Attraction of Minute Particles to Invariant Regions of Volume Preserving Flows by Transients

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Abstract
We find that tracer material can be concentrated into invariant regions of flows due exclusively to transient effects, as are produced when tracers temporarily become more buoyant than the surrounding fluid. This can occur either as a single event, e.g., if the tracer is initially weakly buoyant, or under periodic forcing, e.g., when external effects (such as solar heating) change the tracer density periodically. We study both cases in experiments, in a model, and in direct numerical simulations of laminar flow in a stirred tank. Focusing occurs for very small tracer size and inertia in flows that are instantaneously strictly volume conserving.