Hydrodynamic resistance matrices of colloidal particles with various shapes

Abstract: The hydrodynamic resistance matrix is an important quantity for describing the dynamics of colloidal particles. This matrix encodes the shape- and size-dependent hydrodynamic properties of a particle suspended in a simple liquid at low Reynolds number and determines the particle's diffusion tensor. For this reason, the hydrodynamic resistance matrix is typically needed when modeling the motion of free purely Brownian, externally driven, or self-propelled colloidal particles or the behavior of dilute suspensions of such particles on the basis of Langevin equations, Smoluchowski equations, classical dynamical density functional theory, or other appropriate methods. So far, however, the hydrodynamic resistance matrix was available only for a few particle shapes. In this article, we therefore present the hydrodynamic resistance matrices for various particle shapes that are relevant for current research, including apolar and polar as well as convex and partially concave shapes. The elements of the hydrodynamic resistance matrices are given as functions of shape parameters like the aspect ratio of the corresponding particle so that the results apply not only to discrete but instead to continuous sets of particle shapes. This work shall stimulate and support future studies on colloidal particles with anisometric shapes.