Module Identifier MAM0120  
Module Title COMPLEX FLUIDS: MATHEMATICAL MODELLING  
Academic Year 2005/2006  
Co-ordinator Professor Russell Davies  
Semester Semester 1  
Other staff Professor Russell Davies, Dr Robert J Douglas  
Course delivery Lecture   (16 x 1 hour lectures)  
  Seminars / Tutorials   (4 x 1 hour example classes)  
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Assessment coursework  100%
Supplementary Assessment coursework  100%

Learning outcomes

On completion of this module, students should be able to:
1. Model simple viscoelastic materials.
2. Discuss the predictive capabilities of a range of constitutive models.
3. Derive rheometrical functions for simple flows.
4. Discuss suitability of models for a range of complex flow situations.
5. Describe the dynamics of polymer solutions and melts using coarse-grained kinetic theory models.

Brief description

This module provides a brief introduction to the traditional modelling of complex fluids using constitutive equations of Maxwell/Oldroyd type. Contemporary constitutive theories based on FENE-type kinetic theory models will be introduced in the context of micro-macro modelling of complex fluids. The dynamics of polymer melts will be described using reptation and pom-pom models. The mathematical equivalence between Fokker-Planck equations and stochastic differential equations will be explained as well as the relevance of this result for numerical simulations.

Aims

This module will provide an introduction to the mathematical modelling of complex fluids using both traditional models based on differential and integral constitutive relationships and contemporary models based on kinetic theory.

Reading Lists

Books
** Recommended Text
H. A. Barnes, J. Hutton and K. Walters (1989) An introduction to rheology Elsevier 0444871403
M. J. Crochet, A. R. Davies and K. Walters (1984) Numerical simulation of non-Newtonian Flow Elsevier 0444422927
R. G. Owens and T. N. Phillips (2002) Computational Rheology Imperial College Press 1860941869

Notes

This module is at CQFW Level 7