behaviour, density, shape and dimensions), mechanical (elasticity modulus, maximal deformation and stress) and thermal (heat capacity, thermal conductivity, thermal diffusivity) properties as a function of water content ranging from 11.6 to 67.4% w/w are reported. The electrical conductivity (electrical properties) was described as a function of the temperature and the solid concentration by a semi-empirical equation. The limiting factors to succeed a HTST for heterogeneous products in continuous thermal process were identified and discussed in the light of the properties of the foods involved. The large dispersion of particle mass volume had a simultaneous incidence of the suspension flow and the heat transfer. The volume expansion of particle (+22% between blanched and cooked bean) and the important loss of mechanical properties (68% for elastic properties) constitutes unavoidable limiting factors inducing mechanical degradation and sometimes plugging of the duct. The electrical conductivity is strongly affected by a combined effect of temperature and solid concentration, which will induces irreversible heat treatment heterogeneity between particles. This work stresses that the continuous conventional or ohmic heating of these cooked dishes will be hard to achieve on an industrial scale. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Red bean; Cooked dish; Physical; Mechanical and thermal properties; Electrical conductivity

1. Introduction Commercial food products, such as prepared dishes, are solid–liquid mixtures. The traditional technique used by the food industry to sterilize these products is canning. However, continuous processing of heterogeneous liquid-parti*

Corresponding author. Tel.: +33 561 559 691; fax: +33 561 559 400. E-mail address: [email protected] (L. Fillaudeau).

0260-8774/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2006.11.024

cle food products with conventional or alternative technologies (e.g. ohmic heating) is being increasingly advocated as a substitute for batch sterilization. In continuous processes, the product flows continuously throughout the heating, holding and cooling sections. The expected advantages of a continuous process are an increase in production capacity, a reduction in power consumption, an improved treatment homogeneity and less damage to the particles. However the passage from a batch to continuous processing

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Nomenclature Latin letters A surface area [m2] Bi Biot number [–] CC particle concentration [%w/w] c specific heat [J kg1 K1] e thickness [mm] E elastic modulus [Pa] Eth thermal effusivity [W m2 K1 s0.5] F force [N] f(x) normal distribution function [–] F(x) cumulative normal distribution function [–] G conductance [S] I current intensity [A] k thermal conductivity [W m1 K1] K consistency coefficient [Pa sn] Kc cell constant [m1] l width [mm] L length [mm] m thermal coefficient [J kg1 K2] n flow behaviour index [–] nH2 O absolute moisture content [g H2O/g DM] P power [W] SD standard deviation [x2] t time [s]

(HTST) should satisfy numerous criteria: to produce a constant flow of a homogeneous suspension without blocking or mechanical degradation of particles (Fig. 1), while operating over a range of concentrations or electrical conductivities (ohmic heating). Literature data (Abdelrahim, Ramaswamy, Marcotte, & Toupin, 1993; Chandarana, 1992; Sastry, 1993; Singh & Lee, 1992) indicate that the major factors influencing particle velocity in a stream of carrier fluids are: viscosity, relative density (particle to fluid), relative size (particle to tube), particle shape and concentration of the solid phase in the fluid. Therefore, it is essential to have a perfect knowledge of the physical, mechanical, thermal and electrical properties of the particles and the carrier fluid to develop continuous thermal processing. From scientific and industrial standpoints, the knowledge and the control of the product’s properties lead to the identification of several limiting factors (maximal concentration and mechanical degradation of particles, duct plugging, heterogeneity of the suspension flow or electrical conductivity, heterogeneity in generated heat and heat transfer, widespread of sterilisation or cooking efficiencies) in relation with the process or heating technologies. Industrial users often find that the published physical property data are unsuitable for industrial use because most materials are inhomogeneous and have a complex structure, and model systems tend to omit many of the minor ingredients in commercial formulations. Moisture and air content ranges tend to cover only a relatively narrow band, unrep-

T U v x X H2 O

temperature [°C] voltage [V] volume [mm3] variable relative moisture content [% w/w]

Greek letters a thermal diffusivity [m2 s1] b thermal dependency [S m1 °C1] c_ shear rate [s1] e maximum deformation [%] l apparent viscosity [Pa s] q mass volume [kg m3] r electrical conductivity [S m1] s stress [Pa] Indices max In Out DB HB BB CB

maximum inlet outlet dry bean hydrated bean blanched bean cooked bean

resentative of real systems and data for both elevated temperatures and low temperatures are sparse. Physical properties include density, particle size distribution and the rheological behaviour of the carrier fluid. In a continuous process, the relative density (particle to fluid) appears to be essential to characterize the heterogeneity of a flowing suspension (decantation, flotation). Density differences between solids and fluid, although slight, may be sufficient to generate particle settling (Liu, Pain, Proctor, de alwis, & Fryer, 1993) and consequently different sterilisation and cooking efficiencies between solid and liquid phases and among the solid phases. The particle size is a factor affecting the quality of processed dishes (Grabowski & Ramaswamy, 1995). The length, thickness and width of particles are generally measured using a sliding calliper. However, they could be measured much faster and more accurately using other methods, such as the Machine Vision System or image analysis. Apparent viscosity is a fundamental parameter, not only as a time–temperature integrator (TTI) of final product quality, but also for following intermediate processes for sizing heat exchanger equipment and for estimating mechanical stress. The rheological properties must be known for fluid mechanics studies in order to characterise nature of the flow (Holdsworth, 1971). Determining the flow regime specification (laminar, transition or turbulent) requires the calculation of the Reynolds number. Today, much data has been published on the rheological behaviour of Newtonian and non-Newtonian fluids. In

