Solute Concentration at Membrane Surface Calculator

✖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.ⓘ Bulk Concentration [C_b]			+10% -10%
✖Water flux is defined as the rate at which water flows through a membrane per unit area.ⓘ Water Flux [J_w]			+10% -10%
✖Mass transfer coefficient at membrane surface is defined as the measure of the rate at which solutes can diffuse through the membrane.ⓘ Mass Transfer Coefficient at Membrane Surface [k_l]			+10% -10%
✖Solute rejection is defined as the ability of a membrane to prevent the passage of solutes from a feed solution to the permeate solution.ⓘ Solute Rejection [R_']			+10% -10%

✖Solute concentration at membrane surface is defined as the concentration of solutes in the fluid immediately adjacent to the membrane surface.ⓘ Solute Concentration at Membrane Surface [C_m]

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Formula

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Solute Concentration at Membrane Surface

Formula

`"C"_{"m"} = ("C"_{"b"}*exp("J"_{"w"}/"k"_{"l"}))/("R"_{"'"}+(1-"R"_{"'"})*exp("J"_{"w"}/"k"_{"l"}))`

Example

`"6"=("0.3"*exp("0.0001139m³/(m²*s)"/"0.00003cm/s"))/("0.95"+(1-"0.95")*exp("0.0001139m³/(m²*s)"/"0.00003cm/s"))`

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Solute Concentration at Membrane Surface Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
C_m = (C_b*exp(J_w/k_l))/(R_'+(1-R_')*exp(J_w/k_l))
This formula uses 1 Functions, 5 Variables

Functions Used

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

Variables Used

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.
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.
Water Flux - (Measured in Cubic Meter per Square Meter per Second) - Water flux is defined as the rate at which water flows through a membrane per unit area.
Mass Transfer Coefficient at Membrane Surface - (Measured in Meter per Second) - Mass transfer coefficient at membrane surface is defined as the measure of the rate at which solutes can diffuse through the membrane.
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.

STEP 1: Convert Input(s) to Base Unit

Bulk Concentration: 0.3 --> No Conversion Required
Water Flux: 0.0001139 Cubic Meter per Square Meter per Second --> 0.0001139 Cubic Meter per Square Meter per Second No Conversion Required
Mass Transfer Coefficient at Membrane Surface: 3E-05 Centimeter per Second --> 3E-07 Meter per Second (Check conversion here)
Solute Rejection: 0.95 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_m = (C_b*exp(J_w/k_l))/(R_'+(1-R_')*exp(J_w/k_l)) --> (0.3*exp(0.0001139/3E-07))/(0.95+(1-0.95)*exp(0.0001139/3E-07))

Evaluating ... ...

C_m = 5.99999999999999

STEP 3: Convert Result to Output's Unit

5.99999999999999 --> No Conversion Required

FINAL ANSWER

5.99999999999999 ≈ 6 <-- Solute Concentration at Membrane Surface

(Calculation completed in 00.004 seconds)

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Created by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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Verified by Soupayan banerjee

National University of Judicial Science (NUJS), Kolkata

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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

Solute Concentration at Membrane Surface Formula

What are the Different Types of Membrane Processes?

Microfiltration (MF): This process uses membranes with pore sizes ranging from 0.1 to 10 micrometers to remove larger particles like bacteria, algae, and suspended solids from liquids. It's often used in pre-treatment for other membrane processes and in wastewater treatment.

Ultrafiltration (UF): UF membranes have smaller pore sizes (1-100 nm) and can remove colloids, viruses, and macromolecules like proteins from liquids. It's widely applied in food and beverage processing, pharmaceutical manufacturing, and water purification.

Nanofiltration (NF): NF membranes have even smaller pores (0.1-1 nm) and can separate smaller molecules like divalent ions and organic compounds from water. It's used in water softening, desalination, and wastewater treatment.

How to Calculate Solute Concentration at Membrane Surface?

Solute Concentration at Membrane Surface calculator uses 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)) to calculate the Solute Concentration at Membrane Surface, The solute concentration at membrane surface, also known as the surface concentration, refers to the concentration of a solute (dissolved substance) in the immediate vicinity of a membrane's interface with a bulk solution. Solute Concentration at Membrane Surface is denoted by C_m symbol.

How to calculate Solute Concentration at Membrane Surface using this online calculator? To use this online calculator for Solute Concentration at Membrane Surface, enter Bulk Concentration (C_b), Water Flux (J_w), Mass Transfer Coefficient at Membrane Surface (k_l) & Solute Rejection (R_') and hit the calculate button. Here is how the Solute Concentration at Membrane Surface calculation can be explained with given input values -> 6 = (0.3*exp(0.0001139/3E-07))/(0.95+(1-0.95)*exp(0.0001139/3E-07)).

FAQ

What is Solute Concentration at Membrane Surface?

The solute concentration at membrane surface, also known as the surface concentration, refers to the concentration of a solute (dissolved substance) in the immediate vicinity of a membrane's interface with a bulk solution and is represented as C_m = (C_b*exp(J_w/k_l))/(R_'+(1-R_')*exp(J_w/k_l)) or 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)). 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, Water flux is defined as the rate at which water flows through a membrane per unit area, Mass transfer coefficient at membrane surface is defined as the measure of the rate at which solutes can diffuse through the membrane & Solute rejection is defined as the ability of a membrane to prevent the passage of solutes from a feed solution to the permeate solution.

How to calculate Solute Concentration at Membrane Surface?

The solute concentration at membrane surface, also known as the surface concentration, refers to the concentration of a solute (dissolved substance) in the immediate vicinity of a membrane's interface with a bulk solution is calculated using 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)). To calculate Solute Concentration at Membrane Surface, you need Bulk Concentration (C_b), Water Flux (J_w), Mass Transfer Coefficient at Membrane Surface (k_l) & Solute Rejection (R_'). With our tool, you need to enter the respective value for Bulk Concentration, Water Flux, Mass Transfer Coefficient at Membrane Surface & Solute Rejection 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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