Drag on a large spherical aggregate with self-similar structure: An asymptotic analysis

Abstract

A porous particle with radially varying permeability is used to model a large self-similar (fractal-like) aggregate in the continuum fluid flow regime. The Stokes flow in the viscous fluid around the aggregate is coupled with the solution of the flow inside the aggregate. This internal flow is shown to be composed of a central core governed by Darcy equation and a thin shell at the aggregate edge where the flow is described by Brinkman's equation. Solutions to the governing equations in each of these regions are sought as asymptotic expansions in terms of a suitably small permeability parameter k. The hydrodynamic jumps across the Brinkman layer are systematically established and used to compute the viscous drag experienced by the aggregate. These conditions, which generalize the widely used Saffman (tangential flow) boundary conditions, are more broadly applicable to flows past/through fine-grained deposits of arbitrary shape, and many other configurations of technological interest.