Structural Properties of Corn-Legume Based Extrudates as a Function of Processing Conditions and Raw Material Characteristics

Abstract

The effect of extrusion conditions, including feed rate (2.52–6.84 kg/h), feed moisture content (13–19% wet basis), screw speed (150–250 rpm), and extrusion temperature (150–230°C) on structural properties of corn-legume based extrudates was studied. Four different types of legumes, chickpea, mexican bean, white bean, and lentil were used to form mixtures with corn flour in a ratio ranging from 10 to 90% (corn/legume). A simple power model was used to correlate porosity with extrusion conditions and material characteristics. The influence of feed rate in the extrudates porosity is incorporated into mean residence time. Porosity of extrudates was found to increase with temperature and residence time and to decrease with feed moisture content and corn to legume ratio. Screw speed did not affect extrudates properties. Expansion ratio showed a similar behavior with porosity. The addition of legumes (protein source) led to more dense products. Comparatively, the usage of white bean in mixtures for the production of snacks, led to a product with higher porosity than those with other legumes.

Keywords:

• Chickpea
• Expansion ratio
• Extrusion cooking
• Lentil
• Mexican bean
• Porosity
• White bean

INTRODUCTION

In recent years several studies have suggested that a Mediterranean diet has many benefits in human health. It is associated with lower incidence of cardiovascular disease and cancer via a variety of mechanisms, including improved blood lipid profile, decreased lipid oxidation, antithrombotic, and anti-inflammatory effects, improvement in endothelial function, and decreased insulin resistance and ventricular irritability.[1–3] The Mediterranean diet includes: high monounsaturated: saturated fat ratio, moderate consumption of ethanol, milk and dairy products, low consumption of meat and meat products and high consumption of cereals, fruits, vegetables, and legumes. Legumes are generally good sources of slow release carbohydrates and rich in proteins and dietary fibers. Legumes are normally consumed after processing, which not only improves palatability of foods but also increases the bioavailability of nutrients, by inactivating trypsin inhibitors and haemagglutinins. Starch, the major biopolymeric constituent of legumes, upon processing gets partially modified into resistant starch.[4]

The increasing demand for all types of non-meat, high-protein products has resulted in new and highly profitable ventures for food manufacturers. Proteins derived from plant sources are becoming one of the food industry's fastest-growing and most-innovative ingredient segments. Plant proteins have increased functionality, a bland flavor profile, additional nutritional benefits, and a low-cost advantage as both meat extenders and meat alternatives. Legumes, with their high amount of protein (∼18–25%) can be considered as the best and the cheapest source of plant protein. Although there are several methods for processing plant proteins into texturized products, the use of twin-screw extrusion cooking has proven to be instrumental in the development of many new industry opportunities.

Extrusion cooking is unique among heat processes in that the material is subjected to intense mechanical shear; moistened starchy or proteinaceous foods are worked into a viscous, plastic-like dough and cooked before being forced through the die. The intense structural disruption and mixing facilitates reactions otherwise limited by diffusion of reactants and products.[5] Some results of cooking during the extrusion process are the gelatinization of starch, denaturation of proteins, inactivation of many native enzymes, which causes food deterioration during storage, inactivation of antinutrient factors,[6–8] and reduction of microbial counts in the final product.[9] Product quality can vary considerably depending on the extrusion processing conditions such as extruder type, screw configuration, feed moisture, temperature profile in the barrel sections, screw speed, and feed rate. The influence of processing conditions on the product quality by extrusion of starch based and starch-legumes blends has been investigated.[10–19]

Pores occur in diverse food products, such as cakes, breads, and biscuits, breakfast cereals, fried, dried, and extruded products. During drying the pore formation has been studied widely and many investigators have proposed empirical models for porosity prediction.[20–22] The shrinkage or expansion of food during drying is expressed by shrinkage-expansion coefficient.[21] In extrusion cooking, expansion is the primary quality parameter associated with product crispiness, water absorption, water solubility, and crunchiness. Extrudate expansion can be expressed through porosity and expansion ratio. During extrusion cooking of biopolymers, the viscoelastic material is forced through the die so that the sudden pressure drop causes part of the water to vaporize, giving an expanded porous structure. The resulting extrudate expansion has extrusion contributions from both elastic swell and bubble growth effects.[23] The bubble growth rate is modelled, in the bubble growth theory.[24] A general model of extrudate expansion has been developed including the radial, longitudinal and volumetric expansion.[25] Extrudate expansion has been reported to be most dependent on material moisture content and extrusion temperature. Several theoretical considerations for extrudate expansion have been published.[24–27]

The objective of this study was to investigate porosity and expansion ratio changes of four corn-legumes mixtures (including chickpea, mexican bean, white bean, and lentil) as a function of process conditions (temperature, feed rate, screw speed) and material characteristics (moisture content, corn to legume ratio). A simple mathematical model was developed, to predict porosity as a function of process conditions and material characteristics.

