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.