Membrane Water Concentration Based On Solution Diffusion Model Calculator

Formula Used:

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

Mass Water Flux (J_wm):

kg/s·m²

Temperature (T):

Membrane Layer Thickness (l_m):

Membrane Water Diffusivity (D_w):

m²/s

Partial Molar Volume (V_l):

m³/mol

Membrane Pressure Drop (ΔP_atm):

Osmotic Pressure (Δπ):

Membrane Water Concentration (C_w):

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1. What is Membrane Water Concentration?

Membrane water concentration (MWC) is the concentration of water in a membrane, typically measured in kilograms per cubic meter (kg/m³). It represents the amount of water present within the membrane structure and is a critical parameter in membrane separation processes.

2. How Does the Calculator Work?

The calculator uses the Solution Diffusion Model equation:

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

Where:

\( C_w \) — Membrane water concentration (kg/m³)
\( J_{wm} \) — 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)
\( V_l \) — Partial molar volume (m³/mol)
\( \Delta P_{atm} \) — Membrane pressure drop (Pa)
\( \Delta \pi \) — Osmotic pressure (Pa)

Explanation: This equation describes the relationship between water flux through a membrane and the driving force (pressure difference minus osmotic pressure) based on the solution-diffusion model.

3. Importance of Membrane Water Concentration

Details: Membrane water concentration is crucial for understanding membrane performance in separation processes such as reverse osmosis, nanofiltration, and gas separation. It helps in predicting water permeability, selectivity, and overall membrane efficiency.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure that membrane pressure drop is greater than osmotic pressure to avoid negative driving force. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the solution-diffusion model?
A: The solution-diffusion model is a theoretical framework that describes transport through non-porous membranes where permeants dissolve in the membrane material and then diffuse through it down a concentration gradient.

Q2: Why is temperature important in this calculation?
A: Temperature affects both the diffusion coefficient and the solubility of water in the membrane, making it a critical parameter in membrane transport calculations.

Q3: What is the significance of partial molar volume?
A: Partial molar volume represents the change in volume when one mole of water is added to the membrane system, which affects how water molecules interact with the membrane matrix.

Q4: How does osmotic pressure affect membrane water concentration?
A: Osmotic pressure opposes the applied hydraulic pressure, reducing the effective driving force for water transport through the membrane.

Q5: What are typical values for membrane water diffusivity?
A: Membrane water diffusivity typically ranges from 10⁻¹² to 10⁻⁹ m²/s, depending on the membrane material and structure.