Reconstructing the neutrally-buoyant particle flow near a singular corner

The correction of buoyancy effects is tackled for particles moving close to a singular corner in creeping flow conditions. A few density-mismatched particle trajectories are used to reconstruct the dynamics of a neutrally-buoyant particle all over the target domain. We propose to take advantage of the dissipative dynamics of density-mismatched particles in order to probe the target domain. Thereafter, we retrieve the neutrally-buoyant particle flow all over the domain by reconstructing the phase space of the density-mismatched particulate flow and taking the limit of the particle-to-fluid density ratio tending to one. The robustness of such an approach is demonstrated by deliberately ill-conditioning the reconstruction operator. In fact, we show that our algorithm well performs even when we rely on qualitatively-different density-mismatched orbit topologies or on bundles of close trajectories rather than homogeneously distributed orbits. Potential applications to microfluidics and improvements of the proposed algorithm are finally discussed.