Shear-induced fluid-tracer diffusion in a semidilute suspension of spheres

We calculated tracer diffusion in a sheared suspension of non-Brownian rigid spheres and propose a numerical method based on a boundary element method and Stokesian dynamics method. We present details of the numerical method and examine the accuracy of the method. The limitation of semidiluteness is due to the accuracy of the tracer velocity calculation. The results show that the diffusivity of fluid tracers is greater than that of suspended spheres in the semidilute regime. The diffusivity of the velocity gradient direction is about threefold greater than that in the vorticity direction. Simple scaling demonstrates that the diffusivity of fluid tracers increases with the square of the volume fraction of spheres in the semidilute regime, which is confirmed numerically.