MATHEMATICAL MODELING

Mathematical Model

In order to examine the influences of process conditions and material characteristics on the porosity, a simple power model is used. The proposed equation is:

(1)

where ε is the porosity of extrudates; T is the extrusion temperature (°C); τ is the mean residence time (s); N is the screw rotation speed (rpm); X is the feed moisture content (kg/100kg wb); and C is the materials ratio (kg corn/kg legume). The T _r , τ _r , X _r , C _r and N _r are the respective values in reference conditions. The ε ₀ is a constant with values ranging from 0 to 1, which represents porosity in reference conditions.

The porosity influencing of process conditions, such as, product temperature, residence time and screw speed is expressed by n _T , n _τ, n _N exponents, respectively, while the influence of material characteristics such as feed moisture content and corn to legume ratio is expressed by n _x and n _c exponents, respectively.

The influence of feed rate in the extrudates porosity is incorporated into mean residence time, considering that mean residence time is:

(2)

where e _f is the empty fraction of the extruder; ρ _t is the true density of material (kg/m³); V is the free volume in the extruder barrel; and F is the feed rate (kg/h). The empty fraction of the extruder is the part of its volume which is the void left between barrel and screws during operation.

Extrudates were assumed to have very low levels of moisture content, so their structural properties—namely true density, apparent density, and porosity—are similar to the structural properties of dried materials at zero moisture content. Therefore, the true density of extrudates, ρ _t , is equal to the density of solid material and it is assumed constant.

It is expected that not all of these parameters will influence to the same degree the porosity of extrudates, and this can be revealed through regression analysis.

Regression Analysis

The values of the required parameters are determined by fitting the proposed model to the experimental data. This can be done by minimizing the following residual sum of squares:

(3)

where, ε _ij is the experimental value of porosity of the jth replicate of the ith experiment; ε _i is the predicted value of the model for the ith experiment; n _i is the number of replicates in the ith experiment; and M is the total number of experiments.

The resulting model is considered acceptable if the standard deviation between experimental and predicted values (lack of fit, S _R ) is close to the experimental error (S _E ).

The standard deviation between experimental and predicted values (S _R ) and the standard experimental error (S _E ) can be calculated from the following equations:

(4)

(5)

(6)

(7)

where (K-p) and (K-M) are the degrees of freedom for S _R and S _E , respectively; K is the total number of experimental measurements (including the replicates); M is the number of experiments; p is the number of parameters; and n _i is the number of replicates of the ith experiment.

Following regression analysis procedure, all 6 parameters can be determined simultaneously. However, all of these parameters do not affect the sum of squares of the residuals to the same degree. In order to distinguish between the ones that are necessary to accurately predict the porosity, the following procedure was adopted. Firstly the minimum change in sum of squares (SST) was estimated for all six parameters and mean deviation (S _R ) was evaluated. Secondly, omitting one parameter at a time, the values of S _R was evaluated for all combinations of the five remaining parameters. In this way, the parameter chosen to be eliminated was the one whose elimination produced the minimum S _R . Continuing the former procedure, the minimum values of S _R was evaluated for 4, 3, 2, and 1 parameters, respectively. In Figure 1, it is shown a typical figure of S _R and S _E as a function of the number of parameters. The group of parameters which gives a lack of fit (S _R ) close to mean experimental error (S _E ) is the one that involves the required number of parameters for predicting porosity.

Figure 1 The lack of fit (S _R ) and standard experimental error (S _E ) as a function of the number of parameters.

MATERIALS AND METHODS

Sample Preparation

Yellow corn flour was mixed with legume flour (chickpea, mexican bean, white bean, and lentil) and 0.5% salt. Material characteristics are shown in Table 1. Distilled water was added to adjust moisture content. All the ingredients of each preparation were mixed in a mixer for 15 min, to ensure homogenous mixture. After mixing, the samples were packed under vacuum and stored. The proximate composition of materials used is shown in Table 2.

