MMathPhys Advanced Fluid Dynamics : Part 2 Complex and
Non-Newtonian Fluids (overall
Overall theme: fluids with an extra stress due to (small) embedded
particles, polymer molecules etc, with connections to kinetic theory
Evolving lecture notes (last
updated 16th March 2017 for flow round a translating
sphere) and problem sheet
(with corrections) for HT17.
This year (HT17) Complex and non-Newtonian Fluids will be lectured second.
The class will be 4-6pm on Thursday of 9th week (16th
March) in the Fisher Room, DWB. If you would like work marked,
please leave it for Luuk Metselaar in the Rudolf Peierls Centre by
Thursday of 8th week (9th
• Low Reynolds number hydrodynamics, general mathematical results,
flow past a sphere. Stresses due to suspended rigid particles.
Calculation of the Einstein viscosity for a dilute suspension.
• Stresses due to Hookean bead-spring dumb-bells. Derivation of the
upper convected Maxwell model for a viscoelastic fluid. Properties
of such fluids.
• Suspensions of orientable particles, Jeffery's equation, very
brief introduction to active suspensions and liquid crystals.
See some experiments:
Rheological Behaviour of Fluids (MIT
Low Reynolds Number Flow (
Find the complete set of films by the
(US) National Committee for Fluid Mechanics
Suggested books and chapters:
É. Guazzelli & J. F. Morris
(2011) A Physical Introduction to Suspension Dynamics (CUP,
Chapters 1, 2, 3.1, 3.2, 7.1
M. Renardy (2000) Mathematical Analysis of Viscoelastic Flows
Chapters 1–3. Read this SIAM book online
for free in Oxford.
P. Oswald (2009) Rheophysics:
The Deformation and Flow of Matter
Sections 1.5, 3.7, 7.5.1, appendices 7.A and 7.C.
S. Kim & S. J. Karrila (1991, 2005) Microhydrodynamics:
Principles and Selected Applications (Dover,
, section 2.5, especially example 2.1 on effective stresses
in suspensions of rigid particles, section
on Faxen relations, sections 5.5 & 5.6 on dilute
suspensions of spheroids.
N. Phan-Thien (2015) Introduction to Suspension Rheology
chapter 1 of Rheology of Non-Spherical Particle Suspensions
Concise introduction to suspensions of spheres