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Fundamental:
Taking a specific membrane material as an example, the membrane is fully wetted by a liquid that can penetrate it. The liquid is held within the pores due to surface tension. A gradually increasing gas pressure is applied to one side of the membrane. When the gas pressure exceeds the surface tension in a particular pore size, the liquid inside that pore is pushed out by the gas. Smaller pores require higher pressure to release the liquid because the surface tension is greater in smaller pores. As the pressure increases, the largest pores will open first, allowing gas to pass through. Then, as pressure continues to rise, progressively smaller pores are opened, enabling the gas to permeate until all the pores are clear, achieving the same transmittance as the dry film.
During this process, the pressure and flow rate are recorded in real time to generate a pressure-flow curve. This curve provides information about the pore size distribution and the number of pores at each size. By testing the pressure-flow curve of the dry film, we can calculate key parameters such as the maximum pore size, average pore diameter, minimum pore size, pore size distribution, and overall transmittance using specific formulas.
The relationship between pore size and pressure follows the Washburn equation:
**D = 4γCosθ / p**
Where:
- **D** is the pore diameter,
- **γ** is the surface tension of the liquid,
- **θ** is the contact angle,
- **p** is the pressure difference.
Pore size distribution can be calculated using the formula:
**f(D) = -d[(Fw/Fd) × 100]/dD**
Where:
- **Fw** is the flow rate of the wet sample,
- **Fd** is the flow rate of the dry sample.
This method is widely used in membrane characterization to understand the structural properties and performance of filtration materials. The bubble point pressure is the pressure at which the first pore opens, and it corresponds to the largest pore size in the membrane. The resulting data helps in optimizing membrane design for various industrial applications.
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