Membrane Thickness Based on Solution Diffusion Model Calculator

✖The partial molar volume of a substance in a mixture is the change in volume of the mixture per mole of that substance added, at constant temperature and pressure.ⓘ Partial Molar Volume [V_l]			+10% -10%
✖Membrane water diffusivity is the rate at which water molecules diffuse across a membrane. It is typically measured in square meters per second (m^2/s).ⓘ Membrane Water Diffusivity [D_w]			+10% -10%
✖Membrane water concentration (MWC) is the concentration of water in a membrane. It is typically measured in moles per cubic meter (kg/m^3).ⓘ Membrane Water Concentration [C_w]			+10% -10%
✖Membrane pressure drop is the difference in pressure between the inlet and outlet of a membrane system, housing (pressure vessel), or element.ⓘ Membrane Pressure Drop [ΔP_atm]			+10% -10%
✖Osmotic pressure is the minimum pressure that must be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.ⓘ Osmotic Pressure [Δπ]			+10% -10%
✖Mass Water flux is defined as the rate of movement of water across a surface or through a medium.ⓘ Mass Water Flux [J_wm]			+10% -10%
✖Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness.ⓘ Temperature [T]			+10% -10%

✖Membrane Layer Thickness is the distance between the two outer surfaces of a membrane. It is typically measured in nanometers (nm), which are billionths of a meter.ⓘ Membrane Thickness Based on Solution Diffusion Model [l_m]

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Formula

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Membrane Thickness Based on Solution Diffusion Model

Formula

`"l"_{"m"} = ("V"_{"l"}*"D"_{"w"}*"C"_{"w"}*("ΔP"_{"atm"}-"Δπ"))/("J"_{"wm"}*"[R]"*"T")`

Example

`"1.3E^-5m"=("0.018m³/kmol"*"0.0000000001762m²/s"*"156kg/m³"*("81.32at"-"39.5at"))/("0.000063kg/s/m²"*"[R]"*"298K")`

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Membrane Thickness Based on Solution Diffusion Model Solution

STEP 0: Pre-Calculation Summary

Formula Used

Membrane Layer Thickness = (Partial Molar Volume*Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))/(Mass Water Flux*[R]*Temperature)
l_m = (V_l*D_w*C_w*(ΔP_atm-Δπ))/(J_wm*[R]*T)
This formula uses 1 Constants, 8 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

Membrane Layer Thickness - (Measured in Meter) - Membrane Layer Thickness is the distance between the two outer surfaces of a membrane. It is typically measured in nanometers (nm), which are billionths of a meter.
Partial Molar Volume - (Measured in Cubic Meter per Mole) - The partial molar volume of a substance in a mixture is the change in volume of the mixture per mole of that substance added, at constant temperature and pressure.
Membrane Water Diffusivity - (Measured in Square Meter per Second) - Membrane water diffusivity is the rate at which water molecules diffuse across a membrane. It is typically measured in square meters per second (m^2/s).
Membrane Water Concentration - (Measured in Kilogram per Cubic Meter) - Membrane water concentration (MWC) is the concentration of water in a membrane. It is typically measured in moles per cubic meter (kg/m^3).
Membrane Pressure Drop - (Measured in Pascal) - Membrane pressure drop is the difference in pressure between the inlet and outlet of a membrane system, housing (pressure vessel), or element.
Osmotic Pressure - (Measured in Pascal) - Osmotic pressure is the minimum pressure that must be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.
Mass Water Flux - (Measured in Kilogram per Second per Square Meter) - Mass Water flux is defined as the rate of movement of water across a surface or through a medium.
Temperature - (Measured in Kelvin) - Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness.

STEP 1: Convert Input(s) to Base Unit

Partial Molar Volume: 0.018 Cubic Meter per Kilomole --> 1.8E-05 Cubic Meter per Mole (Check conversion here)
Membrane Water Diffusivity: 1.762E-10 Square Meter per Second --> 1.762E-10 Square Meter per Second No Conversion Required
Membrane Water Concentration: 156 Kilogram per Cubic Meter --> 156 Kilogram per Cubic Meter No Conversion Required
Membrane Pressure Drop: 81.32 Atmosphere Technical --> 7974767.78 Pascal (Check conversion here)
Osmotic Pressure: 39.5 Atmosphere Technical --> 3873626.75 Pascal (Check conversion here)
Mass Water Flux: 6.3E-05 Kilogram per Second per Square Meter --> 6.3E-05 Kilogram per Second per Square Meter No Conversion Required
Temperature: 298 Kelvin --> 298 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_m = (V_l*D_w*C_w*(ΔP_atm-Δπ))/(J_wm*[R]*T) --> (1.8E-05*1.762E-10*156*(7974767.78-3873626.75))/(6.3E-05*[R]*298)

