Surface tension of a torus raindrop


by peripatein
Tags: raindrop, surface, tension, torus
peripatein
peripatein is offline
#1
Nov25-12, 07:55 AM
P: 816
1. The problem statement, all variables and given/known data

When calculating the difference in pressure inside a spherical raindrop, the force exerted by the surface tension is calculated to be 2pi*R*gama, where R is the radius of the drop and gamma is dE/dS (dyne/cm).
When the shape of the raindrop is said to be that of a torus, the force exerted by the surface tension is calculated to be 2pi*R*gamma + 2pi(R+2r)*gamma (please see attachment).
My question is simply why does the force in the case of the torus have two components, whereas in the case of a sphere it has only one?

2. Relevant equations



3. The attempt at a solution
Attached Thumbnails
Torus.JPG  
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
mfb
mfb is offline
#2
Nov25-12, 08:29 AM
Mentor
P: 10,840
In both cases, the expression is the length of the boundary (as seen in a 2D-projection) multiplied by gamma. A circle has one boundary, the torus has 2 (inner+outer).
peripatein
peripatein is offline
#3
Nov25-12, 09:06 AM
P: 816
But isn't the circle's circumference considered a boundary? Or shouldn't it be? Is it not a thin layer of fluid verging on air?

mfb
mfb is offline
#4
Nov25-12, 09:49 AM
Mentor
P: 10,840

Surface tension of a torus raindrop


But isn't the circle's circumference considered a boundary?
Of course. That should be the origin of 2pi*R*gamma.
You get a layer of fluid/air in contact there.
peripatein
peripatein is offline
#5
Nov25-12, 10:49 AM
P: 816
Okay. Thank you.


Register to reply

Related Discussions
Surface Area of a Torus Calculus & Beyond Homework 1
Is Horn-torus a valid genus-1 Riemann Surface? Differential Geometry 2
Surface area of a beaker of water w/ surface tension? Chemistry 1
Surface Integrals and Average Surface Temperature of a Torus Calculus & Beyond Homework 4
Minimal Surface evolution from Torus - reversible? Beyond the Standard Model 0