Mobile-collector capture of particles in a chaotic flow

Removing dispersed material, such as pollutants, from dynamic fluid environments like the ocean or the atmosphere is challenging when the flow is chaotic. Here the capture of passive tracer particles by a mobile collector (MC) is studied in a model two-dimensional chaotic flow with vortices. Four simple capture strategies for determining the MC direction are considered, all of which rely on periodic measurement of the local particle distribution. The ultimate success of a strategy depends on its associated motion and detection parameters as well as the underlying fluid flow. When the flow is fully chaotic or the relative velocity of the MC is large, the four strategies exhibit nearly equal effectiveness. However, when the flow is less chaotic and the relative MC velocity is small, the collector can become trapped in or outside of a vortex. Changing the particle detection parameters can prevent trapping, which improves capture. In the absence of trapping and for both high and low relative velocities of the MC, a scaling analysis explains the dependence of the capture rate on the relevant dimensionless variables based on timescales for the mobile collector and the underlying flow. For a wide range of parameters and all four capture strategies, the capture timescale depends linearly on a combination of the characteristic kinematic timescale related to the relative motion of the collector and the gradient timescale related to the underlying flow field, confirming that the capture process is properly characterized.