Chaining of weakly interacting particles suspended in viscoelastic fluids

An asymptotic theory based on multipole expansions is presented for multiparticle interactions in unbounded, weakly viscoelastic, creeping flows. The theory accounts for non-Newtonian sphere–sphere interactions that are of order O(De(a/R)²)$\text{O}(De{(a/R)}^2)$, where De is the Deborah number, a the sphere radius and R is the sphere–sphere separation. Analytic expressions are derived for the non-Newtonian correction to the multisphere mobility matrix for non-neutrally buoyant sedimenting spheres, and for neutrally buoyant spheres suspended in a shear flow. It is shown that these expressions give rise to particle chaining in simulations of interacting spherical particles.     

An Eulerian–Eulerian model for gravity currents driven by inertial particles

In this work we introduce an Eulerian–Eulerian formulation for gravity currents driven by inertial particles. The model is based on the equilibrium Eulerian approach and on an asymptotic expansion of the two-phase flow equations. The final model consists of conservation equations for the continuum phase (carrier fluid), an algebraic equation for the disperse phase (particles) velocity that accounts for settling and inertial effects, and a transport equation for the disperse phase volume fraction. We present highly resolved two-dimensional (2D) simulations of the flow for a Reynolds number of Re=3450$\mathit{Re}=3450$ (this particular choice corresponds to a value of Grashof number of Gr=Re²/8=1.5×10⁶$\mathit{Gr}={\mathit{Re}}^2/8=1.5\times {10}^6$) in order to address the effect of particle inertia on flow features. The simulations capture physical aspects of two-phase flows, such as particle preferential concentration and particle migration down turbulence gradients (turbophoresis), which modify substantially the structure and dynamics of the flow. We observe the migration of particles from the core of Kelvin–Helmholtz vortices shed from the front of the current as well as their accumulation in the current head. This redistribution of particles in the current affects the propagation speed of the front, bottom shear stress distribution, deposition rate and sedimentation. This knowledge is helpful for the interpretation of the geologic record.