Table 1 Extrusion conditions and material characteristics

Extrusion conditions	Minimum	Maximum
Extrusion temperature (°C)	150	230
Feed rate (kg/h)	2.52	6.84
Screw speed (rpm)	150	250
Materials characteristics
Feed moisture content (kg/100 kg wb)	13	19
Corn/legume ratio	10	90

Table 2 Chemical composition of raw materials (g/100g)

	Protein	Lipids	Total carbohydrates	Dietary fibre	Sugar
Corn	6	1	83	2	1
Chickpea	22	7	58	11	11
Mexican bean	23	1	60	15	2
White bean	23	1	60	15	2
Lentil	28	1	57	30	5

Extrusion Cooking

A prism Eurolab conical, counter-rotating twin screw extruder, model KX-16HC, was used. The general screw geometry was: length 40 cm, diameter 16 mm, maximum rotation speed 500 rpm, and die diameter 3 mm. The material was fed into extruder with a volumetric feeder. The extruder had 5 temperature control zones. The pressure at the die during extrusion was measured with a pressure transducer. All extrusion conditions were displayed on the control panel (barrel and screw die temperature, screw speed). The temperature during extrusion was adjusted by varying the temperature in the barrel, screw and die. The extrusion conditions are shown in Table 1. Steady state conditions were reached after 20 min, and then samples collected dried in air and stored for further structural properties measurement.

Residence time is calculated using Eq. (2). The empty fraction has been correlated with extrusion conditions and it is given by the following equation, which is used for this extruder type:

(8)

where N is the screw speed (rpm), F is the feed rate (kg/s); T is the die temperature; and X is the feed moisture content (kg/100 kg wb).

Measurement of Porosity and Expansion Ratio

The porosity of the extrudates was determined from the true and apparent density, using the equation:

(9)

where ρ _a is the apparent density and ρ _t is the true density of extrudates.

The apparent density was determined by measuring the actual dimensions of the extrudates.[28] The diameter of extrudates was measured with a Vernier caliper. The apparent density of extrudates was determined using the equation:

(10)

where m is the mass of the samples (g); d is the diameter (cm); and L is the length of extrudate (cm). Three replicates of extrudate were selected and an average was taken. The true density of the samples was determined using the equation:

(11)

where m is the mass of the samples (g) and V _t is the true volume (cm³). The true volume was measured using a Quantacrome stereopycnometer (model SPV-3) with the accuracy of 0.001 cm³, assuming no closed pores remain in the sample for helium. The measurement flowchart is shown in Figure 2. Expansion ratio is defined as:[6,10,26,29–31]

(12)

where d is the diameter of the extrudate (cm) and d ₀ is the die diameter (cm). From Eqs. (9) and (12) is derived that expansion ratio can be correlated with extrudate porosity by the following equation:

(13)

where ε is the porosity of the extrudate. The expansion ratio of extrudates was calculated using (Eq. 13).

Figure 2 Measurement flowchart.

RESULTS AND DISCUSSION

The application of regression analysis for each type of sample showed that the optimum number of parameters which affect porosity is 5 (Figure 1). These parameters were ε ₀ , n _T , n _τ, n _X , n _C . The screw rotation speed did not affect significantly the porosity of extrudates. In Table 3, experimental and predicted values of porosity are listed. A comparison between predicted porosity and experimental data is shown in Figures 3 to 5. The corresponding parameter estimates for all materials are shown in Table 4. In 3–5, porosity of extrudates is represented as a function of mean residence time, feed moisture content, extrusion temperature and corn to legume ratio. Solid lines are used for predicted values of porosity using the mathematical model and the parameters of Table 4.

