Mechanical Properties of Corn-Legume Based Extrudates

Figures & data

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)

Figure 1 The lack of fit (S_R ) and standard experimental error (S_E ) as a function of the number of parameters.

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

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).

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

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