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Fig. 1. Passage from a batch to a continuous ohmic heating process for complex solid–liquid food suspension – decision tree (Fillaudeau, 2006).

contrast, not much is available on the rheological behaviour of suspensions, particularly when the carrier fluid is nonNewtonian (Bhamidipati & Singh, 1990). Mechanical properties play an important role in the measuring cooking quality and the magnitude of particle damage along the process. Numerous methods have been developed to determine the texture, but data are frequently incomparable between laboratories due to the lack of standardisation. The incidence of heat treatment on the texture has been studied for various vegetables (Leung, Barron, & Davis, 1983; Rao, Lee, Katz, & Cooley, 1981). The mechanical properties are significantly affected by the mode of cooking (Cheng & Sun, 2004; Xie, Xiong, & Church, 1998). For a lot of fruits and vegetables, the force required to cause a given deformation decreases as the temperature, heating and hydration times increase (Abu-Ghannam, 1998). Correlations between the obtained parameters (elasticity, hardness), the cooking time (Singh, Kaur, Sodhi, & Sekhon, 2005), the physical and chemical properties and the time passage (Nourian, Ramaswamy, & Kushalappa, 2003) were established. Thermal properties (specific heat capacity, thermal conductivity, thermal diffusivity) aid sizing the thermal equipment and understanding the food transformation, e.g. the

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evolution of Biot number along the process affects the heating kinetics inside the particle. Specific heat capacity can be determined using the knowledge of each component in the mixture. Modelling the thermal conductivity is much more difficult because it involves the structure (e.g. porosity, anisotropy). The last three decades have seen much effort and progress in developing measurement techniques to obtain new data on the thermal properties of foodstuffs (Ali, Ramaswamy, & Awuah, 2002; Mayer, 2003; Nesvadba et al., 2004; Pakkala, Reinivuo, & Ovaskainen, 2006). The electrical conductivity of the suspension constitutes a fundamental parameter in ohmic heating. Several authors have reported the electrical conductivities of various liquid foods (El-Hajal, 1997; Marcotte, Piette, & Ramaswamy, 1998; Palaniappan & Sastry, 1991a) and a global equation was proposed by Fillaudeau (2004). A set of electrical conductivity parameters was obtained for particles (Halden, de Alwis, & Fryer, 1990; Marcotte, 1999; Palaniappan & Sastry, 1991b; Wang & Sastry, 1997). Generally, solid vegetable particles have lower electrical conductivities than liquids but many factors affect the electrical conductivity: electrolyte concentration (Wang & Sastry, 1993), particle orientation and shape (de Alwis, Halden, & Fryer, 1989), particle concentration (Zareifard, Ramaswamy, Trigui, & Marcotte, 2003), food composition changes and heating effects (Halden et al., 1990), the specific heat (Zoltai & Swearingen, 1996), the viscosity (Khalaf & Sastry, 1996), the temperature (Marcotte et al., 1998; Wang & Sastry, 1997), the liquid/solid electrical conductivity ratio (Sastry & Palaniappan, 1992). Several authors have proposed correlations according to these experimental parameters (Fryer, de Alwis, Koury, Stapley, & Zhang, 1993; Palaniappan & Sastry, 1991b; Yongsawatdigul, Park, & Kolbe, 1995) but never a single relationship for all products. Finally, although a large amount of data has been published on ohmic heating of homogeneous suspensions, not much is available on the electrical conductivity of heterogeneous liquid products containing large particles. Generally, the size and the shape of the particle are the same (sphere, cylinder) and experiments using real food products as in canned food are insufficient or irrelevant. The present study aims (i) to investigate the physical (density, shape and dimension, rheological properties), mechanical (elasticity modulus, maximal deformation and stress), thermal (heat capacity, thermal conductivity, thermal diffusivity) and electrical (electrical conductivity) properties of red beans (Phaseolus vulgaris L.) and a model nonNewtonian carrier fluid and (ii) to identify the related limiting factors for a transition from a batch to a continuous ohmic heating process. 2. Materials and methods 2.1. Product The product was a cooked dish composed of red beans, Phaseolus vulgaris L. (particles) and a model tomato sauce

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(carrier fluid). Experimental measurements were performed with a model fluid (75.3% w/w water, 0.60% w/w xanthan gum, 22.6% w/w sugar and 1.5% w/w NaCl salt). The carrier fluid was compared to the industrial sauce and adjusted in composition to simulate the rheological behaviour of the real sauce. The model fluid was used to discuss the physical phenomena observed during the process and to carry out experiments on the variability of real products with a complex composition. Furthermore, dry bean (DB) processing requires an initial hydration stage (3 h at 20 °C) to shorten cooking time. Hydrated beans (HB) were blanched by immersion in boiling water at 90 °C for 15 min, to ensure enzymatic inactivation (blanched beans, BB). Analyses were performed on sauces before (inlet) and after (outlet) cooking in cans as well as on dry (DB), hydrated (HB), blanched (BB) and cooked (CB) beans. 2.2. Fluid and particles properties 2.2.1. Physical properties: dimension, density and rheological properties Particle size distribution (Fig. 2) was determined at room temperature (20 °C ± 3). To determine the thickness, a traction-compression press (DY30, Adamel Lhomargy, no. 336, precision ±0.5%) was used and image analysis (Optimas 6.5, Media Cybernetics) of photographs (camera C-2002Z, Olympus Camedia) for the length and width. At least 50 particles were sampled to determine the size distribution and the precision, which was ±0.1 mm in each dimension (Legrand, 2005). For the fluid, the density was measured using a densimeter (type DNA 45, Anton-Paar), and measurements were repeated with twenty samples. A thermostatic bath permitted the density to be determined at various temperatures (20–50 °C) with a precision of ±0.0001 g cm3. For the particles, the volume was measured using a graduated Pyrex cylinder (±0.1 ml) and their weight with a balance (Type 202 A, Precisa Instruments, precision ±0.1 mg). The particle density was measured on 20 samples at room temperature (20 °C ± 3) with a precision of ±0.01 g cm3. The apparent viscosity of fluid was determined using a rotational viscometer (Type Rheomat 30, Contraves).

