MODELING OF THE KINETICS OF CRYOGENIC FREEZING OF LIMA BEAN SEEDS AS A FUNCTION OF INITIAL WATER CONTENT

Luciano, Karina M da F.; Mata, Mario E. R. M. Cavalcanti; Fortes, Mauri; Duarte, Maria E. M.

doi:10.1590/1809-4430-Eng.Agric.v39n3p331-340/2019

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Scientific Paper, Post-Harvest Science and Technology • Eng. agríc. (Online) 39 (3) • May-Jun 2019 • https://doi.org/10.1590/1809-4430-Eng.Agric.v39n3p331-340/2019 copy

MODELING OF THE KINETICS OF CRYOGENIC FREEZING OF LIMA BEAN SEEDS AS A FUNCTION OF INITIAL WATER CONTENT

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Cryopreservation is a technique used to preserve genetic material at ultra-low temperatures in cryogenic germplasm banks. In order to enable the cryopreservation of a seed, it is necessary to study its appropriate freezing temperature and its water content, because seeds reach maximum physiological quality with high water contents, and they tolerate drying when they are orthodox seeds, but they may not tolerate cryopreservation. Therefore, the objective of this study was to analyze the influence of initial water content (50 to 10% wet basis) on the kinetic behavior of the lima bean seed at the temperature of −150 °C, in addition to determining changes in its physiological quality (germination and vigor) when cryopreserved (−150 °C) for 30 days with the variation of initial water contents (50 to 10% wet basis). For this purpose, changes in lima bean size (length, width, and thickness), sphere-equivalent radius and volume, and kinetics of seed cryopreservation as a function of its water content. The Fourier model and the Cavalcanti-Mata & Duarte models I and II were used for cryopreservation modeling, in addition to proposing a new model for cryopreservation kinetics in which water content determines the kinetic behavior. The conclusion was that the water content of 10% wb should be used for the lima bean seed cryopreservation since its physiological quality was not affected by cryopreservation at −150 °C. The model that best represents the experimental data is Cavalcanti Mata & Duarte Model II.

KEYWORDS
Phaseolus lunatus; Cryogenic; Modeling; Germplasm bank

Parameters	Water content, % wet basis
Parameters	10	20	30	40	50
Length, mm	15.968	16.614	16.963	17.766	20.756
Width, mm	11.079	11.176	11.506	11.642	13.412
Thickness, mm	5.626	5.631	5.999	6.274	6.582
Volume, mm³	521.485	546.363	614.217	679.238	966.319
Radius of equivalent sphere, mm	4.983	5.065	5.265	5.446	6.114

Model proposed – Cavalcanti Mata & Duarte
X* %wb	A ₁	A ₂	log X ₁	log X ₂	h ₁	h ₂	R²	P	Residue
40	−0.02703	1.88261	129.555	−19.745	−0.03676	−0.0031	99.36	0.05103	Biased
5	0.02193	1.05358	8.73514	256.106	−0.07038	−0.00547	99.85	0.16512	Biased

X * % wb	Phases	Fourier Model 1^st term of the series α mm²/s	Model Proposed α mm²/s
40 %	Cooling	0.038	0.0368
40 %	Freezing	0.0129	0.0031
	Mean	0.0135
50 %	Cooling	0.0129	0.07038
50 %	Freezing	0.1956	0.00547
	Mean	0.1879

Water content (% wb)	GERMINATION (%)		VIGOR (%)
Water content (% wb)	Before cryopreservation	30 days after cryopreservation	Before cryopreservation	30 days after cryopreservation
10	98.5 Aa	98.5 Aa	87.5 Aa	87.5 Aa
20	98.5 Aa	99.0 Aa	87.5 Aa	86.0 Bb
30	98.5 Aa	98.0 Ab	87.5 Aa	85.0 Cc
40	98.5 Aa	97.0 Bc	87.5 Aa	83.0 Bd
50	98.5 Aa	96.5 Bc	87.5 Aa	73.5 Be
	SMD_line=0.56	SMD_column=0.53	SMD_line=0.63	SMD_column=0.72

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] * Corresponding author. Universidade Federal de Campina Grande/ Campina Grande - PB, Brasil. E-mail: mcavalcantimata@gmail.com

Fourier Model (1st term of the series). Dry matter dominance in kinetics.
*X^ %wb**	J	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R²	SE	P(%)	Residue
10	1.01	0.01779	4.983	24.83	0.3347	0.11202	3.9433	90.05	0.09325	35.29	B
20	1.01	0.01175	5.065	25.65	0.3347	0.11202	2.6905	94.14	0.07606	22.52	B
30	1.01	0.00986	5.265	27.72	0.3347	0.11202	2.4399	95.09	0.06955	18.56	B
Fourier Model (1st term of the series). Water dominance in kinetics.
40	J_liq	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R²	SE	P(%)
	0.992429	0.020837	5.446	29.65	4.0323	16.259443	0.038	98.61	0.007112	0.61	B
	J_cris	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R²	SE	P(%)
	0.839225	0.00198	5.446	29.65	-	-	-	97.41	0.0046410	0.49	R
	J_freez	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R²	SE	P(%)
	0.820172	0.00732	5.446	29.65	4.1127	16.91	0.0129	99.66	0.013507	10.00	R
50	J_liq	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R²	SE	P(%)
	0.981002	0.005637	6.114	37.38	4.0377	16.30302	0.0129	92.19	0.0055514	0.48	B
	J_cris	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R²	SE	P(%)
	0.844514	0.000729	6.114	37.38	-	-	-	92.06	0.0043542	0.46	B
	J_freez	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R²	SE	P(%)
	1.118195	0.00588	6.114	37.38	1.0607	1.12508	0.1956	98.90	0.02825	17.41	B

