Boundary-element simulation of hydrodynamic interaction of two smooth spheres suspended in an unbounded Couette flow

The hydrodynamic interaction between two particles, suspended in shear flows, is fundamental to the macroscopic characterization of suspension flows. Although the understanding of the hydrodynamic interaction between two particles suspended in a quiescent or linear shear flow is mature, studies of the interaction in a non-linear shear field are rare. The current study calculates such interactions between two neutrally-buoyant smooth spheres moving at negligible Reynolds numbers in an unbounded wide-gap Couette flow by three-dimensional boundary-element method (BEM) simulations. Both the identical sphere-pair and the disparate sphere-pair are considered. The numerical results show that there is a preferential cross-streamline migration of the center-of-gravity of the sphere-pair in the plane of shear in the unbounded wide-gap Couette flow that does not arise in simple shear-flow. This migration is always directed towards low-shear regions when the sphere having the larger translational velocity approaches the other sphere, and reverses towards high-shear regions when the faster sphere leads the other sphere in the plane of shear. There is also a cross-streamline migration of the center-of-gravity of the sphere-pair in the plane of vorticity, but this migration does not have a preferential direction. These migrations are symmetric about the point where the spheres are at the minimum separation, and are only significant when the hydrodynamic interaction of the spheres is sufficiently strong. These results show that the migration of the center-of-gravity of the sphere-pair can be attributed to the non-linearity of the shear field. The hydrodynamic interaction between the two spheres has been quantified under various conditions by the BEM simulations for both identical and disparate spheres.