L

l e

Fig. 2. Identification of red beans geometry and main dimensions.

The fluid was placed between two coaxial cylinders with a well-defined shear rate imposed and the resulting shear stress measured. Rheological measurements were performed between 20 and 80 °C with a precision close to ±1% for the apparent viscosity. 2.2.2. Mechanical properties Particles texture was measured using a traction-compression press (DY30, Adamel Lhomargy, no. 336, ±0.5%) attached to data acquisition control (Autotract). A cell load of 10 N was used with a cutting edge of 2.8 mm diameter rod and a plate with a diameter of 70 mm. The stainless steel cutting edge was lowered at a speed of 10 mm min1. The particle was maintained by placing it on its flat side and cutting transversely through the centre up to a distance of 5 mm, and experiment was repeated for 40 particles at room temperature (20 °C ± 3). The precision for force was ±0.1% and the maximum stress, s [Pa], the maximum deformation, e [%] and the Young’s elastic modulus, E [MPa] were calculated from equations (Eq. (1)) s¼

F ; A

e¼

Dl  100 l0

and

E¼

s e

ð1Þ

2.2.3. Thermal properties: specific heat, thermal conductivity Specific heat capacity measurements of each phase was measured with a differential scanning calorimeter (type C80, Setaram) between 20 and 80 °C with an accuracy of ±3%. Thermal conductivity of the particles was determined using a TC Probe sensor (GRC Instruments, USA) which was designed for testing flat solid materials at room temperature (20 °C) with a high repeatability of ±2% and measurements were repeated five times. The probe provides the thermal effusivity value (Eq. (2)). From the experimental specific heat and density experimental data, it is easy to calculate the thermal conductivity pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eth ¼ k  q  c ð2Þ The thermal conductivity of fluid was measured using a prototype developed by HEI (Lille, France). The fluid was placed between two coaxial copper cylinders (L = 160 mm, £ int/ext = 18/34 mm). The interior cylinder was equipped with a heating resistance allowing to dissipate a known quantity of heat and the temperature differences between the two cylinders were measured using two temperature probes placed at mid-height in the cell. The dissipated power was then measured with a voltmeter (Manudax-Appa 105) and an ammeter (MX 575) and the thermal conductivity was calculated with a precision of 4% (Legrand, 2005). 2.2.4. Electrical properties For particles, the electrical conductivity was determined using a conductivity probe (type XE 100, Radiometer Analytical) at room temperature (20 °C ± 3) and measurements were repeated fives times. The electric conductivity of the

A. Legrand et al. / Journal of Food Engineering 81 (2007) 447–458

solution was calculated by using the conductance, G [S] with a precision of ±2% (Eq. (3)) r ¼ G  Kc

ð3Þ

For the suspension and the fluid, experiments were conducted in a static ohmic heater (Fig. 3) consisting of a PTFE box with inner dimensions of 200  80  50 mm. At either end of the box were 40 cm2 titanium electrodes through which 50 Hz current was supplied at up to 250 V via a voltage regulator with a maximum current of 30 A. Five T-Type thermocouples coated with Teflon (£ = 1 mm, L = 150 mm) measured the suspension temperature with a precision of ±1 °C. One thermocouple was placed close (40 mm) to each electrode (ThC1 and ThC5) and one was fitted at the geometric centre of the static ohmic heating cell (ThC3). Two thermocouples were placed at mid-way between the centre of the cell and the electrode in each direction (ThC2 and ThC4). The gap between the thermocouples was the same (30 mm). For control, two thermocouples were used to measure the temperature at the surface and at the centre of the particle. The voltage applied and the current were monitored with a precision of ±2%. During the experiments, temperatures, voltage and current data were recorded versus time on a data-logger (PCMCIA type II) connected to a computer (Eurotherm Chessel 4180M). The heating power, P [W] was controlled and the experiments were carried out between 20 and 80 °C (Legrand, 2005). 3. Results and discussion Food properties constitute the first data that must be known and controlled to investigate the continuous pro-

451

cessing of solid–liquid suspensions with conventional or ohmic heaters (Fig. 1). Overall properties help to establish several recommendations and to define technical limitations previously identified from the analysis of physical, mechanical, thermal and electrical properties in addition to the suspension behaviour under flow condition (Legrand, Berthou, & Fillaudeau, 2007). 3.1. Physical properties: particle size distribution, density and rheological behaviour 3.1.1. Particle size distribution The mean values of the particle dimensions (length, width and thickness), with their standard deviations are summarised in Table 1. Ogunjimi, Aviara, and Aregbesola (2002) reported that particles could be classified into three categories namely small (L < 0.95 cm), medium (0.95 6 L 6 1.10 cm) and large (L > 1.10 cm). In this case, particles were classified as large based on their length or equivalent sphere diameter, dsp. The dimension of the particles (Fig. 4) followed a normal distribution with a relatively high standard deviation but red beans were real and non-uniform particles subjected to a wide dispersion. As expected, the significant amount of absorbed water involved an increase of particle size, and volume and particle dimensions were described versus the moisture content by an empirical model (Eq. (4)) in the range of 11.6–67.4% w/w 8 e ¼ 1:2815  nH2 O þ 5:5645; R2 ¼ 0:95 > > > < l ¼ 1:4924  nH2 O þ 7:8065; R2 ¼ 0:96 ð4Þ > L ¼ 2:113  LnðnH2 O Þ þ 19:75; R2 ¼ 0:99 > > : v ¼ 386:46  nH2 O þ 414:25; R2 ¼ 0:99

Fig. 3. Instrumentation of static ohmic heating cell. Thermocouple positions: ThC1 to 5 in the bulk, Skin ThC at particle surface and Inside ThC at the particles centre.

