Dispersion of heavy particles in an isolated pancake-like vortex

Abstract

The objective of this study is to characterize the dispersion of particles (mainly heavy particles) in a quasi two-dimensional axisymmetric pancake-like vortex. The velocity field for a pancake vortex is substituted into the Maxey-Riley equation, and the resulting equations are solved numerically. Particles that are denser than the surrounding fluid always move away from the vortex center. When the flow is initially seeded with a homogeneous distribution of particles of the same size and density, the particles accumulate in the outer region of the vortex. In addition, overtaking occurs if the Stokes number is large enough. The analysis of the concentration profiles in the horizontal plane of the vortex shows that accumulation of particles takes the form of a concentration wave that grows and travels away from the vortex center. A second peak of concentration appears when overtaking occurs. These concentration peaks dramatically increase the potential for collisions between particles and the potential for flocculation. Three-dimensional simulations show that this second peak only occurs when the vortex is sufficiently thick. Key words: particle dispersion, pancake vortex, Maxey-Riley equation, concentration profiles, flocculation.