Boundary integral simulations of boundary layers in linear viscoelastic flow

Abstract

We investigate the disturbance flow generated by the oscillatory motion of a solid particle in linear viscoelastic (LVE) fluids. We begin with one-mode Maxwell fluids and then add Newtonian components so we can examine a spectrum of Weissenberg numbers and frequency parameters. We compute the fluid dynamics using an accurate boundary integral method with third-order accuracy in space. A unique feature of our method is that we can calculate the stress on the particle surface for a prescribed particle velocity profile. It is well known that a boundary layer develops along an infinite plate under oscillatory motion in a Newtonian fluid. However, when the flow becomes viscoelastic, the boundary layers are fundamentally different from those observed in Newtonian fluids. We perform a series of numerical simulations for the geometry of spheroids, dumbbells, and biconcave disks, and characterize streamlines around these particles and shear stress distributions on the surface of the particles. Specifically, two main results emerge from our investigations: (i) there is a sequence of eddies produced in LVE rather than a single one as in the Newtonian fluid case; and (ii) the eddies develop in the interior of the LVE and barely travel, while in the Newtonian fluid, the eddy is generated on the particle surface and propagates into the fluid. Our numerical findings go beyond the well-known dynamical regimes for Newtonian fluids and highlight the level of complexity of particle dynamics in viscoelastic fluids.