Inertial bifurcation of the equilibrium position of a neutrally-buoyant circular cylinder in shear flow between parallel walls

Abstract

The motion of a neutrally buoyant, rigid circular cylinder in simple shear flow of a Newtonian fluid between parallel walls is calculated for various particle Reynolds numbers, Re_{p}=Ga^{2}/ν, via the lattice Boltzmann method. Here, G is the velocity gradient of the ambient shear, a is the radius of the particle cross section, and ν is the kinematic viscosity of the fluid. An inertial lift force perpendicular to the ambient shear has a single zero crossing at the center of the channel below a critical Re_{p}, corresponding to a single transverse equilibrium position. Above this critical Re_{p}, the equilibrium position undergoes a pitchfork bifurcation, with an unstable zero-force equilibrium at the center and two equidistant stable equilibria off center. The trajectories of a force- and torque-free particle reach the stable equilibria independently of the initial particle position, with the exception of the aforementioned unstable equilibria. The critical Re_{p} increases with increasing confinement ratio κ (i.e., the ratio of the radius of the particle cross section to channel width) and occurs below the transition to unsteady flow. Finally, we suggest how this inertial bifurcation could be used to develop novel particle separation techniques.