Introductory description

N/A.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The module will cover two of the topics listed below, which will differ from year to year.

Topic 1: Interfacial phenomena
a. formulation of surface tension driven flows
i. dynamic BC, kinematic BC, Young’s law
b. exemplars
i. statics (capillary rise, Young-Laplace equation)
ii. dynamics (stability of jets/films, cavitation of bubbles, thin films)
iii. wetting (moving contact line paradox, dynamic contact angles)
c. additional nanoscale physics
i. slip conditions (underlying physics, models,
ii. disjoining pressures (for film breakup)
iii. thermal fluctuations (in stability problems)
Topic 2: Kinetic theory for gas microflows
d. Grad’s method
e. Chapman-Enskog expansions
f. NSF derivation and models that go beyond (e.g. G13)
Topic 3: Molecular dynamics for liquid nanoflows
g. non-equilibrium Molecular Dynamics (algorithms, thermostats, controllers)
h. nano-channel flows
i. carbon nanotube membranes
j. open-source codes (mdFoam+, LAMMPS)
Topic 4: Multiscale fluid dynamics
k. domain decomposition
l. the Heterogeneous Multiscale Method (HMM)
m. time-step multi-scaling
n. applications in micro/nano-scale internal flows
o. machine learning and surrogate micro-model generation.

Learning outcomes

By the end of the module, students should be able to:

• Understand the limitations of classical fluid dynamics.
• Recognise circumstances in which additional microscale physics is required.
• Be confident in formulating models that go beyond NSF.
• Be able to solve computationally the formulated models.

Indicative reading list

Topic 1: Capillarity & Wetting Phenomena: Drops, Bubbles, Pearls & Waves, by deGennes et al
Topic 2: Macroscopic Transport Equations for Rarefied Gas Flows, by Struchtrup
Topic 3: Computer Simulation of Liquids (2nd Edition). M. P. Allen & D. J. Tildesley, Clarendon Press
Topic 4:
W. E, B. Engquist, X. Li, W. Ren, E. Vanden-Eijnden, Heterogeneous multiscale methods: a review, Commun. Comput. Phys. 2 (2007) 367–450.
K.M. Mohamed, A.A. Mohamad, A review of the development of hybrid atomistic-continuum methods for dense fluids, Microfluid. Nanofluid. 8 (2010) 283–302.

Subject specific skills

Understand the limitations of classical fluid dynamics;
Recognise circumstances in which additional microscale physics is required;
Be confident in formulating models that go beyond NSF.
Be able to solve computationally the formulated models.

Transferable skills

Programming, modelling, data analysis