Membrane Thickness Based on Solution Diffusion Model Calculator

Membrane Thickness Formula:

\[ l_m = \frac{V_l \times D_w \times C_w \times (\Delta P_{atm} - \Delta \pi)}{J_{wm} \times [R] \times T} \]

Partial Molar Volume:

m³/mol

Membrane Water Diffusivity:

m²/s

Membrane Water Concentration:

kg/m³

Membrane Pressure Drop:

Osmotic Pressure:

Mass Water Flux:

kg/(s·m²)

Temperature:

Membrane Layer Thickness (m):

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1. What is Membrane Thickness Based on Solution Diffusion Model?

Definition: This calculator determines the thickness of a membrane layer using the solution-diffusion model, which describes permeation in non-porous membranes.

Purpose: It helps researchers and engineers in membrane technology to design and analyze membrane systems for applications like reverse osmosis, gas separation, and pervaporation.

2. How Does the Calculator Work?

The calculator uses the solution-diffusion model formula:

\[ l_m = \frac{V_l \times D_w \times C_w \times (\Delta P_{atm} - \Delta \pi)}{J_{wm} \times [R] \times T} \]

Where:

\( l_m \) — Membrane layer thickness (meters)
\( V_l \) — Partial molar volume (m³/mol)
\( D_w \) — Membrane water diffusivity (m²/s)
\( C_w \) — Membrane water concentration (kg/m³)
\( \Delta P_{atm} \) — Membrane pressure drop (Pa)
\( \Delta \pi \) — Osmotic pressure (Pa)
\( J_{wm} \) — Mass water flux (kg/(s·m²))
\( [R] \) — Universal gas constant (8.314 J/(mol·K))
\( T \) — Temperature (Kelvin)

Explanation: The formula calculates membrane thickness based on the balance between driving forces (pressure difference) and transport resistance.

3. Importance of Membrane Thickness Calculation

Details: Membrane thickness is crucial for determining flux rates, selectivity, and mechanical stability in separation processes. Thinner membranes typically offer higher flux but may compromise mechanical strength.

4. Using the Calculator

Tips:

Default values are provided for typical conditions
All inputs must be positive numbers
Pressure drop must be greater than osmotic pressure
Results are in meters (typically in the range of nanometers to micrometers for membranes)

5. Frequently Asked Questions (FAQ)

Q1: What is the solution-diffusion model?
A: It's a model that describes permeation through dense (non-porous) membranes where molecules dissolve in the membrane material and diffuse through it.

Q2: What's a typical membrane thickness range?
A: Most industrial membranes range from 50 nm to 500 μm, depending on the application and material.

Q3: How does temperature affect membrane thickness calculation?
A: Higher temperatures generally increase diffusivity but also affect other parameters in the equation.

Q4: What if my osmotic pressure is zero?
A: For systems without osmotic pressure difference (like gas separation), set osmotic pressure to zero.

Q5: How accurate is this calculation?
A: It provides theoretical estimates; actual membrane performance may vary due to material properties and manufacturing variations.