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Concentration of Mass at Membrane Surface Formula

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Solute concentration at membrane surface is defined as the concentration of solutes in the fluid immediately adjacent to the membrane surface. Check FAQs

C m = \frac{\exp (\frac{J w}{k l})}{(R' + (1 - R') \cdot \exp (\frac{J w}{k l}))} \cdot C b

C_m - Solute Concentration at Membrane Surface?J_w - Water Flux?k_l - Mass Transfer Coefficient at Membrane Surface?R_' - Solute Rejection?C_b - Bulk Concentration?

Concentration of Mass at Membrane Surface Example

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Here is how the Concentration of Mass at Membrane Surface equation looks like with Values.

Here is how the Concentration of Mass at Membrane Surface equation looks like with Units.

Here is how the Concentration of Mass at Membrane Surface equation looks like.

4.2062 = \frac{\exp (\frac{0.0001}{3E-5})}{(0.95 + (1 - 0.95) \cdot \exp (\frac{0.0001}{3E-5}))} \cdot 0.3

4.2062 = \frac{\exp (\frac{0.0001m³/(m²*s)}{3E-5cm/s})}{(0.95 + (1 - 0.95) \cdot \exp (\frac{0.0001m³/(m²*s)}{3E-5cm/s}))} \cdot 0.3

4.2062 = \frac{\exp (\frac{0.0001}{3E-5})}{(0.95 + (1 - 0.95) \cdot \exp (\frac{0.0001}{3E-5}))} \cdot 0.3

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Concentration of Mass at Membrane Surface Solution

Follow our step by step solution on how to calculate Concentration of Mass at Membrane Surface?

FIRST Step Consider the formula

C m = \frac{\exp (\frac{J w}{k l})}{(R' + (1 - R') \cdot \exp (\frac{J w}{k l}))} \cdot C b

Next Step Substitute values of Variables

∴

C m = \frac{\exp (\frac{0.0001m³/(m²*s)}{3E-5cm/s})}{(0.95 + (1 - 0.95) \cdot \exp (\frac{0.0001m³/(m²*s)}{3E-5cm/s}))} \cdot 0.3

Next Step Prepare to Evaluate

∴

C m = \frac{\exp (\frac{0.0001}{3E-5})}{(0.95 + (1 - 0.95) \cdot \exp (\frac{0.0001}{3E-5}))} \cdot 0.3

Next Step Evaluate

∴

C m = 4.20620545123437

LAST Step Rounding Answer

∴

C m = 4.2062

Concentration of Mass at Membrane Surface Formula Elements

Variables

Functions

Solute Concentration at Membrane Surface

Solute concentration at membrane surface is defined as the concentration of solutes in the fluid immediately adjacent to the membrane surface.

Symbol: C_m

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Solute Concentration at Membrane Surface

Water Flux

Water flux is defined as the rate at which water flows through a membrane per unit area.

Symbol: J_w

Measurement: Membrane FluxUnit: m³/(m²*s)

Note: Value should be greater than 0.

Formulas to find Water Flux

Mass Transfer Coefficient at Membrane Surface

Mass transfer coefficient at membrane surface is defined as the measure of the rate at which solutes can diffuse through the membrane.

Symbol: k_l

Measurement: SpeedUnit: cm/s

Note: Value should be greater than 0.

Formulas to find Mass Transfer Coefficient at Membrane Surface

Solute Rejection

Solute rejection is defined as the ability of a membrane to prevent the passage of solutes from a feed solution to the permeate solution.

Symbol: R_'

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Solute Rejection

Bulk Concentration

Bulk concentration is defined as the concentration of solutes in the bulk fluid, which is the fluid that is not in contact with the membrane.

Symbol: C_b

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Bulk Concentration

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

Other formulas in Basics of Membrane Separation Processes category

Go Hagen Poiseuille Based Flux for Membrane Separation

J wM = \frac{ε \cdot d^{2} \cdot ΔP m}{32 \cdot μ \cdot Τ \cdot l mt}

Go Resistance to flow in Membranes

R m = \frac{ΔP m}{μ \cdot J wM}

Go Liquid Viscosity based on Membrane Resistance

μ = \frac{ΔP m}{R m \cdot J wM}

Go Membrane Flux Based on Resistance

J wM = \frac{ΔP m}{R m \cdot μ}

How to Evaluate Concentration of Mass at Membrane Surface?

Concentration of Mass at Membrane Surface evaluator uses 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 to evaluate the Solute Concentration at Membrane Surface, Concentration of mass at membrane surface is defined as the concentration of solutes in the fluid immediately adjacent to the membrane surface in a membrane separation process. Solute Concentration at Membrane Surface is denoted by C_m symbol.

How to evaluate Concentration of Mass at Membrane Surface using this online evaluator? To use this online evaluator for Concentration of Mass at Membrane Surface, enter Water Flux (J_w), Mass Transfer Coefficient at Membrane Surface (k_l), Solute Rejection (R_') & Bulk Concentration (C_b) and hit the calculate button.

FAQs on Concentration of Mass at Membrane Surface

What is the formula to find Concentration of Mass at Membrane Surface?

The formula of Concentration of Mass at Membrane Surface is expressed as 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. Here is an example- 6 = exp(0.0001139/3E-07)/((0.95+(1-0.95)*exp(0.0001139/3E-07)))*0.3.

How to calculate Concentration of Mass at Membrane Surface?

With Water Flux (J_w), Mass Transfer Coefficient at Membrane Surface (k_l), Solute Rejection (R_') & Bulk Concentration (C_b) we can find Concentration of Mass at Membrane Surface using the formula - 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. This formula also uses Exponential Growth (exp) function(s).

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Concentration of Mass at Membrane Surface Formula

Concentration of Mass at Membrane Surface Example

Concentration of Mass at Membrane Surface Solution

Concentration of Mass at Membrane Surface Formula Elements

Other formulas in Basics of Membrane Separation Processes category

How to Evaluate Concentration of Mass at Membrane Surface?

FAQs on Concentration of Mass at Membrane Surface

Variable Name