Mechanical Properties of Corn-Legume Based Extrudates

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 (150–260°C) on the mechanical properties of corn/legume-based extrudates was studied. White bean and lentil were used in mixtures with corn flour at a ratio of 10:90 up to 90:10 (corn:legume). Simple power models were used to correlate breaking stress and corresponding strain with extrusion conditions and material characteristics. The influence of feed rate on the extrudates mechanical properties was incorporated in the mean residence time. The breaking stress of extrudates decreased with temperature, residence time, and corn to legume ratio, and it increased with feed moisture content. The corresponding strain showed an opposite trend. Screw speed did not affect the extrudate properties. The use of lentil flour led to a product with higher breaking stress. Furthermore, in a previous work, the porosity of these products was modeled and, now, it was found that breaking stress and porosity of the extrudates could be correlated by an exponential relationship.

Keywords:

• Breaking stress
• Extrusion cooking
• Lentil
• Strain
• White bean

INTRODUCTION

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 fast growing and 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 thermal processes in that the material is subjected to intense mechanical shear; moistened, starchy or proteinaceous foods are worked into viscous, plastic-like dough and cooked before being forced through the die. The intense structural disruption and mixing facilitates reactions otherwise limited by the diffusion of reactants and products.[1] Some results of cooking during the extrusion process are the gelatinization of starch, denaturation of proteins, inactivation of many native enzymes, which cause deterioration of foods during storage, inactivation of antinutrient factors, and reduction of microbial counts in the final product.[2,3] 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 during extrusion on the product quality of starch and starch/legumes-based blends has been well.[4–9]

The acceptance of snacks is critical because of the specific quality attributes that attract people. The various sensory attributes of snack foods are appearance, texture, taste, color, and flavor. Among them, texture is one of the most important and this is particularly true for snack food. Crispness is perceived through a combination of tactile, kinesthetic, visual, and auditory sensation, and it represents the key attribute of dry snack products. Crispness is also associated with the rapid drop of force during the mastication process that, in turn, is based on fracture propagation in brittle materials. When a force is applied to brittle snacks, rupture of the cellular structure occurs and, in line with some deformation, generates a typical sound contributing to the crispness sensation. A crispy material usually generates an irregular force-deformation curve.[10] The most common methods to determine the texture of extruded snack foods are compression, puncture, bending and shearing tests, of which the compression test is the most usual.[11–13] The effect of extrusion conditions and material characteristics on the mechanical properties of starch and starch/protein-based extrudates has been discussed extensively during the last decade.[4,12,14,15]. However, the relationships developed were not applied over the whole range of the mentioned materials and process conditions. The relationship between extrusion conditions and physicochemical properties provides a basis for effective product development.

The objective of this study was to investigate the breaking stress changes of two corn/legume mixtures (including white bean and lentil) as a function of process conditions (temperature, feed rate, screw speed) and material characteristics (moisture content and corn to legume ratio). Simple mathematical models were developed for the prediction of breaking stress and the corresponding strain of extrudates as a function of process conditions and material characteristics.

MATHEMATICAL MODELING

Mathematical Models

The mathematical models used to predict the breaking stress and the corresponding strain are summarized on Table 1. The models for breaking stress and corresponding strain involve six parameters: the breaking stress and corresponding strain at reference conditions (σ _B,0 and ϵ _B,0 ), the exponents for residence time (n _τ and m _τ), the exponents for temperature (n_T and m_T ), the exponents for feed moisture content (n_X and m_X ), the exponents for corn to legume ratio (n_C and m_C ), and the exponents for screw rotation speed (n_N and m_N ).

Table 1 Mathematical models

Compression test
Breaking Stress
		(1)
Corresponding Strain
		(2)
Parameters
σ B,0 : Breaking stress at reference conditions	(kPa)
ϵ B,0 : Strain at breaking at reference conditions	(–)
n τ, m τ : Residence time exponents	(–)
n T, mT : Temperature exponents	(–)
nX , mX : Feed moisture exponents	(–)
nC , mC : Materials ratio exponents	(–)
nN , mN : Screw speed exponents	(–)
where,
τ: Mean residence time	(s)
T: Extrusion temperature	(°C)
X: Feed moisture content	(kg/100 kg, wet basis)
C: Corn to legume ratio	(–)
N: Screw rotation speed	(rm)

The breaking stress and strain influence upon process conditions, such as, product temperature, residence time and screw speed is expressed by the n_T , m_T , n _τ, m _τ, n_N , m_N exponents, respectively, while the influence of material characteristics such as feed moisture content and corn to legume ratio is expressed by the n_x , m _x and n_c , m_c exponents, respectively.

