The motion of a single and multiple neutrally buoyant elliptical cylinders in plane Poiseuille flow

In this article, we investigate the motion of neutrally buoyant elliptical cylinders in plane Poiseuille flow of a Newtonian fluid. The method of distributed Lagrange multiplier/fictitious domain was used to solve the Navier-Stokes equations as well as for the motion of elliptical cylinders. The motion of a single elliptical cylinder is shown to be dependent on the channel Reynolds number Re, the particle size ratio K = a*/H*, and the aspect ratio A = a*/b* of the cylinder, where H* is the half height of the channel, a* and b* are the lengths of the semi-major axis and semi-minor axis of the cylinder, respectively. It is found that there is a critical Reynolds number, Rec ∼ 3, which distinguishes the lateral migration of a single elliptical cylinder below and above it. As Re is increased, the equilibrium position of the elliptical cylinder shifts towards the wall when Re ≤ Rec or shifts closer to the central axis when Re ≥ Rec. Moreover, there are interesting correlations between the center-of-mass trajectories and the orientation dynamics, which depend on the ranges of K and Re. The motion of multiple elliptical cylinders is also affected by the total solid area fraction ϕT, which is defined to be the proportion of the area occupied by the cylinders in the domain of computation. For a few elliptical cylinders (the number of cylinders ND = 16 and the corresponding ϕT = 3.77%), the cylinders may scatter into several groups at lower Re (≤ 100), and each group fluctuates about an averaged position. At the higher Re (= 1000), the cylinders may converge to an equilibrium position on each side of the channel center. For a larger number of cylinders (ND = 36, 54, 72, 108, and the corresponding ϕT = 8.48%–25.45%), we observed a significant rheological behavior in the velocity profiles. In addition, there exists a particle-free layer next to each wall, and the thickness of the particle-free layers is increased as A (or K) or Re is increased.