Particle segregation by Stokes number for small neutrally buoyant spheres in a fluid

It is a commonly observed phenomenon that spherical particles with inertia in an incompressible fluid do not behave as ideal tracers. Due to the inertia of the particle, the planar dynamics are described in a four-dimensional phase space and thus can differ considerably from the ideal tracer dynamics. Using finite-time Lyapunov exponents, we compute the sensitivity of the final position of a particle with respect to its initial velocity, relative to the fluid, and thus partition the relative velocity subspace at each point in configuration space. The computations are done at every point in the relative velocity subspace, thus giving a sensitivity field. The Stokes number, being a measure of the independence of the particle from the underlying fluid flow, acts as a parameter in determining the variation in these partitions. We demonstrate how this partition framework can be used to segregate particles by Stokes number in a fluid. The fluid model used for demonstration is a two-dimensional cellular flow.