Tortuosity Factor of Pores Calculator

✖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%
✖Pore diameter is defined as the distance between two opposite walls of a pore.ⓘ Pore Diameter [d]			+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%
✖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%
✖Membrane thickness is defined as the difference between the internal and outernal boundary of the membrane.ⓘ Membrane Thickness [l_mt]			+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 Factor of Pores [Τ]

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Formula

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Tortuosity Factor of Pores

Formula

`"Τ" = ("ε"*"d"^2*"ΔP"_{"m"})/(32*"μ"*"J"_{"wM"}*"l"_{"mt"})`

Example

`"279.9969"=("0.35"*("6.3245μm")^2*"300000Pa")/(32*"0.0009Kg/ms"*"0.0069444m³/(m²*s)"*"75μm")`

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Tortuosity Factor of Pores Solution

STEP 0: Pre-Calculation Summary

Formula Used

Tortuosity = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Flux through Membrane*Membrane Thickness)
Τ = (ε*d^2*ΔP_m)/(32*μ*J_wM*l_mt)
This formula uses 7 Variables

Variables Used

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 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.
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.
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.
Membrane Thickness - (Measured in Meter) - Membrane thickness is defined as the difference between the internal and outernal boundary of the membrane.

STEP 1: Convert Input(s) to Base Unit

Membrane Porosity: 0.35 --> No Conversion Required
Pore Diameter: 6.3245 Micrometer --> 6.3245E-06 Meter (Check conversion here)
Applied Pressure Driving Force: 300000 Pascal --> 300000 Pascal No Conversion Required
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
Membrane Thickness: 75 Micrometer --> 7.5E-05 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Τ = (ε*d^2*ΔP_m)/(32*μ*J_wM*l_mt) --> (0.35*6.3245E-06^2*300000)/(32*0.0009*0.0069444*7.5E-05)

Evaluating ... ...

Τ = 279.99689373012

STEP 3: Convert Result to Output's Unit

279.99689373012 --> No Conversion Required

FINAL ANSWER

279.99689373012 ≈ 279.9969 <-- Tortuosity

(Calculation completed in 00.004 seconds)

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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Membrane Separation » Basics of Membrane Separation Processes » Tortuosity Factor of Pores

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Created by Harsh Kadam

Shri Guru Gobind Singhji Institute of Engineering and Technology (SGGS), Nanded

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< 16 Basics of Membrane Separation Processes Calculators

Concentration of Mass at Membrane Surface

Go 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)))*Bulk Concentration

Partial Molar Volume of Water based on Solution Diffusion Model

Go Partial Molar Volume = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))

Water Permeability based on Initial flux

Go Water Permeability Through Membrane = Volumetric Water Flux Through Membrane/(Applied Pressure Driving Force*(1-(([R]*Temperature*Molecular Weight)/(Initial Volume*Applied Pressure Driving Force))))

Time of Dialysis using Hollow Fiber Haemodialyser

Go Time of Dialysis = (Volume of blood/Volumetric Rate of Blood)*ln(Initial Concentration In Blood/Final Concentration In Blood)*((1-(e^-No of Transfer Units))^-1)

Hagen Poiseuille Based Flux for Membrane Separation

Go Flux through Membrane = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Tortuosity*Membrane Thickness)

Liquid Viscosity Based On Hagen Poiseuille Equation

Go Liquid Viscosity = (Pore Diameter^2*Membrane Porosity*Applied Pressure Driving Force)/(32*Flux through Membrane*Tortuosity*Membrane Thickness)

Tortuosity Factor of Pores

Go Tortuosity = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Flux through Membrane*Membrane Thickness)

Pressure Difference across Pore based on Poiseuille's Law

Go Pressure Difference Across Pore = (Liquid Flow through Pore*128*Viscosity of Liquid*Length of Pore)/(pi*(Membrane Pore Diameter)^(4))

Liquid Flow through Pore Based On Poiseuilles Law

Go Liquid Flow through Pore = ((pi*(Membrane Pore Diameter)^4)/(128*Viscosity of Liquid*Length of Pore))*Pressure Difference Across Pore

Liquid Viscosity based on Poiseuille's Law

Go Viscosity of Liquid = (Pressure Difference Across Pore*pi*(Membrane Pore Diameter)^(4))/(Liquid Flow through Pore*128*Length of Pore)

Liquid Viscosity based on Membrane Resistance

Go Liquid Viscosity = Applied Pressure Driving Force/(Membrane Flow Resistance of Unit Area*Flux through Membrane)

Membrane Flux Based on Resistance

Go Flux through Membrane = Applied Pressure Driving Force/(Membrane Flow Resistance of Unit Area*Liquid Viscosity)

Resistance to flow in Membranes

Go Membrane Flow Resistance of Unit Area = Applied Pressure Driving Force/(Liquid Viscosity*Flux through Membrane)

Applied Pressure Driving Force Based on Permeability of Membrane

Go Applied Pressure Driving Force = Flux through Membrane/Water Permeability Through Membrane

Water Permeability through Membrane

Go Water Permeability Through Membrane = Flux through Membrane/Applied Pressure Driving Force

Membrane Flux Based on Water Permeability

Go Flux through Membrane = Water Permeability Through Membrane*Applied Pressure

Tortuosity Factor of Pores Formula

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

What does Tortuosity factor determines?

The tortuosity factor of the pores is a measure of how winding or convoluted the pore space is in a porous material. It is defined as the ratio of the actual flow path length to the straight distance between the ends of the flow path. The tortuosity factor is an important parameter in the study of fluid flow through porous media, as it affects the rate of flow and the resistance to flow.

How to Calculate Tortuosity Factor of Pores?

Tortuosity Factor of Pores calculator uses Tortuosity = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Flux through Membrane*Membrane Thickness) to calculate the Tortuosity, The Tortuosity Factor of Pores formula is defined as the ratio of the actual flow path length to the straight distance between the ends of the flow path. Tortuosity is denoted by Τ symbol.

How to calculate Tortuosity Factor of Pores using this online calculator? To use this online calculator for Tortuosity Factor of Pores, enter Membrane Porosity (ε), Pore Diameter (d), Applied Pressure Driving Force (ΔP_m), Liquid Viscosity (μ), Flux through Membrane (J_wM) & Membrane Thickness (l_mt) and hit the calculate button. Here is how the Tortuosity Factor of Pores calculation can be explained with given input values -> 700.0045 = (0.35*6.3245E-06^2*300000)/(32*0.0009*0.0069444*7.5E-05).

FAQ

What is Tortuosity Factor of Pores?

The Tortuosity Factor of Pores formula is defined as the ratio of the actual flow path length to the straight distance between the ends of the flow path and is represented as Τ = (ε*d^2*ΔP_m)/(32*μ*J_wM*l_mt) or Tortuosity = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Flux through Membrane*Membrane Thickness). 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, 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, 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 & Membrane thickness is defined as the difference between the internal and outernal boundary of the membrane.

How to calculate Tortuosity Factor of Pores?

The Tortuosity Factor of Pores formula is defined as the ratio of the actual flow path length to the straight distance between the ends of the flow path is calculated using Tortuosity = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Flux through Membrane*Membrane Thickness). To calculate Tortuosity Factor of Pores, you need Membrane Porosity (ε), Pore Diameter (d), Applied Pressure Driving Force (ΔP_m), Liquid Viscosity (μ), Flux through Membrane (J_wM) & Membrane Thickness (l_mt). With our tool, you need to enter the respective value for Membrane Porosity, Pore Diameter, Applied Pressure Driving Force, Liquid Viscosity, Flux through Membrane & Membrane Thickness 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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