Inflow Boundary Conditions For Steady Flows Of Viscoelastic Fluids With Differential Constitutive Laws

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Inflow Boundary Conditions for Steady Flows of Viscoelastic Fluids with Differential Constitutive Laws

Author : Michael Renardy
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Inflow Boundary Conditions for Steady Flows of Viscoelastic Fluids with Differential Constitutive Laws by : Michael Renardy

Download or read book Inflow Boundary Conditions for Steady Flows of Viscoelastic Fluids with Differential Constitutive Laws written by Michael Renardy and published by . This book was released on 1986 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steady flows of viscoelastic fluids can not be uniquely determined by imposing boundary conditions only for the velocities as in the Newtonian case. The reason for this is that the fluids have memory, and therefore the flow inside the domain is affected by what happened before the fluid entered the domain. This leads to the need for extra boundary conditions at an inflow boundary. The nature of these inflow boundary conditions has not been analyzed previously, and it is certainly dependent on the constitutive law. In this paper, we look at the special case of differential constitutive relations with a single relaxation mode. We consider steady transverse flows across a strip which are small perturbations of a flow with constant velocity. It turns out that in this case two extra inflow boundary conditions are required in two dimensions, and four in three dimensions. This is what would be expected from an analysis of characteristics, but it contradicts the belief of many rheologists that it is possible to prescribe the extra stress at an inflow boundary. The problem studied here is of potential relevance for numerical simulations of steady flows. Many of the flows currently simulated are on infinite domains. Numerically, these domains are truncated, and on the inflow boundary of the truncated domain people usually prescribe the extra stress. According to the analysis in this paper, this is an overdetermined problem, and therefore errors must be expected from this procedure unless the artificial boundaries are chosen far enough out. Keywords: Upper Convected Maxwell Model.

Mathematical Analysis of Viscoelastic Flows

Author : Michael Renardy
Publisher : SIAM
ISBN 13 : 0898714575
Total Pages : 110 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Mathematical Analysis of Viscoelastic Flows by : Michael Renardy

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 110 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.

Mathematical Analysis of Viscoelastic Flows

Author : Michael Renardy
Publisher : SIAM
ISBN 13 : 9780898719413
Total Pages : 113 pages
Book Rating : 4.7/5 (194 download)

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Book Synopsis Mathematical Analysis of Viscoelastic Flows by : Michael Renardy

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.

Handbook of Differential Equations: Evolutionary Equations

Author : C.M. Dafermos
Publisher : Elsevier
ISBN 13 : 0080931979
Total Pages : 609 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Handbook of Differential Equations: Evolutionary Equations by : C.M. Dafermos

Download or read book Handbook of Differential Equations: Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2008-10-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts

Constitutive Models of Deformation

Author : J. Chandra
Publisher : SIAM
ISBN 13 : 9780898712179
Total Pages : 196 pages
Book Rating : 4.7/5 (121 download)

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Book Synopsis Constitutive Models of Deformation by : J. Chandra

Download or read book Constitutive Models of Deformation written by J. Chandra and published by SIAM. This book was released on 1987-01-01 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Evolution Equations That Change Type

Author : Barbara L. Keyfitz
Publisher : Springer Science & Business Media
ISBN 13 : 1461390494
Total Pages : 297 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Nonlinear Evolution Equations That Change Type by : Barbara L. Keyfitz

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.

Mathematical Topics in Fluid Mechanics

Author : Jose Francisco Rodrigues
Publisher : CRC Press
ISBN 13 : 1000158039
Total Pages : 282 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Mathematical Topics in Fluid Mechanics by : Jose Francisco Rodrigues

Download or read book Mathematical Topics in Fluid Mechanics written by Jose Francisco Rodrigues and published by CRC Press. This book was released on 2020-09-30 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Research Note presents several contributions and mathematical studies in fluid mechanics, namely in non-Newtonian and viscoelastic fluids and on the Navier-Stokes equations in unbounded domains. It includes review of the mathematical analysis of incompressible and compressible flows and results in magnetohydrodynamic and electrohydrodynamic stability and thermoconvective flow of Boussinesq-Stefan type. These studies, along with brief communications on a variety of related topics comprise the proceedings of a summer course held in Lisbon, Portugal in 1991. Together they provide a set of comprehensive survey and advanced introduction to problems in fluid mechanics and partial differential equations.

