Curvatures of Simple Surfaces

The relation:

$$\input{equations/29-1A}$$ (35-16)

was used above to relate the pressure difference across an interface. If the pressure is to be the same within each phase, then at equilibrium a surface must have constant curvature.

Consider how curvature relates to some geometrical objects that have ``constant mean curvature.''

For the sphere:

$$\input{equations/29-1B}$$ (35-17)

There is one radius of curvature for each perpendicular plane with an axis normal to the surface at each point.

For the cylinder:

$$\input{equations/29-1C}$$ (35-18)