Water and oil permeability of poroelastic potato discs

Figures & data

Table 1. Material properties.

Parameter	Value	Source
Density (kg/m^3)
Water	838.46 + 1.41T – 0.003011T^2 + 3.72X10^−7 T^3	[26]
Oil	1106.11 – 0.64T	[27]
Dynamic Viscosity (Pa.s)
Water	1.38 – 0.02 T + 1.36 × 10^−4 T^2 – 4.65 × 10^−7 T^3 + 8.9 × 10^−10 T^4 – 9.08 × 10^−13 T^5 + 3.85 × 10^16 T^6	[26]
Oil	(0.1569 × 10^−5; e^3108/T)	[28]
Properties of potato
Density (kg/m^3)	1100	[29]
Young’s Modulus (MPa)	0.2	[30]
Porosity	0.6	[31]
Poisson’s ratio	0.4	[32]

Figure 1. (a) A schematic of experimental setup for oil and water permeability measurement for potato discs. (b) Boundary conditions for Darcy’s law equation and structural displacement (P1 = applied pressure, P_atm = atmospheric pressure).

Figure 2. Oil permeability of potatoes at (a) 25°C, (b) 40°C, (c) 50°C, and (d) 70°C.

Figure 3. Water permeability of potatoes at (a) 70°C, (b) 75°C, and (c) 80°C.

Figure 4. (a) The displacement of a raw potato idsc as a function of thickness under the applied pressure of 345 kPa. (b) The 2D view of compression of a raw potato disc under the applied pressure of 345 kPa.

Table 2. Oil permeability data and fluid content of potato at different temperatures.

Temperature	Permeability K°	MSE	Threshold pressure gradient, J	Initial moisture content	Final moisture content	Initial oil content	Final oil content
°C	X10^−15, m^2	X10^−12	kPa	g/g solids (db)
25	2	8	0.24	4.55	3.01	0	0.23
40	3	60	0.11	3.54	3.08	0	0.20
50	8	6	0.12	4.53	1.50	0	0.18
70	12	0.002	0.12	4.03	1.84	0	0.13

Table 3. Water permeability data and fluid content of potato at different temperatures.

Tempe-rature	Permeability K^w	MSE	Threshold pressure gradient, J	Initial moisture content	Final moisture content
°C	X10^−15, m^2	X10^−9	kPa	g/g solids (db)
70	3.50	5	124	4.55	7.33
75	1	9	172	4.26	7.08
80	2	0.04	117	4.26	7.01

Table 4. Change of thickness and weight of potato disc at different temperatures after pressure-driven oil flow.

Temperature of oil	Change of thickness	Change of weight
°C	%	%
25	6↓	21↓
40	14↓	31↓
50	33↓	34↓
70	66↓	53↓

Table 5. Change of thickness and weight of potato disc at different temperatures after pressure-driven water flow.

Temperature of oil	Change of thickness	Change of weight
°C	%	%
25	43↑	7↑
40	18↑	4↑
50	11↓	23↓
70	19↓	19↓
80	20↓	26↓

Table 6. Estimated constant values of oil and water permeability from 13 and 14.

ko	B	R^2
(m^2)	(K^−1)
13 × 10^−26	5639	0.95
kwo	A	R^2
(m^2)	(K^−1)
8 × 10^−26	–7782	0.90

Table

	Fluid velocity (ms^−1)
	Dynamic viscosity of flowing fluid (Pa.s)
K^w	Water permeability of potato (m^2)
K°	Oil permeability of potato (m^2)
Mo	Final oil content of potato(g/g solids)
Mw	Average moisture content of potato (g/g solids)
A,B,k°,k^wo	Constants
∇P	Pressure gradient(kPa)
J	Threshold pressure gradient(kPa)
db	Dry basis(g/g solids)
wb	Wet basis(g/g Total)
MSE	Mean Squared Error
R^2	Determination of coefficient
σ	Stress(Pa)
E	Coefficient of elasticity(Pa)
	Strain tensor
u	Displacement(m)

Poling, B.E.; Prausnitz, J.M.; O’Connell, J.P. The Properties of Gases and Liquids, Vol. 5.; McGraw-Hill: New York, NY, 2001.

 Google Scholar

Esteban, B.; Riba, J.-R.; Baquero, G.; Rius, A.; Puig, R. Temperature Dependence of Density and Viscosity of Vegetable Oils. Biomass and Bioenergy 2012, 42, 164–171.

 Web of Science ®Google Scholar

Santos, J.; Santos, I.; Souza, A. Effect of Heating and Cooling on Rheological Parameters of Edible Vegetable Oils. Journal of food Engineering 2005, 67, 401–405.

 Web of Science ®Google Scholar

Wang, N.; Brennan, J. Changes in Structure, Density and Porosity of Potato During Dehydration. Journal of Food Engineering 1995, 24, 61–76.

 Web of Science ®Google Scholar

Thussu, S.; Datta, A.K. Texture Prediction During Deep Frying: A Mechanistic Approach. Journal of Food Engineering 2012, 108, 111–121.

 Google Scholar

Welti-Chanes, J.; Aguilera, J.M. Engineering and Food for the 21st Century; CRC Press: Boca Raton, FL, 2002.

 Google Scholar

Bourne, M. Food Texture and Viscosity: Concept and Measurement. Academic Press: San Diego, CA, 2002.

 Google Scholar