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

The shear-induced particle self-diffusivity in a concentrated suspension (20%-50% solids volume fraction) of non-colloidal spheres (90 mu m 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 gamma Delta t ranging from 0.05 to 0.5, where gamma is the applied shear rate and Delta t is the correlation time. In both directions, the diffusive displacements scaled linearly with gamma Delta t 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 gamma Delta t. 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 mu m diameter tracer particles dispersed in concentrated suspensions (30%-50% solids volume fraction) of much larger spheres (325 mu m average diameter). These fluid diffusivities were found to be 0.7 times the corresponding particle diffusivities when both were scaled with gamma a(2) (2a = 325 mu m).