Young-Laplace
Equation

For a sphere, R₁ = R₂ = R and the expression simplifies to Δp = 2γ/R.

Small bubbles or drops can therefore exhibit large capillary pressures.

This simple relation underlies phenomena ranging from bubble stability to porous-media capillarity, but the general axisymmetric equation is required for profile analysis of pendant or sessile drops distorted by gravity.

The shape of a millimetric drop results from competition between interfacial tension, which tends to minimize area, and gravity, which deforms the drop.

The density difference Δρ between the phases and gravitational acceleration g determine the hydrostatic pressure variation with height.

By fitting an experimentally measured drop contour to the numerical solution of the Young–Laplace equation, γ can be inferred from the entire profile rather than from a single geometric feature.

The gravitational deformation that contains information about γ scales with Δρ.

In liquid–liquid systems with very small density differences, pendant-drop deformation may be weak even when the optical profile is excellent.

Alternative geometries or capillary-pressure approaches can then become advantageous.

1. 1.T. Young, An Essay on the Cohesion of Fluids, Philosophical Transactions of the Royal Society of London 95 (1805) 65–87.
2. 2.P. S. Laplace, Traité de Mécanique Céleste, Supplement to Book X, Paris, 1805.
3. 3.A. I. Rusanov and V. A. Prokhorov, Interfacial Tensiometry, Studies in Interface Science, Vol. 3, Elsevier, Amsterdam, 1996.
4. 4.D. Möbius and R. Miller (Eds.), Drops and Bubbles in Interfacial Research, Studies in Interface Science, Vol. 6, Elsevier, Amsterdam, 1998.