Lectures for HT24 are 10–11 on Mondays and 12–1 on Tuesdays in the
Lindemann Lecture Theatre
The class will be 4–6pm on Tuesday of 5th week (13th
February 2024) in the Lindemann Lecture Theatre.
Homework is due by 11:59pm on Friday of 4th week (9th
February 2024). Please hand in work via the course
page on Canvas.
In case of problems, please email a scan to the TA and cc to
In HT24 Complex and Non-Newtonian Fluids will be lectured first
• Low Reynolds number hydrodynamics. The Stokes flow regime, general
mathematical results, flow past a sphere. Stresses due to suspended
rigid particles. Calculation of the Einstein viscosity for a dilute
• 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.
Previous handwritten notes from online lectures in HT21:
Lecture 1 Stokes
flow regime – minimum dissipation, uniqueness and reciprocal
theorems Lecture 2 Stokes
flow around a sphere in translation, rotation, and strain Lecture 3 Stokes
drag, Fáxen relations, Einstein viscosity of a dilute suspension of
spheres Lecture 4
Suspensions of bead-spring pairs and the upper convected Maxwell
viscoelastic model Lecture 5
Resistance matrix formulation for arbitrary and axisymmetric bodies.
Jeffery's equation for axisymmetric torque-free bodies Lecture 6
Suspensions of spheroidal particles, anisotropic viscosity,
connection to Braginskii MHD
Find the complete set of films by the
US National Committee for Fluid Mechanics
Suggested books and chapters:
This course will assume the incompressible Navier–Stokes
equations as a starting point. You can find a traditional
continuum mechanics-style derivation of the Navier–Stokes
equations in chapter 1 of the lecture
notes for the Maths Part B course Viscous
Flow. The compressible Navier–Stokes equations were derived
from the Boltzmann equation in MMathPhys/MTP Kinetic Theory.
Link to ORLO
reading list with scans of some material not otherwise available
online (single sign-on required)
É. Guazzelli & J. F. Morris
(2011) A Physical Introduction to Suspension Dynamics (CUP,