NUMERICAL-METHODS FOR COMPUTING INTERFACIAL MEAN-CURVATURE

A procedure is described for computing the mean curvature along condensed phase interfaces in two or three dimensions, without knowledge of the spatial derivatives of the interface. For any point P on the interface, the method consists of computing the portion of volume enclosed by a small template sphere, centered on P, that lies on one side of the interface. That portion of the template volume is shown to be linear in the mean curvature of the surface, relative to the phase lying on the opposite side of the interface, to within terms that can usually be made negligible. An analogous procedure is described in two dimensions. Application of the procedure to compute the mean curvature along a digitized surface is demonstrated. A burning algorithm can be included to improve computational accuracy for interfaces having sharp curvature fluctuations. A minor extension of the method allows computation of the orientation of an interfacial element relative to a fixed reference frame.