Drying kinetics of crushed mass of ‘jambu’: Effective diffusivity and activation energy

Gomes, Francileni P.; Osvaldo, Resende; Sousa, Elisabete P.; Oliveira, Daneil E. C. de; Araújo Neto, Francisco R. de

doi:10.1590/1807-1929/agriambi.v22n7p499-505

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ARTICLE • Rev. bras. eng. agríc. ambient. 22 (7) • July 2018 • https://doi.org/10.1590/1807-1929/agriambi.v22n7p499-505 copy

Drying kinetics of crushed mass of ‘jambu’: Effective diffusivity and activation energy

Cinética de secagem da massa triturada de jambu: Difusividade efetiva e energia de ativação

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The aim of this paper was to analyze the drying kinetics, test the Akaike information criterion (AIC) and Schwarz’s Bayesian information criterion (BIC) in the selection of models, determine the effective diffusivity and activation energy of the crushed mass of ‘jambu’ leaves for different conditions of temperature and layer thicknesses. The experiment was carried out at the Food Laboratory of the Brazilian Agricultural Research Corporation (Embrapa) in Macapá-AP. Drying was carried out in air circulation oven with speed of 1.0 m s^-1 at various temperatures (60, 70 and 80 ºC) and layer thicknesses (0.005 and 0.010 m). The experimental data were fitted to 11 mathematical models. Coefficient of determination (R²), mean relative error (P), mean estimated error (SE), Chi-square test (χ²), AIC and BIC were the selection criteria for the models. For the effective diffusivity, the Fick’s diffusion model was used considering the flat plate geometry. It was found that Midilli and Logarithmic models showed the best fit to the experimental data of drying kinetics. Effective diffusion coefficient increases with increment in the thickness of the material and with the temperature elevation. Activation energy of the material was of 16.61 kJ mol^-1 for the thickness of 0.005 m, and 16.97 kJ mol^-1 for the thickness of 0.010 m. AIC and BIC can be additionally included to select models of drying.

Key words:
vegetable; convective drying; Acmella oleracea

Model	Temp. (°C)	0.005 m					0.010 m
		Coefficients
		a	b	k	n	g	a	b	k	N	g
Approximation of diffusion	60	1.6 x 10⁴	1.8 x 10²	1.2		---	2.6 x 10⁴	2.7 x 10²	0.9		---
	70	3.2 x 10⁴	1.1 x 10²	2.7		---	3.0 x 10⁴	1.2 x 10³	1.7		---
	80	3.4 x 10⁴	7.1 x 10⁴	0.0		---	4.2 x 10³	4.9 x 10³	0.8		---
Two terms	60	1.3 x 10⁶	1.3 x 10⁶	1.2 x 10³		7.7 x 10²	1.3 x 10⁶	1.3 x 10⁶	1.5 x 10²		2.5E+02
	70	9.7 x 10⁵	9.7 x 10⁵	2.3 x 10²		6.5 x 10²	1.9 x 10⁵	1.9 x 10⁵	5.2		5.4
	80	1.3 x 10⁶	1.3 x 10⁶	2.3 x 10²		2.1 x 10²	1.9 x 10⁵	1.9 x 10⁵	7.5		7.3
Two-term Exponential	60	8.4 x 10³	---	8.9		---	1.9E+03	---	2.6		---
	70	2.0 x 10³	---	5.6		---	3.1 x 10³	---	4.4		---
	80	5.1 x 10³	---	11.5		---	6.7 x 10³	---	7.4		---
Thompson	60	5.6 x 10⁵	2.9 x 10³	---		---	5.4 x 10⁵	2.3 x 10³	---		---
	70	3.8 x 10⁵	2.9 x 10³	---		---	6.9 x 10⁵	3.3 x 10³	---		---
	80	7.6 x 10⁵	6.1 x 10³	---		---	6.6E+05	3.7 x 10³	---		---
Verma	60	1.8 x 10⁴	---	1.2		1.2	3.0 x 10⁴	---	0.9		1.0
	70	3.2 x 10⁴	---	2.7		2.8	4.0 x 10⁴	---	1.8		1.8
	80	2.8 x 10²	---	0.1		0.1	5.2 x 10²	---	0.2		0.2

