Water Absorption Index and Water Solubility Index Prediction for Extruded Food Products

Figures & data

Table 1 Number of papers and literature data which were used for analysis

	WAI		WSI
Material	Number of papers	Number of data	Number of papers	Number of data
Cereal Products
Barley cv.	2	54	^FV	^FV
Corn	8	208	7	153
Oat	3	21	3	21
Rice cv.	11	94	9	67
Wheat	5	29	4	21
Legumes
Beans Ph. vulgaris L. cv. and Chickpeas C. Arietinum L. cv.	10	67	7	24
Model Foods
Banana, cassava, corn and wheat starch	15	76	10	80
Blends
Cereal Products
Corn:DDG ^a	2	45	^FV	^FV
Corn:Lentil	1	146	1	146
Rice:DDG ^a	1	18	^NR	^NR
Wheat:DDG ^a	3	33	^FV	^FV
Model Foods
Corn starch ^b :WPC ^c	3	40	3	40
Rice starch SPI ^d	1	28	^NR	^NR
Vegetables
Potato:DDG ^a	1	18	^NR	^NR
^aDried distillers grains from corn and wheat; ^bVarious levels of amylose; ^cWhey protein concentrate; ^dSoy protein isolate; ^FVFew values for statistical analysis; ^NRNot reported.

Table 2 Standard experimental error (), standard deviation between experimental and calculated values (), parameters of the model and the experimental limits of die temperature (T), feed moisture content (X), screw speed (S), and the mixture (M) for the WAI prediction

Material	Se	Sr	a	b	c	d	e	T max (°C)	T min (°C)	X max %	X min %	S max (rpm)	S mix (rpm)	M max %	M min %
Barley cv.	0.60	1.29	4.62	−0.69	0.44	0.86	—	210	110	26	10	230	50	—	—
Corn	0.42	0.69	5.23	0.07	0.16	0.35	—	230	60	28	11	840	30	—	—
Oat	0.24	0.55	2.26	−0.68	−0.14	−0.06	—	240	77	26	11	230	90	—	—
Rice cv.	1.12	1.21	5.97	0.09	0.60	0.01	—	250	95	30	12	500	100	—	—
Wheat	0.26	1.88	4.63	−1.07	−0.46	0.46	—	250	120	24	14	500	60	—	—
Beans and chickpeas cv.	0.42	1.51	4.07	0.11	0.49	0.05	—	205	90	30	15	300	25	—	—
Starch	1.08	3.06	7.54	1.23	0.91	−0.06	—	200	75	70	14.2	750	40	—	—
Blends
Corn:DDG ^a	0.40	0.74	0.04	0.11	−0.06	−7.46	−0.17	250	100	22	11	120	100	40	10
Corn:Lentil	0.28	0.53	4.39	0.28	0.15	1.00	−0.00	230	170	19	13	200	200	50	10
Rice:DDG ^a	0.41	1.21	7.54	0.17	0.32	1.00	−0.08	250	160	22	15	100	100	40	10
Wheat:DDG ^a	0.40	1.78	4.07	−0.60	−0.13	0.34	−0.12	250	120	22	12	350	100	40	10
Corn starch:WPC ^b	1.55	1.21	5.37	0.30	0.54	0.14	−0.08	180	70	30	2	200	45	50	5
Rice starch:SPI ^c	1.02	0.51	19.40	0.15	−0.33	1.00	−0.29	180	140	30	20	42	42	75	25
Potato:DDG^a	0.53	2.07	9.40	0.03	0.19	1.00	−0.12	250	160	22	15	100	100	40	10
^aDried distillers grains from corn and wheat; ^bWhey protein concentrate; ^cSoy protein isolate.

Table 3 Standard experimental error (), standard deviation between experimental and calculated values (), parameters of the model and the experimental limits of die temperature (T), feed moisture content (X), screw speed (S), and the mixture (M) for the WSI prediction

Material	Se	Sr	a	b	c	d	e	T max (°C)	T min (°C)	X max %	X min %	S max (rpm)	S mix (rpm)	M max %	M min %
Corn	5.96	11.99	19.76	−0.16	−0.34	−0.20	—	230	90	28	12.1	400	130	—	—
Oat	0.18	1.20	6.24	−0.08	−0.51	−0.07	—	240	77.5	26	11	230	90	—	—
Rice cv.	2.53	18.70	23.17	1.36	0.10	−0.04	—	200	100	30	12	300	150	—	—
Wheat	3.34	9.96	10.42	2.57	0.02	1.45	—	185	120	24	14	350	60	—	—
Beans and chickpeas cv.	2.96	16.58	33.98	−1.48	1.12	0.26	—	190	130	30	20	300	85	—	—
Starch	7.91	27.30	27.80	0.70	−0.41	−1.09	—	200	90	40	14.2	750	50	—	—
Blends
Corn:Lentil	6.23	7.57	12.76	0.52	−0.72	1.00	−0.11	230	170	19	13	200	200	50	10
Corn starch:WPC ^a	10.00	15.48	27.18	−0.20	0.02	0.60	−0.11	180	70	30	2	200	43	50	5
^aWhey protein concentrate.

