MATHEMATICAL MODELING AND HYSTERESIS OF SORPTION ISOTHERMS FOR PADDY RICE GRAINS

Zeymer, Juliana S.; Corrêa, Paulo C.; Oliveira, Gabriel H. H.; Baptestini, Fernanda M.; Campos, Renata C.

doi:10.1590/1809-4430-Eng.Agric.v39n4p524-532/2019

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Scientific Papers, Post-Harvest Science and Technology • Eng. agríc. 39 (4) • Jul-Aug 2019 • https://doi.org/10.1590/1809-4430-Eng.Agric.v39n4p524-532/2019 copy

MATHEMATICAL MODELING AND HYSTERESIS OF SORPTION ISOTHERMS FOR PADDY RICE GRAINS

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Knowledge on sorption isotherms is important for predicting drying and storage processes of a product. A sorption isotherm can be generated from two processes: desorption and adsorption. The lag between these two curves is called hysteresis. Static method was used to obtain the equilibrium moisture content of paddy rice grains, in different temperature (10, 20, 30, 40 and 50 ± 1°C) and relative humidity (between 11 and 76% ± 2%) conditions. Equilibrium moisture content data were correlated with eight mathematical models and. The Chung Pfost model had the best fit to the experimental data. Desorption and adsorption isotherms, represented by the Chung Pfost model, showed a sigmoidal shape, characteristic of type II curve. Equilibrium moisture content values obtained by desorption were higher than those obtained by adsorption, evidencing the hysteresis phenomenon.

adsorption; desorption; hygroscopic equilibrium; relative humidity; temperature

Saline solution	Temperature (°C)

	10	20	30	40	50
LiCl	11.3	11.3	11.3	11.2	11.1
MgCl₂	33.5	33.1	32.4	31.6	30.5
Mg(NO₃)₂	57.4	54.4	51.4	49.9	45.4
NaCl	75.7	75.5	75.1	74.7	74.4

Model name	Model	Equation number
Modified Henderson	$U_{e} = {[\frac{\ln (1 - a_{w})}{- a (T + b)}]}^{\frac{1}{c}}$	(1)
Modified Halsey	$U_{e} = {[\frac{\exp (a - bT)}{- \ln (a_{W})}]}^{\frac{1}{c}}$	(2)
Modified Oswin	$U_{e} = (a + bT) {[\frac{a_{W}}{1 - a_{W}}]}^{\frac{1}{c}}$	(3)
Copace	$U_{e} = \exp [a - (bT) + ({ca}_{W})]$	(4)
Sigma-Copace	$U_{e} = \exp [a - (bT) + c \exp (a_{W})]$	(5)
Chung Pfost	$U_{e} = a - b \ln [- (T + c) \ln (a_{W})]$	(6)
Smith	$U_{e} = a - (bT) - cln (1 - a_{W})$	(7)
Harkins Jura	$U_{e} = \frac{\exp (a - bT)}{c - \ln (a_{W})}$	(8)

Model	Parameters*	R² (%)	SEE (decimal)	MRE (%)	Residual plot
Modified Henderson	a = 0.00005 b = 59.29579 c = 2.01760	99.08	0.74	8.07	Random
Modified Halsey	a = 4.978758 b = 0.011060 c = 2.044422	97.43	1.19	13.65	Biased
Modified Oswin	a = 14.25468 b = -0.06960 c = 2.84464	98.80	0.84	8.89	Biased
Copace	a = 1.839119 b = 0.005876 c =1.639578	98.14	1.04	11.45	Biased
Sigma-Copace	a = 1.032387 b = 0.005735 c = 0.959289	96.86	1.35	15.65	Biased
Chung Pfost	a = 37.41332 b = 6.23300 c = 49.64200	99.60	0.49	5.16	Random
Smith	a = 7.669984 b = 0.080895 c = 9.388660	98.34	0.99	11,45	Biased
Harkins-Jura	a = 2.965899 b = 0.005945 c = 0.620576	98.92	0.80	8.69	Random

Model	Parameters*	R² (%)	SEE (decimal)	MRE (%)	Residual plot
Modified Henderson	a = 0.00008 b = 62.29053 c = 1.87538	99.11	0.70	9.59	Random
Modified Halsey	a = 4.478713 b = 0.010657 c = 1.915281	97.81	1.11	14.78	Biased
Modified Oswin	a = 13.11786 b = -0.06562 c = 2.65584	98.96	0.76	9.88	Random
Copace	a = 1.700181 b = 0.006091 c =1.754145	98.45	0.93	12.22	Random
Sigma-Copace	a = 0.841173 b = 0.005930 c = 1.024176	97.35	1.21	16.84	Biased
Chung Pfost	a = 35.93673 b = 6.08728 c = 50.48329	99.64	0.45	5.99	Random
Smith	a = 6.747202 b = 0.077581 c = 9.217345	98.80	0.82	11.25	Biased
Harkins-Jura	a = 2.809354 b = 0.006131 c = 0.531248	99.02	0.74	9.82	Random

Temperature (°C)	Relative humidity (%)	U_e desorption (% d.b.)	U_e adsorption (% d.b.)	Hysteresis (% d.b.)
10	13.30	7.20	6.50	0.700
	40.00	12.30	11.00	1.300
	59.00	15.60	14.50	1.100
	81.00	21.50	20.60	0.900
20	12.00	6.50	5.80	0.700
	35.00	11.40	10.20	1.200
	55.00	13.70	12.60	1.100
	75.50	18.90	18.00	0.900
30	11.20	5.50	5.00	0.500
	32.40	10.20	9.00	1.200
	47.20	12.20	11.10	1.100
	75.60	18.10	17.20	0.900
40	11.50	4.70	4.10	0.600
	32.10	8.90	8.00	0.900
	49.80	11.80	10.70	1.100
	75.40	17.50	16.60	0.900
50	11.40	2.60	2.00	0.600
	31.40	8.00	7.10	0.900
	46.30	10.10	9.20	0.900
	74.50	16.00	15.30	0.700

Associação Brasileira de Engenharia Agrícola SBEA - Associação Brasileira de Engenharia Agrícola, Departamento de Engenharia e Ciências Exatas FCAV/UNESP, Prof. Paulo Donato Castellane, km 5, 14884.900 | Jaboticabal - SP, Tel./Fax: +55 16 3209 7619 - Jaboticabal - SP - Brazil
E-mail: revistasbea@sbea.org.br

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[1] 1* Corresponding author. Federal University of Viçosa/ Viçosa - MG, Brazil. E-mail: jujuszeymer@gmail.com