Model		60 °C – 0.005 m					70 °C – 0.005 m								80 °C – 0.005 m
Model		SE (decimal)	P (%)	χ² (decimal) x 10^-3	R² (%)		SE (decimal)		P (%)		χ² (decimal) x 10^-3		R² (%)		SE (decimal)		P (%)		χ² (decimal) x 10^-3		R² (%)
Wang & Singh		0.007	4.2	0.05	99.94		0.011		6.2		0.13		99.87		0.011		2.3		0.13		99.84
Page		0.030	18.5	0.90	99.06		0.025		22.1		0.62		99.38		0.026		6.9		0.65		99.22
Newton		0.063	41.1	3.94	95.72		0.058		51.2		3.35		96.50		0.065		18.8		4.21		94.71
Midilli		0.007	3.5	0.05	99.96		0.008		4.1		0.07		99.94		0.008		1.5		0.06		99.93
Logarithmic		0.007	3.8	0.05	99.96		0.009		5.8		0.08		99.92		0.008		1.7		0.06		99.93
Henderson & Pabis		0.056	36.4	3.17	96.70		0.050		44.5		2.49		97.52		0.055		15.4		3.04		96.36
	60 °C – 0.010 m							70 °C – 0.010 m								80 °C – 0.010 m
	SE (decimal)		P (%)	χ² (decimal) x 10^-3		R² (%)		SE (decimal)		P (%)		χ² (decimal) x 10^-3		R² (%)		SE (decimal)		P (%)		χ² (decimal) x 10^-3		R² (%)
Wang & Singh	0.009		7.3	0.09		99.91		0.013		4.2		0.18		99.81		0.008		1.8		0.06		99.93
Page	0.028		24.1	0.78		99.16		0.023		8.6		0.54		99.45		0.026		8.1		0.70		99.19
Newton	0.061		52.2	3.71		95.88		0.067		26.7		4.52		95.19		0.061		20.4		3.78		95.42
Midilli	0.007		5.1	0.05		99.95		0.007		1.6		0.05		99.95		0.006		1.3		0.04		99.96
Logarithmic	0.007		6.2	0.05		99.94		0.010		3.1		0.10		99.90		0.006		1.3		0.04		99.96
Henderson & Pabis	0.054		46.5	2.91		96.89		0.058		22.6		3.35		96.58		0.054		17.5		2.89		96.65

Model/Treatments	Wang & Singh		Midilli		Logarithmic
Model/Treatments	BIC	AIC	BIC	AIC	BIC	AIC
60 °C – 0.005 m	-166.91	-170.57	-166.66	-172.75	-169.44	-174.32
60 °C – 0.010 m	-159.29	-163.39	-182.00	188.84	-167.35	-172.81
70 °C – 0.005 m	-133.46	-136.87	-144.68	-150.35	-141.36	-145.90
70 °C – 0.010 m	-148.28	-152.17	-177.95	-184.43	-161.70	-166.88
80 °C – 0.005 m	-121.09	-124.22	-132.93	-138.16	-134.09	-138.26
80 °C – 0.010 m	-162.98	-166.63	-172.85	-178.94	-175.79	-180.67

Model	Temperature (°C)	0.005 m				0.010 m
		Coefficients
		a	b	k	n	a	b	k	n
Midilli	60	1.003416	-0.044528	0.073914	1.061702	1.004232	-0.025116	0.043710	1.115153
	70	1.005617	-0.032338	0.139091	1.123543	1.001743	-0.024922	0.051771	1.249553
	80	1.010381	-0.090987	0.075519	1.129995	1.007867	-0.055776	0.048866	1.048359
Logarithmic	60	3.286140	-2.279470	0.037430	-	3.378600	-2.368020	0.022860	-
	70	1.951988	-0.936192	0.095699	-	4.302200	-3.286370	0.022420	-
	80	12.695900	-11.680600	0.013600	-	6.177150	-5.167520	0.017370	-

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[1] fpgleni@yahoo.com.br (Corresponding author)