Evolution of interfacial curvatures of a bicontinuous structure generated via nonconserved dynamics

While coarsening of spherical particles has been well documented, our understanding of coarsening of complex microstructures is still limited. The first step in developing a theory of coarsening of microstructures with complex morphologies is to study coarsening of microstructures that evolve self-similarly. In this paper, we examine the morphological evolution of a self-similar two-phase bicontinuous structure generated via nonconserved dynamics (i.e., motion by mean curvature) to elucidate the complex dynamics of coarsening. We find that the evolution proceeds with some interfaces evolving toward topological singularities (pinching) while the majority of interfaces flatten. These two processes were also illustrated through the evolution equation for the mean curvature, which has a term that depends solely on the local curvatures, as well as a term that is proportional to the surface Laplacian of the mean curvature. The first term causes an increase in the magnitude of the mean curvature, while the second term causes smoothing of the mean curvature in a manner similar to diffusion of chemical species on a surface. The second term causes a large dispersion in the values of the time derivative of mean curvature at various locations in the structure, characterized neither by the mean curvature nor the Gaussian curvature.