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of solids in a liquid medium. It affects the distribution of groundwater, the
moistening of soils, and a variety of biological and other natural processes.

3.7. Surface Curvature and Laplace Pressure

The Laplace pressure is the pressure difference between the inside and
the outside of a curved surface. The pressure difference is caused by the
surface tension of the interface between liquid and gas.

The Laplace pressure is determined from the Young–Laplace equation

given as

 1 1 

p     (3.7.1)
 
R
 1 R 2 
where and are the radii of

curvature (fig.3.7.1) and  is the
surface tension. Although signs for
these values vary, sign convention

usually dictates positive curvature
when it is convex and negative when
concave. The Laplace pressure is
commonly used to determine the

pressure difference in spherical shapes
such as bubbles or droplets. When this
is the case the radiuses of curvature are

equal ( = ) and the equation is
Figure 3.7.1 simplified to

2 
p  (3.7.2)
R

A common example of use is finding the pressure inside an air bubble in
pure water, where = 72 mN/m at 25°C (298 K). The extra pressure inside
the bubble is given here for three bubble sizes:

Bubble diameter (2r) (µm) (Pa) (atm)
1000 288 0.00284

3.0 96000 0.947

0.3 960000 9.474

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