Free Surface next to a Wet Wall

The height of a gas-liquid interface near a wet vertical surface is given by , the solution of the nonlinear ODE , where is the capillary length (expressed in unit length), is the surface tension (in force per unit length) and is the liquid density (in unit weight per unit volume). The following boundary conditions apply:
and , with the contact angle, which is a property of the three phases (solid, liquid and gas). The wetting assumption requires that . Here, is measured from the vertical wall.
This Demonstration displays the gas-liquid interface near the wet vertical wall for various values of the capillary length and contact angle.

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W. M. Deen, Analysis of Transport Phenomena, New York: Oxford University Press, 1998.
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