Numerical simulations of the competition between the effects of inertia and viscoelasticity on particle migration in Poiseuille flow

In this work, we present 2D numerical simulations on the migration of a particle suspended in a viscoelastic fluid under Poiseuille flow at finite Reynolds numbers, in order to clarify the simultaneous effects of viscoelasticity and inertia on the lateral particle motion. The governing equations are solved through the finite element method by adopting an Arbitrary Lagrangian-Eulerian (ALE) formulation to handle the particle motion. The high accuracy provided by such a method even for very small particle-wall distances, combined with proper stabilization techniques for viscoelastic fluids, allow obtaining convergent solutions at relatively large flow rates, as compared to previous works. As a result, the detailed non-linear dynamics of the migration phenomenon in a significant range of Reynolds and Deborah numbers is presented. The simulations show that, in agreement with the previous literature, a mastercurve relating the migration velocity of the particle to its vertical position completely describes the phenomenon. Remarkably, we found that, for comparable values of the Deborah and Reynolds numbers, inertial effects are negligible: migration is in practice driven by fluid viscoelasticity only. At moderate Reynolds numbers (20 <Re <200) and by lowering De, the transition from viscoelasticity-driven to inertia-driven regimes occurs through two intermediate regimes characterized by multiple stable solutions. In particular, two bifurcations appear, a saddle-node and a pitchfork, whose simultaneous presence determines the establishment of an hysteresis loop where three stable solutions do exist. At low but non zero Reynolds numbers, the saddle-node disappears and two stable solutions are found for any Deborah number in the investigated range.