Boundary layer in linear viscoelasticity

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.