Mathematical Modeling for Complex Fluids and Flows

Book Preface

The book is intended to provide researchers and engineering practitioners in fluid flows with a state-of-the-art knowledge in continuum concepts and the associated fluid dynamics. It further exploits the implicit link between the turbulent flow of classical Newtonian fluids and the laminar and turbulent flow of non-Newtonian fluids needed in many applications such as food processing and polymeric flows. The underlying basis of the presentation will be primarily continuum modeling and will focus on tensorial constitutive relations needed to solve complex flow situations. The notion of complexity will be defined for both the fluids and the flows, and the interplay between the observed phenomena and the capabilities offered by the continuum theory will be highlighted where possible.

The reader is assumed to have a basic knowledge in standard continuum and fluid mechanics, that is, tensor algebra, and basic concepts of kinematics or dynamics of the fluid and flow stress tensor. The monograph will present the mathematical foundation to write meaningful constitutive equations and relevant fluid flow models. These equations are nonlinear most of the time and quite complicated to solve. In order to aid in the clarity, an effort has been made to conserve the usual topical mathematical notation within the complex fluid (viz. the continuum mechanics) and complex flow (viz. turbulent dynamics) communities. The solution methods require numerical methods and algorithms. However, this book does not address this topic as it deserves by itself a full manuscript. We refer the reader to the available specialized literature that covers these subjects.