Curved surfaces
A liquid surface is not generally flat. This has two consequences.
1. The curvature of the surface affects the vapor pressure.
2. The capillary rise or of liquids in narrow tubes results.
We consider bubbles (vapor trapped in liquid) or droplets (liquid
in vapor) as spheres of area 4pR2. Here we consider a bubble
where the pressure inside the cavity is Pin. The outward force is
4pR2Pin . The force inwards arises from the external pressure
Pout and the surface tension. The differential change in area is:
ds = 4p(R + dR)2 - 4pR2 = 8pRdR
Since, dw = 8pgRdR the force is F = 8pgR. Pressure is force per
4pR2 Pin = 4pR2 Pout + 8pgR