Bulk Concentration of Membrane Calculator

Bulk Concentration Formula:

\[ C_b = \frac{C_m}{\frac{\exp\left(\frac{J_w}{k_l}\right)}{R' + (1-R')\exp\left(\frac{J_w}{k_l}\right)}} \]

Solute Concentration at Membrane Surface (C_m):

mol/m³

Water Flux (J_w):

m³/m²·s

Mass Transfer Coefficient (k_l):

m/s

Solute Rejection (R'):

Bulk Concentration (C_b): mol/m³

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1. What is Bulk Concentration in Membrane Processes?

Definition: Bulk concentration refers to the concentration of solutes in the main body of fluid, away from the membrane surface.

Purpose: This calculator helps determine the bulk concentration based on membrane surface conditions and transport properties.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_b = \frac{C_m}{\frac{\exp\left(\frac{J_w}{k_l}\right)}{R' + (1-R')\exp\left(\frac{J_w}{k_l}\right)}} \]

Where:

\( C_b \) — Bulk concentration (mol/m³)
\( C_m \) — Solute concentration at membrane surface (mol/m³)
\( J_w \) — Water flux (m³/m²·s)
\( k_l \) — Mass transfer coefficient (m/s)
\( R' \) — Solute rejection (dimensionless, 0-1)

Explanation: The formula accounts for concentration polarization effects at the membrane surface.

3. Importance of Bulk Concentration Calculation

Details: Accurate bulk concentration determination is crucial for membrane process design, performance prediction, and fouling control.

4. Using the Calculator

Tips: Enter all required parameters. Solute rejection (R') defaults to 0.95 (95%) but can be adjusted from 0 to 1.

5. Frequently Asked Questions (FAQ)

Q1: What is concentration polarization?
A: It's the accumulation of rejected solutes near the membrane surface, creating a higher concentration layer than in the bulk solution.

Q2: How does water flux affect bulk concentration?
A: Higher water flux typically increases concentration polarization, leading to greater differences between bulk and surface concentrations.

Q3: What factors influence the mass transfer coefficient?
A: Flow velocity, channel geometry, solution viscosity, and solute diffusivity all affect the mass transfer coefficient.

Q4: Why is solute rejection important in this calculation?
A: Solute rejection determines how much of the solute is retained at the membrane surface versus passing through.

Q5: What are typical units for these parameters?
A: Concentrations are in mol/m³, water flux in m³/m²·s, and mass transfer coefficient in m/s.