Figure 1 Effect of (a) die temperature °C; (b) feed moisture content %; (c) screw speed rpm on WAI for barley (▴), corn (•), oat (■), rice (x), wheat (◊), beans (○), and starch (□). Lines are calculated model values using parameters given in Table 2.

Figure 2 Effect of (a) die temperature °C; (b) feed moisture content %; (c) screw speed rpm on WSI for corn (•), oat (■), rice (x), wheat (◊), beans (○), and starch (□). Lines are calculated model values using parameters given in Table 3.

Figure 3 Effect of (a) die temperature °C; (b) feed moisture content %; (c) mix lever % on WAI for: (1) (▲) corn:DDG, (2) (•) corn:lentil, (3) (■) rice:DDG, (4) (x) wheat:DDG, 5 (◊) corn starch:WPC, (6) (○) rice starch:SPI, and (7) (□) potato:DDG. Lines are calculated model values using parameters given in Table 2.

Figure 4 The lack of fit () and standard experimental error () as a function of the number of parameters: (a) predicted model for WAI of rice; (b) predicted model for WSI of blend corn:lentil.

Table 4 Confidence intervals (95%) for the parameters of the model for the WAI prediction

	Confidence interval
	a		b		c		d		e
Material	Lower	Upper	Lower	Upper	Lower	Upper	Lower	Upper	Lower	Upper
Barley cv.	3.96	5.29	−1.45	−0.02	−0.14	1.02	0.59	1.15	—	—
Corn	5.15	5.31	0.09	0.23	0.09	0.23	0.31	0.39	—	—
Oat	2.01	2.53	−1.00	−0.37	−0.52	0.23	−0.47	0.34	—	—
Rice cv.	5.71	6.25	0.43	0.77	0.43	0.77	−0.11	0.14	—	—
Wheat	3.10	4.64	−1.66	−0.49	−1.07	0.15	0.28	0.66	—	—
Beans and chickpeas cv.	4.18	5.16	−0.26	0.48	0.08	0.91	−0.06	0.17	—	—
Starch	6.19	8.94	0.78	1.69	0.07	1.75	−0.24	0.11	—	—
Blends
Corn:DDG ^a	0.03	0.06	−0.01	0.23	−0.18	−0.05	−8.00	−6.91	−0.22	−0.14
Corn:Lentil	4.27	4.54	0.20	0.37	0.08	0.22	1.00	1.00	−0.02	−0.01
Rice:DDG ^a	7.04	8.21	−0.03	0.37	0.13	0.51	1.00	1.00	−0.15	−0.02
Wheat:DDG ^a	3.32	4.83	−1.12	−0.09	−0.72	0.46	0.09	0.59	−0.27	0.03
Corn starch:WPC ^b	3.58	7.14	−0.07	0.69	0.21	0.86	−0.16	0.45	−0.28	0.1
Rice starch:SPI ^d	14.60	24.78	−1.40	1.70	−1.29	0.62	1.00	1.00	−0.50	−0.08
Potato:DDG ^a	9.00	10.01	−0.10	0.18	0.06	0.33	1.00	1.00	−0.17	−0.08
^aDried distillers grains from corn and wheat; ^bWhey protein concentrate; ^cSoy protein isolate.

Table 5 Confidence intervals (95%) for the parameters of the model for the WSI prediction

	Confidence interval
	a		b		c		d		e
Material	Lower	Upper	Lower	Upper	Lower	Upper	Lower	Upper	Lower	Upper
Corn	16.00	30.47	0.45	0.12	−0.73	0.04	−0.51	0.12	—	—
Oat	5.52	7.77	−0.32	0.16	−0.75	−0.26	−0.34	0.19	—	—
Rice cv.	4.27	43.81	0.45	2.27	−0.64	0.85	−0.92	0.83	—	—
Wheat	0.09	6.31	−0.33	4.80	−1.78	1.82	0.65	2.26	—	—
Beans and chickpeas cv.	11.83	42.99	−3.32	0.35	0.03	2.22	−0.36	0.89	—	—
Starch	51.44	82.76	−0.20	1.61	−1.05	0.22	−0.49	−0.70	—	—
Blends
Corn:Lentil	10.91	14.65	0.14	0.92	−1.02	−0.42	1.00	1.00	−0.18	−0.05
Corn starch:WPC ^a	13.66	40.71	−1.30	0.89	−0.30	0.34	−0.05	1.26	−0.48	0.25
^aWhey protein concentrate.