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X H2 O [% w/w] nH2 O [g H2O/g DM] L [mm] l [mm] e [mm] vp [mm3] dsp [mm] q [kg m3] E [MPa] smax [MPa] emax [%]

1.2

DB

HB

BB

CB

11.6 [0.2] 0.15 15.6 [1.4] 7.9 [0.6] 5.8 [0.4] 467 [28] 9.6 1181 [67] 21.7 [2.0] 26.3 [6.0] 15.7 [6.5]

53.2 [1.1] 1.14 20.4 [1.7] 9.7 [0.7] 6.9 [0.5] 883 [50] 11.9 1057 [34] 17.6 [2.4] 3.6 [1.3] 24.8 [6.2]

62.0 [1.1] 1.64 20.7 [1.2] 10.4 [0.8] 7.4 [0.6] 1005 [73] 12.4 1116 [64] 3.8 [1.3] 1.6 [0.6] 45.7 [7.4]

67.4 [0.7] 2.07 21.1 [1.7] 10.7 [0.8] 8.5 [0.8] 1230 [35] 13.3 1105 [31] 1.2 [0.4] 0.24 [0.08] 29.5 [4.8]

Dry beans (DB) Blanched beans (BB)

Cumulative and distribution function, F(x) and f(x) [-]

0.8 0.6 0.4 0.2 0 5

6

7 8 Thickness, e [mm]

9

0.007 0.006

ρp = 1116 kg/m3 ρf = 1108 kg/m3

0.8 0.7

0.005

0.6

0.004

0.5 0.003

0.4 0.3

0.002

Cumulative function F(x)

0.2

Experiment

0.001

Mass volume of carrier fluid

0.1

Distribution function f(x)

0

0 900

1000

1100 1200 1300 Mass volume, ρ [kg.m-3]

1400

1500

Fig. 5. Cumulative distribution of the mass volume of blanched beans and inlet fluid.

oping a stationary or a moving bed of particles (Legrand et al., 2007). Only particles with lower density ratios tend to float (around 40% of the population).

Hydrated beans (HB) Cooked beans (CB)

1

4

1 0.9

Distribution function, f(x) [-]

Table 1 Relative and absolute water contents, particle dimensions (length, width, thickness, volume, equivalent diameter), density, elastic modulus and maximal stress and deformation for red beans (Phaseolus vulgaris L.) at 20 °C – mean value [standard deviation] – DB: dry beans, HB: hydrated beans, BB: blanched beans, CB: cooked beans

Cumulative function, F(x) [-]

452

10

Fig. 4. Normal distribution of particle thickness versus water content along the process.

3.1.2. Density Model inlet and industrial outlet fluids had a density of 1112 [±2] and 1061 [±1] kg m3 at the room temperature (20 °C) before and after cooking respectively. These data are significantly different from the density of water at the same temperature (1000 kg m3) and could be explained by the fluid composition. Moreover, the density increased linearly with temperature in the range of 20–50 °C (Eq. (5))  qIn ¼ 1126:1  0:709  T ; model fluid ð5Þ qOut ¼ 1068:6  0:390  T ; industrial fluid For red beans, the density values are summarised in Table 1, but no significant trend versus water content was observed. The density of the particles was strongly dispersed with a standard deviation of ±67 kg m3 and Fig. 5 represents the cumulative distribution of blanched beans and the mean density value of the inlet fluid (1108 kg m3) at 20 °C. It emphasizes that two particle populations existed because almost 60% of the particles had a density higher than the fluid density. In continuous heat treatment, it thus caused solid to settle out at the bottom of the pipe, devel-

3.1.3. Rheological behaviour of carrier fluid The rheological behaviour showed that an increase in the shear rate resulted in a decrease in apparent viscosity, suggesting pseudo-plastic behaviour for a shear rate between 0.1 and 100 s1 (Table 2). For a power law model, the consistency and structure indexes were modelled versus the temperature in the range 20–80 °C. The flow behaviour indexes were between 0.1 and 0.5 and increased linearly with temperature, whereas consistency indexes exhibited a power-law model with temperature. Fagla (2002) highlighted that the heterogeneous suspension can be easily taken into account by the hypothesis of the homogeneous medium or by the effective model approach based on Quemada’s law. 3.1.4. Limiting factors correlated to physical properties Red beans (Phaseolus vulgaris L.) are large particles with an equivalent diameter of the same order of magnitude as the pipe (dsp/£ > 0.10), irregular shape, with a wide range of surface areas and mechanical properties depending on their moisture content and their natural dispersion. In continuous processes, an increase of particle dimension limits the maximal particle concentration at the inlet due to a volume expansion along the process. Legrand et al. (2007) analysed the flow behaviour of the same product and defined quantitative criteria to describe the suspension. Table 2 Rheological behaviour of carrier fluids (20–80 °C) at inlet and outlet of process Carrier fluid

l [Pa s] at 20 °C

n [–]

