Boundary layer in linear viscoelasticity

TL;DR

This paper extends the classical oscillatory boundary layer theory from Newtonian fluids to linear viscoelastic fluids, deriving new formulas and developing a boundary integral method for numerical analysis of complex particle geometries.

Contribution

The work generalizes boundary layer theory to linear viscoelastic fluids and introduces a numerical boundary integral method for complex geometries.

Findings

Derived a boundary layer formula for LVE that includes Stokes layer as a special case.

Developed and verified a boundary integral numerical method.

Applied the method to study particles with various shapes in LVE.

Abstract

It is well known that a boundary layer develops along an infinite plate under oscillatory motion in a Newtonian fluid. In this work, this oscillatory boundary layer theory is generalized to the case of linear viscoelastic(LVE) flow. We demonstrate that the dynamics in LVE are generically different than those for flow of similar settings in Newtonian fluids, in several aspects. These new discoveries are expected to have consequences on related engineering applications. Mimicking the theory for Stokes oscillatory layers along an infinite plate in Newtonian flow, we derive a similar oscillatory boundary layer formula for the case of LVE. In fact, the new theory includes the Stokes layer theory as a special case. For the disturbance flow caused by particles undergoing oscillatory motion in linear viscoelasticity(LVE), a numerical investigation is necessary. A boundary integral method is developed for this purpose. We verify our numerical method by comparing its results to an existing analytic solution, in the simple case of a spherical particle. Then the numerical method is applied in case studies of more general geometries. Two geometries are considered because of their prevalence in applications: spheroids; dumbbells and biconcave disks.