Bulk Concentration of Membrane Calculator

✖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]			+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%

✖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 of Membrane [C_b]

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Formula

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Bulk Concentration of Membrane

Formula

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

Example

`"0.299557"=("4.2")/((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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Bulk Concentration of Membrane Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
C_b = (C_m)/((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

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.
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.
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 Centimeter 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

Solute Concentration at Membrane Surface: 4.2 --> 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-05 Centimeter per Second No Conversion Required
Solute Rejection: 0.95 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_b = (C_m)/((exp(J_w/k_l))/(R_'+(1-R_')*exp(J_w/k_l))) --> (4.2)/((exp(0.0001139/3E-05))/(0.95+(1-0.95)*exp(0.0001139/3E-05)))

Evaluating ... ...

C_b = 0.299557407408674

STEP 3: Convert Result to Output's Unit

0.299557407408674 --> No Conversion Required

FINAL ANSWER

0.299557407408674 ≈ 0.299557 <-- Bulk Concentration

(Calculation completed in 00.020 seconds)

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Created by Harsh Kadam

Shri Guru Gobind Singhji Institute of Engineering and Technology (SGGS), Nanded

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Verified by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

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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

Bulk Concentration of Membrane Formula

Where is the Application of Bulk Concentration of Membrane?

ulk membrane concentration can be used to concentrate a wide variety of solutes, including metals, organic compounds, and proteins. It is a particularly useful technique for concentrating solutes from dilute solutions, or for concentrating solutes that are difficult to concentrate using other methods.

How to Calculate Bulk Concentration of Membrane?

Bulk Concentration of Membrane calculator uses 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))) to calculate the Bulk Concentration, Bulk Concentration of Membrane is defined as a process of using a semipermeable membrane to separate a mixture of solutes into two or more fractions. Bulk Concentration is denoted by C_b symbol.

How to calculate Bulk Concentration of Membrane using this online calculator? To use this online calculator for Bulk Concentration of Membrane, enter Solute Concentration at Membrane Surface (C_m), Water Flux (J_w), Mass Transfer Coefficient at Membrane Surface (k_l) & Solute Rejection (R_') and hit the calculate button. Here is how the Bulk Concentration of Membrane calculation can be explained with given input values -> 0.21 = (4.2)/((exp(0.0001139/3E-07))/(0.95+(1-0.95)*exp(0.0001139/3E-07))).

FAQ

What is Bulk Concentration of Membrane?

Bulk Concentration of Membrane is defined as a process of using a semipermeable membrane to separate a mixture of solutes into two or more fractions and is represented as C_b = (C_m)/((exp(J_w/k_l))/(R_'+(1-R_')*exp(J_w/k_l))) or 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 is defined as the concentration of solutes in the fluid immediately adjacent to the membrane surface, 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 Bulk Concentration of Membrane?

Bulk Concentration of Membrane is defined as a process of using a semipermeable membrane to separate a mixture of solutes into two or more fractions is calculated using 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))). To calculate Bulk Concentration of Membrane, you need Solute Concentration at Membrane Surface (C_m), 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 Solute Concentration at Membrane Surface, 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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