Handbook of Numerical Analysis

Author : Philippe G. Ciarlet
Publisher : Gulf Professional Publishing
ISBN 13 : 9780444509062
Total Pages : 698 pages
Book Rating : 4.5/5 (9 download)

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Book Synopsis Handbook of Numerical Analysis by : Philippe G. Ciarlet

Download or read book Handbook of Numerical Analysis written by Philippe G. Ciarlet and published by Gulf Professional Publishing. This book was released on 1990 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes following subjects: Solution of equations in Rn, Finite difference methods, Finite element methods, Techniques of scientific computing, Optimization theory and systems science, Numerical methods for fluids, Numerical methods for solids, Specific applications

Thermodynamics of Flowing Systems

Author : Antony N. Beris
Publisher : Oxford University Press
ISBN 13 : 9780195344882
Total Pages : 704 pages
Book Rating : 4.3/5 (448 download)

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Book Synopsis Thermodynamics of Flowing Systems by : Antony N. Beris

Download or read book Thermodynamics of Flowing Systems written by Antony N. Beris and published by Oxford University Press. This book was released on 1994-05-26 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This much-needed monograph presents a systematic, step-by-step approach to the continuum modeling of flow phenomena exhibited within materials endowed with a complex internal microstructure, such as polymers and liquid crystals. By combining the principles of Hamiltonian mechanics with those of irreversible thermodynamics, Antony N. Beris and Brian J. Edwards, renowned authorities on the subject, expertly describe the complex interplay between conservative and dissipative processes. Throughout the book, the authors emphasize the evaluation of the free energy--largely based on ideas from statistical mechanics--and how to fit the values of the phenomenological parameters against those of microscopic models. With Thermodynamics of Flowing Systems in hand, mathematicians, engineers, and physicists involved with the theoretical study of flow behavior in structurally complex media now have a superb, self-contained theoretical framework on which to base their modeling efforts.

Scientific and Technical Aerospace Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 920 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1987 with total page 920 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Existence of Slow Steady Flows of Viscoelastic Fluids with Differential Constitutive Equations

Author : Michael Renardy
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (216 download)

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Book Synopsis Existence of Slow Steady Flows of Viscoelastic Fluids with Differential Constitutive Equations by : Michael Renardy

Download or read book Existence of Slow Steady Flows of Viscoelastic Fluids with Differential Constitutive Equations written by Michael Renardy and published by . This book was released on 1984 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions of existence and uniqueness of steady flows of viscoelastic fluids have thus far not been understood, even for slow flows perturbing rest. This paper provides an existence result for slow flows with no in- and outflow boundaries. The fluid is assumed to be described by constitutive equations of a differential nature. The method used to prove existence is constructive and in fact very close to procedures used in numerical calculations.

Rheological Fundamentals of Polymer Processing

Author : J.A. Covas
Publisher : Springer Science & Business Media
ISBN 13 : 9401585717
Total Pages : 470 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Rheological Fundamentals of Polymer Processing by : J.A. Covas

Download or read book Rheological Fundamentals of Polymer Processing written by J.A. Covas and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experts in rheology and polymer processing present up-to-date, fundamental and applied information on the rheological properties of polymers, in particular those relevant to processing, contributing to the physical understanding and the mathematical modelling of polymer processing sequences. Basic concepts of non-Newtonian fluid mechanics, micro-rheological modelling and constitutive modelling are reviewed, and rheological measurements are described. Topics with practical relevance are debated, such as linear viscoelasticity, converging and diverging flows, and the rheology of multiphase systems. Approximation methods are discussed for the computer modelling of polymer melt flow. Subsequently, polymer processing technologies are studied from both simulation and engineering perspectives. Mixing, crystallization and reactive processing aspects are also included. Audience: An integrated and complete view of polymer processing and rheology, important to institutions and individuals engaged in the characterisation, testing, compounding, modification and processing of polymeric materials. Can also support academic polymer processing engineering programs.

Theoretical, Experimental and Numerical Contributions to the Mechanics of Fluids and Solids

Author : Paul Mansour Naghdi
Publisher : Springer Science & Business Media
ISBN 13 : 9783764351397
Total Pages : 866 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis Theoretical, Experimental and Numerical Contributions to the Mechanics of Fluids and Solids by : Paul Mansour Naghdi

Download or read book Theoretical, Experimental and Numerical Contributions to the Mechanics of Fluids and Solids written by Paul Mansour Naghdi and published by Springer Science & Business Media. This book was released on 1995-07-27 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: ZAMP special issue, Vol. 46 This is a comprehensive and up-to-date collection of papers on the mechanics of fluids and solids by leading researchers. It encompasses theoretical, experimental and numerical work on a variety of topics, including nonlinear elasticity, plastici- ty, dynamics, water waves, and turbulence. The collection is published in celebration of Professor Paul M. Naghdi's lifelong contributions to the field of mechanics. It will be of interest to graduate students and researchers in all branches of continuum mechanics.

