Towards a reliable method for predicting the rheological properties of multiphase fluids

Abstract

Measurement of the constitutive behavior of multiphase fluids is one of the most interesting and difficult problems in rheology. The boundary element method is particularly suited to modeling the flow of such fluids because of the relative ease of representing their complex geometry accurately without excessive meshing difficulties. Many papers have been published on the subject, but to the author's knowledge, the literature on the actual implementation of such methods is scarce. Here, a parallel implementation of a code based on the completed double layer boundary integral equation, with Barnes–Hut multipole acceleration, is described briefly. After determining the level of mesh refinement required to obtain convergent results, the code is used to predict the rheological behavior of suspensions of rigid particles of different shapes. The effect of concentration and spatial distributions on the rheological behavior of the suspensions is investigated. It is found that the properties of suspensions of rigid particles are correctly predicted for concentrations up to 30% solids, while at higher concentrations accurate predictions require excessively fine discretization. A new hybrid numerical-asymptotic technique is proposed, which produces a significant improvement in accuracy accompanied by a reduction in computational cost.