Object floating on the surface of water

[xyd]

How to use a function f[x,y,z] to describe the shape of water surface when a tiny object is floating on it based on surface tension ONLY?

Assume there is a tiny object floating on the water surface because of the surface tension, then the water surface will be deformed obviously. So how can we use a function f[x,y,z] to describe the shape of water surface? (x,y,z) is a set of coordinate system of 3D space.

 

[Andy Resnick]

AFAIK, this is a solved problem (it's a meniscus) even though I can't find a reference... interesting

The idea is to balance the pressure: the surface will deform in accordance with Laplace's equation (\Delta P = -\sigma\kappa), and the boundary condition is given by the contact angle. The pressure is given by hydrostatic and contact line forces.

This reference may be a useful starting point:

http://www.springerlink.com/content/ux52v7274110l023/

Or this:

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WHR-4CX72MT-NR&_user=7774119&_coverDate=12%2F31%2F1990&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1276525828&_rerunOrigin=google&_acct=C000062847&_version=1&_urlVersion=0&_userid=7774119&md5=888045530331985fdc846499027a23cd

 

[xyd]

Hey, why no one seems interested in this question?