Particle accumulation in incompressible laminar flows due to particle-boundary interaction

Abstract

The accumulation of particles in laminar incompressible fluid flows is investigated. Boundary-driven closed systems are considered. We deal with a thermocapillary liquid bridge, a lid-driven cavity and a partially liquid-filled rotating drum. In all three the configurations we consider flows after the onset of a steady three-dimensional instability. The corresponding fluid dynamics systems are equivalent to a Hamiltonian system of 1.5 degrees of freedom and we consider flow parameters for which chaotic and regular regions coexist. Owing to the boundary-driving mechanism, the quasi-periodic streamlines (Kolmogorov-Arnold-Moser or KAM tori) are mainly located near the moving wall or the free-surface. Finite-size particles with small Stokes numbers are introduced in these fluid flow systems to study the so-called particle accumulation structures (PAS). In the following we extend the classical framework of investigation of PAS, passing from thermocapillary to boundary-driven flows. We further aim at clarifying the fundamental mechanism PAS is based on, regardless of the specific system in which it is considered. The main flow features basically required in these set-ups are KAM tori located near the boundaries and particles of finite-size. The particles which move close to a wall or a free-surface may be transferred from the chaotic to the regular regions of the flow because of the repulsion exerted by the boundaries. The particle--boundary interaction represents the main dissipative mechanism responsible for the formation of PAS. For simulating particles moving close to the driving boundaries we employ fully-resolved simulations produced via a discontinuous Galerkin finite element method (DG-FEM) in combination with the smoothed profile method (SPM). The simulations aim at clarifying the dependence of the lubrication gap width on particle size and density ratio after that a single particle is trapped (within a certain tolerance) in 2-D PAS. To this end, small particles in a shear--stress- and a lid-driven cavity are investigated. The fully-resolved simulation results are employed to improve an existing particle--boundary interaction (PSI) model. A one-way coupling approach which includes such an improved PSI model is used to simulate two- and three-dimensional particle-laden flows. A comparison of the numerically predicted PAS with experimental data is finally made to confirm the numerical results. All the main phenomenological explanations given for understanding PAS will be commented and discussed in details. Our principal aim is to show that the strong correlation between particle accumulation structures and flow topology, together with the particle--boundary interaction dissipative effect, provides a universal mechanism for explaining PAS for all set-ups investigated.