Modelling of rheological behaviour of macaíba pulp at different temperatures

Brasileiro, Jéssica L. O.; Figueirêdo, Rossana M. F. de; Queiroz, Alexandre J. de M.; Feitosa, Regilane M.

doi:10.1590/1807-1929/agriambi.v26n3p198-203

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Articles • Rev. bras. eng. agríc. ambient. 26 (3) • Mar 2022 • https://doi.org/10.1590/1807-1929/agriambi.v26n3p198-203 copy

Modelling of rheological behaviour of macaíba pulp at different temperatures¹ 1 Research developed at Universidade Federal de Campina Grande, Campina Grande, PB, Brazil

Modelagem do comportamento reológico da polpa de macaíba em diferentes temperaturas

Authorship SCIMAGO INSTITUTIONS RANKINGS

HIGHLIGHTS:

The rheological behaviour of macaíba pulp can be represented by the Mizrahi-Berk equation.

The fluid behaviour index (n) was below unity, characterizing a pseudoplastic behaviour for the macaíba pulp.

The effect of temperature can be evaluated using the Arrhenius-type equation for the viscous flow of the macaíba pulp.

ABSTRACT

Fruit pulps undergo temperature variations during processing, leading to viscosity changes. This study aimed to analyse the rheological behaviour of macaíba pulp at different temperatures (10 to 50 ºC, with 5 ºC increments) and speeds (2.5 to 200 rpm, totalling 17 speeds). Experimental measurements were performed in a Brookfield viscometer, fitting the Ostwald-de-Waele, Mizrahi-Berk, Herschel-Bulkley, and Casson models to the experimental data of shear stress as a function of shear rate. Among the models used, the Mizrahi-Berk model (R² > 0.9656 and average percentage deviation - P ≤ 4.1%) was found to best fit the rheogram data. Macaíba pulp exhibited a non-newtonian behaviour and was characterised as pseudoplastic. It showed fluid behaviour indexes below unity under the studied conditions, with decreases in apparent viscosity as temperature and shear rate increased. Such behaviour could be described by the Arrhenius equation. The Mizrahi-Berk and Falguera-Ibarz models (R² > 0.99 and P ≤ 10%) best fitted the data and were used to represent the viscosity behaviour of macaíba pulp. The activation energy values of macaíba pulp ranged between 17.53 and 25.37 kJ mol^-1, showing a rheological behaviour like other fruit pulps.

Key words:
Acrocomia intumescens; apparent viscosity; non-newtonian fluid; pseudoplastic; Arrhenius equation

Model	Equation
Casson	$τ^{0.5} = K_{O C} + {K_{C \dot{γ}}}^{0.5}$	(1)
Herschel-Bulkley	$τ = τ_{O H} + {K_{H \dot{γ}}}^{n_{H}}$	(2)
Mizrahi-Berk	$τ^{0.5} = K_{O M} + {K_{\dot{γ}}}^{n}$	(3)
Ostwald-de-Waele	$τ = {K_{\dot{γ}}}^{n}$	(4)

Model	Equation
Mizrahi-Berk	$η_{a p} = \frac{{(K_{O M} + {K_{γ}}^{n})}^{2}}{\dot{γ}}$	(6)
Power Law	$η_{a p} = {K_{\dot{γ}}}^{n - 1}$	(7)
Sisko	$η_{a p} = η_{\infty} + {K_{s \dot{γ}}}^{n_{s} - 1}$	(8)
Faguelra-Ibarz	$η_{a p} = η_{\infty} + (η_{0} - η_{\infty}) {\dot{γ}}^{- k}$	(9)

Casson
Temperature (ºC)		K_0C (Pa)				K_C (Pa s)			R²			P (%)
10		5.52				0.94			0.8778			13.97
15		5.35				0.83			0.9183			5.15
20		3.19				1.06			0.9766			3.15
25		3.30				0.90			0.9902			2.30
30		3.35				0.80			0.9826			2.65
35		3.87				0.93			0.9282			7.07
40		3.07				0.85			0.9458			6.30
45		2.64				0.72			0.9749			4.26
50		2.58				0.72			0.9788			3.59
Herschel Bulkley
Temperature (ºC)		τ_0H (Pa)	K_H (Paⁿ)				n			R²			P (%)
10		-667.78	693.99				0.0372			0.9846			5.87
15		-72.41	100.69				0.1613			0.9843			3.59
20		6.49	9.26				0.6219			0.9675			8.56
25		7.22	8.49				0.5832			0.9929			3.12
30		5.98	9.13				0.5285			0.9858			4.14
35		-30.23	45.96				0.2698			0.9781			6.38
40		-0.30	12.64				0.4692			0.9447			8.28
45		-2.66	11.22				0.4257			0.9917			5.29
50		3.56	5.99				0.5613			0.9769			5.23
Mizrahi-Berk
Temperature (ºC)	K_0M (Pa)			K_M (Pa sⁿ)				n			R²			P (%)
10	-145.97			151.40				0.0105			0.9799			2.57
15	-1166.01			1171.34				0.0012			0.9865			1.76
20	2.83			1.34				0.4517			0.9771			3.50
25	2.22			1.76				0.3637			0.9945			1.52
30	2.04			1.88				0.3298			0.9894			2.02
35	-48.04			51.97				0.0285			0.9833			3.07
40	-0.79			4.25				0.2097			0.9656			4.11
45	0.24			2.78				0.2470			0.9919			2.39
50	1.34			1.75				0.3253			0.9860			2.69
Ostwald-de-Waele
Temperature (ºC)	K (Pa s)				n				R²			P (%)
10	38.52				0.3278				0.9567			10.27
15	33.56				0.3232				0.9770			6.37
20	13.02				0.5483				0.9661			10.60
25	13.17				0.4898				0.9909			5.73
30	13.32				0.4505				0.9843			5.74
35	20.44				0.4145				0.9729			10.09
40	12.43				0.4727				0.9447			8.28
45	9.27				0.4638				0.9913			4.98
50	8.33				0.4912				0.9758			5.94

