On micropolar fluid theory

Abstract

New fundamental solutions for an incompressible micropolar fluid have been obtained in an explicit form by considering a three-dimensional Oseen flow due to a point force and a point couple. Fundamental solutions that do not exist in classical flows have also emerged in this study owning to the existence of the microrotation velocity field in a micropolar fluid. The newly-found fundamental solutions, together with the representations that have been derived based on the Stokes approximation, are believed to be useful in the application of the boundary integral method and the singularity method in seeking for solutions to flow problems. These flow problems are not trivial, as they deal with rheologically complex fluids and the mechanics of fluids at microscale and nanoscale, where classical theories have been found to be invalid there.