Abstract
Using recent generalizations of the Laplace equation based on the curvature expansion for surface internal energy, the lowest-order surface curvature correction to the standard macroscopic energy minimization model of liquid droplet profiles is explained. Including this correction, the nonlinear differential equation governing cylindrical profile shape is derived and its numerical solutions under suitable boundary conditions are presented. The results show qualitative agreement with recent experiments in the production of melted microlenses. The standard spherical solution is recovered as the special case of global constant curvature.
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