Stochastic Processes in Polymeric Fluids PDF Download
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Author: Hans Christian Öttinger
Publisher:
ISBN:
Category : Technology & Engineering
Languages : en
Pages : 396
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Book Description
This book consists of two strongly interweaved parts: the mathematical theory of stochastic processes and its applications to molecular theories of polymeric fluids. The comprehensive mathematical background provided in the first part should be equally useful in many other branches of engineering and the natural sciences. As a benefit from the second part one gains a more direct understanding of polymer dynamics, one can more easily identify exactly solvable models, and one can develop efficient computer simulation algorithms in a straightforward manner. In view of the many examples and exercises, on the one hand, and the numerous applications to problems from the front line of science, on the other hand, this volume may be used equally well as a basic textbook or as an up-to-date reference book.
Author: Hans Christian Öttinger
Publisher:
ISBN:
Category : Technology & Engineering
Languages : en
Pages : 396
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Book Description
This book consists of two strongly interweaved parts: the mathematical theory of stochastic processes and its applications to molecular theories of polymeric fluids. The comprehensive mathematical background provided in the first part should be equally useful in many other branches of engineering and the natural sciences. As a benefit from the second part one gains a more direct understanding of polymer dynamics, one can more easily identify exactly solvable models, and one can develop efficient computer simulation algorithms in a straightforward manner. In view of the many examples and exercises, on the one hand, and the numerous applications to problems from the front line of science, on the other hand, this volume may be used equally well as a basic textbook or as an up-to-date reference book.
Author: Hans C. Öttinger
Publisher: Springer Science & Business Media
ISBN: 3642582907
Category : Technology & Engineering
Languages : en
Pages : 384
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Book Description
This book consists of two strongly interweaved parts: the mathematical theory of stochastic processes and its applications to molecular theories of polymeric fluids. The comprehensive mathematical background provided in the first section will be equally useful in many other branches of engineering and the natural sciences. The second part provides readers with a more direct understanding of polymer dynamics, allowing them to identify exactly solvable models more easily, and to develop efficient computer simulation algorithms in a straightforward manner. In view of the examples and applications to problems taken from the front line of science, this volume may be used both as a basic textbook or as a reference book. Program examples written in FORTRAN are available via ftp from ftp.springer.de/pub/chemistry/polysim/.
Author: Hans C. Öttinger
Publisher: Springer
ISBN: 9783642582912
Category : Technology & Engineering
Languages : en
Pages : 362
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Book Description
This book consists of two strongly interweaved parts: the mathematical theory of stochastic processes and its applications to molecular theories of polymeric fluids. The comprehensive mathematical background provided in the first section will be equally useful in many other branches of engineering and the natural sciences. The second part provides readers with a more direct understanding of polymer dynamics, allowing them to identify exactly solvable models more easily, and to develop efficient computer simulation algorithms in a straightforward manner. In view of the examples and applications to problems taken from the front line of science, this volume may be used both as a basic textbook or as a reference book. Program examples written in FORTRAN are available via ftp from ftp.springer.de/pub/chemistry/polysim/.
Author: Francisco Chinesta
Publisher: Springer
ISBN: 3319700014
Category : Technology & Engineering
Languages : en
Pages : 132
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Book Description
This SpringerBrief covers the main scales of description of matter, starting at its finest level, the quantum scale, moving through ab-initio, molecular dynamics, coarse grained approaches, to finish at the scale of kinetic theory models that allows a nice compromise between the rich but expensive microscopic descriptions and the computationally cheap but sometimes too coarse macroscopic descriptions. The book addresses undergraduate and graduate students, as well as beginners in multi-scale modeling of materials.
Author: David C. Venerus
Publisher: Cambridge University Press
ISBN: 1107129206
Category : Science
Languages : en
Pages : 537
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Book Description
Integrating nonequilibrium thermodynamics and kinetic theory, this unique text presents a novel approach to the subject of transport phenomena.
Author: Michael Grinfeld
Publisher: John Wiley & Sons
ISBN: 3527411887
Category : Science
Languages : en
Pages : 634
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Book Description
The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.
Author: Roger I. Tanner
Publisher: OUP Oxford
ISBN: 0191590169
Category : Mathematics
Languages : en
Pages : 590
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Book Description
This book sets out to provide a guide, with examples, for those who wish to make predictions about the mechanical and thermal behaviour of non-Newtonian materials in engineering and processing technology. After an introductory survey of the field and a review of basic continuum mechanics, the radical differences between elongational and shear behaviour are shown. Two chapters, one based on a continuum approach and the other using microstructural approaches, lead to useful mathematical desriptions of materials for engineering applications. As examples of nearly-viscometric and nearly-elongational flows, there is a discussion of lubrication and related shearing flows, and fibre- spinning and film-blowing respectively. A long chapter is devoted to the important new field of computational rheology, and this is followed by chapters on stability and turbulence and the all-important temperature effects in flow. This new edition contains much new material not available in book form elsewhere-for example wall slip, suspension rheology, computational rheology and new results in stability theory.