The effect of the feed rate, on the extrudates mechanical properties, is incorporated into the mean residence time, assuming that the latter is expressed as:

(3)

where e_f is the void fraction of the extruder; ρ _t is the true density of material (kg/m³); V is the free volume in the extruder barrel (m³); and F is the feed rate (kg/s). The void fraction of the extruder is the portion of its volume, which is the void left between barrel and screws during operation. It is expected that not all of these parameters influence the mechanical properties of the extrudates in the same degree and this can be revealed by 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:

(4)

(5)

where, σ _B,ij and ϵ _B,ij are the experimental values of breaking stress and corresponding strain of the j^th replicate of the i^th experiment; σ _B,i and ϵ _B,i are the predicted values of the model for the i^th experiment; n_i is the number of replicates in the i^th 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:

(6)

(7)

(8)

(9)

(10)

(11)

(12)

where (K-p) and (K-M) are the degrees of freedom for S _R,σ, S _R,ϵ, and S _E,σ, S _E,ϵ, 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 i^th experiment.

Following the regression analysis procedure, all six parameters can be determined simultaneously. However, not all of these parameters affect the sum of squares of the residuals to the same degree. In order to distinguish between the ones that are important for the accurate prediction of the mechanical properties, the following procedure was adopted. Firstly, the minimum change in the sum of squares (SST _σ, SST _ϵ) was estimated for all six parameters and the mean deviation (S _R,σ, S _R,ϵ) was evaluated. Secondly, omitting one parameter at a time, the values of S _R,σ, S _R,ϵ were 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,σ S _R,ϵ. Continuing the former procedure, the minimum values of S _R,σ, S _R,ϵ were evaluated for 4, 3, 2, and 1 parameters, respectively. In Fig. 1 a typical plot of S_R and S_E as a function of the number of parameters is shown. The group of parameters which gives a lack of fit (S _R,σ, S _R,ϵ) close to the mean experimental error (S _E,σ, S _E,ϵ) is the one that involves the required number of parameters for the prediction of the mechanical properties.

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 (white bean and lentil) and 0.5 g salt per 100 g of mixture was added for taste reasons. Material characteristics are shown on Table 2. Distilled water was added to adjust the moisture content. All the ingredients of each preparation were put in a mixer for 15 min, to ensure a homogeneous mixture. After mixing, the samples were packed under vacuum and stored until experimentation time.

Table 2 Extrusion conditions and material characteristics

Extrusion conditions	Minimum	Maximum
Extrusion Temperature (°C)	150	260
Feed Rate (kg/h)	2.52	6.84
Screw Speed (rpm)	150	250
Materials Characteristics
Feed Moisture Content (kg/100 kg, wet basis)	13	19
Corn/Legume Ratio	10	90

Extrusion Cooking

A co-rotating twin-screw extruder (Prism Eurolab, model KX-16HC, Staffordshire, UK) was used. The screw geometry was length 40 cm, diameter 16 mm, maximum rotation speed 500 rpm. It was used a cylindrical die with diameter 3 mm and length 17.5 mm. The material was fed into the extruder using a volumetric feeder. The extruder had five temperature control zones. The temperature during extrusion was adjusted by varying the temperature in the barrel, screw, and die using electric heaters. The extrusion conditions are shown on Table 2. Steady-state conditions were reached after 20 min, after which samples collected, were dried in air and stored for further properties' measurements.

Residence time is calculated using Eq. (3). The void fraction has been correlated with the extrusion conditions and is given by the following equation, which is applicable to this particular extruder type [16]:

(13)

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 sample, wet basis) (unpublished correlations).

