Nonlinear Phenomena in Flows of Viscoelastic Polymer Fluids

This monograph presents theoretical and experimental studies of flows of elastic liquids. Falling into this category are particularly the melts and concentrated solutions of such flexible-chain polymers as polyethylene, polyisobutylene and polypropylene, all of which are widely used in polymer processing. These polydisperse polymers vary greatly, from batch to batch, in their mechanical properties and 20% variation in a property is believed to be good enough. l 7 All recent books - devoted to the rheology of polymers do not answer the question of which constitutive equations should be used for solving the fluid mechanic problems of polymer processing in the usual case of an appreciable nonlinear region of deformation where nonlinear effects of shear and extensional elasticity are very important. Viscoelastic constitut ive equations cited commonly (see, e.g. Refs 5 and 6) do not describe simultaneously even the simplest cases of deformations, viz. simple shear and uniaxial extension. Moreover, some of them are internally inconsist ent and sometimes display highly unstable behaviour in simple flows without any fundamental reasons. Even more respected molecular ap free from these defects.

Klappentext

This book presents detailed studies of flows in elastic liquids, from theory, through experiment, to applications. Falling into the category of elastic liquids in particular, are the melts and concentrated solutions of such flexible-chain polymers as polyethylene, polyisobutylene and polypropylene, all of which are widely used in polymer processing. The reading material is presented with an emphasis on practical applications. Applications of results to industrial problems are also discussed.

Inhalt
1 Constitutive Equations with a Recoverable Strain Tensor as an Internal Parameter.- 2 Other Constitutive Equations for Elastic Liquids.- 3 Analyses of Simple Constitutive Equations for Viscoelastic Liquids.- 4 Experimental Methods in the Rheology of Viscoelastic Liquids.- 5 Theoretical and Experimental Investigation of Shear Deformations in Elastic Polymeric Liquids.- 6 Experimental and Theoretical Studies of Uniaxial Uniform Extension of Polymeric Liquids.- 7 On Hardening Phenomena in Flows of Polymeric Liquids.- 8 Flows of Polymeric Viscoelastic Liquids in Channels and Pipes.- 9 Non-isothermal Flows of Polymeric Liquids.- 10 Flows Close to Simple Shear and Simple Extension.- 11 Melt Flow Instabilities.- 12 Additional Problems in the Rheology of Polymeric Fluids.- Appendices.- A1 Kinematics of continuum.- A1.1 Eulerian and Lagrangian descriptions.- A1.2 Basis vectors and tensors.- A1.3 Strain gradient tensors.- A1.4 Cayley polar decomposition.- A1.5 Strain measures.- A1.6 Invariants of tensors and Hamilton-Cayley identity. D(ensity).- A1.7 Scalar functions of tensors and their tensor derivatives.- A1.8 Strain rate and vorticity tensors.- A1.9 Evolution equation for strains.- A1.10 Continuity equation.- A2 A brief introduction into non-equilibrium thermodynamics.- A2.1 Conservation laws: the local formulation of the First Law of Thermodynamics.- A2.2 Local equilibrium assumption: Gibbs' relation. A local formulation of the Second Law of Thermodynamics.- A2.3 Expressions for entropy production, entropy flux and heat capacity.- A2.4 Generalized thermodynamic forces and fluxes.- A3 Component-wise expressions for basic equations.- A3.1 The equations of momentum balance and continuity for incompressible media.- A3.2 Equation for temperature variations.- A3.3Component-wise expressions for the velocity gradient tensor and the upper-convected time derivative of recoverable strain tensor.- References.