Table 3 Experimental and predicted porosity of extrudates

	Extrusion Conditions & Material Characteristics				Porosity		Standard Deviation
Material	C (%)	X (% wb)	T (°C)	τ (s)	ε (−)	ε i (−)	S R (−)
Corn/Chickpea	10	16	150	36	0.556	0.553	0.003
	50	16	150	28	0.613	0.618	0.005
	50	16	150	36	0.632	0.635	0.004
	50	16	150	40	0.640	0.643	0.003
	50	16	150	49	0.667	0.659	0.008
	50	16	150	58	0.669	0.672	0.003
	10	13	200	38	0.700	0.703	0.003
	10	14.5	200	38	0.692	0.690	0.002
	10	16	200	39	0.674	0.679	0.004
	10	17.5	200	39	0.670	0.668	0.002
	10	19	200	40	0.663	0.659	0.004
	50	13	200	38	0.804	0.801	0.003
	50	14.5	200	38	0.792	0.789	0.003
	50	16	200	28	0.748	0.746	0.002
	50	16	200	30	0.750	0.753	0.003
	50	16	200	39	0.775	0.776	0.001
	50	16	200	50	0.800	0.798	0.002
	50	16	200	55	0.814	0.808	0.006
	50	16	200	58	0.816	0.813	0.003
	50	17.5	200	39	0.760	0.764	0.004
	50	19	200	40	0.757	0.755	0.001
	90	13	200	38	0.850	0.844	0.006
	90	14.5	200	38	0.826	0.828	0.002
	90	16	200	39	0.808	0.815	0.006
	90	17.5	200	39	0.805	0.802	0.003
	90	19	200	40	0.788	0.791	0.003
	10	16	230	40	0.744	0.741	0.003
	50	16	230	28	0.820	0.818	0.002
	50	16	230	31	0.828	0.829	0.001
	50	16	230	40	0.847	0.854	0.008
	50	16	230	50	0.879	0.876	0.003
	50	16	230	58	0.891	0.892	0.001
Corn/Mexican Bean	10	16	150	30	0.696	0.697	0.001
	50	16	150	25	0.737	0.739	0.002
	50	16	150	26	0.742	0.740	0.002
	50	16	150	26	0.742	0.740	0.002
	50	16	150	26	0.742	0.740	0.002
	50	16	150	26	0.742	0.740	0.002
	50	16	150	30	0.745	0.746	0.001
	50	16	150	30	0.745	0.746	0.001
	50	16	150	35	0.750	0.754	0.004
	50	16	150	40	0.765	0.761	0.004
	50	16	150	40	0.765	0.761	0.004
	50	16	150	40	0.765	0.761	0.004
	50	16	150	48	0.772	0.770	0.002
	10	13	200	31	0.786	0.781	0.005
	10	14.5	200	32	0.760	0.764	0.004
	10	16	200	32	0.757	0.749	0.008
	10	17.5	200	32	0.730	0.736	0.006
	10	19	200	33	0.728	0.724	0.004
	50	13	200	31	0.843	0.837	0.006
	50	14.5	200	32	0.814	0.818	0.004
	50	16	200	25	0.794	0.790	0.004
	50	16	200	28	0.795	0.796	0.001
	50	16	200	32	0.802	0.803	0.000
	50	17.5	200	32	0.794	0.789	0.005
	50	19	200	33	0.775	0.777	0.001
	90	13	200	31	0.863	0.859	0.004
	90	14.5	200	32	0.837	0.840	0.003
	90	16	200	32	0.831	0.823	0.007
	90	17.5	200	32	0.814	0.809	0.005
	90	19	200	33	0.792	0.796	0.004
	10	16	230	33	0.776	0.780	0.004
	50	16	230	32	0.802	0.803	0.000
	50	16	230	32	0.802	0.803	0.000
	50	16	230	45	0.824	0.821	0.003
	50	16	230	45	0.824	0.821	0.003
	50	16	230	48	0.825	0.824	0.001
Corn/White Bean	10	16	150	33	0.783	0.791	0.008
	50	16	150	28	0.815	0.815	0.000
	50	16	150	33	0.818	0.821	0.003
	50	16	150	36	0.825	0.824	0.001
	50	16	150	45	0.835	0.831	0.004
	50	16	150	53	0.835	0.836	0.001
	10	13	200	35	0.859	0.860	0.001
	10	14.5	200	35	0.842	0.838	0.004
	10	16	200	36	0.814	0.819	0.004
	10	17.5	200	36	0.805	0.801	0.004
	10	19	200	36	0.785	0.786	0.001
	50	13	200	35	0.900	0.901	0.001
	50	14.5	200	35	0.871	0.878	0.007
	50	16	200	28	0.848	0.849	0.001
	50	16	200	36	0.860	0.858	0.002
	50	16	200	42	0.860	0.863	0.003
	50	16	200	51	0.870	0.870	0.000
	50	16	200	53	0.872	0.871	0.001
	50	17.5	200	36	0.843	0.840	0.004
	50	19	200	36	0.823	0.823	0.000
	90	13	200	35	0.910	0.917	0.007
	90	14.5	200	35	0.890	0.894	0.004
	90	16	200	36	0.878	0.872	0.006
	90	17.5	200	36	0.860	0.854	0.006
	90	19	200	36	0.837	0.837	0.001
	10	16	230	37	0.834	0.835	0.001
	50	16	230	28	0.859	0.867	0.008
	50	16	230	37	0.874	0.876	0.002
	50	16	230	45	0.886	0.883	0.003
	50	16	230	53	0.898	0.889	0.009
Corn/Lentil	10	16	150	29	0.691	0.693	0.002
	50	16	150	25	0.743	0.746	0.002
	50	16	150	29	0.746	0.753	0.007
	50	16	150	40	0.759	0.768	0.010
	50	16	150	45	0.780	0.774	0.006
	10	13	200	31	0.769	0.762	0.007
	10	14.5	200	31	0.750	0.746	0.004
	10	16	200	32	0.727	0.730	0.004
	10	17.5	200	32	0.723	0.717	0.006
	10	19	200	33	0.702	0.705	0.003
	50	13	200	31	0.834	0.829	0.006
	50	14.5	200	31	0.801	0.810	0.009
	50	16	200	25	0.777	0.781	0.004
	50	16	200	28	0.782	0.787	0.005
	50	16	200	32	0.795	0.794	0.001
	50	16	200	37	0.804	0.802	0.002
	50	16	200	45	0.813	0.811	0.001
	50	17.5	200	32	0.774	0.779	0.006
	50	19	200	33	0.764	0.766	0.003
	90	13	200	31	0.861	0.854	0.007
	90	14.5	200	31	0.842	0.836	0.006
	90	16	200	32	0.817	0.818	0.002
	90	17.5	200	32	0.798	0.803	0.005
	90	19	200	33	0.796	0.790	0.006
	10	16	230	33	0.751	0.749	0.002
	50	16	230	25	0.793	0.800	0.007
	50	16	230	33	0.807	0.814	0.007
	50	16	230	33	0.807	0.814	0.007
	50	16	230	40	0.830	0.824	0.006
	50	16	230	45	0.835	0.830	0.005