Cavalcanti-Mata & Duarte Model I Dry matter dominance in kinetics.
*X wb**	J	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm2	M1	M²1	α mm²/s	R²	SE	P(%)	Residue
10	1.01	0.08532	4.983	24.83	0.3347	0.11202	18.9117	99.14	0.02774	10.24	B
20	1.01	0.0525	5.065	25.65	0.3347	0.11202	12.0213	99.00	0.03311	12.82	B
30	1.01	0.04121	5.265	27.72	0.3347	0.11202	10.1976	99.10	0.03017	10.61	B
Modelo I Cavalcanti- Mata & Duarte. Domínio da água na cinética.
40	J_liq	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R²	SE	P(%)
	1.0097	0.04763	5.446	29.65	0.3111	0.09678	14.597	96.87	0.0125	1.07	B
	J_cris	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R²	SE	P(%)
	0.4947	0.76137	5.446	29.65	-	-	-	91.96	0.00893	0.79	B
	J_freez	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R²	SE	P(%)
	0.7775	0.00389	5.446	29.65	4.132	17.0767	0.0068	99.78	0.01044	8.58	R
50	J_liq	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R2	SE	P(%)
	0.9972	0.0110	6.114	37.38	4.03	16.241	0.0254	98.86	0.00549	0.44	B
	J_cris	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R2	SE	P(%)
	0.6373	0.52421	6.114	37.38	-	-	-	93.81	0.00445	0.36	B
	J_freez	$\frac{M_{1}^{2} α}{r_{m}^{2}}$	r_m mm	$r_{m}^{2}$ mm	M ₁	$M_{1}^{2}$	α mm²/s	R2	SE	P(%)
	1.0761	0.00571	6.114	37.38	0.858	0.73616	0.2905	98.83	0.02834	18.07	B

Cavalcanti–Mata & Duarte Model II. Dry matter dominance in kinetics.
*X (%wb)**	A_liq	$\frac{φ_{1}}{r_{m}^{2}}$	N ₁	$r_{m}^{2}$	B_liq	$\frac{φ_{2}}{r_{m}^{2}}$	N ₂	R²	SE	P (%)	Residue
10	0.59476	0.00926	0.99949	24.83	0.40524	0.32228	0.46436	99.70	0.02750	9,76	B
20	0.30955	0.00022	1.62527	25.65	0.69045	0.10878	0.58386	99.83	0.01389	7,01	R
30	−0.46390	0.04312	4.02×10⁻¹⁰	27.72	1.46347	0.04840	0.53200	99.89	0.01098	4,53	R
Cavalcanti–Mata & Duarte Model II. Water dominance in kinetics.
40	A_liq	$\frac{φ_{1}}{r_{m}^{2}}$	N ₁	$r_{m}^{2}$	B_liq	$\frac{φ_{2}}{r_{m}^{2}}$	N ₂	R²	SE	P (%)
	0.58093	0.08671	1.00108	29.65	0.418749	0.055439	0.78201	99.78	0.00424	0,27	R
	A_cris	$\frac{φ_{1}}{r_{m}^{2}}$	N ₁	$r_{m}^{2}$	B_cris	$\frac{φ_{2}}{r_{m}^{2}}$	N ₂	R²	SE	P (%)
	0.27399	0.979026	0.09515	29.65	−0.10158	1.08866	0.0879	92.46	0.0106	0,77	B
	A_freez	$\frac{φ_{1}}{r_{m}^{2}}$	N ₁	$r_{m}^{2}$	B_cong	$\frac{φ_{2}}{r_{m}^{2}}$	N ₂	R²	SE	P (%)
	0.72343	0.00287	1.15972	29.65	0.04453	0.000278	1.98666	99.81	0.01035	1,91	B
50	A_liq	$\frac{φ_{1}}{r_{m}^{2}}$	N ₁	$r_{m}^{2}$	B_liq	$\frac{φ_{2}}{r_{m}^{2}}$	N ₂	R²	SE	P (%)
	0.3995	0.005014	1.2659	37.38	0.600138	0.02387	0.4683	99.10	0.00477	0,41	B
	A_cris	$\frac{φ_{1}}{r_{m}^{2}}$	N ₁	$r_{m}^{2}$	B_cris	$\frac{φ_{2}}{r_{m}^{2}}$	N ₂	R²	SE	P (%)
	0.0655	0.54815	0.0257	37.38	0.45778	0.73031	0.14548	94.08	0.004194	0,34	B
	A_freez	$\frac{φ_{1}}{r_{m}^{2}}$	N ₁	$r_{m}^{2}$	B_cong	$\frac{φ_{2}}{r_{m}^{2}}$	N ₂	R²	SE	P (%)
	1.53071	4.49816	0.32395	37.38	−2.4584	11.95193	0.74817	99.03	0.02537	14,8	B