SURFACES OF CONSTANT MEAN-CURVATURE WITH PRESCRIBED CONTACT-ANGLE

A Galerkin weighted residual formulation of the surface divergence theorem is used with finite element basis functions to compute prototype geometric models of foam and emulsion structure. The models are surfaces of constant mean curvature arranged on a simple cubic lattice so that they meet the boundary planes of the unit cells at prescribed contact angles. Surfaces are computed for a variety of contact angles and mean curvatures. With a contact angle between 5-degrees and 133-degrees, the structure inverts as the mean curvature decreases, whereas with a contact angle between 134-degrees and 180-degrees, the structure fills the unit cell as the mean curvature decreases, passes through a turning point, and then increases.