On the asymptotics of the fluid flow past an array of fixed obstacles

Abstract

It is known that the asymptotics of slow fluid flow past an array of fixed obstacles is described in several situations by Brinkman's law or Darcy's law (with or without interaction between different obstacles). We show that there exists a continuous transition between the asymptotic structures corresponding to the different situations. Consequently, the asymptotic structure for concentrations of particles 0(1) gives by a limit process the asymptotic schemes for small concentration. Some results of existence, uniqueness and symmetry of the translation tensor are given for flow in 2 dimensions.