# Laplace pressure

Written by Yuhang Jin, AP225 2011 Fall.

The Laplace pressure is the pressure difference across a curved surface or interface [2]. This pressure jump arises from surface tension or interfacial tension, whose presence tends to compress the curved surface or interface. At equilibrium, this trend is balanced by an extra pressure at the concave side. The Laplace pressure is given as

$P_L=\gamma(\frac{1}{R_1}+\frac{1}{R_2})$,

where $R_1$ and $R_2$ are the orthogonal (principle) radii of the curvature, and $\gamma$ is the surface tension or interfacial tension. For a spherical droplet or bubble with a radius of $R$, the formula reduces to

$P_L=2\frac{\gamma}{R}$.

The Laplace pressure is usually insignificant for macroscopic droplets or bubbles with a diameter of 10 cm or larger. However, this capillary effect is especially important for small bubbles. For instance, an air bubble in water whose diameter is 1 μm can have an extra pressure of 2.9 atm inside. This explains the extra energy required to generate emulsions such as droplets in droplet microfluidics etc.

## References

[2] J. N. Israelachvili, "Intermolecular and Surface Forces", Academic Press, 2011.