**Instructor**:

Dr. James J. Feng
Office: MATX 1206

Phone:
604-822-4936
Email: james.feng@ubc.ca

(Office hour by appointment; please email.)

**Reference
books**:

¥ R. G. Larson, The Structure and Rheology of Complex Fluids, Oxford (1999).

¥ R. B. Bird, R. C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, Vols. 1 & 2, Wiley and Sons (1987).

¥ P. G. deGennes and J. Prost, The Physics of Liquid Crystals, Clarendon (1993).

¥ D. Barthes-Biesel, Microhydrodynamics and Compex Fluids, Taylor & Francis (2012).

¥ M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford (1988).

**Course outline:**

This course will give students an overview of Non-Newtonian Fluid Dynamics, and discuss two approaches to building constitutive models for complex fluids: continuum modeling and kinetic-microstructural modeling. In addition, it will provide an introduction to multiphase complex fluids and to numerical models and algorithms for computing complex fluid flows.

** **

1.
Background and motivation

2.
Review of required mathematics

1.
Oldroyd's theory for viscoelastic fluids

2.
Ericksen-Leslie theory for liquid crystals

3.
Viscoplastic theories

1.
Dumbbell theory for polymer solutions

2.
Bead-rod-chain theories

3.
Doi-Edwards theory for entangled systems

4. Doi
theory for liquid crystalline materials

**IV.
Heterogeneous/multiphase systems**

1.
Suspension theories (Einstein, Batchelor, Acrivos, etc.)

2.
Kinetic theory for emulsions and drop dynamics

3.
Energetic formalism for interfacial dynamics

4.
Numerical methods for moving boundary problems

**Prerequisites:**

Undergraduate-level course on Partial Differential Equations (MATH 257 or MATH 400), and graduate-level course on Fluid Mechanics (one of MATH 519, CHBE 557, MECH 502).

**Evaluation:**

The instructional format for the course will consist of lectures of 3 hours per week. The final grade is computed as such: 50% from cumulative marks of biweekly homework assignments, and 50% on a final presentation based on a cluster of research papers. There is no final exam.

Problem 1 (PDF), due Sept. 25, 2015 (bring to class)

Problem 2 (PDF), due Oct. 9, 2015

Problem 3 (PDF), due Nov. 2, 2015

Problem 4 (PDF), due Nov. 13, 2015