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Membrane Thickness Based on Solution Diffusion Model Formula

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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. Check FAQs

l m = \frac{V l \cdot D w \cdot C w \cdot (ΔP atm - Δπ)}{J wm \cdot [R] \cdot T}

l_m - Membrane Layer Thickness?V_l - Partial Molar Volume?D_w - Membrane Water Diffusivity?C_w - Membrane Water Concentration?ΔP_atm - Membrane Pressure Drop?Δπ - Osmotic Pressure?J_wm - Mass Water Flux?T - Temperature?[R] - Universal gas constant?

Membrane Thickness Based on Solution Diffusion Model Example

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Here is how the Membrane Thickness Based on Solution Diffusion Model equation looks like with Values.

Here is how the Membrane Thickness Based on Solution Diffusion Model equation looks like with Units.

Here is how the Membrane Thickness Based on Solution Diffusion Model equation looks like.

1.3E-5 = \frac{0.018 \cdot 1.8E-10 \cdot 156 \cdot (81.32 - 39.5)}{6.3E-5 \cdot 8.3145 \cdot 298}

1.3E-5m = \frac{0.018m³/kmol \cdot 1.8E-10m²/s \cdot 156kg/m³ \cdot (81.32at - 39.5at)}{6.3E-5kg/s/m² \cdot 8.3145 \cdot 298K}

1.3E-5 = \frac{0.018 \cdot 1.8E-10 \cdot 156 \cdot (81.32 - 39.5)}{6.3E-5 \cdot 8.3145 \cdot 298}

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Membrane Thickness Based on Solution Diffusion Model Solution

Follow our step by step solution on how to calculate Membrane Thickness Based on Solution Diffusion Model?

FIRST Step Consider the formula

l m = \frac{V l \cdot D w \cdot C w \cdot (ΔP atm - Δπ)}{J wm \cdot [R] \cdot T}

Next Step Substitute values of Variables

∴

l m = \frac{0.018m³/kmol \cdot 1.8E-10m²/s \cdot 156kg/m³ \cdot (81.32at - 39.5at)}{6.3E-5kg/s/m² \cdot [R] \cdot 298K}

Next Step Substitute values of Constants

∴

l m = \frac{0.018m³/kmol \cdot 1.8E-10m²/s \cdot 156kg/m³ \cdot (81.32at - 39.5at)}{6.3E-5kg/s/m² \cdot 8.3145 \cdot 298K}

Next Step Convert Units

∴

l m = \frac{1.8E-5m³/mol \cdot 1.8E-10m²/s \cdot 156kg/m³ \cdot (8E+6Pa - 3.9E+6Pa)}{6.3E-5kg/s/m² \cdot 8.3145 \cdot 298K}

Next Step Prepare to Evaluate

∴

l m = \frac{1.8E-5 \cdot 1.8E-10 \cdot 156 \cdot (8E+6 - 3.9E+6)}{6.3E-5 \cdot 8.3145 \cdot 298}

Next Step Evaluate

∴

l m = 1.29992026139213E-05m

LAST Step Rounding Answer

∴

l m = 1.3E-5m

Membrane Thickness Based on Solution Diffusion Model Formula Elements

Variables

Constants

Membrane Layer Thickness

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.

Symbol: l_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Membrane Layer Thickness

Partial Molar Volume

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.

Symbol: V_l

Measurement: Molar VolumeUnit: m³/kmol

Note: Value should be greater than 0.

Formulas to find Partial Molar Volume

Membrane Water Diffusivity

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).

Symbol: D_w

Measurement: Kinematic ViscosityUnit: m²/s

Note: Value should be greater than 0.

Formulas to find Membrane Water Diffusivity

Membrane Water Concentration

Membrane water concentration (MWC) is the concentration of water in a membrane. It is typically measured in moles per cubic meter (kg/m^3).

Symbol: C_w

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Membrane Water Concentration

Membrane Pressure Drop

Membrane pressure drop is the difference in pressure between the inlet and outlet of a membrane system, housing (pressure vessel), or element.

Symbol: ΔP_atm

Measurement: PressureUnit: at

Note: Value should be greater than 0.

Formulas to find Membrane Pressure Drop

Osmotic Pressure

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.

Symbol: Δπ

Measurement: PressureUnit: at

Note: Value should be greater than 0.

Formulas to find Osmotic Pressure

Mass Water Flux

Mass Water flux is defined as the rate of movement of water across a surface or through a medium.

Symbol: J_wm

Measurement: Mass FluxUnit: kg/s/m²

Note: Value should be greater than 0.

Formulas to find Mass Water Flux

Temperature

Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value should be greater than 274.15.

Formulas to find Temperature

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

Other formulas in Membrane Characteristics category

Go Pressure Driving Force in Membrane

ΔP m = R m \cdot μ \cdot J wM

Go Membrane Pore Diameter

d = {(\frac{32 \cdot μ \cdot J wM \cdot Τ \cdot l mt}{ε \cdot ΔP m})}^{0.5}

How to Evaluate Membrane Thickness Based on Solution Diffusion Model?

Membrane Thickness Based on Solution Diffusion Model evaluator uses Membrane Layer Thickness = (Partial Molar Volume*Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))/(Mass Water Flux*[R]*Temperature) to evaluate 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 evaluate Membrane Thickness Based on Solution Diffusion Model using this online evaluator? To use this online evaluator 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.

FAQs on Membrane Thickness Based on Solution Diffusion Model

What is the formula to find Membrane Thickness Based on Solution Diffusion Model?

The formula of Membrane Thickness Based on Solution Diffusion Model is expressed as Membrane Layer Thickness = (Partial Molar Volume*Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))/(Mass Water Flux*[R]*Temperature). Here is an example- 1.3E-5 = (1.8E-05*1.762E-10*156*(7974767.78-3873626.75))/(6.3E-05*[R]*298).

How to calculate Membrane Thickness Based on Solution Diffusion Model?

With 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) we can find Membrane Thickness Based on Solution Diffusion Model using the formula - Membrane Layer Thickness = (Partial Molar Volume*Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))/(Mass Water Flux*[R]*Temperature). This formula also uses Universal gas constant .

Can the Membrane Thickness Based on Solution Diffusion Model be negative?

Yes, the Membrane Thickness Based on Solution Diffusion Model, measured in Length can be negative.

Which unit is used to measure Membrane Thickness Based on Solution Diffusion Model?

Membrane Thickness Based on Solution Diffusion Model is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Membrane Thickness Based on Solution Diffusion Model can be measured.

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Membrane Thickness Based on Solution Diffusion Model Formula

Membrane Thickness Based on Solution Diffusion Model Example

Membrane Thickness Based on Solution Diffusion Model Solution

Membrane Thickness Based on Solution Diffusion Model Formula Elements

Other formulas in Membrane Characteristics category

How to Evaluate Membrane Thickness Based on Solution Diffusion Model?

FAQs on Membrane Thickness Based on Solution Diffusion Model

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