BEM simulation of hydrodynamic interaction between two identical neutrally buoyant smooth spheres freely moving in a wide gap Couette flow

Abstract

Abstract In this paper, the hydrodynamic interaction between two identical neutrally buoyant smooth spheres freely moving at negligible Reynolds numbers in an unbounded wide gap Couette flow is investigated by three dimensional boundary element method (BEM) simulations. Such information is fundamental to the macroscopic characterization of suspension flows. The numerical results show that the hydrodynamic interaction of the sphere-pair causes both spheres to experience repulsive cross-streamline displacements, which are in opposite directions, when the trailing sphere is approaching the leading one. These cross-streamline displacements reach their maxima when the sphere-pair is at their closest center-to-center distance due to the strongest hydrodynamic interaction at this instant. After that, the initially trailing sphere becomes the leading one, and the sphere-pair begins to separate, causing the hydrodynamic interaction to decrease gradually and the spheres to return to their individual initial streamlines. The center of gravity of the sphere-pair in this non-linear shear field experiences a preferential cross-streamline migration in the plane of shear when they meet, firstly moving from regions of higher shear rates towards those of lower ones before the meeting and then experiencing a “reverse migration”, that is, moving from regions of low shear rates to those of higher ones, after the meeting, which is not presented in a linear shear field such as in a simple shear flow. 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. All these results suggest that the non-linearity of the shear field is responsible for the preferential cross-streamline displacement and the particle migration in concentrated suspensions undergoing inhomogeneous shearing. In addition, the hydrodynamic interaction between the sphere-pair has also been quantified under various conditions by the BEM simulations.