(118b) Simulation of Pattern Formation in a Rotating Suspension of non-Brownian Settling Particles

We present the numerical results of pattern formation for a settling suspension of non-Brownian spherical particles in a completely filled horizontal rotating cylinder. The experimental results have been recently reported by S.G. Lipson, J. Phys: Condens. Matter 13, 5001 (2001) and W.R.Maston, B.J. Ackerson, and P. Tong, Phys. Rev. E 67, 050301(R) (2003). We assume that these phenomena are modeled by the Navier-Stokes equations for incompressible Newtonian viscous fluids coupled to the Euler-Newton equations describing rigid-solid motions. The numerical methodology relies on the combination of a finite element approximation with time-discretization by operator-splitting and a Lagrange multiplier based fictitious domain method allowing the flow calculations to take place in a fixed simple shape space region [R. Glowinski, T.W. Pan el al, J. Comp. Phys. 169, 363 (2001)]. We have studied interaction of 160 particles and that of 320 particles. Through the histories of each particle position associated with different angular speed, we can investigate how these particles interact with each other. They have formed subclusters within each cluster at higher angular speed. Also a drafting and kissing phenomenon has been observed happening with each subcluster. This could be an important factor for forming of these clusters.