Mizrahi-Berk
Temperature (°C)	K_0M (Pa)			K (Pa s)			n				R²				P (%)
10	-184.71			352.45			0.1248				0.9928				9.96
15	-465.84			632.95			0.0680				0.9942				7.85
20	113.75			22.94			0.5853				0.9982				6.02
25	65.73			60.80			0.3405				0.9993				3.31
30	71.69			52.56			0.3527				0.9980				4.51
35	-3.19			123.39			0.1920				0.9958				5.41
40	69.73			41.59			0.4010				0.9980				6.59
45	69.29			30.18			0.4595				0.9973				6.68
50	69.52			29.77			0.4535				0.9979				6.19
Power Law
Temperature (°C)		K (Pa s)			n			R²						P (%)
10		27658.44			0.4320			0.9908						14.64
15		27969.69			0.4587			0.9904						15.19
20		19002.87			0.3488			0.9819						18.51
25		16131.87			0.3941			0.9968						8.66
30		15576.38			0.3691			0.9952						9.19
35		14444.42			0.3922			0.9958						5.25
40		12510.83			0.3946			0.9922						9.11
45		10005.24			0.4013			0.9869						12.03
50		9973.82			0.3887			0.9887						12.57
Sisko
Temperature (°C)		η_∞ (Pa s)				K_s (Pa s)				n			R²			P (%)
10		-3102.36				31018.97				0.5705			0.9947			5.67
15		4169171.46				-4144439.37				1.0015			0.9245			34.52
20		1820.69				16929.56				0.1154			0.9981			6.06
25		786.72				15304.08				0.3067			0.9994			3.38
30		738.65				14783.40				0.2788			0.9979			4.85
35		125.55				14313.67				0.3786			0.9958			4.78
40		817.33				11647.95				0.2693			0.9970			7.81
45		866.61				9084.41				0.2238			0.9962			8.01
50		2254253.31				-2245794.79				1.0009			0.8293			35.08
Falguera–Ibarz
Temperature (°C)			η_∞ (Pa s)			η₀ (Pa s)			k			R²				P (%)
10			-3102.36			27916.61			0.4295			0.9947				5.67
15			-2698.87			27650.35			0.4602			0.9950				7.55
20			1820.69			18750.25			0.8846			0.9981				6.06
25			786.72			16090.79			0.6933			0.9994				3.38
30			738.65			15522.06			0.7212			0.9979				4.85
35			125.55			14439.22			0.6214			0.9958				4.78
40			817.33			12465.28			0.7307			0.9970				7.81
45			866.61			9951.02			0.7762			0.9962				8.01
50			801.24			9915.94			0.7773			0.9970				7.64

Rotation speed (rpm)	µ₀ (mPa s)	E_a (kJ mol^-1)	R²
2.5	9.0322	19.3957	0.9686
10	1.0660	22.5343	0.9181
20	0.2300	25.3743	0.8624
60	1.6967	18.7464	0.8738
80	2.4368	17.5666	0.9535
100	1.6051	18.4104	0.9872
135	1.6883	17.8294	0.9665
160	1.0846	18.4554	0.9848
200	1.4405	17.5284	0.9809

Unidade Acadêmica de Engenharia Agrícola Unidade Acadêmica de Engenharia Agrícola, UFCG, Av. Aprígio Veloso 882, Bodocongó, Bloco CM, 1º andar, CEP 58429-140, Campina Grande, PB, Brasil, Tel. +55 83 2101 1056 - Campina Grande - PB - Brazil
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[1] * Corresponding author - E-mail: jessicalisana@gmail.com

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Modelling of rheological behaviour of macaíba pulp at different temperatures1 1 Research developed at Universidade Federal de Campina Grande, Campina Grande, PB, Brazil

Modelagem do comportamento reológico da polpa de macaíba em diferentes temperaturas

HIGHLIGHTS:

ABSTRACT

Modelling of rheological behaviour of macaíba pulp at different temperatures¹ 1 Research developed at Universidade Federal de Campina Grande, Campina Grande, PB, Brazil