K [Pa sn]

Model fluid (inlet) Industrial fluid (outlet)

8:206  c_ 0:84

0.146 + 7.0  104  T

14.072  T0.18

5:737  c_ 0:553

0.421 + 1.3  103  T

18.456  T0.39

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Suspension heterogeneity and the flow pattern depends on four major parameters: the orientation of the tubes and the density differences (and associated dispersion) between the carrier fluid and the particles; but the shape and the mechanical properties of particles are factors which limit particle concentration increase and cause fluids to tend toward homogeneity. The rheological behaviour of the carrier fluid affects the particle residence time and a high viscosities afforded some degree of protection to the particle, but also influenced the velocity profiles in the continuous system. Knowing the distribution of both liquid and particle velocities is essential for a sound process design. 3.2. Mechanical properties 3.2.1. Elastic modulus, maximal deformation and stress The mechanical properties (elastic modulus, maximal stress and deformation) were measured in one dimension (thickness) whereas beans exhibited a strong anisotropy in mechanical properties. In beans, the compressive force on the particles increased with an increase in deformation. There was a sharp decrease in the force after particle rupture. The force required causing a given deformation decreased as the moisture content increased, as reported by Abu-Ghannam (1998). This may be due to the fact that at higher moisture contents, the particles became softer and required less force to break them. The particles were assumed to exhibit elastic behaviour, obeying Hooke’s law. Young’s modulus was properly determined from the initial section of the stress–strain curve, at relatively low deformation (Shitanda, Nishiyama, & Koide, 2002). The elastic modulus, the maximal stress and deformation are given in Table 1. The elastic modulus quantified the textural changes of particles during heat treatment and followed a normal distribution (Fig. 6). The particles lost their elastic properties during the process (21.7– 1.2 MPa) in close correlation with water content (Eq. (5)). The general trend also showed that the standard deviation was very high (±2.4 MPa) which illustrates the heterogeneity of a real product. Before cooking, the elastic

453

modulus of blanched beans was of 3.82 MPa. In Fig. 7, the maximal stress is plotted versus deformation. The maximal stress decreased sharply with the moisture content (Eq. (6)) whereas the maximal deformation remained near 30–40%. It meant that particles could support a deformation of up to 45.7% of the initial state and a stress of 1.62 MPa before cooking whereas, after they could only be deformed by 29.5% and support a stress of 0.24 MPa  smax ¼ 42:206  Expð2:2886  nH2 O Þ ð6Þ E ¼ 25:09  11:30  nH2 O 3.2.2. Limiting factors correlated to mechanical properties The shape and mechanical properties of the particles are limiting factors in increasing their concentration (maximal volume fractions). Indeed, mechanical properties define the ability of particles to flow through a pipe with mechanical inter-particle and particle-wall interactions. Beans tend to break due to the presence of the many bends and obstacles (enlargements, reductions) in the continuous process. An insufficient mechanical resistance leads to a severe reduction in particle size generally involving blockage of the pilot plant (Legrand, 2005). In order to keep the particle whole, a low solid concentration is required but this could be far from economic reality. Bean dimensions, and hence volume increase along the process and this should be taken into account in determining the maximum packing volume fraction in continuous heat treatment in order to avoid duct blocking and mechanical degradation. However, at a low solid concentration, the density differences observed between each phase can be sufficient to cause a severe suspension heterogeneity, which will naturally contribute to the mechanical damage of the beans. Decantation or flotation will firstly generate the collisions with the wall and secondly the flow of two separate phases. During processing, red beans lost their elasticity (E reduced from 3.8 for BB to 1.2 MPa for CB) and become softer and rather prone to breaking (smax reduced from 1.62 for BB to 0.24 MPa for CB) with increasing moisture content which tends to be incompatible with continuous heat treatment. 100

0.8

0.8 Dry bean (DB) Hydrated bean (HB) Blanched bean (BB) Cooked bean (CB) Cumulative function, F(x) Distribution function, f(x)

0.6

0.4

0.2

0.6

0.4

0.2

0 0

10

20 30 Elastic modulus, E [Pa]

0 40

Fig. 6. Elastic modulus, E versus particles hydration rate along the process.

Maximal stress, σ [Pa]

1 Distribution functions, f(x) [-]

Cumulative function, F(x) [-]

1

Dry bean (DB) Hydrated bean (HB) Blanched bean (BB) Cooked bean (CB)

10

1

0.1 0

10

20

30

40

50

60

Maximal Deformation, ε [%]

Fig. 7. Maximal stress versus maximal deformation for particles hydration rate along the process.

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3.3. Thermal properties 3.3.1. Specific heat For the carrier fluids, the mean values of specific heat, obtained at 20 °C, were of 3660 and 3326 J kg1 K1 before and after cooking, respectively. Empirical equations (Eq. (7)) model the slight increase of the specific heat versus temperature between 20 and 80 °C. At the same temperature, these results (Table 3) are significantly different from the specific heat of water (4180 J kg1 K1) or tomato paste (3302 J kg1 K1), which could be explained by their composition. A simple linear equation versus temperature is commonly used in order to establish a global model integrating the moisture content, even if the curve fitting is sometime very low (R2  0.50) and a non-linear multivariable regression is feasible ( cIn ¼ 1:5415  T þ 3596:1; R2 ¼ 0:65; model fluid ð7Þ cOut ¼ 1:9953  T þ 3620:5; R2 ¼ 0:52; industrial fluid 8 cDB ¼ 5:6347  T þ 1631:8; R2 ¼ 0:89 > > > < c ¼ 4:0597  T þ 2789:6; R2 ¼ 0:59 HB > cBB ¼ 1:8096  T þ 3114:8; R2 ¼ 0:72 > > : cCB ¼ 1:2627  T þ 3310:7; R2 ¼ 0:54 ð8Þ

