| Some macroscopic features of non-uniform disperse two-phase flows are investigated in both analytical and numerical ways.;Based on Cauchy's principle, a physical explanation of the mixture stress is presented in chapter 2. Not only the known results are recovered but also some new effects attributed to the inhomogeneity are shown to arise. One particular effect is the antisymmetric stress induced by the interphase force. The axial vector of the antisymmetric stress tensor for both zero- and finite Reynolds number is studied numerically.;In addition to the antisymmetric stress, the interphase force also contributes to the symmetric stress. In chapter 3, the symmetric mixture stress for slow viscous flow is investigated in detail. In the analysis for small concentrations, Batchelor's (1972) renormalization technique is extended to a non-uniform situation and applied to the calculation of the average stresslet. The transport coefficients in the closure relation are obtained analytically and numerically.;In chapter 4, this generalized renormalization method is used to analyze the particle momentum equation for spheres in Stokes flow. In addition to the shear-induced diffusion which is perpendicular to the flow, it is found that in general the particles move relative to the mixture in the flow direction. Some limited analysis on the particle rotation is also presented in chapter 4.;As a powerful tool for multiphase flow modelling, the ensemble averaging technique is briefly introduced and some relations are re-derived in chapter 5. In the last chapter, calculations of stress moments for a sphere in Stokes flow are presented. |