Evaluating ... ...

l_m = 1.29992026139213E-05

STEP 3: Convert Result to Output's Unit

1.29992026139213E-05 Meter --> No Conversion Required

FINAL ANSWER

1.29992026139213E-05 ≈ 1.3E-5 Meter <-- Membrane Layer Thickness

(Calculation completed in 00.020 seconds)

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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 Thickness Based on Solution Diffusion Model Formula

By which factors is the Membrane thickness affected?

the membrane thickness can also be affected by the following:

The age of the organism: The membranes of older organisms are generally thicker than the membranes of younger organisms.
The presence of disease: Some diseases can cause the membranes to become thicker.
The use of certain medications: Some medications can also cause the membranes to become thicker.

How to Calculate Membrane Thickness Based on Solution Diffusion Model?

Membrane Thickness Based on Solution Diffusion Model calculator uses Membrane Layer Thickness = (Partial Molar Volume*Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))/(Mass Water Flux*[R]*Temperature) to calculate the Membrane Layer Thickness, Membrane thickness based on solution diffusion model is defined as the thickness of the membrane that is required to achieve a desired permeation rate and selectivity. Membrane Layer Thickness is denoted by l_m symbol.

How to calculate Membrane Thickness Based on Solution Diffusion Model using this online calculator? To use this online calculator for Membrane Thickness Based on Solution Diffusion Model, enter Partial Molar Volume (V_l), Membrane Water Diffusivity (D_w), Membrane Water Concentration (C_w), Membrane Pressure Drop (ΔP_atm), Osmotic Pressure (Δπ), Mass Water Flux (J_wm) & Temperature (T) and hit the calculate button. Here is how the Membrane Thickness Based on Solution Diffusion Model calculation can be explained with given input values -> 1.3E-5 = (1.8E-05*1.762E-10*156*(7974767.78-3873626.75))/(6.3E-05*[R]*298).

FAQ

What is Membrane Thickness Based on Solution Diffusion Model?

Membrane thickness based on solution diffusion model is defined as the thickness of the membrane that is required to achieve a desired permeation rate and selectivity and is represented as l_m = (V_l*D_w*C_w*(ΔP_atm-Δπ))/(J_wm*[R]*T) or Membrane Layer Thickness = (Partial Molar Volume*Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))/(Mass Water Flux*[R]*Temperature). The partial molar volume of a substance in a mixture is the change in volume of the mixture per mole of that substance added, at constant temperature and pressure, Membrane water diffusivity is the rate at which water molecules diffuse across a membrane. It is typically measured in square meters per second (m^2/s), Membrane water concentration (MWC) is the concentration of water in a membrane. It is typically measured in moles per cubic meter (kg/m^3), Membrane pressure drop is the difference in pressure between the inlet and outlet of a membrane system, housing (pressure vessel), or element, Osmotic pressure is the minimum pressure that must be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane, Mass Water flux is defined as the rate of movement of water across a surface or through a medium & Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness.

How to calculate Membrane Thickness Based on Solution Diffusion Model?

Membrane thickness based on solution diffusion model is defined as the thickness of the membrane that is required to achieve a desired permeation rate and selectivity is calculated using Membrane Layer Thickness = (Partial Molar Volume*Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))/(Mass Water Flux*[R]*Temperature). To calculate Membrane Thickness Based on Solution Diffusion Model, you need Partial Molar Volume (V_l), Membrane Water Diffusivity (D_w), Membrane Water Concentration (C_w), Membrane Pressure Drop (ΔP_atm), Osmotic Pressure (Δπ), Mass Water Flux (J_wm) & Temperature (T). With our tool, you need to enter the respective value for Partial Molar Volume, Membrane Water Diffusivity, Membrane Water Concentration, Membrane Pressure Drop, Osmotic Pressure, Mass Water Flux & Temperature 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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