This observation was also supported by Subramanian and Viswanathan (2003), who reported a rise in specific heat of millet grains from 1500 to 2400 J kg1 K1 with a rise in moisture from 10 to 30% w/w. Table 3 indicated that for dry beans, the experimental data were identical to those predicted by these authors. On the other hand, no satisfactory agreement could be found between the other data for higher moisture contents (Loncin, 1985; Subramanian & Viswanathan, 2003). 3.3.2. Thermal conductivity For the fluids, the thermal conductivity measurements were modelled versus temperature (20 < T < 50 °C, Eq. (11)) and Table 3 indicates that the thermal conductivities of fluids at 20 °C were of 0.54 W m1 K1 and 0.52 W m1 K1, respectively before and after heat treatment. At the same temperature, these results were significantly different from the thermal conductivity of water (0.6 W m1 K1) but close to that of tomato paste reported by Drusas and Saravacos (1985), that the model fluid is supposed to mitigate ( k In ¼ 0:00576  T þ 0:29254; R2 ¼ 0:75; model fluid k Out ¼ 0:003357  T þ 0:410221; R2 ¼ 0:93; industrial fluid ð11Þ

General equation : c ¼ c0  C þ m  T with c0  C ¼ 1226:5 þ 30:378  X H2 O and m ¼ 6:6628  0:0793  X H2 O

The specific heat of red beans at 20 °C was found to lie between 1730 and 3300 J kg1 K1 (Table 3) and increased linearly with moisture content with a negligible contribution of temperature (Eq. (8)). Experimental values were compared to those from the literature (Eq. (9) proposed by Subramanian & Viswanathan (2003) and Eq. (10) by Loncin (1985)) and confirmed that particle specific heat was generally lower than that of liquids, resulting in lower moisture content c ¼ 1210 þ 40:4  X H2 O

for 10 < X H2 O < 30% w=w

c ¼ cH2 O  ð1  0:005  ð100  X H2 O ÞÞ for X H2 O > 40% w=w and h < 100  C

ð9Þ ð10Þ

The thermal conductivity of particles at 20 °C changed from 0.22 W m1 K1 (HB) to 0.34 W m1 K1 (CB) and varied linearly with moisture content (Eq. (12)) for 50 < X H2 O < 70% w=w k ¼ 0:2125 þ 7:8  103  X H2 O

ð12Þ

Several models useful in predicting the thermal conductivity of solids have appeared in the literature. Zuritz, Sastry, McCoy, Murakami, and Blaisdell (1989) measured the thermal conductivity of beans using a modified Fitch device. A linear increase of thermal conductivity with water content expressed as percent by weight has been deduced from their experimental results (Eq. (13)). Ali et al. (2002) proposed an expression developed from experimental data to predict the thermal conductivity of vegetables as a function of temperature, moisture content and density.

Table 3 Experimental and predicted thermal properties (q, c, k, a) of particles and liquids at 20 °C – mean value, NR: not recorded q [kg/m3]

c [J kg1 K1]

k [W m1 K1]

a  10+7 [m2 s1]

Exp

Exp

Eq. (9)

Eq. (10)

Exp

Eq. (13)

Eq. (14)

Exp

Eq. (15)

Eq. (16)

Particles DB HB BB CB

1181 1057 1116 1105

1731 2893 3147 3300

1679 3359 3719 3933

2332 3202 3386 3499

NR 0.20 0.27 0.31

NR 0.24 0.27 0.29

NR 0.41 0.48 0.50

NR 0.61 0.74 0.79

0.95 1.18 1.23 1.26

0.91 1.15 1.20 1.23

Fluids Fluid inlet Fluid outlet Tomato paste (Drusas & Saravacos, 1985)

1112 1061 1163

3767 3728 3302

NR NR NR

NR NR NR

0.54 0.52 0.525

NR NR NR

NR NR NR

1.31 1.30 1.37

NR NR NR

1.29 1.29 NR

A. Legrand et al. / Journal of Food Engineering 81 (2007) 447–458

This correlation is valid for a large range of temperatures and water content and for various vegetables (Eq. (14)) k ¼ 0:0671 þ 0:003284  X H2 O 3

ð13Þ 4

5

k ¼ ð2:35  10 Þ  T þ ð6:68  10 Þ  q þ ð2:516  10 Þ  X 2H2 O þ 0:145  log X H2 O  0:222  log q

ð14Þ

Experimental thermal conductivities at 20 °C were compared to those calculated by Zuritz et al. (1989) and Ali et al. (2002). It may be noted in this table that the mean thermal conductivities measured by Zuritz et al. (1989) were within ±4% of the calculated values, which is approximately within the experimental error. Moreover, the measured values were found close to those calculated by this author, due to the similarity of the particles used (beans). On the other hand, major differences between the experimental data and the values calculated by Ali et al. (2002) were observed. They could be explained by the parameters included in the equation. The correlation of Zuritz et al. (1989) allows the determination of thermal conductivity only according to the moisture content, whereas the expression developed by Ali et al. (2002) allows the prediction of thermal conductivity as a function of water content, density and temperature. Possible sources of error are also associated with density and moisture content measurement. 3.3.3. Thermal diffusivity Properties previously studied such as thermal conductivity, specific heat and density play an important role in the design and analysis of food processes and processing equipment. Thermal diffusivity is a ratio of these three properties and results obtained at 20 °C are given in Table 3. Singh (1982) observed that the thermal diffusivities of liquids and vegetables vary from 1 to 2  107 m2 s1, whatever the product, the temperature and the moisture content. Martens (1980) performed multiple regression analysis on 246 published values of thermal diffusivity for a variety of food products and established a regression equation (Eq. (15), precision: ±0.014  106 m2 s1). Loncin (1985) proposed a semi-empirical model to predict the thermal diffusivity (Eq. (16)) a ¼ ½0:0005736  X H2 O þ 0:000288  ðT þ 273Þ  106 a ¼ 0:0885  10

