Static Hysteresis Contact Angles of Drops

A similar approach is used in the following example for drops of liquids that form equilibrium contact angles 0 with a flat substrate. For the sake of simpUcity, we limit the discussion to drops of a cyUndrical shape, where the Uquid profile depends on only one variable x This permits the reduction of the problem to a two-dimensional one, as in the case of slit capillaries. 

In the case of an equilibrium drop for solving Equation 3.3II instead of condition (3.312), a different boundary condition should be used  

Condition (3.313) for equilibrium of a drop with an equilibrium flat film of thickness h h 0 h h, is written now in the form / = Y- Using these conditions, we derive from Equation 3.335 that 

The excess pressure P, is negative in the case of a drop, and P = where 91 is the radius of curvature of the spherical part of the surface of the drop. It follows from simple geometrical considerations that cos0 = 

By substituting these expressions in Equation 3.336, we derive the condition of equilibrium of a drop with a film that is identical with Equation 3.55 derived 

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