The measurement of the shear-induced particle and fluid tracer diffusivities in concentrated suspensions by a novel method

Abstract

The shear-induced particle self-diffusivity in a concentrated suspension (20%–50% solids volume fraction) of non-colloidal spheres (90 μm average diameter) was measured using a new correlation technique. This method is based on the correlation between the positions of tracer particles in successive images and can be used to determine the self-diffusivity in non-colloidal suspensions for different time scales. These self-diffusivities were measured in the velocity gradient and vorticity directions in a narrow-gap Couette device for values of the strain γΔt ranging from 0.05 to 0.5, where γ is the applied shear rate and Δt is the correlation time. In both directions, the diffusive displacements scaled linearly with γΔt over the range given above and the corresponding diffusivities were found to be in good agreement with the experimental results of Leighton & Acrivos (1987a) and of Phan & Leighton (1993), even though these earlier studies were performed at much larger values of γΔt. The self-diffusivity in the velocity gradient direction was found to be about 1.7 times larger than in the vorticity direction. The technique was also used to determine the shear-induced fluid tracer by measuring the mean square displacement of 31.5 μm diameter tracer particles dispersed in concentrated suspensions (30%–50% solids volume fraction) of much larger spheres (325 μm average diameter). These fluid diffusivities were found to be 0.7 times the corresponding particle diffusivities when both were scaled with γ a² (2a = 325 μm).