The rotation of two-dimensional elliptical porous particles in a simple shear flow with fluid inertia

Abstract

The motion of porous particles in fluid flow is of fundamental importance in both natural and industrial processes. Recent work shows that fluid inertia can essentially alter the rotation of spherical porous particles in a simple shear flow. In this contribution, we examined the influence of fluid inertia on the rotation of elliptical porous particles in shear flow by solving the volume-averaged macroscopic equations with a two-dimensional lattice Boltzmann model. It is confirmed that the Darcy number Da has only a minor effect on the rotation of elliptical porous particles if fluid inertia is neglected. At finite fluid inertia, the elliptical porous particles, however, manifested time-periodic rotation with a non-uniform angular rate. For particles with small to intermediate Da, the period of rotation increases with Reynolds number Re up to a critical Rec above which the particle would stop rotating. It is shown that the maximum and minimum angular rates, as well as the inclination angle at which the particle has a minimum angular rate, are significantly affected by Da. A scaling law for the period of rotation initially proposed for solid impermeable particles can be extended to elliptical porous particles at finite fluid inertia. For a highly permeable ellipse, however, Rec has not been observed, and thus, the scaling law breaks down. We calculated the relative viscosity and intrinsic viscosity for simple shear flow containing elliptical porous particles. A formula developed for suspensions with vanishing Re can also be extended to correlate the intrinsic viscosity to Da at finite Re.