I met a problem to solve the Navier-stoke equation in a confined geometry. Here geometry is a sphere on a flat plate. The liquid was load in the gap between two surfaces. This liquid will evaporate.

And the radius of sphere is larger compared with the gap disatance between two surface. So N-V equation was used lubrication approximation.

I want to how the is veloticy field in such condition caused by evaporation. and also I want to know the interface evolution with time.

Could anyone tell me how to establish a coordinate to solve my problem.

Thank you very much

Boundary element method ( stokelets in particular ) would be a possible way.

-Harish

Thank you