# Laplace pressure

Written by Yuhang Jin, AP225 2011 Fall.

The Laplace pressure is the pressure difference across a curved surface or interface. 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

<math>P_L=\gamma(\frac{1}{R_1}+\frac{1}{R_2})</math>,

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

<math>P_L=2\frac{\gamma}{R}</math>.

## References

[1] High-throughput injection with microfluidics using picoinjectors