Basic Principle:
Consider a specific membrane material. The membrane is fully wetted with a liquid that can be infiltrated into it. The infiltrating liquid is held within the pores of the membrane due to surface tension. A gradually increasing gas pressure is applied on one side of the membrane. When the gas pressure exceeds the surface tension of the liquid in a particular pore size, the liquid in that pore is pushed out by the gas. Since smaller pores have higher surface tension, they require higher gas pressure to expel the liquid. As the pressure increases, the smallest pores are opened first, allowing gas to pass through. Then, as the pressure continues to rise, larger pores are sequentially opened until all pores are clear, resulting in a transmittance similar to that of a dry membrane.
The pressure at which the first pore opens is called the bubble point pressure, and the corresponding pore size is referred to as the bubble point diameter. During this process, both pressure and flow rate are recorded in real time to generate a pressure-flow curve. The pressure data provides information about the pore size, while the flow rate reflects the number of pores of a given size. By testing the pressure-flow curve of the dry membrane, it is possible to calculate various parameters such as pore size, average pore size, minimum pore size, pore size distribution, and transmittance using appropriate formulas.
The relationship between pore size and pressure follows the Washburn equation:
D = 4γCosθ / p
In this formula, D represents the pore diameter, γ is the surface tension of the liquid, θ is the contact angle, and p is the pressure difference.
Pore size distribution can be calculated using the following expression:
f(D) = -d[(Fw/Fd) × 100]/dD
Where Fw is the flow rate of the wet sample, and Fd is the flow rate of the dry sample.
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