# Object floating on the surface of water

1. Mar 31, 2010

### 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.

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Last edited: Mar 31, 2010
2. Mar 31, 2010

### 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: