Abstract In this article, we consider the flow of a Burgers’ fluid transient electro-osmotic type in small tube with circular cross-section. Analytical results are found for velocity and, electric potential profile by solving Navier–Stokes and linearized Poisson–Boltzmann equations. Moreover, these equations solved help integral transform method. We cases which changes time those does not chang...

A conservative finite difference method designed to capture elastic wave propagation in viscoelastic fluids in two space dimensions is presented. The governing equations are the incompressible Navier-Stokes equations coupled to the Oldroyd-B constitutive equations for viscoelastic stress. The equations are cast into a hybrid conservation form to make use of a second-order upwind method to treat...

Start-up times in viscoelastic channel and pipe flows generated by the sudden imposition of a pressure gradient are here determined by a mixed analytical/numerical procedure. The rheological models considered are the upper convected Maxwell and the Oldroyd-B equations. With these models the flow evolves asymptotically to the steady state solution after a transient regime presenting strong oscil...

This paper is concerned with regular flows of incompressible weakly viscoelastic fluids which obey a differential constitutive law of Oldroyd type. We study the newtonian limit for weakly viscoelastic fluid flows in IR or T N for N = 2, 3, when the Weissenberg number (relaxation time measuring the elasticity effect in the fluid) tends to zero. More precisely, we prove that the velocity field an...

Abstract: Studied is a flow between two infinite planes, one of which performs periodic oscillations. Non-Newtonian fluid is described by the Voight-Oldroyd model applicable for the motion of an emulsion of one liquid in another. Such liquid possesses relaxation properties, which give rise to a relaxation wave. The generated results may be used to determine viscosity and the relaxation constant...

Numerical simulations reveal the formation of singular structures in the polymer stress field of a viscoelastic fluid modeled by the Oldroyd-B equations driven by a simple body force. These singularities emerge exponentially in time at hyperbolic stagnation points in the flow and their algebraic structure depends critically on the Weissenberg number. Beyond a first critical Weissenberg number t...

Abstract We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form-valued 2-forms, their divergence covariant exterior derivative. review necessary tools differential geometry obtain corresponding coordinate-free form equations motion for variety inviscid models—compressible incompressible Euler equ...

In this chapter we introduce the fundamental concepts in Newtonian and complex fluid mechanics, beginning with the basic underlying assumptions in continuum mechanical modeling. The equations of mass and momentum conservation are derived, and the Cauchy stress tensor makes its first of many appearances. The Navier–Stokes equations are derived, along with their inertialess limit, the Stokes equa...

We measure the swimming speed of a cylindrical version of Taylor's swimming sheet in viscoelastic fluids, and find that depending on the rheology, the speed can either increase or decrease relative to the speed in a Newtonian viscous fluid. The swimming stroke of the sheet is a prescribed propagating wave that travels along the sheet in the azimuthal direction. The measurements are performed wi...