Drying kinetics of Brazil nuts

SILVA, Patrícia Cardoso; RESENDE, Osvaldo; FERREIRA JUNIOR, Weder Nunes; SILVA, Lígia Campos de Moura; QUEQUETO, Wellytton Darci; SILVA, Fabio Adriano Santos e

doi:10.1590/fst.64620

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Original Article • Food Sci. Technol (Campinas) 42 • 2022 • https://doi.org/10.1590/fst.64620 copy

Drying kinetics of Brazil nuts

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

The drying is one of the stages of processing Brazil nuts, being an important stage due to the high moisture content and water activity of the product. This study aimed to adjust mathematical models to the drying kinetics data of Brazil nuts, calculating the effective diffusion coefficient and obtaining activation energy for the drying process. Brazil nuts were collected in amazon region, and then the product was homogenized for processing. The nuts were subjected to drying in a forced ventilation oven at temperatures of 40, 50, 60, 70 and 80 °C in 4 replicates, each one consisting of approximately 200 g of samples in aluminum containers. Mathematical models were adjusted to the experimental data of the moisture content ratio. Thompson, Midilli, Logarithmic and Two Terms models are suitable for estimating the drying of Brazil nuts. The Two Terms model was selected to represent the drying phenomenon for presenting better results in the analyzed parameters. The effective diffusion coefficient increased with increasing temperature and the activation energy for the liquid diffusion in the drying was 35.69 kJ mol^-1.

Keywords:
Bertholletia excelsa H. B. K.; Two Terms model; coefficient of diffusion

Model designation	Model
$RX = 1 + a \cdot t + b \cdot t^{2}$	Wang and Sing	(2)
$RX = a \cdot exp (-k \cdot t) + (1-a) \cdot exp ({-k}_{1} \cdot t)$	Verma	(3)
$RX = exp ((-a- {(a^{2} +4 \cdot b \cdot t)}^{0 .5}) /2 \cdot b)$	Thompson	(4)
$RX = exp-k \cdot t^{n}$	Page	(5)
$RX = exp (-k \cdot t)$	Newton	(6)
$RX = a \cdot exp (-k \cdot t^{n}) + b \cdot t$	Midilli	(7)
$RX = a \cdot exp (-k \cdot t) + c$	Logarithmic	(8)
$RX = a \cdot exp (-k \cdot t)$	Henderson and Pabis	(9)
$RX = a \cdot exp (-k \cdot t) + (1-a) exp (-k \cdot a \cdot t)$	Two-Term Exponential	(10)
$RX = a \cdot exp ({-k}_{0} \cdot t) + b \cdot exp ({-k}_{1} \cdot t)$	Two Terms	(11)
$RX = a \cdot exp (-k \cdot t) + (1-a) \cdot exp (-k \cdot b \cdot t)$	Approximation of Diffusion	(12)

Model	40 °C		50 °C		60 °C		70 °C		80 °C
Model	SE	χ²	SE	χ²	SE	χ²	SE	χ²	SE	χ²
2	0.057	33.33	0.085	72.28	0.096	93.76	0.108	117.34	0.033	11.34
3	0.056	31.74	0.139	195.76	0.228	521.69	0.080	65.57	0.036	13.45
4	0.024	5.87	0.031	9.64	0.026	7.20	0.026	6.93	0.033	11.44
5	0.033	11.03	0.042	18.12	0.033	11.34	0.037	13.72	0.035	12.28
6	0.051	26.67	0.074	55.40	0.064	41.33	0.076	58.28	0.033	11.38
7	0.022	4.95	0.023	5.75	0.018	3.53	0.016	3.61	0.014	2.16
8	0.021	4.69	0.020	4.09	0.015	2.26	0.015	2.53	0.023	5.46
9	0.049	24.49	0.068	47.06	0.066	44.50	0.087	47.36	0.032	10.69
10	0.030	9.34	0.050	25.35	0.049	24.44	0.053	28.59	0.033	11.27
11	0.015	2.25	0.012	1.59	0.006	0.49	0.007	0.62	0.022	5.05
12	0.020	4.18	0.018	3.28	0.010	1.04	0.080	65.57	0.036	13.45

Model	40 °C		50 °C		60 °C		70 °C		80 °C
Model	R²	P	R²	P	R²	R²	P	R²	P	R²
2	96.55	14.37	87.20	22.86	90.08	96.55	14.37	87.20	22.86	90.08
3	96.83	12.32	82.50	24.70	47.36	96.83	12.32	82.50	24.70	47.36
4	99.39	4.76	98.98	7.36	99.23	99.39	4.76	98.98	7.36	99.23
5	98.86	6.58	98.09	10.33	98.42	98.86	6.58	98.09	10.33	98.42
6	97.15	14.04	93.97	23.62	94.04	97.15	14.04	93.97	23.62	94.04
7	99.52	5.28	99.44	5.88	99.66	99.52	5.28	99.44	5.88	99.66
8	99.53	5.95	99.58	5.88	99.77	99.53	5.95	99.58	5.88	99.77
9	97.47	12.76	95.06	20.19	95.29	97.47	12.76	95.06	20.19	95.29
10	99.25	7.48	97.34	16.35	97.41	99.25	7.48	97.34	16.35	97.41
11	99.78	3.29	99.84	2.28	99.95	99.78	3.29	99.84	2.28	99.95
12	99.58	4.23	99.66	3.30	99.89	99.58	4.23	99.66	3.30	99.89

Models	40 °C		50 °		60 °C		70 °C		80 °C
Models	AIC	BIC	AIC	BIC	AIC	BIC	AIC	BIC	AIC	BIC
4	-143	-139	-115	-111	-58	-54	-80	-78	-51	-49
7	-147	-140	-128	-122	-117	-111	-91	-86	-73	-70
8	-150	-144	-139	-134	-129	-124	-99	-95	-61	-58
11	-171	-165	-166	-159	-165	-159	-124	-120	-80	-78

Coefficients	40 °C	50 °C	60 °C	70 °C	80 °C
a	0.49788^ Significant at 1% probability level by t-test. nsNot significant by t-test.	0.67734**	0.30919**	0.31076**	0.00947^ns
k₀	0.05021**	0.39032**	0.05610**	0.08349**	-0.44738^ns
b	0.54105**	0.36077**	0.71286**	0.69761**	1.03581**
k₁	0.29317**	0.04324**	0.51527**	0.79612**	0.59619**

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[1] *Corresponding author: wedernunesiftm@gmail.com