Modeling Inertial Particle Focusing in Curvilinear Microchannels

The focusing of particles in curvilinear microchannels at high Reynolds number has received great attention in recent years as a tool to separate bioparticles. However, in order to design a curvilinear channel for a specific separation process one must rely on empirical results, as no complete theoretical model currently exists. This is because the existing models that predict the total forces on a particle in a curvilinear geometry do so by superposing inertial forces with a Dean force calculated using a point particle assumption. The ability to add these two forces may hold under certain regimes, but as the inertia associated with the Dean flow increases, it is crucial to take into account the finite size of the particle. In our work we model the full flow physics of a particle migrating in a curvilinear channel in a reference frame that is rotating with the particle by including both Coriolis and Centripetal forces. Here we investigate the three dimensional focusing behavior of inertial particles and the applicability of the point particle assumption previous models have proposed. Finally, we propose a new linear model that takes into account the full physics, but relies on a perturbation expansion where the perturbation parameter is the curvature ratio of the channel.