Surface Tension

Date: 11/09/2000 at 20:14:38
From: Derek Schimpf
Subject: Calculating the force of surface tension

Dr. Math,

The unit of surface tension is N/m. If I want to calculate the force 
in newtons exerted by a liquid, do I multiply the surface tension by 
the distance that the surface has been deformed (without breaking the 
surface)?

Thanks.
Derek

Date: 11/10/2000 at 06:34:23
From: Doctor Mitteldorf
Subject: Re: Calculating the force of surface tension

Dear Derek,

It's not that simple. The force can be related to the radius of 
curvature, which may be different at different points along your 
surface. The geometry of the problem is often the complicating factor.

Surface tension is the amount of force on a given liquid area. You'd 
think it would be newtons per meter squared, N/m^2. How did it get to 
be N/m?
  
The reason is that surface tension depends on the curvature of the 
surface, and the units of curvature are 1/m. Think of curvature as 
being the reciprocal of the radius of curvature.  
   
To get the force, multiply the surface tension times the area times 
the reciprocal of the radius of curvature.

The complication comes in the geometry. A 2-dimensional surface can 
have 2 principal radii of curvature, because it curves differently in 
2 directions. A free surface, like a soap bubble, will obey a 
"constant curvature" rule that says the sum of these two reciprocals 
is the same everywhere. It's the sum of the two reciprocals that gives 
you the effective curvature that you can use to calculate a force.

- Doctor Mitteldorf, The Math Forum
  http://mathforum.org/dr.math/