Measuring shear-induced self-diffusion in a counterrotating geometry

The novel correlation method to measure shear-induced self-diffusion in concentrated suspensions of noncolloidal hard spheres which we developed recently [J. Fluid Mech. 375, 297 (1998)] has been applied in a dedicated counterrotating geometry. The counterrotating nature of the setup enables experiments over a wider range of well-controlled dimensionless time $(\dot{\gamma }\Delta t$ in the range 0.03–3.5, compared to 0.05–0.6 in previous experiments; here $\dot{\gamma }$ denotes the shear rate and $\Delta t$ the correlation time). The accessible range of timescales made it possible to study the nature of the particle motion in a more detailed way. The wide radius geometry provides a well-defined flow field and was designed such that there is optical access from different directions. As a result, shear-induced self-diffusion coefficients could be determined as a function of particle volume fraction φ (0.20–0.50) in both the vorticity and velocity gradient direction. A transition could be observed to occur for $\dot{\gamma }\Delta t$ of $O\left(1\right),$ above which the particle motion is diffusive. The corresponding self-diffusion coefficients do not increase monotonically with particle volume fraction, as has been suggested by numerical calculations and theoretical modeling of Brady and Morris [J. Fluid Mech. 348, 103 (1997)]. After an exponential growth up to $\phi =0.35,$ the diffusion coefficients level off. The experiments even suggest the existence of a maximum around $\phi =\mathrm{0.40.}\mathrm{}$ The results are in good agreement with experimental literature data of Phan and Leighton [J. Fluid Mech. (submitted)], although these measurements were performed for much larger values of the dimensionless time $\dot{\gamma }\Delta t.\mathrm{}$