Membrane Water Diffusivity Based on Solution Diffusion Model Calculator

✖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 Layer Thickness [l_m]			+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%
✖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 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%

✖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 Based on Solution Diffusion Model [D_w]

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Formula

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Membrane Water Diffusivity Based on Solution Diffusion Model

Formula

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

Example

`"1.8E^-10m²/s"=("0.000063kg/s/m²"*"[R]"*"298K"*"0.000013m")/(("156kg/m³"*"0.018m³/kmol")*("81.32at"-"39.5at"))`

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Membrane Water Diffusivity Based on Solution Diffusion Model Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

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).
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.
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.
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).
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 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.

STEP 1: Convert Input(s) to Base Unit

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
Membrane Layer Thickness: 1.3E-05 Meter --> 1.3E-05 Meter No Conversion Required
Membrane Water Concentration: 156 Kilogram per Cubic Meter --> 156 Kilogram per Cubic Meter No Conversion Required
Partial Molar Volume: 0.018 Cubic Meter per Kilomole --> 1.8E-05 Cubic Meter per Mole (Check conversion here)
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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D_w = (J_wm*[R]*T*l_m)/((C_w*V_l)*(ΔP_atm-Δπ)) --> (6.3E-05*[R]*298*1.3E-05)/((156*1.8E-05)*(7974767.78-3873626.75))

Evaluating ... ...

D_w = 1.7621080831119E-10

STEP 3: Convert Result to Output's Unit

1.7621080831119E-10 Square Meter per Second --> No Conversion Required

FINAL ANSWER

1.7621080831119E-10 ≈ 1.8E-10 Square Meter per Second <-- Membrane Water Diffusivity

(Calculation completed in 00.020 seconds)

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< 25 Properties of Fluids Calculators

Water Flux Based on Solution Diffusion Model

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

Torque on Cylinder given Angular Velocity and Radius of Inner Cylinder

Go Torque = (Dynamic Viscosity*2*pi*(Radius of Inner Cylinder^3)*Angular Velocity*Length of Cylinder)/(Thickness of Fluid Layer)

Height of Capillary Rise in Capillary Tube

Go Height of Capillary Rise = (2*Surface Tension*(cos(Contact Angle)))/(Density*[g]*Radius of Capillary Tube)

Torque on Cylinder given Radius, Length and Viscosity

Go Torque = (Dynamic Viscosity*4*(pi^2)*(Radius of Inner Cylinder^3)*Revolutions per Second*Length of Cylinder)/(Thickness of Fluid Layer)

Weight of Liquid Column in Capillary Tube

Go Weight of Liquid Column in Capillary = Density*[g]*pi*(Radius of Capillary Tube^2)*Height of Capillary Rise

Wetted Surface Area

Go Wetted Surface Area = 2*pi*Radius of Inner Cylinder*Length of Cylinder

Enthalpy given Flow Work

Go Enthalpy = Internal Energy+(Pressure/Density of Liquid)

Enthalpy given Specific Volume

Go Enthalpy = Internal Energy+(Pressure*Specific Volume)

Tangential Velocity given Angular Velocity

Go Tangential Velocity of Cylinder = Angular Velocity*Radius of Inner Cylinder

Angular Velocity given Revolution Per Unit Time

Go Angular Velocity = 2*pi*Revolutions per Second

Mach Number of Compressible Fluid Flow

Go Mach Number = Velocity of Fluid/Speed of Sound

Specific Gravity of Fluid given Density of Water

Go Specific Gravity = Density/Density of Water

Relative Density of Fluid

Go Relative Density = Density/Density of Water

Specific Total Energy

Go Specific Total Energy = Total Energy/Mass

Flow Work given Density

Go Flow Work = Pressure/Density of Liquid

Flow Work given Specific Volume

Go Flow Work = Pressure*Specific Volume

Shear Stress Acting on Fluid Layer

Go Shear Stress = Shear Force/Area

Shear Force given Shear Stress

Go Shear Force = Shear Stress*Area

Weight Density given Density

Go Specific Weight = Density*[g]

Specific Weight of Substance

Go Specific Weight = Density*[g]

Specific Volume of Fluid given Mass

Go Specific Volume = Volume/Mass

Coefficient of Volume Expansion for Ideal Gas

Go Coefficient of Volume Expansion = 1/(Absolute Temperature)

Volume Expansivity for Ideal Gas

Go Coefficient of Volume Expansion = 1/(Absolute Temperature)

Density of Fluid

Go Density = Mass/Volume

Specific Volume given Density

Go Specific Volume = 1/Density

Membrane Water Diffusivity Based on Solution Diffusion Model Formula

What is the Solution Diffusion Model?

The solution–diffusion model assumes that the pressure within a membrane is uniform and that the chemical potential gradient of a permeant across the membrane is represented only as a concentration gradient.
The pore-flow model assumes that the permeant. concentration within a membrane is uniform.

How to Calculate Membrane Water Diffusivity Based on Solution Diffusion Model?

Membrane Water Diffusivity Based on Solution Diffusion Model calculator uses Membrane Water Diffusivity = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/((Membrane Water Concentration*Partial Molar Volume)*(Membrane Pressure Drop-Osmotic Pressure)) to calculate the Membrane Water Diffusivity, Membrane water diffusivity based on solution diffusion model is the rate at which water molecules diffuse across a membrane driven by a concentration gradient. Membrane Water Diffusivity is denoted by D_w symbol.

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

FAQ

What is Membrane Water Diffusivity Based on Solution Diffusion Model?

Membrane water diffusivity based on solution diffusion model is the rate at which water molecules diffuse across a membrane driven by a concentration gradient and is represented as D_w = (J_wm*[R]*T*l_m)/((C_w*V_l)*(ΔP_atm-Δπ)) or Membrane Water Diffusivity = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/((Membrane Water Concentration*Partial Molar Volume)*(Membrane Pressure Drop-Osmotic Pressure)). 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, 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 water concentration (MWC) is the concentration of water in a membrane. It is typically measured in moles per cubic meter (kg/m^3), 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 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.

How to calculate Membrane Water Diffusivity Based on Solution Diffusion Model?

Membrane water diffusivity based on solution diffusion model is the rate at which water molecules diffuse across a membrane driven by a concentration gradient is calculated using Membrane Water Diffusivity = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/((Membrane Water Concentration*Partial Molar Volume)*(Membrane Pressure Drop-Osmotic Pressure)). To calculate Membrane Water Diffusivity Based on Solution Diffusion Model, you need Mass Water Flux (J_wm), Temperature (T), Membrane Layer Thickness (l_m), Membrane Water Concentration (C_w), Partial Molar Volume (V_l), Membrane Pressure Drop (ΔP_atm) & Osmotic Pressure (Δπ). With our tool, you need to enter the respective value for Mass Water Flux, Temperature, Membrane Layer Thickness, Membrane Water Concentration, Partial Molar Volume, Membrane Pressure Drop & Osmotic Pressure 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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