High-throughput particle sorting and focusing using rectification of flow and forces

Inertial forces on fluid-borne objects arising due to nonlinear interactions of spatial flow gradients of a “fast" oscillatory flow are a powerful way to reliably and consistently steer particles in microfluidics, without the need for charges or chemistry. In many practical applications, the background oscillatory flow is driven by acoustically-excited bubbles, which typically simultaneously engender steady streaming and/or transport flows that deliver particles close to the bubble interface. While in earlier work we described previously unrecognized inertial forces due to the primary oscillatory driving in isolation, here we rigorously integrate these forces acting on particles in a realistic two dimensional bubble streaming flow. We account for streaming as well as for the presence of a nearby interface. A rigorous separation of time scales in two dimensions yields an overdamped system of equations for particle motion that is computationally efficient and accurately predicts particle displacements across streamlines in comparison to experiments. Our theory also suggests new particle manipulation strategies using oscillating bubbles as actuators of inertial forces, e.g., marker-less flow cytometry based on particle size or density, important for biomicrofluidics.