Flow of spatially non-uniform suspensions. Part III. Closure relations forporous media and spinning particles

The methods developed in the earlier papers of this series are applied to t he systematic derivation of averaged equations for two situations: slow vis cous flow past a system of rigid spheres fixed in space (which may be consi dered as approximating a porous medium), and the flow induced by a system o f fixed spheres all spinning with the same angular velocity. When the same closure relations used in the earlier papers are applied, it is found that the closure coefficients are different. This finding implies that broadly a pplicable closure relations expressed solely in terms of volume fraction, v elocities, and pressure (as usually found in models of the 'two-fluid' type ) are insufficient: it must be that one or more additional variables need t o be specified to achieve some degree of universality independent of the pa rticular flow considered. It is also shown that the difficulties in the pre scription of the viscosity parameter for use in the Brinkman equation deriv e from the fact that the correct parameter is actually the combination of t wo different viscosities that accidentally end up combined into a single te rm when the particles are fixed. (C) 2001 Elsevier Science Ltd. All rights reserved.