Author: R.R. Huilgol
Publisher: Elsevier
ISBN: 0080531741
Category : Science
Languages : en
Pages : 508
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Book Description
The areas of suspension mechanics, stability and computational rheology have exploded in scope and substance in the last decade. The present book is one of the first of a comprehensive nature to treat these topics in detail. The aim of the authors has been to highlight the major discoveries and to present a number of them in sufficient breadth and depth so that the novice can learn from the examples chosen, and the expert can use them as a reference when necessary.The first two chapters, grouped under the category General Principles, deal with the kinematics of continuous media and the balance laws of mechanics, including the existence of the stress tensor and extensions of the laws of vector analysis to domains bounded by fractal curves or surfaces. The third and fourth chapters, under the heading Constitutive Modelling, present the tools necessary to formulate constitutive equations from the continuum or the microstructural approach. The last three chapters, under the caption Analytical and Numerical Techniques, contain most of the important results in the domain of the fluid mechanics of viscoelasticity, and form the core of the book.A number of topics of interest have not yet been developed to a theoretical level from which applications can be made in a routine manner. However, the authors have included these topics to make the reader aware of the state of affairs so that research into these matters can be carried out. For example, the sections which deal with domains bounded by fractal curves or surfaces show that the existence of a stress tensor in such regions is still open to question. Similarly, the constitutive modelling of suspensions, especially at high volume concentrations, with the corresponding particle migration from high to low shear regions is still very sketchy.
Author: Michael Kotelyanskii
Publisher: CRC Press
ISBN: 0824751310
Category : Technology & Engineering
Languages : en
Pages : 572
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Book Description
Author: Shikha Somani
Publisher: Stanford University
ISBN:
Category :
Languages : en
Pages : 135
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Book Description
Polymers undergo a sharp coil to stretch conformational transition in extension dominated flows when the strain rate exceeds a critical value. Dramatic change in flow behavior is known to occur at the coil-stretch transition, making it useful for several commercial applications. Despite decades of study, this phenomenon remains surrounded with controversy as the effect of solvent properties and fluid flow elements on this transition is not fully understood. In this work, we present a study of the coil-stretch transition and related hysteresis phenomenon using stochastic computer simulations. We first investigate the effect of solvent quality on the coil-stretch transition using Brownian dynamics simulations. Unlike experiments, which are plagued with problems related to polydispersity of polymers and inaccurate control over flow profiles, simulations offer a powerful platform to systematically study the effect of solvent quality while keeping all other parameters in the system constant. The system consists of a polymer subjected to planar elongational flow in both theta solvents and good solvents. The polymer is represented by a bead-spring chain model undergoing elongational flow. Solvent-mediated effects such as fluctuating hydrodynamic interactions (HI) and excluded volume (EV) are included rigorously. Conformational hysteresis is understood in terms of a 1-D energy landscape theory with an activation energy barrier for transition. At steady state, depending upon the flow rate, the energy landscape can either have one or two energy wells. An energy landscape with one well corresponds to the coiled state at low flow rate and stretched state at high flowrate. The double welled landscape corresponds to the hysteretic regime where both coiled and stretched conformational states coexist across the ensemble population. A key factor in determining the effect of solvent quality is the use of a proper measure of solvent quality. In almost all earlier studies, the effect of molecular weight on solvent quality has been neglected, producing inconsistent results. Here, the solvent quality is quantified carefully such that the effect of molecular weight and temperature is taken into account. Contrary to earlier findings, it is observed that with improvement in solvent quality, the chains unravel faster and the critical strain rate at which the coil to stretch transition takes place decreases. Furthermore, the solvent quality has a profound effect on the scaling of the critical strain rate with molecular weight and on both the transient and steady state properties of the system. Universal functions are shown to exist for the observed dynamic and static properties, which will prove useful in determining the operating parameters for experiments. In particular, the ratio of the two different relaxation times (longest relaxation time and zero shear rate viscosity) is found to be a universal function of solvent quality independent of molecular weight. The relaxation times (both the longest relaxation time and the zero shear rate viscosity) increase while the critical strain rate is found to decrease with solvent quality. Next, the study of conformational hysteresis is extended to more complicated 3-D flows to understand the effect of flow vorticity on this phenomenon. Heretofore, there has been no systematic methodology for studying the dynamical interactions between polymer molecules and elementary flow patterns in three-dimensional flows. Such a framework is essential not just for gaining valuable insights into the physics of complex fluids at a fundamental level, but it is also crucial for various important applications like turbulent drag reduction where the underlying physical mechanisms involve dynamical interactions between polymers and turbulence fine scale flow features. Such a study is presented here to provide a framework to interpret complex fluid phenomenon in terms of elementary flow patterns. We investigate the conformational hysteresis using rigorous Brownian dynamics simulations and specifically explore the effect of flow vorticity on the lifetime and width of the hysteresis window in 3-D flows. A systematic procedure is developed with careful eigenvalue analysis to explore the sole effect of vorticity on polymer dynamics keeping the principal strain rate fixed. It is observed that the hysteresis width shrinks due to increase in flow vorticity irrespective of the flow type (bi-extensional, bi-compressional, spiral-inwards, spiral-outwards etc). This is further traced to the alignment of eigenvectors with the principal eigenvector direction leading to enhanced fluctuations. Vorticity is found to have a significant effect on both the transient and the steady state properties. Understanding the effect of vorticity on polymer conformational hysteresis can further help in understanding the fundamental processes in complex flows.