Table 4 Results of parameter estimation

	ε 0	n T	n τ	n X	n C	S R	S E
Corn/chickpea	0.863	0.661	0.117	−0.170	0.083	0.032	0.104
Corn/mexican bean	0.904	0.236	0.064	−0.200	0.043	0.032	0.067
Corn/white bean	0.974	0.142	0.041	−0.244	0.029	0.140	0.014
Corn/lentil	0.907	0.165	0.062	−0.214	0.052	0.132	0.022

Figure 3 Porosity of extrudates as a function of residence time and temperature (CP: corn/chickpea; CM: corn/mexican bean; CB: corn/white bean; CL: corn/lentil).

Figure 4 Porosity of extrudates as a function of feed moisture content and corn to legume ratio (CP: corn/chickpea; CM: corn/mexican bean; CB: corn/white bean; CL: corn/lentil).

Figure 5 Comparative figures of porosity for all extrudates (CP: corn/chickpea; CM: corn/mexican bean; CB: corn/white bean; CL: corn/lentil). a. Porosity as a function of residence time; b. porosity as a function of corn/legume ratio; c. porosity as a function of temperature; and d. porosity as a function of feed moisture content.

As can be seen, in all extrudates, porosity was increased with temperature. Such a trend had been observed for various extruded products in the past.[6,11,12,15,16,29–32] An increase in the barrel temperature will decrease the melt viscosity. The reduced viscosity effect would favour the bubble growth during extrusion. Moreover, the degree of superheating of water in the extruder would be increased at higher temperatures, also leading to greater expansion.