Computational Rheology

Author : Robert G Owens
Publisher : World Scientific
ISBN 13 : 1783261951
Total Pages : 437 pages
Book Rating : 4.7/5 (832 download)

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Book Synopsis Computational Rheology by : Robert G Owens

Download or read book Computational Rheology written by Robert G Owens and published by World Scientific. This book was released on 2002-05-29 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern day high-performance computers are making available to 21st-century scientists solutions to rheological flow problems of ever-increasing complexity. Computational rheology is a fast-moving subject — problems which only 10 years ago were intractable, such as 3D transient flows of polymeric liquids, non-isothermal non-Newtonian flows or flows of highly elastic liquids through complex geometries, are now being tackled owing to the availability of parallel computers, adaptive methods and advances in constitutive modelling.Computational Rheology traces the development of numerical methods for non-Newtonian flows from the late 1960's to the present day. It begins with broad coverage of non-Newtonian fluids, including their mathematical modelling and analysis, before specific computational techniques are discussed. The application of these techniques to some important rheological flow problems of academic and industrial interest is then treated in a detailed and up-to-date exposition. Finally, the reader is kept abreast of topics at the cutting edge of research in computational applied mathematics, such as adaptivity and stochastic partial differential equations.All the topics in this book are dealt with from an elementary level and this makes the text suitable for advanced undergraduate and graduate students, as well as experienced researchers from both the academic and industrial communities.

Existennce of Slow Steady Flows of Viscoelastic Fluids with Differential Constitutive Equations

Author : Michael Renardy
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (245 download)

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Book Synopsis Existennce of Slow Steady Flows of Viscoelastic Fluids with Differential Constitutive Equations by : Michael Renardy

Download or read book Existennce of Slow Steady Flows of Viscoelastic Fluids with Differential Constitutive Equations written by Michael Renardy and published by . This book was released on 1984 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Micro-Injection Moulding

Author : Cécile Jeggy
Publisher : Presses univ. de Louvain
ISBN 13 : 9782930344553
Total Pages : 296 pages
Book Rating : 4.3/5 (445 download)

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Book Synopsis Micro-Injection Moulding by : Cécile Jeggy

Download or read book Micro-Injection Moulding written by Cécile Jeggy and published by Presses univ. de Louvain. This book was released on 2004 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Micro-injection moulding is a new process, and as such it has not been thoroughly investigated until now. The peculiarities related to the three dimensional aspect of the cavity and the very small length and time scales at stake make it a very specific technology compared to conventional injection moulding. The aim of this thesis is to pave the way for micro-injection moulding modelling with a special emphasis on micro-cavity filling. Besides giving insight into the process, this work demonstrates the importance of visco-elastic effects and investigates further related issues. The different steps adopted in this work are the following ones: first an extensive review of the process is proposed, followed by a reflection on micro-cavity filling and polymer behaviour which ends up with the choice of the Giesekus model as an appropriate viscoelastic model for some polymers used in this process. A chapter dedicated to polymer characterization conducted on PC Lexan HF11110R, a micro-injection suited amorphous material, shows that the Newtonian viscosity is very low. In this case, the model admissibility from a mathematical and thermodynamic point of view is not guaranteed. This admissibility is the object of a chapter which provides an analysis for the Giesekus model completed with the PC Lexan material parameters. A further mathematical consequence of a vanishing Newtonian viscosity is that the number of inlet boundary conditions to be prescribed for the extra-stress tensor is reduced to 4 instead of 6 in case of a non-vanishing Newtonian viscosity. A specific numerical scheme to tackle this problem is proposed along with a theta-splitting based method which allows us to separate the viscous and visco-elastic effects in the governing equations and to treat subsequently a modified Stokes sub-problem and a transport sub-problem. Finally, a micromixer design and prototyping is presented as an application of this promising process.

Drop, Bubble and Particle Dynamics in Complex Fluids

Author : Pengtao Yue
Publisher : MDPI
ISBN 13 : 3039282964
Total Pages : 142 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Drop, Bubble and Particle Dynamics in Complex Fluids by : Pengtao Yue

Download or read book Drop, Bubble and Particle Dynamics in Complex Fluids written by Pengtao Yue and published by MDPI. This book was released on 2020-03-19 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: The presence of drops, bubbles, and particles affects the behavior and response of complex multiphase fluids. In many applications, these complex fluids have more than one non-Newtonian component, e.g., polymer melts, liquid crystals, and blood plasma. In fact, most fluids exhibit non-Newtonian behaviors, such as yield stress, viscoelastity, viscoplasticity, shear thinning, or shear thickening, under certain flow conditions. Even in the complex fluids composed of Newtonian components, the coupling between different components and the evolution of internal boundaries often lead to a complex rheology. Thus the dynamics of drops, bubbles, and particles in both Newtonian fluids and non-Newtonian fluids are crucial to the understanding of the macroscopic behavior of complex fluids. This Special Issue aims to gather a wide variety of papers that focus on drop, bubble and particle dynamics in complex fluids. Potential topics include, but are not limited to, drop deformation, rising drops, pair-wise drop interactions, drop migration in channel flows, and the interaction of particles with flow systems such as pastes and slurries, glasses, suspensions, and emulsions. We emphasize numerical simulations, but also welcome experimental and theoretical contributions.