Control Theory in Rheology

This book bridges the gap between theoretical rheology and practical industry applications by introducing Control Theory (CT) and the linear Unified Model. This approach enables the modelling and analysis of various viscoelastic flows as well as polymer and macromolecular structures. In practical engineering, the design of machinery and equipment for polymers often relies on handbooks, respective textbooks, and numerous CAD-aided software tools based on empirical formulas. This book presents many useful viscoelastic constitutive equations for analysing and model shear and complex flows, relaxation modulus and spectrum, elongation, transient viscosity, and for computing the Molecular Weight Distribution (MWD) from viscoelastic measurements.

The book adopts a counterintuitive approach, starting afresh and proceeding chronologically from steady-state viscosity and other flows relevant to practical engineering to the theoretical formulas of relaxation phenomena. It simplifies unnecessary complexity while still drawing on the well-documented motions of molecular chains. Furthermore, the book offers deeper insights into the background of power-law theories and the Cox-Merz rule, supplying new formulas for the relaxation modulus, spectrum, and various modules through the application of unified formulas. Professionals and scholars alike will find it a handy reference tool.

Provides new viscoelastic equations for accurately modelling shear and complex flows Bridges the gap between theoretical rheology and industry using scientifically approved control theory Offers a fresh platform for analysing flow behaviours and macromolecular structures, including polydispersity

Autorentext

Tommi Borg has been active in plastics conversion since the 1960s, starting as a trainee at extrusion and polymerization plants in Finland and Sweden. He studied physics and computer science at the University of Oulu during the 1970s, leading to his first Finnish patent being granted in 1977, followed by his first international patent in 1989. He has decades of experience in engineering extrusion lines and die designs. He worked at extrusion plants from 1979 to 1993, after which he became an independent researcher and an international consultant in plastics and software. He focused on developing viscoelasticity models that were more accurate than existing Maxwell and power-law models.

Inhalt

1.Theoretical and Practical Rheology.- 2.The Principle of Control Theory (CT).- 3.Basics of distribution Functions.- 4.Steady Shear Viscosity.- 5.Complex Viscosit.- 6.Relaxation Modulus.- 7.Converting RED function to MWD.- 8.From MWD to RED and back again.- 9.From measured viscosity data to MWD.- 10.Start-up and transient flow effects.- 11.Elongational viscosity.- 12.Temperature and viscoelastic relations.- 13.Computation Cases.- 14.Overview of the Unified Model.- 15.Hemorheological method for analyses.- 16.Comparison With other known models.