In this article we rst provide a priori estimates of the solution for the nonsta tionary two dimensional viscoelastic uid motion equations with periodic bound ary condition We then present an modi ed nonlinear Galerkin method for solving such equations By comparing the convergence rates of the proposed method with the standard Galerkin method we conclude that the modi ed nonlinear Galerkin meth...

The dynamics of a fluid in a vertical tube, subjected to an oscillatory pressure gradient, is studied experimentally for both a Newtonian and a viscoelastic shear-thinning fluid. Particle image velocimetry is used to determine the two-dimensional velocity fields in the vertical plane of the tube axis, in a range of driving amplitudes from 0.8 to 2.5 mm and of driving frequencies from 2.0 to 11....

We present an experimental method allowing a direct measurement of the local rheological behavior of complex fluids. A magnetic probe is inserted into the bulk of the fluid and submitted to a controlled magnetic force or torque, which induces a mechanical perturbation of the fluid. The geometry of the perturbation can be varied using two kinds of probes: a magnetic bead submitted to a homogeneo...

Because of their various applications during the past several years, generalizations of the Navier-Stokes model to highly nonlinear constitutive laws have been proposed and studied (see [4, 5, 7]). Several different models have been introduced to explain such nonstandard features, as normal stress effect, rod climbing, shear thinning, and shear thickening. Among the differential-typemodels, Old...

The relaxation processes of a wide variety of soft materials frequently contain one or more broad regions of power-law–like or stretched exponential relaxation in time and frequency. Fractional constitutive equations have been shown to be excellent models for capturing the linear viscoelastic behavior of such materials, and their relaxation modulus can be quantitatively described very generally...

A survey of secondary flows of viscoelastic liquids in straight tubes is given including recent work pointing at striking analogies with transversal deformations associated with the simple shearing of solid materials. The importance and implications of secondary flows of viscoelastic fluids in heat transfer enhancement are explored. Recent new work by the author and colleagues of both the stead...