Instabilities in Shear Flow of Viscoelastic Fluids with Fading Memory
Instabilities in Shear Flow of Viscoelastic Fluids with Fading Memory

Author: Bradley J. Plohr

Publisher:

Published: 1988

Total Pages: 17

ISBN-13:

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For certain models of viscoelastic fluids with fading memory, classical steady channel flow does not exist beyond a maximal wall shear stress. This occurs when the shear stress for steady flow decreases with strain. For generalized Newtonian models of viscoelastic flow, such a decrease implies that the flow is unstable. Because of this example, a constitutive relation that exhibits a maximal wall shear stress in regarded as defective. The author reports on work showing that, contrary to this intuition, such models correctly describe the experimentally observed spurt phenomenon: exceeding this critical stress results in large increase in volumetric flow rate. The transition to spurt flow is analogous to a dynamically generated phase transition. To analyze this phenomenon, we derive a system of conservation laws that govern the flow; these equations take the form of gas dynamics with relaxation terms. We solve the Riemann problem for this non-strictly-hyperbolic system, and incorporate this solution into the random choice method. Numerical simulation of channel flow, with the maximal wall shear stress exceeded, shows that a discontinuity forms at the wall, allowing the fluid to slip; no steady state exists. However, when a small Newtonian viscosity is included in the model, a slip layer forms and the flow approaches a discontinuous steady state. (KR).

Flow Behavior and Instabilities in Viscoelastic Fluids
Flow Behavior and Instabilities in Viscoelastic Fluids

Author: Boyang Qin

Publisher:

Published: 2018

Total Pages: 0

ISBN-13:

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The flow of complex fluids, especially those containing polymers, is ubiquitous in nature and industry. From blood, plastic melts, to airway mucus, the presence of microstructures such as particles, proteins, and polymers, can impart nonlinear material properties not found in simple fluids like water. These rheological behaviors, in particular viscoelasticity, can give rise to flow anomalies found in industrial settings and intriguing transport dynamics in biological systems. The first part of my work focuses on the flow of viscoelastic fluids in physical systems. Here, I investigate the flow instabilities of viscoelastic fluids in three different geometries and configurations. Realized in microfluidic channels, these experiments mimic flows encountered in technology spanning the oil extraction, pharmaceutical, and chemical industries. In particular, by conducting high-speed velocimetry on the flow of polymeric fluid in a micro-channel, we report evidence of elastic turbulence in a parallel shear flow where the streamline is without curvature. These turbulent-like characteristics include activation of the flow at many time scales, anomalous increase in flow resistance, and enhanced mixing associated with the polymeric flow. Moreover, the spectral characteristics and spatial structures of the velocity fluctuations are different from that in a curved geometry. Measured using novel holographic particle tracking, Lagrangian trajectories show spanwise dispersion and modulations, akin to the traveling waves in the turbulent pipe flow of Newtonian fluids. These curvature perturbations far downstream can generate sufficient hoop stresses to sustain the flow instabilities in the parallel shear flow. The second part of the thesis focuses on the motility and transport of active swimmers in viscoelastic fluids that are relevant to biological systems and human health. In particular, by analyzing the swimming of the bi-flagellated green algae Chlamydomonas reinhardtii in viscoelastic fluid, we show that fluid elasticity enhances the flagellar beating frequency and the wave speed. Yet the net swimming speed of the alga is hindered for fluids that are sufficiently elastic. The origin of this complex response lies in the non-trivial change in flagellar gait due to elasticity. Numerical simulations show that such change in gait reduces elastic stress build up in the fluid and increases efficiency. These results further illustrate the complex coupling between fluid rheology and swimming gait in the motility of micro-organisms and other biological processes such as mucociliary clearance in mammalian airways.

Mathematical Analysis of Viscoelastic Flows
Mathematical Analysis of Viscoelastic Flows

Author: Michael Renardy

Publisher: SIAM

Published: 2000-01-01

Total Pages: 113

ISBN-13: 9780898719413

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This monograph is based on a series of lectures presented at the 1999 NSF-CBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics.