Increased residence time led to a slight increase of extrudate porosity at all type of corn-legume blends. That is, increased feed rate led to a decrease in porosity (Eq. 2). Increased feed rate would influence the degree of fill, inducing the degradation of amylopectin networks, and change the melt rheological characteristics thus leading to greater elastic effect and changes in product porosity. Exactly, a rise in feed rate leads to an increase of final viscosity and consequently porosity decreases.[6,26,31,33,34]

Feed moisture content seems to have an influence to porosity; as it raised porosity decreased. Moisture content during extrusion provides the driving force for the expansion and also contributes to the rheological properties of the melt, which in turn affect expansion. Moisture is the main plasticizer of flours, which enables them to undergo a glass transition during the extrusion process and thus facilitates the deformation of the matrix and its expansion.[35] Similar results have been observed in the past.[13,26,30,31,36,37]

It was observed that increasing the amount of legume, porosity decreased. This trend could be attributed to legume proteins. Proteins have an effect on expansion through their ability to affect water distribution in the matrix and through their macromolecular structure and conformation, which affects the extensional properties of extruded melts. They also contribute to extensive networking through covalent and nonbonding interactions that take place in extrusion.[38,39] Similar results have been observed previously.[40–43]

From Figure 5, it is clear that the extrudates containing chickpea had the lowest values of porosity and the extrudates containing white bean had the highest value of porosity. This might be due to shortening effect in chickpea blends which exhibit higher lipid content (Table 2). A stronger influence on corn/chickpea blend porosity by temperature was observed. Generally differences in values observed among different legume blends could be attributed to differences in legume proteins and especially in protein quality.

The expansion ratio of extrudates is presented in Figure 6. It is obvious that expansion ratio depends on residence time, extrusion temperature, feed moisture content and corn to legume ratio. More specifically, expansion ratio increased with residence time and temperature and decreased with feed moisture content and corn to legume ratio. It should be pointed out that porosity and expansion ratio were depended in a similar way by the same parameters. This trend is well described by Eq. (13). Furthermore, these two properties represent the swelling of the product, so a similar dependence from process variables and material characteristics is expected.

Figure 6 Comparative figures of expansion ratio for all extrudates (CP: corn/chickpea; CM: corn/mexican bean; CB: corn/white bean; CL: corn/lentil). e. Expansion ratio as a function of residence time; f. expansion ratio as a function of corn/legume ratio; g. expansion ratio as a function of temperature; and h. Expansion ratio as a function of feed moisture content.

The values of true density for each type of extrudate are shown in Table 5. It is evident that the Corn/Lentil extrudate had the minimum value of true density, while Corn/Chickpea extrudate had the maximum value.

Table 5 True density

	True density, ρp, (kg/m)
Corn/chickpea	1703 ± 387
Corn/mexican bean	1400 ± 107
Corn/white bean	1561 ± 134
Corn/lentil	1392 ± 61

CONCLUSIONS

Structural properties of expanded corn-legume snacks produced on a twin screw extruder were depended on several process conditions. Extrusion temperature and residence time as well as material characteristics (feed moisture content, corn to legume ratio) had some significant effect on extrudate porosity. Porosity of extrudates was found to increase with temperature and residence time and to decrease with feed moisture content and ratio of legume. A similar trend was observed for expansion ratio. The addition of legumes (protein source) produces more dense products. Comparatively, the usage of white bean in mixtures for the production of snacks, leads to product with greater porosity than those with other legumes.

NOMENCLATURE

C	=	Corn/legume ratio (−)
d	=	Diameter (cm)
d 0	=	Die diameter (cm)
E	=	Expansion ratio (−)
e f	=	Empty fraction (−)
F	=	Feed rate (kg/s)
K	=	Number of experimental measurements (−)
L	=	Extrudates length (cm)
m	=	Extrudates mass (g)
M	=	Number of experiments (−)
N	=	Screw speed (rpm)
n C	=	Corn/legume ratio constant (−)
n i	=	Number of replicates (−)
n N	=	Screw speed constant (−)
n T	=	Temperature constant (−)
n X	=	Feed moisture content constant (−)
n τ	=	Residence time constant (−)
p	=	Number of parameters (−)
S E	=	Standard experimental error (−)
S R	=	Standard deviation between experimental and predicted values (−)
SST	=	Total sum of squares (−)
T	=	Extrusion temperature (°C)
V t	=	True volume (cm3)
X	=	Feed moisture content (kg/100kg wb) Greek Symbols ε = porosity (−) ρ a = apparent density (g/cm3) ρ t = true density (g/cm3) τ = mean residence time (s) Subscripts i = ith experiment j = jth replicate r = reference

ACKNOWLEDGMENTS

The project is co-funded by the European Social Fund (75%) and National Resources (25%)—EPEAEK II—PYTHAGORAS. The authors wish to thank Mr. Panagiotis Mermigas for technical assistance.