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For a spherical particle that is at least several times larger than the solvent molecules and is moving in a bulk fluid, its diffusivity is simply the ratio between thermal energy and its drag coefficient according to the Stokes-Einstein equation. This work focuses on transport of spherical particles through a row of parallel cylinders. Because the drag coefficient of the particle becomes anisotropic, the particle diffusivity, instead of being a scalar, is a second order tensor which can be calculated from the mobility tensor of the particle. In addition, in the presence of a pressure gradient, the convective hindrance factor of the particle, the change in its convective rate due to a particle-cylinder hydrodynamic interaction, is also a second order tensor. In this work, the anisotropic drag coefficient are calculated using finite element method, assuming Low Reynolds number. The obtained diffusivity and convective hindrance factor tensor are then substituted in the steady-state convection diffusion equation which is solved in order to determine the particle concentration and the particle sieving coefficient. The effect of coupling between particle translation and rotation as well as that of the off-diagonal terms of the mobility tensor are also investigated.
