On the combined effect of diffusion and agglomeration in shear flow of suspensions

In this paper, a simple model will be proposed concerning the combined effect of diffusion, agglomeration and agglomerate break-up on the rheology of shear flow. Basic underlying assumptions are: In shear flow, suspended particles form agglomerates and agglomerates break up. These processes are reversible. In homogeneous steady shear flow, the equilibrium size distribution of agglomerates is determined by the shear stress. In non-equilibrium situations, the rate of change of the size distribution is proportional to the distance of the state from equilibrium. Due to diffusion, agglomerates migrate perpendicular to the direction of flow. At walls, agglomerates may be built up or destroyed. The viscosity of the suspension depends on the agglomerate size distribution. Possible effects of these mechanisms on the rheology of shear flow will be discussed, and it will be shown that the "viscosity" may depend on geometry. Furthermore, a simple theory of wall slip will be proposed, assuming that agglomerates are destroyed at the wall. This results in a thin wall layer with reduced viscosity, of which the thickness is determined by diffusion and the time constant of agglomeration.