Osmotic Pressure Drop Based on Solution Diffusion Model Calculator

Osmotic Pressure Formula:

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

Membrane Pressure Drop (ΔP):

Mass Water Flux (J_wm):

kg/(s·m²)

Temperature (T):

Membrane Layer Thickness (l_m):

Membrane Water Diffusivity (D_w):

m²/s

Membrane Water Concentration (C_w):

kg/m³

Partial Molar Volume (V_l):

m³/mol

Osmotic Pressure (Δπ): Pa

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1. What is Osmotic Pressure Drop Based on Solution Diffusion Model?

Definition: This calculator determines the osmotic pressure drop across a semipermeable membrane using the solution-diffusion model.

Purpose: It helps in understanding and predicting membrane performance in reverse osmosis and other membrane separation processes.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the osmotic pressure by accounting for the driving force (pressure drop) and subtracting the resistance terms related to membrane properties and operating conditions.

3. Importance of Osmotic Pressure Calculation

Details: Accurate osmotic pressure calculation is crucial for designing efficient membrane systems, predicting water flux, and optimizing energy consumption in desalination and water purification processes.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Default values are provided for typical membrane conditions, but these should be adjusted based on your specific membrane properties.

5. Frequently Asked Questions (FAQ)

Q1: What is the solution-diffusion model?
A: It's a theoretical model that describes transport through non-porous membranes where permeants dissolve in and diffuse through the membrane material.

Q2: How do I determine membrane water diffusivity?
A: This is typically measured experimentally or provided by membrane manufacturers. For RO membranes, it's usually in the range of 10^-10 to 10^-12 m²/s.

Q3: What affects membrane water concentration?
A: It depends on membrane material, water activity, and temperature. For polymeric membranes, it's typically 100-200 kg/m³.

Q4: Why is temperature important in this calculation?
A: Temperature affects both the diffusion coefficient and the thermodynamic properties of water in the membrane.

Q5: How does membrane thickness impact osmotic pressure?
A: Thicker membranes generally result in higher resistance to water transport, requiring greater pressure differences to achieve the same flux.