Membrane Pore Diameter Calculator

✖Liquid viscosity is defined as the measure of a fluid's resistance to flow or its internal friction when subjected to an external force.ⓘ Liquid Viscosity [μ]			+10% -10%
✖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.ⓘ Flux through Membrane [J_wM]			+10% -10%
✖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.ⓘ Tortuosity [Τ]			+10% -10%
✖Membrane thickness is defined as the difference between the internal and outernal boundary of the membrane.ⓘ Membrane Thickness [l_mt]			+10% -10%
✖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.ⓘ Membrane Porosity [ε]			+10% -10%
✖Applied Pressure Driving Force is defined as the force or pressure that is intentionally exerted or applied to induce or facilitate process.ⓘ Applied Pressure Driving Force [ΔP_m]			+10% -10%

✖Pore diameter is defined as the distance between two opposite walls of a pore.ⓘ Membrane Pore Diameter [d]

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Formula

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Membrane Pore Diameter

Formula

`"d" = ((32*"μ"*"J"_{"wM"}*"Τ"*"l"_{"mt"})/("ε"*"ΔP"_{"m"}))^0.5`

Example

`"6.324535μm"=((32*"0.0009Kg/ms"*"0.0069444m³/(m²*s)"*"280"*"75μm")/("0.35"*"300000Pa"))^0.5`

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Membrane Pore Diameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pore Diameter = ((32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Membrane Porosity*Applied Pressure Driving Force))^0.5
d = ((32*μ*J_wM*Τ*l_mt)/(ε*ΔP_m))^0.5
This formula uses 7 Variables

Variables Used

Pore Diameter - (Measured in Meter) - Pore diameter is defined as the distance between two opposite walls of a pore.
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.
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.
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)
Membrane Porosity: 0.35 --> No Conversion Required
Applied Pressure Driving Force: 300000 Pascal --> 300000 Pascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = ((32*μ*J_wM*Τ*l_mt)/(ε*ΔP_m))^0.5 --> ((32*0.0009*0.0069444*280*7.5E-05)/(0.35*300000))^0.5

Evaluating ... ...

d = 6.32453508172735E-06

STEP 3: Convert Result to Output's Unit

6.32453508172735E-06 Meter -->6.32453508172735 Micrometer (Check conversion here)

FINAL ANSWER

6.32453508172735 ≈ 6.324535 Micrometer <-- Pore Diameter

(Calculation completed in 00.004 seconds)

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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 Pore Diameter Formula

Pore Diameter = ((32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Membrane Porosity*Applied Pressure Driving Force))^0.5
d = ((32*μ*J_wM*Τ*l_mt)/(ε*ΔP_m))^0.5

How can membrane pore diameter be measured?

The membrane pore diameter 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.
Atomic force microscopy (AFM): This method uses a probe to scan the surface of a membrane and measure the height of the pores.

How to Calculate Membrane Pore Diameter?

Membrane Pore Diameter calculator uses Pore Diameter = ((32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Membrane Porosity*Applied Pressure Driving Force))^0.5 to calculate the Pore Diameter, Membrane Pore Diameter formula is defined as property of membranes which determines the size of the molecules that can pass through the membrane. Pore Diameter is denoted by d symbol.

How to calculate Membrane Pore Diameter using this online calculator? To use this online calculator for Membrane Pore Diameter, enter Liquid Viscosity (μ), Flux through Membrane (J_wM), Tortuosity (Τ), Membrane Thickness (l_mt), Membrane Porosity (ε) & Applied Pressure Driving Force (ΔP_m) and hit the calculate button. Here is how the Membrane Pore Diameter calculation can be explained with given input values -> 6.3E+6 = ((32*0.0009*0.0069444*280*7.5E-05)/(0.35*300000))^0.5.

FAQ

What is Membrane Pore Diameter?

Membrane Pore Diameter formula is defined as property of membranes which determines the size of the molecules that can pass through the membrane and is represented as d = ((32*μ*J_wM*Τ*l_mt)/(ε*ΔP_m))^0.5 or Pore Diameter = ((32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Membrane Porosity*Applied Pressure Driving Force))^0.5. 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, 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 & 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 Pore Diameter?

Membrane Pore Diameter formula is defined as property of membranes which determines the size of the molecules that can pass through the membrane is calculated using Pore Diameter = ((32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Membrane Porosity*Applied Pressure Driving Force))^0.5. To calculate Membrane Pore Diameter, you need Liquid Viscosity (μ), Flux through Membrane (J_wM), Tortuosity (Τ), Membrane Thickness (l_mt), Membrane Porosity (ε) & Applied Pressure Driving Force (ΔP_m). With our tool, you need to enter the respective value for Liquid Viscosity, Flux through Membrane, Tortuosity, Membrane Thickness, Membrane Porosity & 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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