Push and pull: attractors and repellors of a dynamical system can localize inertial particles

Recent experiments in a laminar flow stirred tank found that particles, initially moving throughout the fluid domain, undergo an instability and cluster into subdomains of the fluid when the flow Reynolds number exceeds a critical value that depends on particle and fluid inertia. As the dynamical system for inertial particles in fluid flow has both attracting and repelling regions, I show how the interplay of these regions can localize particles and derive an expression for the instability boundary that is suitable for comparison to data. Moreover, I model a master curve for the particle clustering rate in terms of excess inertia past the instability.