6

ð15Þ

6

þ ðaH2 O  0:0885  10 Þ  ðX H2 O =100Þ ð16Þ

Satisfactory agreement was found for the fluids between the present data and the literature. For the particles, the predicted data (Eqs. (14) and (15)) were higher than the experimental values. For solids, a possible source of error is associated with the high standard deviation for density and specific heat, resulting from the natural dispersion of properties. Consequently, for the fluids, satisfactory agreement was found between the present results and those of Loncin (1985). On the other hand, for particles, the difference may be attributed to the standard deviation of density and the moisture content.

455

3.3.4. Limiting factors correlated to thermal properties Sterilisation of a suspension could appear complex. Heterogeneity and settling suspensions have a simultaneous incidence on the flow of the suspension and on heat transfer (Legrand, 2005; Legrand et al., 2007). Conventional thermal processing can be successful for single-phase fluids, but is limited in its applicability to multiphase foods. In this case, the time required to conduct heat to and from the centres of the particles during a process could be a limiting factor. Heat transfer from the surface to the centre of particle is defined by the Biot number, Bi, which characterizes the heterogeneity between the heating kinetics of the fluid and of the particles. Particle size and relative velocity intervene primarily on the heat transfer coefficient between the fluid and the particle, hfp and heat transfer is strongly influenced by the cross-sectional distribution of the solid phase in the pipe and the flow of each phase. In addition, the dimension and thermal conductivity of particles evolve along the process and affect the Biot number. The sterilization efficiency concerning the particles and carrier fluid will be closely correlated to the flow behaviour of the suspension, especially when particle density shows a wide dispersion, as in the case of a real particles (high standard deviation). Hence, under such conditions a fastest-particle process design strategy would lead to overprocessing the majority of particles. This phenomenon may cause local overheating, when the moving bed pattern is considered, the heat transfer increases above the bed by the mixing effect of the particles. But when the cooking time is too high, particles become softer and lead to degradation of the solid tissue and consequent loss of product quality. In many cases, the extent of particle damage observed during the heat treatment would be unacceptable for a consumer product. 3.4. Electrical properties: electrical conductivity of the suspension Ohmic heating is defined as purely volume and direct resistance heating, in opposition to heating by conduction from the hot surface of a heat exchanger. The heat transfer coefficient between the hot wall and the fluid is irrelevant, as there is no hot wall at all, which constitutes a major advantage for food applications. The degradation of thermo-sensitive compounds through overheating (change in taste, undesirable reactions, burning) as well as heat exchanger fouling are theoretically strongly reduced. However, the homogeneity of treatment depends on the electrical conductivity of each phase and the flow behaviour of the suspension. To be able to process food by ohmic heating, its electrical conductivity should be in the range 0.01 and 10 S m1 at 25 °C. Blanched beans and fluid (0.8% w/w xanthan gum, 1.5% w/w NaCl salt and 97.7% w/w water) have an electrical conductivity of 0.22 S m1 and 1.43 S m1, respectively. Consequently, the mixture can be heated by the direct Joule effect heater. The fluid has a considerably greater electrical conductivity than the solid food particle,

A. Legrand et al. / Journal of Food Engineering 81 (2007) 447–458

3.4.1. Temperature and particle concentration effect Values of five thermocouples were used to determine the mean temperature of the suspension. The initial temperature of the suspension, for the different thermocouples was almost the same, a large difference was observed between the temperatures at the beginning of heating, which increased with time. For example, the maximum temperature deviation between two thermocouples can reach 10 °C whatever the particle concentration. Marcotte et al. (1998) also found major differences between temperatures at different positions within the static ohmic heating cell for hydrocolloid samples. Fryer et al. (1993) reported that the issue of non-uniformities arises in static heating systems where there is a lack of convection in high viscosity solutions. Therefore, the non-uniformity explanation might rely on another parameter that could also influence the heat transfer efficiency: the viscosity of the solutions. In this study, the experiments were carried out with strongly viscous fluids. The suspension viscosity decreased with the temperature, but remained less significant than that of fluid alone (Antonini & Francßois, 1985). Consequently, major deviations between the temperatures of the thermocouples appeared. Fig. 8 plots electrical conductivity versus particle concentration and temperature. The general trend shows that electrical conductivity increases linearly with temperature between 20 and 80 °C. This result was confirmed by Palaniappan and Sastry (1991b), Fryer et al. (1993) and Yongsawatdigul et al. (1995). It may be noticed that electrical conductivity decreased with particle concentration. Zareifard et al. (2003) also noted that overall values of electrical conductivity ranged from 0.2 to 1.8 S m1, increasing linearly with the process temperature as it ranged from 20 to 80 °C and decreasing as carrot cube concentration increased.