Compression Test

The compression tests were performed at room temperature (25°C) using a Zwick Universal Testing Machine (Zwick, model 1120, Ulm, Germany). The samples were compressed between two parallel plates of diameter 10 cm each, at a crosshead speed of 0.5 mm/s, with 100 N load cell. Force and deformation were recorded and the resulting stress-strain compression curves were constructed. A drop of ≥1 N force during compression was considered as the major fracture. At the fracture point, breaking stress was calculated as:

(14)

where F_B in the breaking force (N); and A the area of the compressed specimen (mm²).

Corresponding strain was calculated as:

(15)

where ΔL is deformation (mm); and L₀ is the length of compressed specimen (mm). The results presented are the mean values of four replications.

RESULTS AND DISCUSSION

Typical compression curves of legume extrudates are presented in Fig. 2. The compression curve indicates the presence of three zones. In the first zone, there is a sharp rise of stress with deformation, which may be attributed to the toughness of the product. In the second zone, multiple fractures occur, as evidenced by several ups and downs in the curve, which still show a marginal increasing trend. The third zone is characterized by a sharp increase of the stress with an increase in the extent of compression. The breaking stress can be considered as the end of the linear part of the compression curve (first zone).

Figure 2 Typical stress-strain curve for corn legume extudates at 200°C, 200 rpm, 4.68 kg/h, 16% feed moisture content and 50% corn to legume ratio (CB: corn/white bean, CL: corn/lentil).

The application of regression analysis for each type of sample showed that the optimum number of parameters, which affect breaking stress and corresponding strain, is five. These parameters are σ _B0, n_T , n _τ, n_x , and n_c for breaking stress and ϵ _B0 , m_T , m _τ, m_x , and m_c, for the corresponding strain. The screw rotation speed did not affect significantly the mechanical properties of the extrudates. The corresponding parameter estimates for all materials are shown on Table 3. In 3–6, mechanical properties of the extrudates are shown 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 mechanical properties using the mathematical model and the parameters of Table 3. Table 4 summarizes experimental and predicted values of mechanical properties for all extrudates.

Table 3 Results of parameter estimation

	Breaking stress parameters
	σB0	nT	nτ	nX	nC	SR,B	SE,B
Corn/White Bean	24.483	−0.648	−0.898	2.149	−0.248	3.241	18.747
Corn/Lentil	37.234	−1.195	−0.866	1.832	−0.309	2.508	30.315
	Strain parameters
	ϵB0	mT	mτ	mX	mC	SR,ϵ	SE,ϵ
Corn/White Bean	0.595	0.870	0.526	−0.855	0.195	0.015	0.057
Corn/Lentil	0.687	0.578	1.077	−0.811	0.240	0.014	0.055

Table 4 Experimental and predicted values of mechanical properties of corn-legume based extrudates

