Journal of the Chinese Institute of Chemical Engineers, Vol.29, No.1, 55-63, 1998
Diffusion of a dilute monodisperse system of fluid drops
A study of diffusion for a dispersion which the suspending droplets are spherical and have the same radius and fluid viscosity is considered, Droplets are assumed to be close enough to interact hydrodynamically. Based on the Einstein's prescription of Brownian motion that invokes an equilibrium and the droplets will be exerted by a thermodynamic force, the Brownian diffusivities in two different types of situation are deduced analytically, The first concerns a homogeneous dilute suspension which is being deformed locally, and the relative diffusivity of two spherical droplets with a given separation distance is derived from the properties of mobility functions due to the low-Reynolds-number flow caused by two hydrodynamically interacting droplets, The second concerns a suspension in which there is a gradient of concentration of droplets. The thermodynamic force on each droplet in this case is shown to be equal to the gradient of the chemical potential of droplets, which brings considerations of the multi-droplet excluded volume into the problem, Determination of the sedimentation velocity of droplets falling through fluid under gravity for which a theoretical result correct to the first order in volume fraction of the droplets is available, The diffusivity of the droplets is found to increase slowly as the concentration rises from zero, The results, presented in simple closed forms, agree very well with the existing solutions for the limiting cases of solid particles, Also, the limiting diffusion situation of spherical gas bubbles are considered in this article.