2

1

0 20

30

40

50

ð17Þ

The values of parameters r0 °C and b were obtained from the regression equations. A combined effect of temperature and particle concentration on electrical conductivity is noticeable as shown in Fig. 9, and the evolution of parameters r0 °C and b versus solid concentration can be described by exponential functions (Eq. (18)) rðhÞ ¼ bðCCÞ  T þ r0  C ðCCÞ with r0  C ¼ 0:6381  Expð0:021  CCÞ; and b ¼ 0:0336  Expð0:018  CCÞ;

R2 ¼ 0:96

R2 ¼ 0:98

ð18Þ

Overall, this semi-empirical correlation gave satisfactory predictions of the electrical conductivity (±20%) for a homogeneous suspension and became interesting in continuous ohmic heating, but its application still remains limited to a temperature range between 20 and 80 °C. 3.4.3. Limiting factors linked to suspension properties In ohmic heating, if solid and liquid have identical electrical conductivities, both phases will generate heat at the same rate and the suspension will heat both rapidly and uniformly. Unfortunately, in practice, the problem is more complex, because the electrical conductivity of each phase (particle and surrounding fluid) is often significantly different and the mean residence time of liquid and particle could also be different (Legrand et al., 2007). Consequently, it is possible for one phase to heat more rapidly so as to create a large temperature difference. If a temperature gradient appears between fluid and particle, a convective–conductive heat transfer will be generated to reach a thermal balance between the two phases. In our case, the solid generates heat at a slower rate than the liquid. However, a suitable holding section could balance the cooking efficiency and the mean temperature of the product. 0.07

0.7

-1

3

r ¼ r0  C þ b  T

Thermal dependency, β, [S.m-1.˚C ]

Carrier fluid 20% w/w particles 40% w/w particles 60% w/w particles 100% w/w mashed particles

-1

Electrical conductivity, σ [S.m ]

4

3.4.2. Electrical conductivity model For each solid concentration, the electrical conductivity of a two-phase food system was modelled by an empirical linear equation (Eq. (17)) according to the temperature and expressed like Davies, Kemp, and Fryer (1999) Li, Li, and Tatsumi (2004):

60

70

80

Temperature, T [˚C]

Fig. 8. Electrical conductivity versus temperature and particle concentration (red bean suspension in carrier fluid).

Thermal dependency, [S.m-1.˚C-1]

0.06

0.6

Conductivity at 0˚C, [S.m-1]

0.05

0.5

0.04

0.4

0.03

0.3

0.02

0.2

0.01

0.1

0.00

-1

as frequently reported in literature. Typical values ranging from 0.5 to 1.6 S m1 over temperatures of 20–80 °C have been reported for low viscosity liquids such as orange, tomato and carrot juices (Palaniappan & Sastry, 1991b).

Conductivity at 0˚C, σ0˚C [S.m ]

456

0 0

10

20

30

40

50

60

70

80

90

100

Particle concentration, CC [%w/w]

Fig. 9. Evolution of r0 °C and b parameters versus solid concentration (red beans suspension in carrier fluid).

A. Legrand et al. / Journal of Food Engineering 81 (2007) 447–458

The electrical conductivity of the suspension is affected by a combined effect of temperature and solid concentration. In a direct Joule effect heater, any heterogeneity in the suspension (e.g. capsule flow or settling) generates non-uniformity in the delivery of the electric field and in the heating rate (microbiological destruction, enzymatic inactivation, cooking). In the worse case, the suspension heterogeneity leads to the instability of electrical parameters and precludes the use of a direct Joule effect heater. The relative electrical conductivity of the mixture at different particle concentration and the flow behaviour of the suspension will be determinant in the decision as to whether the direct Joule effect heater can be considered as a relevant technology or not.

457

 Electrical conductivity is closely dependent on temperature and particle concentration, which may be important limiting factors during ohmic heating. Any fluid overheating or suspension heterogeneity would lead to the instability of electrical parameters. In conclusion, the mixture composed of red beans in a highly viscous sauce stands as a complex product. Due to the evolution of the properties along the process and current knowledge of the flow behaviour of suspensions, heat treatment in continuous processes with conventional or ohmic heaters does not appear to be an industrial reality at present time. Acknowledgement

4. Conclusion The passage from a batch to a continuous thermal process for the sterilisation of heterogeneous products, notably suspensions of fragile particles in viscous carrier fluids, remains an empirical and random operation even with alternative technologies such as ohmic heating. A high-temperature treatment in a short time (HTST) is feasible but requires a perfect knowledge of the properties of both phases (carrier fluid and particles properties). The present work reports (i) the properties for a real foodstuff composed of red beans (Phaseolus vulgaris L.) and a model non-Newtonian carrier fluid and (ii) the limiting factors for a transition from a batch to a continuous thermal process and specifically ohmic heating. Physical (density, shape and dimensions, rheological properties), mechanical (elasticity modulus, maximal deformation and stress) and thermal (heat capacity, thermal conductivity, thermal diffusivity) properties are reported versus the water content, as are the electrical property (electrical conductivity) versus the temperature and the solid concentration. All these properties could not be discussed without considering the flow behaviour of the suspension because all these properties interact closely with hydrodynamics. With a suspension composed of red beans in a highly viscous carrier fluid, several points were identified as limiting factors for continuous heat treatment:  The volume expansion of the particle (+22% between blanched and cooked beans) increases the particle concentration and may affect the homogeneity of the suspension along the process.  An important loss of mechanical properties (E reduced from 3.8 to 1.2 MPa and smax from 1.62 to 0.24 MPa during cooking) will enhance the physical degradation of particles.  The large size of the particles (dsp > 10 mm) and their complex shape associated with the loss of their mechanical properties could lead to extensive quality degradation of the product and induce duct plugging.

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