The governing equation
A liquid that wets the pore walls is held in a pore by capillary pressure. Gas can only displace it when the applied pressure difference exceeds the Young–Laplace pressure of the narrowest constriction along the pore path:
Unlike mercury porosimetry (non-wetting liquid pushed in), porometry pushes a wetting liquid out. Both rely on the same capillary physics; compare the Washburn equation.
| Wetting liquid | γ (mN/m) | ΔP for 1 μm | ΔP for 0.2 μm |
|---|---|---|---|
| Low-surface-tension fluorinated liquid (e.g. Galwick) | 15.9 | 0.64 bar (9.2 psi) | 3.2 bar (46 psi) |
| Silicone oil type (e.g. Silwick) | 20.1 | 0.80 bar (11.7 psi) | 4.0 bar (58 psi) |
| Water (20 °C) | 72.8 | 2.9 bar (42 psi) | 14.6 bar (211 psi) |
Values use the ideal 4γ/ΔP. Low-surface-tension liquids wet almost any material spontaneously and keep pressures moderate, which is why they are the default for most filter media.
The three curves
- Wet curve. Start with the sample saturated and raise the pressure. Nothing flows until the bubble point, then flow rises as progressively smaller pores empty.
- Dry curve. Measure flow through the dry sample over the same pressure range.
- Half-dry curve. The dry-curve flow divided by two.
| Result | Where it is read | Formula |
|---|---|---|
| Largest pore (bubble point) | First continuous flow on the wet curve | dmax = 4γ/PBP |
| Mean flow pore (MFP) | Wet curve crosses the half-dry curve | dMFP = 4γ/PMFP |
| Smallest pore | Wet curve meets the dry curve | dmin = 4γ/Pmin |
| Flow-based distribution | Between bubble point and smallest pore | % flow = [(Fw/Fd)i − (Fw/Fd)i−1] × 100 |
Half of the gas flow through the fully open sample passes through pores larger than the mean flow pore, and half through smaller ones. The MFP is a flow-weighted size, not a number-weighted or volume-weighted mean.
Worked example
A membrane wetted with Galwick (γ = 15.9 mN/m) shows its bubble point at 15 psi (103.4 kPa), and the wet curve crosses the half-dry curve at 40 psi (275.8 kPa).
dMFP = 4 × 0.0159 / 275,790 Pa = 2.31 × 10⁻⁷ m ≈ 0.23 μm
Using the ASTM F316 constant instead (d = 0.415 γ / p[psi]) gives 0.44 μm and 0.16 μm. That is the same data with a different convention, which is why reports must state the formula used.
Bubble point calculator
Pitfalls
- Incomplete wetting gives a false, low “bubble point”. Soak under vacuum if needed.
- Evaporation of the wetting liquid during a slow scan shifts the wet curve.
- Diffusion flow through liquid-filled pores can be mistaken for the first bubble in very tight membranes. Use a defined flow threshold.
- Compressible media (nonwovens, foams) can change pore size as pressure rises.
- Dead-end pores are invisible. Porometry only sees through-pores; for total porosity use porosimetry.
Standards
- ASTM F316-03(2019) — bubble point (Method A) and mean flow pore test (Method B) for membrane filters, maximum pore sizes about 0.1–15 μm.
- ASTM D6767 — pore size characteristics of geotextiles by capillary flow test.
- ISO 2942 — hydraulic filter elements: fabrication integrity and first bubble point.
- ASTM E1294 (automated liquid porosimeter) was withdrawn in 2008.
Related guides
Frequently asked questions
How is mean flow pore size calculated?
Record the gas flow through the dry sample (dry curve) and through the wetted sample (wet curve). The half-dry curve is the dry curve divided by two. The pressure where the wet curve crosses the half-dry curve is the mean flow pore pressure P_MFP, and d_MFP = 4γcosθ / P_MFP (θ ≈ 0 for a fully wetting liquid).
What is the bubble point?
The bubble point is the lowest pressure at which a continuous gas flow passes through the wetted sample. It is set by the largest through-pore constriction: d_max = 4γcosθ / P_bubble.
Why does ASTM F316 use 0.415 instead of 4?
ASTM F316 writes d = Cγ/p with C = 2860 (p in Pa, d in μm) or 0.415 (p in psi). That is about 0.715 times the ideal 4γ/ΔP for a cylindrical capillary. The empirical factor is a shape correction. State which convention you use, because the two differ by about 30 %.
Is the Gurley number the same as pore size?
No. A Gurley number is the time for a set volume of air (typically 100 cm³) to pass through a set area under a small fixed pressure. It measures air permeability, which depends on pore size, porosity and thickness together, and does not give a pore size distribution.