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.

Dynamics of a sphere in inertial shear flow between parallel walls

“…As demonstrated by Asmolov (1999), a neutrally buoyant sphere in shear flow bounded by a single wall experiences no equilibrium position, as the lift force is always directed away from the wall. We previously showed that the equilibrium position of a circular cylinder in confined shear flow experienced a similar inertial bifurcation as a result of the second confining wall (Fox et al 2020). Our present findings indicate that this phenomenon persists in three-dimensional confined shear flows.…”

“…We previously showed that the equilibrium position of a circular cylinder in confined shear flow experienced a similar inertial bifurcation as a result of the second confining wall (Fox et al. 2020). Our present findings indicate that this phenomenon persists in three-dimensional confined shear flows.…”

“…This study revealed that, up to Re p = 0.625, the equilibrium position for a particle in bounded shear flow remained at the centre of the channel for a cylinder of κ = 0.125. In our previous work, lattice Boltzmann simulations were performed to extend the study of a neutrally buoyant circular cylinder in confined shear flow to higher Re p (Fox, Schneider & Khair 2020). Our analysis revealed a supercritical pitchfork bifurcation of the equilibrium position above a critical Re p dependent on κ, switching from a single stable equilibrium position at the centre of the channel to three equilibrium positions: two stable equilibria equidistant from the centre and an unstable equilibrium position at the centre.…”

Behaviour of a magnetic nanogel in a shear flow

“…Over the past 50 years, not less than 20 experimental, analytical and computational studies have been devoted to the WLF, see works [111,112] and references therein. We also could not resist the temptation to measure this effect in our system.…”

“…We chose WLF as a benchmark to check the accuracy of the LB algorithm in our simulations. Therefore, the obtained results were compared with two recent computational studies: one for low translational Reynolds numbers [111] Re γ = {0.1, 0.01} and other one for intermediate-low [112] -Re γ = {1, 3, 10};…”