Membrane Porosity Solution

STEP 0: Pre-Calculation Summary
Formula Used
Membrane Porosity = (32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Pore Diameter^2*Applied Pressure Driving Force)
ε = (32*μ*JwM*Τ*lmt)/(d^2*ΔPm)
This formula uses 7 Variables
Variables Used
Membrane Porosity - Membrane porosity is defined as the void volume fraction of a membrane. It is the volume of the pores divided by the total volume of the membrane.
Liquid Viscosity - (Measured in Pascal Second) - Liquid viscosity is defined as the measure of a fluid's resistance to flow or its internal friction when subjected to an external force.
Flux through Membrane - (Measured in Cubic Meter per Square Meter per Second) - Flux through membrane is defined as the rate of movement or transfer of a substance per unit area across a porous barrier known as a membrane.
Tortuosity - Tortuosity is an intrinsic property of a porous material usually defined as the ratio of actual flow path length to the straight distance between the ends of the flow path.
Membrane Thickness - (Measured in Meter) - Membrane thickness is defined as the difference between the internal and outernal boundary of the membrane.
Pore Diameter - (Measured in Meter) - Pore diameter is defined as the distance between two opposite walls of a pore.
Applied Pressure Driving Force - (Measured in Pascal) - Applied Pressure Driving Force is defined as the force or pressure that is intentionally exerted or applied to induce or facilitate process.
STEP 1: Convert Input(s) to Base Unit
Liquid Viscosity: 0.0009 Kilogram per Meter per Second --> 0.0009 Pascal Second (Check conversion ​here)
Flux through Membrane: 0.0069444 Cubic Meter per Square Meter per Second --> 0.0069444 Cubic Meter per Square Meter per Second No Conversion Required
Tortuosity: 280 --> No Conversion Required
Membrane Thickness: 75 Micrometer --> 7.5E-05 Meter (Check conversion ​here)
Pore Diameter: 6.3245 Micrometer --> 6.3245E-06 Meter (Check conversion ​here)
Applied Pressure Driving Force: 300000 Pascal --> 300000 Pascal No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ε = (32*μ*JwM*Τ*lmt)/(d^2*ΔPm) --> (32*0.0009*0.0069444*280*7.5E-05)/(6.3245E-06^2*300000)
Evaluating ... ...
ε = 0.350003882880426
STEP 3: Convert Result to Output's Unit
0.350003882880426 --> No Conversion Required
FINAL ANSWER
0.350003882880426 0.350004 <-- Membrane Porosity
(Calculation completed in 00.005 seconds)

Credits

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Created by Harsh Kadam
Shri Guru Gobind Singhji Institute of Engineering and Technology (SGGS), Nanded
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13 Membrane Characteristics Calculators

Bulk Concentration of Membrane
​ Go Bulk Concentration = (Solute Concentration at Membrane Surface)/((exp(Water Flux/Mass Transfer Coefficient at Membrane Surface))/(Solute Rejection+(1-Solute Rejection)*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)))
Solute Concentration at Membrane Surface
​ Go Solute Concentration at Membrane Surface = (Bulk Concentration*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface))/(Solute Rejection+(1-Solute Rejection)*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface))
Initial Flux of Membrane
​ Go Volumetric Water Flux Through Membrane = (Water Permeability Through Membrane*Applied Pressure Driving Force)*(1-((Universal Gas Constant)*Temperature*Molecular Weight/Initial Volume*(1/Applied Pressure Driving Force)))
Osmotic Pressure Drop Based on Solution Diffusion Model
​ Go Osmotic Pressure = Membrane Pressure Drop-((Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*Partial Molar Volume))
Membrane Thickness Based on Solution Diffusion Model
​ Go Membrane Layer Thickness = (Partial Molar Volume*Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))/(Mass Water Flux*[R]*Temperature)
Membrane Pressure Drop Based On Solution Diffusion Model
​ Go Membrane Pressure Drop = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*Partial Molar Volume)+Osmotic Pressure
Membrane Temperature
​ Go Temperature = Initial Volume*((Applied Pressure Driving Force*Water Permeability Through Membrane)-Volumetric Water Flux Through Membrane)/([R]*Water Permeability Through Membrane*Molecular Weight)
Initial Membrane Volume
​ Go Initial Volume = ([R]*Temperature*Molecular Weight)/(Applied Pressure Driving Force-(Volumetric Water Flux Through Membrane/Water Permeability Through Membrane))
Membrane Pore Diameter
​ Go Pore Diameter = ((32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Membrane Porosity*Applied Pressure Driving Force))^0.5
Membrane Pressure Drop
​ Go Applied Pressure Driving Force = (Tortuosity*32*Liquid Viscosity*Flux through Membrane*Membrane Thickness)/(Membrane Porosity*(Pore Diameter^2))
Membrane Thickness
​ Go Membrane Thickness = (Pore Diameter^2*Membrane Porosity*Applied Pressure Driving Force)/(32*Liquid Viscosity*Flux through Membrane*Tortuosity)
Membrane Porosity
​ Go Membrane Porosity = (32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Pore Diameter^2*Applied Pressure Driving Force)
Pressure Driving Force in Membrane
​ Go Applied Pressure Driving Force = Membrane Flow Resistance of Unit Area*Liquid Viscosity*Flux through Membrane

