Stokes layers in oscillatory flows of viscoelastic fluids

Abstract

<h2>Abstract</h2> Oscillatory fluid flows play an important role in industrial problems such as pumping, drilling, and oil recovery, and in physiological processes such as mucous flow in respiration and blood pumping. A key concept in oscillatory flows is the Stokes layer, i.e. the region of fluid adjacent to a wall that is in motion as a result of the wall oscillatory motion along its own plane. In this talk we will discuss oscillatory flows of viscoelastic fluids from the perspective of Stokes viscoelastic layers. We will first revisit Stokes' second problem for a viscoelastic fluid modelled by a single-mode Maxwell constitutive equation, and the generation of viscoelastic shear waves. Next, we will turn the attention to wall-bounded zero-mean oscillatory flows, for which we will identify the governing dimensionless variables and discuss the presence of resonances in the one-dimensional base flow. Finally, we will present experimental evidence of the destabilization of the one-dimensional base flow for a wormlike micellar solution in a cylindrical pipe as the oscillatory forcing increases, and sketch a perturbative analysis based on the Giesekus constitutive equation that links the first instability of the base flow to the divergence of normal radial stresses. If there is enough time, we will also present recent experimental results of oscillatory pipe flow of shear-thinning non-elastic solutions.