Trapping and leakage of heavy inertial particles in an unequal strength counter-rotating vortex pair

The clustering of inertial particles in turbulent flows is ubiquitous in many applications. This phenomenon is attributed to the influence of multiscale vortex structures in turbulent flows on particle motion. In this study, our primary goal is to further investigate the vortex effect on particle motion. We perform analytical and numerical simulations to examine the motion of particles in a counter-rotating vortex pair (CVP) with circulation ratio $\gamma \in (-1,0)$ . The small, dilute, heavy inertial particles with a low particle Reynolds number are considered. In particular, the particle Stokes number and density factor satisfy $St\in (0,0.3)$ and $ R\in (0,1)$ , respectively. We validate the existence of a particle-attracting ring within the CVP, which provides a simple mechanism for particle trapping. Meanwhile, there exists a critical Stokes number $St_{{cr}}$ limiting the occurrence of particle trapping. We provide a formula to predict the value of $St_{{cr}}$ , which depends on both $\gamma$ and $R$ . Only when $St\lt St_{{cr}}$ can the attracting ring trap the particle initially located within its basin of attraction and eventually lead to the formation of a particle clustering ring. Particles with a larger $R$ are more likely to be trapped in the CVP. While $St\gt St_{{cr}}$ , the dynamics of the particles exhibits finite-time ‘leakage’. The attracting ring in the phase space coincides with the saddle point from which particles escape. Although all particles eventually escape, some may remain trapped in the vortex core region for a duration (represented by residence time). The distribution of residence time exhibits a localised exponential-like feature, indicating transient chaos.