Inertial Lift Velocities For Particles In Curvilinear Background Flow

Inertial lift forces are used within microfluidic particles to position, segregate, and sort particles and droplets. Previous theoretical results can accurately predict this phenomena in rectilinear flows but have avoided looking at curvilinear flows to avoid the unsteady terms and nonlinearity that arise. Here, we use asymptotic methods to construct a singularity approximation method for efficiently calculating inertial lift in curvilinear background flow.  We will use our new theory to explore under what conditions particles will get trapped in cavity flow.