Physics of Transitional Shear Flows
Physics of Transitional Shear Flows

Author: Andrey V. Boiko

Publisher: Springer Science & Business Media

Published: 2011-09-15

Total Pages: 286

ISBN-13: 9400724985

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Starting from fundamentals of classical stability theory, an overview is given of the transition phenomena in subsonic, wall-bounded shear flows. At first, the consideration focuses on elementary small-amplitude velocity perturbations of laminar shear layers, i.e. instability waves, in the simplest canonical configurations of a plane channel flow and a flat-plate boundary layer. Then the linear stability problem is expanded to include the effects of pressure gradients, flow curvature, boundary-layer separation, wall compliance, etc. related to applications. Beyond the amplification of instability waves is the non-modal growth of local stationary and non-stationary shear flow perturbations which are discussed as well. The volume continues with the key aspect of the transition process, that is, receptivity of convectively unstable shear layers to external perturbations, summarizing main paths of the excitation of laminar flow disturbances. The remainder of the book addresses the instability phenomena found at late stages of transition. These include secondary instabilities and nonlinear features of boundary-layer perturbations that lead to the final breakdown to turbulence. Thus, the reader is provided with a step-by-step approach that covers the milestones and recent advances in the laminar-turbulent transition. Special aspects of instability and transition are discussed through the book and are intended for research scientists, while the main target of the book is the student in the fundamentals of fluid mechanics. Computational guides, recommended exercises, and PowerPoint multimedia notes based on results of real scientific experiments supplement the monograph. These are especially helpful for the neophyte to obtain a solid foundation in hydrodynamic stability. To access the supplementary material go to extras.springer.com and type in the ISBN for this volume.

Stability and Transition in Shear Flows
Stability and Transition in Shear Flows

Author: Peter J. Schmid

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 561

ISBN-13: 1461301858

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A detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. It presents analytical results and numerical simulations, linear and selected nonlinear stability methods. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It is equally of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Stability theory has seen a rapid development over the past decade, this book includes such new developments as direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem.

Channel Flow Instabilities of Complex Fluids
Channel Flow Instabilities of Complex Fluids

Author: Hugo A. Castillo Sánchez

Publisher:

Published: 2019

Total Pages: 294

ISBN-13:

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Complex fluids are present in our daily life: food, paints, plastics, pharmaceuticals, to name just a few, and thus, their study is of great interest to the industry. In many industrial processes, raw materials are transformed into finished products with specific rheological properties. Such a transformation may consist of many intermediate physical processes (extruding, melting, coating, pumping, among others). However, the complex nature of these materials might be problematic in many of these operations. More specifically, when complex fluids are under flow conditions, an unexpected behaviour may be observed: for instance, the presence of non-ideal velocity fields during steady flow. In fluid mechanics, we refer to these undesired behaviours as \textit{flow instabilities}; they can occur in a variety of commercially important processing operations. This thesis is a study of instabilities in inertialess viscoelastic flows, also known as \textit{purely elastic instabilities}. The main research content of the thesis is split into three main chapters. In the first, we extend previous theoretical work on a newly discovered elastic instability in planar channel flow of highly shear-thinning viscoelastic fluids. Our motivation was to answer whether the mechanism of such instability observed is truly elastic or principally as a result of strong shear-thinning; we found that both components were critical for the existence of the instability. In the second chapter, we carried out a similar analysis to study instabilities in channel flow of fluids that exhibit much more complex rheological behaviour: thixotropic-viscoelasto-plasticity (TVEP). For the most unstable flows, we showed that the growth rate of instability scales with the rate of recovery of thixotropic structure. Finally, in a third chapter, we extended the scope of the fluids we could consider by including the shear-banding phenomenon in the flows of TVEP fluids; this allowed us to identify distinct bulk and interfacial modes of instability.

Fluid Dynamics of Viscoelastic Liquids
Fluid Dynamics of Viscoelastic Liquids

Author: Daniel D. Joseph

Publisher: Springer Science & Business Media

Published: 2013-11-27

Total Pages: 772

ISBN-13: 1461244625

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This book is about two special topics in rheological fluid mechanics: the elasticity of liquids and asymptotic theories of constitutive models. The major emphasis of the book is on the mathematical and physical consequences of the elasticity of liquids; seventeen of twenty chapters are devoted to this. Constitutive models which are instantaneously elastic can lead to some hyperbolicity in the dynamics of flow, waves of vorticity into rest (known as shear waves), to shock waves of vorticity or velocity, to steady flows of transonic type or to short wave instabilities which lead to ill-posed problems. Other kinds of models, with small Newtonian viscosities, give rise to perturbed instantaneous elasticity, associated with smoothing of discontinuities as in gas dynamics. There is no doubt that liquids will respond like elastic solids to impulses which are very rapid compared to the time it takes for the molecular order associated with short range forces in the liquid, to relax. After this, all liquids look viscous with signals propagating by diffusion rather than by waves. For small molecules this time of relaxation is estimated as lQ-13 to 10-10 seconds depending on the fluids. Waves associated with such liquids move with speeds of 1 QS cm/s, or even faster. For engineering applications the instantaneous elasticity of these fluids is of little interest; the practical dynamics is governed by diffusion, ·say, by the Navier-Stokes equations. On the other hand, there are other liquids which are known to have much longer times of relaxation.