This paper deals with three related problems. First, we consider the effective viscosity of a neutrally-buoyant concentrated Brownian suspension of identical hard spheres with allowance for shear-thinning of the suspension, and we also formulate a set of mean normal stresses due to particle thermal and shear-induced fluctuations. Secondly, the effect of these stresses on particle distribution in suspension flow is modeled, the resultant model being verified by comparing its predictions with particle concentration profiles experimentally found for rotational Couette flow. Thirdly, the model is applied to suspension flow in plane and cylindrical where the lateral segregation of particles affects the hydraulic flow characteristics to quite a considerable extent by making them essentially non-Newtonian. The theoretical results are compared with experimental evidence available for steady flow of non-Brownian suspensions. (C) 1999 Elsevier Science B.V. All rights reserved.