We provide a mathematical analysis of the spectrum of the linear stability problem for one and two layer channel flows of the upper-convected Maxwell (UCM) and Oldroyd-B fluids at zero Reynolds number. For plane Couette flow of the UCM fluid, it has long been known (Gorodstov and Leonov, J. Appl. Math. Mech. (PMM) 31 (1967) 310) that, for any given streamwise wave number, there are two eigenval...

Peristaltic pumping is a mechanism for transporting fluid or immersed particles in a channel by waves of contraction. It occurs in many biological organisms as well as in several human designed systems. In this study, we investigate numerically the peristaltic pumping of an incompressible viscoelastic fluid using the simple Oldroyd-B model coupled to the Navier-Stokes equations. The pump’s wall...

Analytical solutions corresponding to the starting flow of an Oldroyd-B fluid between rotating cylinders are established. If the radius of the inner cylinder tends to zero the flow within a circular cylinder is obtained. The well-known solutions for a Navier-Stokes fluid, as well as those corresponding to a Maxwell fluid and to a second grade one, appear as limiting cases of our solutions. The ...

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally...

Understanding the behavior of complex fluids in biology presents mathematical, modeling, and computational challenges not encountered in classical fluid mechanics, particularly in the case of fluids with large elastic forces that interact with immersed elastic structures. We discuss some of the characteristics of strongly elastic flows and introduce different models and methods designed for the...

The breakdown of finite element (FEM) computations for the flow of an Oldroyd-B fluid around a cylinder confined between parallel plates, at Weissenberg numbers Wi = O(1), is shown to arise due to a coil-stretch transition experienced by polymer molecules traveling along the centerline in the wake of the cylinder. With increasing Wi, the coil-stretch transition leads to an unbounded growth in t...