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Polymer rheology and plastics processing
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Journal of Non-Newtonian Fluid Mechanics, 1 (1976) 305-308 @ Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
Book Reviews
Polymer Rheology and Plastics Processing, Proceedings of the Symposium of the British Society of Rheology and the Plastics and Rubber Institute, held at the University of Loughborough, 17-19 September, 1975, 320 pages. For many years theoretical rheologists and applied mathematicians happily evolved theories for the continuum mechanics and fluid mechanics of viscoelastic materials and idealized processes. At the same time, design and production engineers threw up their hands in despair at the complexity of their real processes and tinkered with their machines as enormous black boxes. Gradually, the theoreticians realized that their work required interpretation and translation if industrialists were to comprehend their analyses. At the same time, practitioners have increased their understanding of the analyses as they have seen them attack pertinent industrial problems. The papers included in this volume reflect the progress and frustrations which have beset the marriage of these disparate philosophies of work. Parnaby shows in a paper on machine design how the lumped parameter analysis used by engineers can incorporate some of the complex properties of polymers. Although the calculations err in detail, the results are often accurate enough for devising control schemes. The level of analysis used depends upon a tradeoff between the costs of calculations and the improved accuracy of the results. A series of papers by Halmos et al., Lindt, Worth and Helmy and Janssen and Smith on single- and twin-screw extruders extends the sophistication of the analysis by another step. In these papers, the complex flows in an extruder are considered as distributed systems. Because of the complexity of the coupled momentum and energy equations and the geometry, a number of assumptions on the flow behaviour of the molten or melting polymer are needed. The primary unsolved problems in these papers are how to calculate the stresses on the compressed bed of solid particles in a plasticating extruder and how to calculate the shape of the bed as a result of these stresses. The shape and position of the bed may have a large influence on the rate of melting in the extruder, hence on the maximum flow rates and pressures developed. Another sequence of papers treats the experimental and theoretical problems in describing elongational flow. Despite the elegant experimental procedures described by Dealy, little is known about the elongational behaviour of polymer melts with large strains, high strain rates and non-isothermal conditions. Czarnecki and Plochocki show how important melt elasticity can be in the elongational flow of a film-blowing process. Mackley and Hinch, in a pair of papers, have shown how orientation due to elongational flow in either solutions or melt
306
can lead to unusual flow behaviour including phase changes and highly elastic effects. Unfortunately, even some of the basic ideas of fluid mechanics have been baldy misused. Hansen and Cogswell mistake secondary flow in the entrance region of a reservoir as indicative of “structure”. Deprez and Bontnick neglect the fact that fibre spinning is not a constant elongation rate process. The stated objective of the conference was to bring together theoreticians and engineers to exchange ideas and methods. Somce of the papers in this volume reflect a real collaboration between these groups of workers. However, on the whole, the sad conclusion is that often the two groups are talking past one another with the exchanged information garbled beyond recognition. As a collection of research papers, the contents of the volume present few new ideas not published before and do little to advance the state of the art. J.M. FUNT
to Non-Linear Continuum Thermodynamics, by Gianni Astarita, Societa Editricedi Chimica, Milan, Italy, 1975, 133 pages, approx. $10.
An Introduction
The conventional engineering course in classical thermodynamics begins with a discussion of compression of an ideal gas. Using everyday notions of mechanical work, the concept of an inexact differential, whose line integral is the total work, is developed. Then notions of heat are similarly developed and the internal energy, the First Law and the Second Law are discussed. The concepts rely on naturalistic arguments and the idea that real processes can be treated as quasistatic processes. The quasi-static process consists of a sequence of steps, each of which is in equilibrium and which can be described using state functions of state variables. Following a review of kinematics and tensor analysis in the first chapter, Astarita develops a critical review of the conventional theory of thermodynamics. The first objection to the classical approach is that work defined in that theory cannot account for even simple linear friction of a Newtonian fluid. The concept of a quasi-static process contains implicit assumptions on the smoothness and differentiability of state functions which may not hold for real processes. Thirdly, the classical theory makes no statements on the dynamics of a process. In Chapter 3 the stress tensor as a functional of the kinematics and temperature field is introduced. The Second Law is presented as an inequality of the rate of entropy change and the First Law is presented as a dynamic energy balance. From this point it is shown that classical thermodynamics is a special case of a more general theory. More particularly, the assumptions on smoothness are made explicit and the theory can treat dynamic processes. In the remaining chapters the consequences of various constitutive assumptions, such as an ideal elastic solid, a Newtonian liquid or a simple fluid with fading memory are explored. The subject of the book is an introduction to the theories developed by Coleman, Truesdell and others. It assumes some familiarity with classical thermodynamics and kinematics. As such, it makes an excellent basis for exploring the concepts and limitations of the conventional thermodynamics course. The text
