Solute Concentration at Membrane Surface Calculator

Solute Concentration Formula:

\[ C_m = \frac{C_b \times e^{(J_w/k_l)}}{R' + (1 - R') \times e^{(J_w/k_l)}} \]

Bulk Concentration (C_b):

Water Flux (J_w):

m³/m²/s

Mass Transfer Coefficient (k_l):

m/s

Solute Rejection (R'):

Solute Concentration at Membrane Surface (C_m):

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1. What is Solute Concentration at Membrane Surface?

Definition: This is the concentration of solutes in the fluid immediately adjacent to the membrane surface during filtration processes.

Purpose: It helps in understanding membrane fouling phenomena and optimizing membrane filtration systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_m = \frac{C_b \times e^{(J_w/k_l)}}{R' + (1 - R') \times e^{(J_w/k_l)}} \]

Where:

\( C_m \) — Solute concentration at membrane surface
\( C_b \) — Bulk concentration in the feed solution
\( J_w \) — Water flux through the membrane (m³/m²/s)
\( k_l \) — Mass transfer coefficient at membrane surface (m/s)
\( R' \) — Solute rejection coefficient (0 to 1)

Explanation: The formula accounts for concentration polarization at the membrane surface due to solute accumulation.

3. Importance of This Calculation

Details: Accurate calculation helps predict membrane performance, fouling potential, and optimize operating conditions.

4. Using the Calculator

Tips: Enter bulk concentration, water flux, mass transfer coefficient, and solute rejection (default 0.95). All values must be valid (k_l > 0, 0 ≤ R' ≤ 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 than in the bulk solution.

Q2: How is mass transfer coefficient determined?
A: It can be estimated from empirical correlations or measured experimentally for specific systems.

Q3: What affects solute rejection?
A: Membrane properties, solute characteristics, operating pressure, and cross-flow velocity.

Q4: Why does C_m increase with higher flux?
A: Higher flux brings more solutes to the membrane surface faster than they can diffuse back to the bulk.

Q5: How can I reduce C_m?
A: Increase cross-flow velocity (higher k_l), reduce flux, or use membranes with lower rejection.