THE COAGULATION RATE OF SMALL PARTICLES IN A SEDIMENTING DISPERSION

The rate of coagulation is considered for small particles when both co nvection and Brownian motions simultaneously exist. By solving the equ ation for the pair-distribution function for the case of large and sma ll Peclet numbers, which provides the measure of the ratio of the grav ity-induced convection to Brownian diffusion between two rigid particl es, it is shown that there are nonlinear interactions between Brownian diffusion and the gravity-induced convection, so the additivity assum ption is not valid in these regimes. Based on the above work and using an interpolation method, we obtain the complete pictures of the dimen sionless coagulation rate Nu (Nusselt number) as a function of the dim ensionless parameter Pe (Peclet number). The dependence of Nu curves o n the size ratio lambda and reduced density ratio gamma and the numeri cal errors made by the additivity assumption are also discussed. It is only a theoretical result and needs to be verified by experiments. (C ) 1996 Academic Press, Inc.