Evaluating Some Empirical Models for Predicting Water Absorption in African Breadfruit (Treculia Africana) Seeds

Figures & data

Table 1 Some physical characteristics of ABF seeds

Parameter	Mean values
1,000 seed mass (g)	210.50 ± 4.50
aMajor diameter (mm)	10.57 ± 0.75
aMinor diameter (mm)	5.76 ± 0.52
aThickness (mm)	5.12 ± 0.46
bSeed coat thickness (mm)	0.34 ± 0.12
Sphericity (%)	64.3

^a N = 100.

^b N = 10.

Figure 1. Water absorption characteristics curves for T. africana seeds at various soaking temperatures.

Table 2 Original and linear forms of the water absorption models

Model	Original form	Linear form
aPilosof et al.18:			(1)
bSingh–Kulshrestha19:			(2)
cPeleg13:			(3)

^a M—Total moisture uptake at time t (g/100 g solid); A-water absorption capacity (g/g dry solid); B-half-life (hour).

^b M _o —Initial moisture content (g/g dry basis); M—moisture content at any time t (g/g dry solid); A—water absorption capacity (g/g dry solid); B—water absorption rate constant (per hour).

^c M _o —Initial moisture content (% dry wt. basis); M—moisture content after time t (% dry wt. basis); A—water absorption rate constant (hour per % dry wt. Basis not clear); B—characteristic water absorption constant (per % dry wt. basis).

Table 3 Regression coefficients in the water absorption models

Model	Temperature (°C)	A	B	r ^2
Pilosof	30	70.122	4.877	0.970
	40	73.552	3.630	0.995
	50	68.721	0.892	0.968
	60	73.611	1.158	0.948
	70	70.029	0.617	0.984
Peleg	30	7.421 × 10^−2	1.383 × 10^−2	0.916
	40	4.887 × 10^−2	1.373 × 10^−2	0.991
	50	1.170 × 10^−2	1.503 × 10^−2	0.992
	60	1.801 × 10^−2	1.298 × 10^−2	0.950
	70	6.689 × 10^−3	1.451 × 10^−2	0.995
Singh–Kulshreshta	30	0.918	0.136	0.992
	40	0.807	0.256	0.997
	50	0.846	0.700	0.956
	60	0.772	1.024	0.915
	70	0.829	1.268	0.969

Table 4 Temperature dependence of the absorption rate constants

Model	Preexponential (K o ) (g/100 g per h)	Activation energy (E a ) (MJ/mole)	r ^2
Peleg	22.61	50.37	a0.856
Singh–Kulshrestha	22.91	50.91	b0.955
Pilosof	18.65	38.92	a0.875

^aSignificant at P < 0.05.

^bSignificant at P < 0.01.

Table 5 Published water absorption parameters for some cereals and legumes

Material	Temperature range (°C)	M e (g/100 g db)	E a (MJ/mol)	Source
Maize	10–50	a35–70	16.23	Sopade et al.15
Millet	10–50	a72–80	15.88	Sopade et al.15
Sorghum	10–50	a99–110	13.99	Sopade et al.15
Soybean	37–80	187–206	a38.52	Singh and Kulshrestha19
	2–40	125–177	a19.02	Sopade and Obekpa14
Cowpea		a163–176	19.04	Sopade and Obekpa14
Groundnut		a80–94	19.56	Sopade and Obekpa14
Pigeon pea	35–65	a222–348	50.85	Singh and Kulshrestha19
Chickpea	5–42	14.8–15.1	27–30	Hung et al.16
Field pea	5–42	16.2–17.8

^aValues calculated from the reported kinetic parameter by authors.

Figure 2. Temperature dependence of the absorption rate constants.

Table 6 Estimates of equilibrium moisture (M _e ) and time to reach equilibrium (t _e )

Parameter	Temperature (°C)	Pilosof	Peleg	Singh–Kulshreshta
M e (g/100 g solid)	30	70.12	81.59	91.80
	40	73.88	82.11	80.70
	50	68.72	75.81	84.60
	60	73.61	86.32	77.20
	70	70.03	78.19	82.90
Mean		71.21	79.84	83.35
Coefficient of variation (%)		3.14	5.39	5.83
*t e (h)	30	53.09	139.71	139.71
	40	42.65	74.22	74.21
	50	13.32	27.14	27.14
	60	15.81	18.56	18.55
	70	9.25	14.98	14.98

Table 7 Chi-square and root mean square deviation (RMSD) values

		Pilosof		Peleg		Singh–Kulshrestha
Temperature (°C)	df	χ ^2	RMSD	χ ^2	RMSD	χ ^2	RMSD
30	14	2.05	0.63	4.61	1.10	2.20	0.71
40	14	0.36	0.21	0.51	0.36	0.42	0.31
50	11	2.15	0.72	2.34	0.74	2.53	0.87
60	10	3.07	0.93	3.52	0.95	3.35	0.99
70	10	1.24	0.61	1.31	0.60	0.95	0.54
				df = 14	df = 11		df = 10
Critical χ ^2 values at 5% sig. level:				23.68	19.68		18.31
at 1% sig. level:				29.14	27.42		23.21

Figure 3. Comparism of the predicted moisture contents (M and M − M _o ) with the experimental data at 30^oC.

Figure 4. Experimental and predicted moisture contents at 30^oC.

Figure 5. Experimental and predicted moisture contents at 40^oC.

Figure 6. Experimental and predicted moisture contents at 50^oC.

Figure 7. Experimental and predicted moisture contents at 60^oC.

Figure 8. Experimental and predicted moisture contents at 70^oC.

Figure 9. Residual plot of moisture content based on Pilosof's absorption model.

Figure 10. Residual plot of moisture content based on Peleg's absorption model.

Figure 11. Residual plot of moisture content based on Singh–Kulshrestha absorption model.

Pilosof , A.M.R. , Boquet , R. and Bartholomai , G.B. 1985 . Kinetics of water uptake by food powders . Journal of Food Science , 50 : 278 – 282 .

 Google Scholar

Singh , B.P.N. and Kulshrestha , S.P. 1987 . Kinetics of water sorption by Soybean and Pigeonpea grains . Journal of Food Science , 52 : 1538 – 1541, 1544 .

 Web of Science ®Google Scholar

Peleg , M.A. 1988 . An empirical model for the description of moisture sorption curves . Journal of Food Science , 53 : 1216 – 1219 .

 Web of Science ®Google Scholar

Sopade , P.A. , Ajisegiri , E.S. and Badau , M.H. 1992 . The use of Peleg's equation to Model water absorption in some cereal grains during soaking . Journal of Food Engineering , 15 : 269 – 283 . [CROSSREF]

 Web of Science ®Google Scholar

Sopade , P.A. and Obekpa , J.A. 1990 . Modelling water absorption in soybean, cowpea and peanuts at three temperatures using Peleg's equation . Journal of Food Science , 55 : 1084 – 1087 .

 Web of Science ®Google Scholar

Hung , T.V. , Liv , L.H. , Black , R.G. and Trewhella , M.A. 1993 . Water absorption in chickpea (C. arientum) and field pea (P. sativum) cultivars using Peleg's model . Journal of Food Science , 58 : 848 – 852 .

 Google Scholar