Viscoelastic lift forces on non-spherical particles in pressure-driven flows: theory and experiment

When particles are in a pressure-driven flow of a non-Newtonian fluid, the particles can acquire lift forces due to the imbalance of normal stresses on the particle surface. This phenomenon has been well-studied for spherical particles, but the role of particle shape is still in its early stages. In this work, we develop a theory to describe the rigid body motion of a non-spherical particle in a polymeric fluid. The theory is based on a retarded expansion in the Deborah number (i.e., second order fluid model), for the case when the particle is in a quadratic (i.e., pressure-driven) flow. We find that for particles in a circular tube flow, spherical particles move to the center of the tube faster than prolate and oblate particles of the same volume, due to the unique orientation dynamics of the spheroids in the polymeric fluid. We also find that prolate particles move slower than oblate particles of the same aspect ratio. These trends are verified by performing microfluidic experiments where we visualize polystyrene particles of various shapes moving through circular capillaries in a Boger fluid with weak viscoelasticity (De~O(10^-2)) and vanishing inertia (Re~O(10^-4)). The work here gives crucial understanding of how viscoelastic lift forces are altered by particle shape.