Microhydrodynamics and Complex Fluids

A self-contained textbook, Microhydrodynamics and Complex Fluidsdeals with the main phenomena that occur in slow, inertialess viscous flows often encountered in various industrial, biophysical and natural processes. It examines a wide range of situations, from flows in thin films, porous media and narrow channels to flows around suspended particles. Each situation is illustrated with examples that can be solved analytically so that the main physical phenomena are clear. It also discusses a range of numerical modelling techniques.

Two chapters deal with the flow of complex fluids, presented first with the formal analysis developed for the mechanics of suspensions and then with the phenomenological tools of non-Newtonian fluid mechanics. All concepts are presented simply, with no need for complex mathematical tools. End-of-chapter exercises and exam problems help you test yourself.

Dominique Barthès-Biesel has taught this subject for over 15 years and is well known for her contributions to low Reynolds number hydrodynamics. Building on the basics of continuum mechanics, this book is ideal for graduate students specializing in chemical or mechanical engineering, material science, bioengineering, and physics of condensed matter.

Dominique Barthès-Biesel graduated from Ecole Centrale Paris and then earned a PhD in chemical engineering from Stanford University. She has been a professor at both Ecole Polytechnique and at Compiègne University of Technology, where she taught various classes in classical and complex fluid mechanics, biomechanics, and microfluidics. Professor Barthès-Biesel’s field of interest is fluid mechanics with a special emphasis on suspensions of deformable particles such as drops, cells, and capsules. She is well-known for her pioneering work on the motion and deformation of encapsulated droplets. She has directed 27 PhD theses, published over 70 papers, and also worked on industrial projects.

Fundamental Principles
Mass Conservation
Equation of Motion
Newtonian Fluid
Navier-Stokes Equations
Energy Dissipation
Dimensional Analysis


General Properties of Stokes Flows
Stationary Stokes Equations
Simple Stokes Flow Problem
Linearity and Reversibility
Uniqueness
Minimum Energy Dissipation
Reciprocal Theorem
Solution in Terms Of Harmonic Functions
Problems


Two-Dimensional Stokes Flow
Stream Function
Two-Dimensional Stokes Equation
Wedge with a Moving Boundary
Flow in Fixed Wedges
Problems


Lubrication Flows
Two-Dimensional Lubrication Flows
Three-Dimensional Lubrication Flow
Flow between Fixed Solid Boundaries
Flow in Porous Media
Problems


Free Surface Films
Interface between Two Immiscible Fluids
Gravity Spreading of a Fluid on a Horizontal Plane
Stability of a Film down an inclined plane
Problems


Motion of a Solid Particle in a Fluid
Motion of a Solid Particle in a Quiescent Fluid
Isotropic Particles
Flow around a Translating Sphere
Flow around a Rotating Sphere
Slender Particles
Problems


Flow of Bubbles and Droplets
Freely Suspended Liquid Drop
Translational Motion of a Bubble in a Quiescent Fluid
Translational Motion of a Liquid Drop in a Quiescent Fluid
Problems

General Solutions of the Stokes Equations
Flow Due to a Point Force
Irrotational Solutions
Series of Fundamental Solutions: Singularity Method
Integral Form of the Stokes Equations
Problems


Introduction to Suspension Mechanics
Homogenisation of a Suspension
Micro-Macro Relationship
Dilute Suspension
Highly Concentrated Suspension of Spheres
Numerical Modelling of a Suspension
Conclusion
Problems


O(Re) Correction to Some Stokes Solutions
Translation of a Sphere: Oseen Correction
Translation of a Cylinder: Stokes Paradox
Validity Limits of the Stokes Approximation
Problem


Non-Newtonian Fluids
Introduction
Non-Newtonian Fluid Mechanics
Viscous Non-Newtonian Liquid
Viscoelastic Fluid
Linear Viscoelastic Laws
Non-Linear Viscoelastic Laws
Non-Newtonian Flow Examples
Conclusion
Problems


Appendix A Notations
Vectors and Tensors
Einstein Summation Convention
Integration on a Sphere

Appendix B Curvilinear Coordinates
Cylindrical Coordinates
Spherical Coordinates


Bibliography


Index