Numerical simulations of the pressure-driven flow of pairs of rigid spheres in elastoviscoplastic fluids

Abstract

We investigate through numerical simulations the hydrodynamic interactions between two rigid spherical particles suspended on the axis of a cylindrical tube filled with an elastoviscoplastic fluid subjected to pressure-driven flow. The simulations are performed by the finite element method with the arbitrary Lagrangian-Eulerian formulation. We carry out a parametric analysis to examine the impact of the yield stress and relaxation time of the fluid and of particle confinement on the dynamics of the system. We identify master curves of the particle relative velocity as a function of the inter-particle distance. When the yield stress of the suspending phase is much lower than the viscous stress, those curves highlight short-range attractive interactions and long-range repulsive interactions between particles, with the latter specifically promoting their alignment. As the yield stress increases, the attractive interaction is replaced by stasis at short distance, characterized by a vanishing relative velocity and the formation of an unyielded region that connects the two spheres, where the fluid behaves like a viscoelastic solid. Additionally, the combined effects of plasticity and elasticity enhance the repulsion between the particles, promoting their ordering. Also increasing the confinement of the particles enhances repulsion, thus allowing to achieve ordering within shorter lengths in the flow direction. Reducing shear thinning amplifies peak relative velocities and expands the attractive region due to increased viscoelastic stresses and stress gradients. While a stable equilibrium may appear at larger separations, its impact is limited by low relative velocities.