Attraction of neutrally buoyant deformable particles towards a vortex

We conduct direct numerical simulations (DNS) by the full Eulerian finite difference method of a neutrally buoyant hyperelastic particle in Taylor-Green vortical flow. We investigate the case that the initial shape of the particle is spherical with a diameter compa-rable with the vortex radius. The particle orbit depends on the degree of its deformation due to the flow. When the particle is stiffer (i.e., the capillary number Ca is smaller than about 0.1), the particle is hardly deformed and slowly swept out from the vortex. In contrast, softer particles with Ca >= 0.1 are significantly deformed, in an initial period, and they are attracted towards the vortex; then, afterward, the deformation is relaxed so that they can stay around the vortex center. Such an attraction of anisotropic neutrally buoyant particles towards a vortex occurs, even if particles are rigid. We demonstrate this phenomenon by additional DNS of a rigid prolate spheroidal particle in the vortical flow. We also develop analytical arguments to show that the angle between the major axis of the particle and the pathline determines whether the vortex attracts or repulses the particle. This feature well explains the radial motion of neutrally buoyant elastic particles in vortical flow.