Related papers: Viscoelastic Flows In A Rough Channel: A Multiscal…
We derive a unidirectional asymptotic model for one-dimensional blood flow in viscoelastic arteries. We prove local well-posedness of strong solutions in Sobolev spaces for general parameters and mean-zero periodic data. In the purely…
We consider a family of linear viscoelastic shells with thickness $2\varepsilon$ ( $\varepsilon$ , small parameter), clamped along a portion of their lateral face, all having the same middle surface $S$. We formulate the three-dimensional…
In this paper, we discuss whether the instability of viscoelastic flow around a circular cylinder is subcritical or supercritical by numerical simulation. The Oldroyd-B model is selected to describe the viscoelastic constitutive…
We study the flow of a generalized Newtonian fluid, characterized by a power-law model, through a channel consisting of a wall with a flexible membrane under longitudinal tension. It is assumed that at steady state the flow through the…
Viscoelastic rate-type fluids are popular models of choice in many applications involving flows of fluid-like materials with complex micro-structure. A well-developed mathematical theory for the most of these classical fluid models is…
In this work we study stochastic Oldroyd type models for viscoelastic fluids in $\mathbb{R}^d, d= 2, 3$. We show existence and uniqueness of strong local maximal solutions when the initial data are in $H^s$ for $s>d/2, d= 2, 3$.…
We formulate the flow of thick fluids as evolution variational and quasi-variational inequalities, with a variable threshold on the absolute value of the deformation rate tensor. In the variational case, we show the existence and uniqueness…
The problem of oscillating flows inside pipes under periodic forcing of viscoelastic fluids is addressed here. Starting from the linear Oldroyd-B model, a generalized Darcy's law is obtained in frequency domain and an explicit expression…
Recently, detailed experiments on visco-elastic channel flow have provided convincing evidence for a nonlinear instability scenario which we had argued for based on calculations for visco-elastic Couette flow. Motivated by these experiments…
We consider the Cauchy problem for incompressible viscoelastic fluids in the whole space $\mathbb{R}^d$ ($d=2,3$). By introducing a new decomposition via Helmholtz's projections, we first provide an alternative proof on the existence of…
We present a combined experimental, numerical and theoretical investigation of the geometric scaling of the onset of a purely-elastic flow instability in a serpentine channel. Good qualitative agreement is obtained between experiments,…
The steady flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens model for blood) in a two-dimensional channel, partly bound by a deformable, finite thickness neo-Hookean solid, is computed. The limiting Weissenberg number beyond…
Diverse processes rely on the viscous flow of polymer solutions through porous media. In many cases, the macroscopic flow resistance abruptly increases above a threshold flow rate in a porous medium---but not in bulk solution. The reason…
Amplification of deterministic disturbances in inertialess shear-driven channel flows of viscoelastic fluids is examined by analyzing the frequency responses from spatio-temporal body forces to the velocity and polymer stress fluctuations.…
The global existence of solutions to incompressible viscoelastic flows has been a longstanding open problem, even for the global weak solution. Under some special structure ("div-curl" condition) the global small smooth solution was…
The flow of viscoelastic fluids in porous media is encountered in many practical applications, such as in the enhanced oil recovery process or in the groundwater remediation. Once the flow rate exceeds a critical value in such flows, an…
The velocity and friction properties of laminar pipe flow of a viscoelastic solution are bounded by the corresponding values for two Newtonian fluids, namely, the solvent and a fluid with a viscosity identical to the total viscosity of the…
Viscoelastic flows transition from steady to time-dependent, chaotic dynamics under critical flow conditions, but the implications of geometric disorder for flow stability in these systems are unknown. Utilizing microfluidics, we flow a…
Long, shallow microchannels embedded in thick soft materials are widely used in microfluidic devices for lab-on-a-chip applications. However, the bulging effect caused by fluid--structure interactions between the internal viscous flow and…
We investigate the dynamics of the two-dimensional periodic Kolmogorov flow of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct numerical simulations. Above a critical Weissenberg number the flow displays a…