Membrane Porosity Formula

Membrane Porosity = (32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Pore Diameter^2*Applied Pressure Driving Force)
ε = (32*μ*JwM*Τ*lmt)/(d^2*ΔPm)

How can Membrane Porosity be measured?




Membrane porosity can be measured using a variety of methods, including:

Mercury porosimetry: This method uses mercury, which is a non-wetting liquid, to measure the pore size distribution of a membrane.
Gas permeation: This method uses gases of different molecular sizes to measure the pore size distribution of a membrane.
Electrical resistance tomography: This method uses electrical resistance measurements to map the pore space.
Nuclear magnetic resonance imaging (NMR): This method uses NMR signals to map the pore space.

How to Calculate Membrane Porosity?

Membrane Porosity calculator uses Membrane Porosity = (32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Pore Diameter^2*Applied Pressure Driving Force) to calculate the Membrane Porosity, Membrane porosity is defined as the void volume fraction of the membrane.It is defined as the volume of the pores divided by the total volume of the membrane. Membrane Porosity is denoted by ε symbol.

How to calculate Membrane Porosity using this online calculator? To use this online calculator for Membrane Porosity, enter Liquid Viscosity (μ), Flux through Membrane (JwM), Tortuosity (Τ), Membrane Thickness (lmt), Pore Diameter (d) & Applied Pressure Driving Force (ΔPm) and hit the calculate button. Here is how the Membrane Porosity calculation can be explained with given input values -> 0.139999 = (32*0.0009*0.0069444*280*7.5E-05)/(6.3245E-06^2*300000).

FAQ

What is Membrane Porosity?
Membrane porosity is defined as the void volume fraction of the membrane.It is defined as the volume of the pores divided by the total volume of the membrane and is represented as ε = (32*μ*JwM*Τ*lmt)/(d^2*ΔPm) or Membrane Porosity = (32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Pore Diameter^2*Applied Pressure Driving Force). Liquid viscosity is defined as the measure of a fluid's resistance to flow or its internal friction when subjected to an external force, Flux through membrane is defined as the rate of movement or transfer of a substance per unit area across a porous barrier known as a membrane, Tortuosity is an intrinsic property of a porous material usually defined as the ratio of actual flow path length to the straight distance between the ends of the flow path, Membrane thickness is defined as the difference between the internal and outernal boundary of the membrane, Pore diameter is defined as the distance between two opposite walls of a pore & Applied Pressure Driving Force is defined as the force or pressure that is intentionally exerted or applied to induce or facilitate process.
How to calculate Membrane Porosity?
Membrane porosity is defined as the void volume fraction of the membrane.It is defined as the volume of the pores divided by the total volume of the membrane is calculated using Membrane Porosity = (32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Pore Diameter^2*Applied Pressure Driving Force). To calculate Membrane Porosity, you need Liquid Viscosity (μ), Flux through Membrane (JwM), Tortuosity (Τ), Membrane Thickness (lmt), Pore Diameter (d) & Applied Pressure Driving Force (ΔPm). With our tool, you need to enter the respective value for Liquid Viscosity, Flux through Membrane, Tortuosity, Membrane Thickness, Pore Diameter & Applied Pressure Driving Force and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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