Abstract
The authors examine the inertial lift on a neutrally-buoyant circular cylinder in confined shear flow. Through two-dimensional lattice Boltzmann simulations, it is shown that the transverse equilibrium position of the cylinder will undergo a pitchfork bifurcation above a critical Reynolds number, with the stable equilibrium position shifting away from the centerline of the channel. The study demonstrates that this critical Reynolds number is dependent on the ratio of particle size to channel width, and occurs below the transition to unsteady flow.
Highlights
Observations of fluid inertia inducing particle migration across streamlines were reported by Segre and Silberberg [1,2]
This phenomenon only occurs at nonzero Reynolds numbers, as the linearity and reversibility of the Stokes equations prevents its occurrence in purely viscous flows
The inertial lift force per unit length on a circular cylinder of κ = 0.125 in shear flow was calculated by fixing the transverse position y0 of the particle
Summary
Observations of fluid inertia inducing particle migration across streamlines were reported by Segre and Silberberg [1,2]. Schoenberg and Hinch [12] observed that while Ho and Leal [11] assumed Rec 1, the channel Reynolds number in the experiments of Segre and Silberberg was not small; to reconcile these results, they investigated a sphere in Poiseuille flow at Rec = O(1) They used a singular perturbation expansion in the limit of small κ (and small Rep) to calculate the lift force on the sphere, via a finite-difference solution of the Fourier-transformed linearized Navier-Stokes equations, which govern the inertially dominated flow at the channel scale. Their results showed that the equilibrium position moved toward the wall of the channel as Rec increased, in agreement with Segre and Silberberg [1,2].
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