Membrane Water Diffusivity Based On Solution Diffusion Model Calculator

Formula Used:

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

Mass Water Flux (J_wm):

kg/s·m²

Temperature (T):

Membrane Layer Thickness (l_m):

Membrane Water Concentration (C_w):

kg/m³

Partial Molar Volume (V_l):

m³/mol

Membrane Pressure Drop (ΔP_atm):

Osmotic Pressure (Δπ):

Membrane Water Diffusivity (D_w):

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1. What is Membrane Water Diffusivity?

Membrane water diffusivity is the rate at which water molecules diffuse across a membrane. It is typically measured in square meters per second (m²/s) and is a crucial parameter in membrane separation processes, particularly in reverse osmosis and other filtration technologies.

2. How Does the Calculator Work?

The calculator uses the Solution Diffusion Model equation:

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

Where:

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

Explanation: This equation describes the diffusion of water through a membrane based on the solution-diffusion model, which is fundamental to understanding membrane transport phenomena.

3. Importance of Membrane Water Diffusivity Calculation

Details: Accurate calculation of membrane water diffusivity is essential for designing efficient membrane separation systems, optimizing filtration processes, and predicting membrane performance in various applications including water purification, desalination, and industrial separation processes.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure that membrane pressure drop is greater than osmotic pressure for valid results. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range 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.

Q2: How does temperature affect membrane water diffusivity?
A: Higher temperatures generally increase water diffusivity due to increased molecular mobility and reduced viscosity.

Q3: What is the significance of the solution-diffusion model?
A: The solution-diffusion model is widely used to describe transport through non-porous membranes, where permeants dissolve in the membrane material and then diffuse through it.

Q4: How does membrane thickness affect water diffusivity?
A: Thicker membranes generally result in lower flux rates, but the intrinsic diffusivity (D_w) is a material property that should be independent of thickness.

Q5: What are common applications of this calculation?
A: This calculation is crucial in reverse osmosis system design, membrane characterization, water treatment process optimization, and research on membrane materials.