Drops and Puddles in the Partial Wetting Regime

The solutions to this last equation are of the form z = Zq exp Kx). In the problem at hand, we are restricted to z — 0 when x — oo. Therefore, we retain only the exponentially decaying solution  

Conclusion, Surface perturbations decay exponentially with distance with a characteristic length which is the capillary length. In the immediate vicinity of the wall, the exact solution is more complicated because the height z is no longer necessarily small. This case will be discussed shortly (section 2.3). 

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