Download or read book Instabilities in Shear Flow of Viscoelastic Fluids with Fading Memory written by Bradley J. Plohr and published by . This book was released on 1988 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Shear Flow Instabilities in Viscoelastic Fluids written by Helen Jane Wilson and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stability of Non Linear Constitutive Formulations for Viscoelastic Fluids written by Dennis A. Siginer and published by Springer Science & Business Media. This book was released on 2013-12-05 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids provides a complete and up-to-date view of the field of constitutive equations for flowing viscoelastic fluids, in particular on their non-linear behavior, the stability of these constitutive equations that is their predictive power, and the impact of these constitutive equations on the dynamics of viscoelastic fluid flow in tubes. This book gives an overall view of the theories and attendant methodologies developed independently of thermodynamic considerations as well as those set within a thermodynamic framework to derive non-linear rheological constitutive equations for viscoelastic fluids. Developments in formulating Maxwell-like constitutive differential equations as well as single integral constitutive formulations are discussed in the light of Hadamard and dissipative type of instabilities.
Download or read book Shear Flow Instabilities in Viscoelastic Fluids written by Joel C. Miller and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Breadth and Depth of Continuum Mechanics written by Constantine M. Dafermos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers dedicated to Jerry Ericksen on his sixtieth birthday, December 20, 1984. They first appeared in Volumes 82-90 (1983-1985) of the Archive for Rational Mechanics and Analysis. At the request of the Editors the list of authors to be invited was drawn up by C. M. Dafermos, D. D. Joseph, and F. M. Leslie. The breadth and depth of the works here reprinted reflect the corresponding qualities in Jerry Ericksen's research, teaching, scholarship, and inspiration. His interests and expertness center upon the mechanics of materials and extend to everything that may contribute to it: pure analysis, algebra, geometry, through all aspects of theoretical mechanics to fundamental experiment, all of these illumi nated by an intimate and deep familiarity with the sources, even very old ones. He is independent of school and contemptuous of party spirit; his generosity in giving away his ideas is renowned, but not everyone is capable of accepting what is offered. His writings are totally free of broad claims and attributions beyond his own study. Some are decisive, some are prophetic, and all are forthright. His work has served as a beacon of insight and simple honesty in an age of ever more trivial and corrupt science. The authors of the memoirs in this volume are his students, colleagues, admirers, and (above all) his friends.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mechanics of Viscoelastic Fluids written by S. Zahorski and published by Springer. This book was released on 1982-10-31 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elements of Stability of Viscoelastic Fluids written by J. Dunwoody and published by Longman. This book was released on 1989 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Viscoelasticity and Rheology written by Arthur S. Lodge and published by Academic Press. This book was released on 2014-06-28 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Viscoelasticity and Rheology covers the proceedings of a symposium by the same title, conducted by the Mathematics Research Center held at the University of Wisconsin-Madison on October 16-18, 1984. The contributions to the symposium are divided into four broad categories, namely, experimental results, constitutive theories, mathematical analysis, and computation. This 16-chapter work begins with experimental topics, including the motion of bubbles in viscoelastic fluids, wave propagation in viscoelastic solids, flows through contractions, and cold-drawing of polymers. The next chapters covering constitutive theories explore the molecular theories for polymer solutions and melts based on statistical mechanics, the use and limitations of approximate constitutive theories, a comparison of constitutive laws based on various molecular theories, network theories and some of their advantages in relation to experiments, and models for viscoplasticity. These topics are followed by discussions of the existence, regularity, and development of singularities, change of type, interface problems in viscoelasticity, existence for initial value problems and steady flows, and propagation and development of singularities. The remaining chapters deal with the numerical simulation of flow between eccentric cylinders, flow around spheres and bubbles, the hole pressure problem, and a review of computational problems related to various constitutive laws. This book will prove useful to chemical engineers, researchers, and students.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1972 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transactions of the Army Conference on Applied Mathematics and Computing written by and published by . This book was released on 1989 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Equations written by K.D. Elworthy and published by Routledge. This book was released on 2017-11-22 with total page 984 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents recent developments in the areas of differential equations, dynamical systems, and control of finke and infinite dimensional systems. Focuses on current trends in differential equations and dynamical system research-from Darameterdependence of solutions to robui control laws for inflnite dimensional systems.
Download or read book Mathematical Analysis of Viscoelastic Flows written by Michael Renardy and published by SIAM. This book was released on 2000-01-01 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Evolution Equations That Change Type written by Barbara L. Keyfitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications NONLINEAR EVOLUTION EQUATIONS THAT CHANGE TYPE is based on the proceedings of a workshop which was an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshop focussed on prob lems of ill-posedness and change of type which arise in modeling flows in porous materials, viscoelastic fluids and solids and phase changes. We thank the Coordinat ing Committee: James Glimm, Daniel Joseph, Barbara Lee Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the workshop organizers, Barbara Lee Keyfitz and Michael Shearer, for their efforts in bringing together many of the major figures in those research fields in which theories for nonlinear evolution equations that change type are being developed. A vner Friedman Willard Miller, J r. ix PREFACE During the winter and spring quarters of the 1988/89 IMA Program on Non linear Waves, the issue of change of type in nonlinear partial differential equations appeared frequently. Discussion began with the January 1989 workshop on Two Phase Waves in Fluidized Beds, Sedimentation and Granular Flow; some of the papers in the proceedings of that workshop present strategies designed to avoid the appearance of change of type in models for multiphase fluid flow.
Download or read book Technical Reports Awareness Circular TRAC written by and published by . This book was released on 1989-03 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Flow Behavior and Instabilities in Viscoelastic Fluids written by Boyang Qin and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Current Progress in Hyperbolic Systems Riemann Problems and Computations written by W. Brent Lindquist and published by American Mathematical Soc.. This book was released on 1989 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Current Progress in Hyperbolic Systems: Riemann Problems and Computations, held at Bowdoin College in July 1988.