Extrusion conditions & material characteristics						Mechanical properties
Material	C (%)	X (% wb)	T (°C)	N (rpm)	τ (s)	σB, exp (kPa)	σB, pre (kPa)	APE* %	ϵB, exp	ϵB, pre	APE* %
Corn/white bean	10	13	200	200	35	75	71	5.69	0.31	0.32	2.26
	10	16	150	200	33	137	140	2.01	0.21	0.20	4.35
	10	16	200	200	51	80	79	1.62	0.34	0.32	4.75
	10	16	200	200	36	107	108	0.79	0.26	0.27	3.57
	10	16	200	200	28	136	136	0.18	0.25	0.24	5.88
	10	16	260	200	38	87	86	1.52	0.36	0.35	2.69
	10	19	200	200	36	156	153	1.94	0.23	0.24	2.25
	30	16	200	200	36	79	82	3.94	0.33	0.33	1.07
	50	13	150	200	37	55	54	2.07	0.36	0.35	3.36
	50	13	150	200	32	64	62	3.61	0.33	0.32	2.14
	50	13	200	200	49	38	35	7.78	0.53	0.52	2.26
	50	13	200	200	35	48	47	1.88	0.44	0.43	1.43
	50	13	200	200	27	61	59	2.50	0.39	0.38	2.57
	50	13	260	200	37	36	38	4.54	0.56	0.57	0.91
	50	14.5	200	200	35	59	59	0.62	0.39	0.40	2.07
	50	16	150	200	45	69	71	2.86	0.33	0.32	1.96
	50	16	150	200	38	84	82	2.21	0.30	0.30	1.01
	50	16	150	200	33	93	94	0.81	0.28	0.27	1.84
	50	16	150	250	31	99	100	0.81	0.27	0.26	1.87
	50	16	170	200	34	81	84	3.28	0.32	0.31	2.37
	50	16	200	150	38	71	68	4.85	0.37	0.38	3.40
	50	16	200	200	51	51	53	3.53	0.43	0.44	3.05
	50	16	200	200	42	63	63	0.66	0.41	0.40	2.19
	50	16	200	200	36	71	72	1.89	0.36	0.37	2.34
	50	16	200	200	30	88	85	3.05	0.32	0.34	4.80
	50	16	200	250	34	75	76	1.93	0.35	0.36	1.92
	50	16	230	200	53	44	46	4.55	0.52	0.51	1.06
	50	16	230	200	37	63	64	2.36	0.42	0.42	0.97
	50	16	230	200	28	80	81	1.07	0.36	0.37	2.59
	50	16	230	250	49	50	50	0.69	0.50	0.49	1.61
	50	16	260	200	56	40	41	3.47	0.58	0.59	0.97
	50	16	260	200	38	56	58	2.34	0.49	0.48	2.18
	50	17.5	200	200	36	83	87	4.59	0.33	0.34	4.04
	50	19	150	200	34	134	133	0.99	0.25	0.24	3.85
	50	19	200	200	52	75	74	1.02	0.38	0.39	2.38
	50	19	200	200	36	105	103	2.25	0.33	0.32	2.50
	50	19	200	200	28	127	130	2.09	0.29	0.28	3.25
	50	19	260	200	39	84	82	2.19	0.43	0.42	2.76
	70	16	200	200	36	67	67	0.18	0.38	0.39	3.52
	90	13	200	200	35	40	41	3.27	0.48	0.49	1.32
	90	16	150	200	33	82	81	0.87	0.32	0.31	3.69
	90	16	200	200	51	47	46	2.66	0.51	0.50	2.57
	90	16	200	200	36	64	63	2.90	0.42	0.41	1.64
	90	16	200	200	28	81	79	2.93	0.36	0.36	0.27
	90	16	260	200	38	52	50	4.40	0.54	0.54	0.47
	90	19	200	200	36	89	89	0.32	0.37	0.36	2.49
Corn/lentil	10	13	200	200	31	128	126	1.42	0.32	0.31	3.63
	10	16	150	200	29	270	273	1.00	0.21	0.21	0.83
	10	16	200	200	45	132	133	0.80	0.38	0.39	3.03
	10	16	200	200	32	182	180	0.96	0.27	0.27	0.62
	10	16	200	200	25	226	225	0.41	0.21	0.20	3.06
	10	16	260	200	34	124	124	0.33	0.34	0.34	1.39
	10	19	200	200	33	241	242	0.55	0.23	0.24	3.89
	30	16	200	200	32	129	128	0.71	0.36	0.35	2.96
	50	13	150	200	32	105	107	1.48	0.40	0.39	2.08
	50	13	150	200	30	110	112	1.75	0.36	0.37	2.34
	50	13	200	200	43	56	57	2.26	0.65	0.65	0.44
	50	13	200	200	31	78	77	1.66	0.44	0.45	3.15
	50	13	200	200	27	88	86	2.08	0.38	0.39	3.33
	50	13	260	200	33	52	53	1.57	0.58	0.57	1.94
	50	14.5	200	200	31	94	93	1.57	0.41	0.42	2.91
	50	16	150	200	40	128	127	0.73	0.42	0.43	1.91
	50	16	150	200	29	167	166	0.73	0.31	0.31	1.13
	50	16	170	200	30	140	138	1.21	0.35	0.34	2.09
	50	16	200	150	34	101	103	1.98	0.44	0.43	3.06
	50	16	200	200	45	83	81	2.55	0.59	0.58	2.33
	50	16	200	200	37	93	95	2.49	0.47	0.47	0.05
	50	16	200	200	32	107	110	2.41	0.38	0.39	3.93
	50	16	200	200	28	122	123	1.16	0.33	0.34	2.29
	50	16	200	200	25	135	137	1.34	0.29	0.30	3.32
	50	16	200	250	30	116	116	0.09	0.38	0.37	2.73
	50	16	230	200	33	92	90	2.31	0.44	0.45	1.16
	50	16	260	200	34	77	76	1.19	0.48	0.49	2.80
	50	17.5	200	200	32	130	128	1.65	0.36	0.37	3.28
	50	19	150	200	30	224	222	0.74	0.28	0.27	2.23
	50	19	200	200	47	106	108	1.69	0.52	0.52	0.24
	50	19	200	200	33	149	147	1.13	0.36	0.35	2.31
	50	19	200	200	25	185	185	0.07	0.26	0.27	2.20
	50	19	260	200	35	104	102	2.05	0.44	0.44	0.36
	50	19	150	200	30	224	222	0.74	0.28	0.27	2.23
	70	16	200	200	32	100	99	1.25	0.44	0.43	2.69
	90	13	200	200	31	62	64	3.15	0.53	0.52	1.39
	90	16	150	200	29	135	138	2.39	0.36	0.35	1.95
	90	16	200	200	45	69	67	2.26	0.65	0.66	2.09
	90	16	200	200	32	90	91	1.52	0.46	0.45	1.13
	90	16	200	200	25	112	114	1.85	0.33	0.35	4.56
	90	16	260	200	34	61	63	3.38	0.58	0.57	2.02
	90	19	200	200	33	121	123	1.51	0.40	0.40	1.25
*APE: absolute percentage error.

