(483a) Equilibrium Position Bifurcation and Manipulation for a Sphere in Inertial Shear Flow between Parallel Walls

Inertial hydrodynamic forces can enable particle separations in microfluidic devices without the need for external forces (e.g magnetic or electric). Here, we calculate the migration of a rigid sphere in ambient inertial shear flow of a Newtonian fluid between infinite parallel walls using the lattice Boltzmann method. A neutrally buoyant sphere migrates to an equilibrium position at the center of the shear cell when the flow is below a critical particle Reynolds number Re_p, in agreement with previous asymptotic analyses at small Re_p(e.g. Ho and Leal, JFM 1974). Surprisingly, we demonstrate that a pitchfork bifurcation of the equilibrium position occurs above this critical Re_p, resulting in an unstable center equilibrium position and two stable equilibria equidistant from the center. The bifurcation occurs below the transition to unsteady flow, and the critical Re_p increases with the confinement ratio κ. Next, we show that the equilibrium position of a non-neutrally buoyant sphere moves toward the channel wall in a manner that is dependent on the orientation of the channel. For a horizontally-aligned channel, the equilibrium position shifts toward the bounding wall in the direction of the gravitational force. For a vertically-aligned channel, the equilibrium position moves toward the confining wall translating in the opposite direction of the gravitational force. Finally, we present the migration of a neutrally buoyant sphere above the critical Re_p in a time dependent shear flow. Following flow cessation, the sphere migrates toward the center of the channel while the fluid motion ceases, the migration distance and time dependent on the duration over which the flow is stopped. A sphere in reversing flow translates toward the channel center before returning to the original equilibrium position prior to flow reversal. In summary, our work suggests that the equilibrium position of a sphere in confined shear flow can be controlled to potentially create novel particle separation devices.