Complex fluids exist in nature and are continually engineered for specific applications
involving the addition of macromolecules to a solvent, among other means. This imparts …

The Oldroyd-B model has been used extensively to predict a host of instabilities in shearing
flows of viscoelastic fluids, often realized experimentally using polymer solutions. The …

The Oldroyd-B fluid has become the starting point for almost all complex flow calculations
and analysis involving the behavior of dilute polymer solutions. The reasons for this are …

We review progress and open challenges for a number of problems related to the Oldroyd B
model which are of current interest to the mathematical community. We discuss existence …

The log-conformation formulation, proposed by Fattal and Kupferman [J. Non-Newt. Fluid
Mech. 123 (2004) 281], has helped to provide further insights into the High-Weissenberg …

The flow of polymer solutions past solid obstacles or through porous media gives rise to rich
physical phenomena over a wide range of spatial and temporal scales. Viscoelasticity, in …

The principles of suspension mechanics in Newtonian fluids particularly at low Reynolds
number were established on a rigorous basis via a bevy of papers from George Batchelor …

Viscoelastic particulate suspensions play a key role in many energy applications. Our goal is
to develop a simulation-based tool for engineering such suspensions. This study is …

In this article, we analyze the stability of various numerical schemes for differential models of
viscoelastic fluids. More precisely, we consider the prototypical Oldroyd-B model, for which a …

This paper is an introduction to the modelling of viscoelastic fluids, with an emphasis on
micromacro (or multiscale) models. Some elements of mathematical and numerical analysis …