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About this book

The book is designed for advanced graduate students as well as postdoctoral researchers across several disciplines (e.g., mathematics, physics and engineering), as it provides them with tools and techniques that are essential in performing research on the flow problems of visco-plastic fluids. The following topics are treated:

analysis of classical visco-plastic fluid models

mathematical modeling of flows of visco-plastic fluids

computing flows of visco-plastic fluids

rheology of visco-plastic fluids and visco-plastic suspensions

application of visco-plastic fluids in engineering sciences

complex flows of visco-plastic fluids.

Table of Contents


Background Lectures on Ideal Visco-Plastic Fluid Flows

These notes are intended to supplement a short lecture course covering the theoretical background of the dynamics of ideal visco-plastic fluids, e.g. Bingham fluids, Herschel-Bulkley fluids. They are targeted at an applied mathematics or engineering audience. The intention is to give a non-rigorous introduction to those parts of the theory that: (a) appear to have use in applications; (b) are needed for computational methods; (c) mark out visco-plastic fluids from purely viscous generalised Newtonian fluids.
I. A. Frigaard

Viscoplastic Asymptotics and Other Analytical Methods

The goal of these lectures is to outline some of the ideas behind the use of asymptotic analysis and other analytical methods in viscoplastic fluid mechanics
Neil J. Balmforth

Computational Methods for Viscoplastic Fluid Flows

This document constitutes the lecture notes that I used over the summer school Visco-plastic fluids: From theory to application organized in the International Centre for Mechanical Sciences of Udine, Italy, from May 30th to June 3rd, 2016. It contains five sections corresponding to the five lectures I gave on Computational Methods for Viscoplastic Fluid Flows. We discuss solution algorithms, discretization schemes, weak/strong coupling, mesh generation and high performance computing for the numerical solution of viscoplastic fluid flow problems. We present ready-on-the-shelf algorithms that practitioners can easily implement and illustrate their performance on a variety of flows (weakly compressible, non-isothermal, two-phase and thixotropic).
Anthony Wachs

Rheometry of Visco-Plastic Fluids

This chapter deals with experimental methods for the measurement of the rheological properties of materials, with a focus on yield stress fluids. Section 2 provides the basis of rheometry. Standard equations for viscosimetric flows are given and their application to visco-plastic fluids is discussed. The third section deals with the measurements of the main properties of simple yield stress fluids: solid viscoelastic properties, yield stress, and visco-plastic properties. The fourth section is devoted to the measurements of the properties of thixotropic yield stress fluids, with a focus on the dependence of their behaviour on shear history and on their aging at rest. The phenomena of shear localisation and shear banding are finally discussed in the fifth section, together with possible material inhomogeneities.
Guillaume Ovarlez

Rheology of Visco-Plastic Suspensions

This chapter deals with the rheological properties of viscoplastic suspensions. In Sect. 2, we discuss the theoretical behavior of suspensions of rigid particles in linear and nonlinear media. In Sect. 3, we present appropriate model systems, experimental setups and methods. The main experimental observations are presented in Sect. 4: we present the evolution of the elastic, plastic, and flow properties with the particle volume fraction, and we discuss the emergence of a shear-dependent microstructure. Finally, shear-induced migration and its link with normal stress differences are briefly discussed in Sect. 5.
Guillaume Ovarlez

Industrial Applications of Yield Stress Fluids

Industry has been working with yield stress fluids for many years. In many cases they are known as viscoplastic fluids (VPFs).
D. Ian Wilson
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