PHYM423 Classical and Quantum Fluids

2007-2008

Code: PHYM423
Title: Classical and Quantum Fluids
Instructors: Dr C.D.H. Williams and Dr A.S. Plaut
CATS credits: 10
ECTS credits: 5
Availability: unrestricted
Level: M
Pre-requisites: N/A
Co-requisites: N/A
Background Assumed: Fundamental Electromagnetism II (PHY2006), Solid State Physics I (PHY3102) and Statistical Mechanics (PHYM421)
Duration: Semester I
Directed Study Time: 22 lectures
Private Study Time: 78 hours
Assessment Tasks Time: -
Observation report: 2001/02 SJM (CDHW)

Aims

Fluids exhibit an enormous range of behaviours. Examples of classical fluid behaviour in nature include: the circulation of blood, the winds, currents in seas, and convection mechanisms in stars. In in the human world, our understanding of fluid mechanics has made essential contributions to the design of aircraft, the generation of power, the distribution of water, and even the processing of food.

This module also introduces the astonishing properties of quantum fluids. In some cases these are extreme examples of qualities also possessed by classical fluids, but quantum fluids also have many unique properties which are manifestations of quantum mechanics acting on a macroscopic scale such as quantised vorticity, zero viscosity and superfluidity. Many of the examples to be discussed arise from research being conducted in the Quantum Interacting Systems Group at Exeter.

Intended Learning Outcomes

After completion of this module the student should be able to:

• analyze fluid-mechanics problems using basic equations such as Newton's viscosity equation, Bernoulli's theorem, the continuity equation and the momentum equation for steady flow;
• calculate Reynolds numbers and use them to describe the laminar/turbulent transition in the context of flow through pipes and in boundary layers;
• describe the basic properties of liquid helium at low temperatures and the experiments that demonstrate these properties;
• interpret superfluid phenomena by applying the two-fluid and excitation-model theories;
• explain the operation of a dilution refrigerator;
• solve problems involving the properties of thin-films, and/or surfaces, of liquids.

Transferable Skills

Abilty to use physics techniques in a multi-disciplinary context.

Learning and Teaching Methods

Lectures and problems classes.

Assignments

Problems for problems classes.

Assessment

One 90-minute examination (100%).

Syllabus Plan and Content

1. Basics and Simple Applications
   Viscosity; Non-Newtonian behaviour; Euler's equation; Bernoulli's theorem; Continuity equation; Flow measurement using Bernoulli's theorem; The momentum equation for steady flow.
2. Laminar/Turbulent Flow
   Flow regimes; Steady flow in pipes.
3. Flow around bodies
   Boundary layers; Drag coefficient.
4. Introduction to the Navier-Stokes equation.
5. Liquid ⁴He
   1. Weakly and strongly interacting Bose systems, Bose condensation, liquid ⁴He at T > T_lambda.
   2. Two-fluid model and phenomena of superfluidity at T < T_lambda, video of demonstrations.
   3. Excitation model of ⁴He, dispersion curve, Landau's criterion for the critical velocity, heat capacity, quantum evaporation London's macroscopic wave function, superflow, rotating superfluids.
   4. Connection between the two-fluid model and excitations.
6. Normal ³He and Dilute Mixtures of ³He in ⁴He.
   1. ³He as a fermion system in the liquid and solid state.
   2. Thermal and magnetic properties of ³He using kinetic theory.
   3. Dilution refrigeration.
7. Thin Films and Two-Dimensional Systems.
   1. Surface tension (fundamentals and thermodynamics).
   2. Saturated and unsaturated films of liquid helium.
   3. Wetting.
   4. Defects on the surface of helium-II.
8. Phase Coherence in a Bose Condensed System.
   1. Macroscopic phase coherence, number-phase uncertainty.
   2. Excitations, quantised circulation and vortices, phase slippage.

Core Text

Tritton D.J. (1988), Physical Fluid Dynamics (2^nd edition), Oxford University Press, ISBN 0-19-854493-6 (UL: 532 TRI)

Supplementary Text(s)

Faber T.E. (1995), Fluid Dynamics for Physicists, Cambridge University Press, ISBN 0-521-42969-2 (UL: 532.05 FAB)
Massey B.S. (1998), Mechanics of Fluids (7^th edition), Nelson Thorne, ISBN 0-7487-4043-0 (UL: 532 MAS)
McClintock P.V.E., Meredith D.J. and Wigmore J.K. (1992), Low Temperature Physics, Blackie & Son Ltd, ISBN 0-13-110362-8 (UL: 536.56 MCC)
McClintock P.V.E., Meredith D.J. and Wigmore J.K. (1984), Matter at Low Temperatures, Blackie & Son Ltd, ISBN 0-216-91594-5 (UL: 536.56 MACC)
Tilley R. and Tilley J. (1990), Superfluidity and Superconductivity (3^rd edition), IoP Publishing, ISBN 750300337 (UL: 537.623 TIL)

Formative Mechanisms

Students are able to monitor their learning by attempting the problems set for the problem classes. Model solutions are discussed in the problem classes.

Evaluation Mechanisms

The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.