Figure 3 Breaking stress and corresponding strain of extrudates as a function of residence time and temperature (CB: corn/white bean; CL: corn/lentil).

Figure 4 Breaking stress and corresponding strain of extrudates as a function of feed moisture content and corn to legume ratio (CB: corn/white bean, CL: corn/lentil).

Figure 5 Comparative figures of breaking stress for all extrudates (CB: corn/white bean, CL: corn/lentil). (a) Breaking stress as a function of residence time. (b) Breaking stress as a function of corn/legume ratio. (c) Breaking stress as a function of temperature. (d) Breaking stress as a function of feed moisture content.

Figure 6 Comparative figures of corresponding strain for all extrudates (CB: corn/white bean, CL: corn/lentil). (a) Corresponding strain as a function of residence time. (b) Corresponding strain as a function of corn/legume ratio. (c) Corresponding strain as a function of temperature. (d) Corresponding strain as a function of feed moisture content.

Figure 3 shows that the breaking stress of the extrudates decreased with residence time, while the corresponding strain increased. That is, increased feed rate led to an increase in breaking stress and a decrease in strain (Eq. 3). Increased feed rate would influence the degree of fill, inducing the degradation of amylopectin networks, and change the melt rheological characteristics, thus leading to a greater elastic effect and changed product's porosity.[2,4,17] In particular, a rise in feed rate leads to an increased final viscosity and, consequently, to a decreased porosity. The latter may be responsible for the increased breaking stress and the reduction of the corresponding strain.

The extrusion temperature seems to affect the mechanical properties of corn/legume-based extrudates. As can be seen in Fig. 3, the breaking stress decreased with temperature, while the corresponding strain increased. Similar results were found in the past.[4,6,9] Increasing the temperature would decrease the melt viscosity, which favors the bubble growth and produces low density products with small and thin cells, thus increasing the crispness of extrudates and decreasing breaking stress.