Journal of Non-Newtonian Fluid Mechanics, 1 (1976) 305-308 @ Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
Book Reviews
Polymer Rheology and Plastics Processing, Proceedings of the Symposium of the British Society of Rheology and the Plastics and Rubber Institute, held at the University of Loughborough, 17-19 September, 1975, 320 pages. For many years theoretical rheologists and applied mathematicians happily evolved theories for the continuum mechanics and fluid mechanics of viscoelastic materials and idealized processes. At the same time, design and production engineers threw up their hands in despair at the complexity of their real processes and tinkered with their machines as enormous black boxes. Gradually, the theoreticians realized that their work required interpretation and translation if industrialists were to comprehend their analyses. At the same time, practitioners have increased their understanding of the analyses as they have seen them attack pertinent industrial problems. The papers included in this volume reflect the progress and frustrations which have beset the marriage of these disparate philosophies of work. Parnaby shows in a paper on machine design how the lumped parameter analysis used by engineers can incorporate some of the complex properties of polymers. Although the calculations err in detail, the results are often accurate enough for devising control schemes. The level of analysis used depends upon a tradeoff between the costs of calculations and the improved accuracy of the results. A series of papers by Halmos et al., Lindt, Worth and Helmy and Janssen and Smith on single- and twin-screw extruders extends the sophistication of the analysis by another step. In these papers, the complex flows in an extruder are considered as distributed systems. Because of the complexity of the coupled momentum and energy equations and the geometry, a number of assumptions on the flow behaviour of the molten or melting polymer are needed. The primary unsolved problems in these papers are how to calculate the stresses on the compressed bed of solid particles in a plasticating extruder and how to calculate the shape of the bed as a result of these stresses. The shape and position of the bed may have a large influence on the rate of melting in the extruder, hence on the maximum flow rates and pressures developed. Another sequence of papers treats the experimental and theoretical problems in describing elongational flow. Despite the elegant experimental procedures described by Dealy, little is known about the elongational behaviour of polymer melts with large strains, high strain rates and non-isothermal conditions. Czarnecki and Plochocki show how important melt elasticity can be in the elongational flow of a film-blowing process. Mackley and Hinch, in a pair of papers, have shown how orientation due to elongational flow in either solutions or melt
306
can lead to unusual flow behaviour including phase changes and highly elastic effects. Unfortunately, even some of the basic ideas of fluid mechanics have been baldy misused. Hansen and Cogswell mistake secondary flow in the entrance region of a reservoir as indicative of “structure”. Deprez and Bontnick neglect the fact that fibre spinning is not a constant elongation rate process. The stated objective of the conference was to bring together theoreticians and engineers to exchange ideas and methods. Somce of the papers in this volume reflect a real collaboration between these groups of workers. However, on the whole, the sad conclusion is that often the two groups are talking past one another with the exchanged information garbled beyond recognition. As a collection of research papers, the contents of the volume present few new ideas not published before and do little to advance the state of the art. J.M. FUNT
to Non-Linear Continuum Thermodynamics, by Gianni Astarita, Societa Editricedi Chimica, Milan, Italy, 1975, 133 pages, approx. $10.
An Introduction
The conventional engineering course in classical thermodynamics begins with a discussion of compression of an ideal gas. Using everyday notions of mechanical work, the concept of an inexact differential, whose line integral is the total work, is developed. Then notions of heat are similarly developed and the internal energy, the First Law and the Second Law are discussed. The concepts rely on naturalistic arguments and the idea that real processes can be treated as quasistatic processes. The quasi-static process consists of a sequence of steps, each of which is in equilibrium and which can be described using state functions of state variables. Following a review of kinematics and tensor analysis in the first chapter, Astarita develops a critical review of the conventional theory of thermodynamics. The first objection to the classical approach is that work defined in that theory cannot account for even simple linear friction of a Newtonian fluid. The concept of a quasi-static process contains implicit assumptions on the smoothness and differentiability of state functions which may not hold for real processes. Thirdly, the classical theory makes no statements on the dynamics of a process. In Chapter 3 the stress tensor as a functional of the kinematics and temperature field is introduced. The Second Law is presented as an inequality of the rate of entropy change and the First Law is presented as a dynamic energy balance. From this point it is shown that classical thermodynamics is a special case of a more general theory. More particularly, the assumptions on smoothness are made explicit and the theory can treat dynamic processes. In the remaining chapters the consequences of various constitutive assumptions, such as an ideal elastic solid, a Newtonian liquid or a simple fluid with fading memory are explored. The subject of the book is an introduction to the theories developed by Coleman, Truesdell and others. It assumes some familiarity with classical thermodynamics and kinematics. As such, it makes an excellent basis for exploring the concepts and limitations of the conventional thermodynamics course. The text