(108d) Combined Hydrodynamic and Static Force Interactions of Two Rough Spheres in Nonlinear

The phenomenon of particle migration in nonlinear viscous shear flow has been under investigation now for several decades. Although there has been significant progress in the understanding of suspension flows, there still remains several significant open questions. For example, the migration rate appears to scale with slightly less than the cube of the characteristic particle size in Couette flow whereas, for Poiseuille flow, the rate appears to scale with slightly less than the square of the characteristic particle size. The resolution of this discrepancy in the migration rate between Poiseuille and Couette flow is currently an open question. As another example, in periodic flow, it has been shown that there is a critical amplitude below which the flow is reversible, and above which, irreversibilities accumulate rapidly with increasing amplitude. Further, for large amplitude oscillatory Poiseuille flows, particles migrate to the low shear-rate region of the flow field, whereas for small amplitude, particles actually migrate to the high shear-rate region of the flow field. However, current rheological models do not differentiate between small and large amplitude osciallation. Hence, another open question is to determine the physics currently lacking in these rheological models.

In fact, the underpinnings of current rheological models are based almost entirely on multi-body interactions, and hence, the answers to these open questions have been primarily sought by analyzing dense suspension flows. In the current research, a much simpler system is considered of two rough spheres undergoing nonlinear shear flow in which the hydrodynamic interactions are augmented by an adjustible electrostatic force. Numerical simulations are performed using a traction-corrected boundary element formulation. It is shown in this research that the magnitude and even the direction of the particle migration is strongly affected by the static force. Many of the behaviors observed in dense suspensions can be replicated in these two-particle systems. Some conjectures are put forward based on these two-particle simulations that could potentially resolve outstanding issues in suspension modeling.