The effect of the feed moisture content during extrusion cooking is important as it greatly affects the extrudate texture. Figure 4 indicates that the breaking stress of the extrudates increased with increasing feed moisture content and the corresponding strain decreased. These trends are in agreement with previous works.[9–11,14,15] It is known that the decrease of moisture content in extrusion cooking tends to increase the specific mechanical energy and, consequently, favors the macromolecular degradation of the starch through dextrinisation. The resulting melt gives more fragile structures, which leads to low-resistance cell walls and more structural fractures. Furthermore water leads to plasticization of food materials, which makes the snack, behave like a semi-solid mass rather than a brittle material. Hence, extrudates with high moisture content show enhanced levels of strain tolerance during compression with delayed fracture or even absence of fracture or failure.[10]

The addition of legume flour had a significant effect on the extrudates mechanical properties. As the corn to legume ratio increased the breaking stress decreased, while the corresponding strain increased (Fig. 4). Therefore, the addition of legume caused an increase of the breaking stress of the extrudates. This trend can be attributed to the legume proteins. Proteins can affect the water distribution in the produced matrix through their macromolecular structure and conformation, which affect the extensional properties of the extruded melts. They also contribute to extensive networking through covalent and non-bonding interactions that take place during extrusion. Similar results have been observed by other investigators.[6,13,15]

Figures 5 and 6 make clear that the product containing lentil flour had higher values of breaking stress and corresponding strain than the product with white bean. Furthermore, a stronger influence of temperature on lentil extrudate breaking stress was observed. Figure 6 shows the similarity of the corresponding strain of the two products. The main differentiation is that the lentil extrudate strain is more strongly affected by the residence time. In general speaking, differences in values observed among different legume blends could be attributed to differences in legume proteins and, especially, in protein quality.

It has been proven that the processing conditions and the material characteristic affect the porosity of corn-legume based extrudates.[16] The mechanical properties of extrudates, including breaking stress and corresponding strain, have in general been found to correlate positively with the extrudates' apparent density; increased apparent density corresponds to an increased breaking stress.[6,18,19] It is known that porosity and apparent density are negatively correlated.[16] The correlation of the extrudate porosity with breaking stress and corresponding strain showed that the properties had an exponential correlation. An increase in porosity can lead to a product with a lower breaking stress. Figure 7 depicts these trends.

Figure 7 Breaking stress and corresponding strain as a function of product porosity (CB: corn/white bean, CL: corn/lentil).

CONCLUSIONS

Mechanical properties of expanded corn-legume snacks produced on a twin-screw extruder depend on several process conditions. Extrusion temperature and residence time as well as material characteristics (feed moisture content, corn to legume ratio) have a significant effect on the extrudate breaking stress and the corresponding strain. Breaking stress of extrudates was found to decrease with temperature and residence time and to increase with feed moisture content and the ratio of legume. An opposite trend was observed for the corresponding strain. The use of lentil in mixtures for the production of snacks leads to a product with a higher breaking stress than the white bean. In addition, a stronger influence of temperature on the breaking stress was observed. With regard to the corresponding strain, the product with lentil has a slightly higher value than the others have, and it exhibits a stronger influence on residence time. The breaking stress and the porosity of the extrudates were correlated by an exponential relationship. An increase in porosity can lead to a product with lower breaking stress. A similar exponential relationship was produced between porosity and strain at fracture with the opposite trend. In conclusion, the addition of legumes (protein source) leads to harder extruded products. The breaking stress and the porosity are related to the crispness of the product, which is the most important textural attribute of ready-to-eat extruded snacks.

NOMENCLATURE

=

Table C corn/legume ratio (–) ef voidfraction (–) F feed rate (kg/s) K number of experimental measurements (–) M number of experiments (–) N screw speed (rpm) nC , mC corn/legume ratio constants (–) ni number of replicates (–) nN , mN, screw speed constants (–) nT , mT temperature constants (–) nX , mX feed moisture content constants (–) n τ, mτ residence time constants (–) p number of parameters (–) SE standard experimental error (kPa) or (–) SR standard deviation between experimental and predicted values (kPa) or (–) SST total sum of squares (kPa)^2 or (–) T extrusion temperature (°C) Vt true volume (cm^3) X feed moisture content (kg/100 kg wet basis) Greeks ϵ corresponding strain (–) σ breaking stress (kPa) τ mean residence time (s) Subscripts B at breaking stress i i^th experiment j j^th replicate r reference ϵ refers to strain σ refers to breaking stress

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 and Mr. Panagiotis Michailidis for technical assistance.