Professor Stephen Wilson

Contact Details

Room No.	LT1003 (L903)
Telephone	+44 (0)141 548 3820
Fax	+44 (0)141 548 3345
email	s.k.wilson@strath.ac.uk

Research Interests

Mathematical solutions to real world problems, and in particular problems involving any of the following.

Thin fluid films (especially rivulet flows).
Surface tension gradient (Marangoni) phenomena.
Stability of fluid flows.
Asymptotic methods.
Non-Newtonian fluid mechanics.
Boiling phenomena.
Mathematical medicine and biology.
Mathematical models of "industrial" problems.

Graduate Research Students

Adam Leslie (Ph D, 2007-)
Stuart Kennedy (Ph D, 2007-)
Yazariah Mohd Yatim (Ph D, 2006-)
Julie Sullivan (Ph D, 2004-)
Gavin Dunn (Ph D, 2004-)
Neil Manson (Ph D, 2002-06)
Judit Quintans Carou (Ph D, 2002-07)
Gavin Black (M Phil, 2001-02)
David Holland (Ph D, 1998-2002)
Andrew Ross (Ph D, 1996-2000)
Iain McKinley (Ph D, 1995-99)
Ishak Hashim (Ph D, 1994-98)
Darren Wall (Ph D, 1991-96)

Postdoctoral Research Assistants

Together with Dr David Kenning and Prof. Zhanfeng Cui (Department of Engineering Science, University of Oxford) I had an EPSRC grant to support a three-year post-doctoral research assistant at the University of Strathclyde to work on "A Theoretical Investigation of Flow Boiling in Capillaries'' of which I am the PI. Dr Kausik Das has recently finished working on this project.

In collaboration with Profs Colin Please (PI), Alistair Fitt (University of Southampton) and Leo Pyle (University of Reading) I had an EPSRC grant to support a two-year post-doctoral research assistant at the University of Southampton to work on "Practical Mathematical Models for Scraped-Surface Heat Exchangers''. This collaboration arose as a result of the Smith Institute for Industrial Mathematics and System Engineering Faraday Partnership (now the Knowledge Transfer Network for Industrial Mathematics (external link)). Dr Michael Lee (University of Southampton) has recently finished working on this project. A nice layman's summary of the project can be found here.

Recent Meetings

International Workshop on Rain Wind Induced Vibrations

On 30th March to 1st April 2008 myself, Dr Brian Duffy and Dr Ian Taylor (Mechanical Engineering) organised an International Workshop on Rain Wind Induced Vibrations at Ross Priory with the support of the University of Strathclyde Research Enhancement Fund.

Ben Lomond seen from Ross Priory.

The participants gathered in the sunshine on the front steps of Ross Priory during the workshop.

17th Annual Scottish Fluid Mechanics Meeting

On 19th May 2004 we hosted the 17th Annual Scottish Fluid Mechanics Meeting. A brief history of the meeting since its inception in 1988 can be found here.

The participants at the 17th Scottish Fluid Mechanics Meeting in the Rottenrow Gardens at the University of Strathclyde.

Back in the last century I was the main organiser of the workshop The Dynamics of Thin Fluid Films which was held at the International Centre for Mathematical Sciences, 14 India Street, Edinburgh on 11-14th July 1999. Some of the papers presented at this meeting were published in a special issue of the European Journal of Applied Mathematics [12 (3) 233-252 (2001)].

Journal of Engineering Mathematics

Along with Profs M. H. Holmes (RPI, New York) and C. Pozrikidis (UCSD, San Diego) I am one of three Executive Associate Editors of the Journal of Engineering Mathematics. This excellent journal promotes the application of mathematics to physical problems, and in particular to the general area of Engineering Science. Papers intended for this journal should be submitted via the journal website.

Selected Publications

Asymptotic and numerical analysis of a simple model for blade coating: Quintans Carou J, Wilson SK, Mottram NJ and Duffy BR
J. Eng. Math., 2009, 63(2-4), 155-176.
Large-Biot-number non-isothermal flow of a thin film of a stationary or rotating cylinder: Duffy BR and Wilson SK
Eur. J. Phys. - Special Topics "Recent Advances in Coating, Drying and Dynamical Wetting", 2009, 166(1), 147-150.
A mathematical model of the evaporation of a thin sessile liquid droplet: comparison between experiment and theory: Dunn GJ, Wilson SK, Duffy BR, David S and Sefiane K
Colloid. Surf. A PhysicoChem. Eng. Aspects, 2008, 323, 50-55.
A thin rivulet of perfectly wetting fluid subject to a longitudinal surface shear stress: Sullivan JS, Wilson SK and Duffy BR
Q. J. Mech. Appl. Math., 2008, 61 (1), 25--61.
A mathematical model of fluid flow in a scraped-surface heat exchanger: Duffy BR, Wilson SK and Lee MEM
J. Eng. Math., 2007, 57 (4), 381-405.
A mathematical model for blade coating of a nematic liquid crystal: Quintans Carou J, Mottram NJ, Wilson SK and Duffy BR
Liq. Cryst., 2007, 34 (5), 621-631.
Shear-driven and pressure-driven flow of a nematic liquid crystal in a slowly varying channel: Quintans Carou J, Duffy BR, Mottram NJ and Wilson SK
Phys. Fluids, 2006, 18 (2), 027105.
Confined growth of a vapour bubble in a capillary tube at initially uniform superheat: Experiments and modelling: Kenning DBR, Wen DS, Das KS and Wilson SK
Int. J. Heat Mass Trans., 2006, 49 (23-24), 4653-4671.
Towards a Model of Atherosclerosis: McKay C, McKee S, Mottram N, Mulholland T, Wilson S, Kennedy S and Wadsworth R
University of Strathclyde Mathematics Research Report, 2005, #4
When is it energetically favorable for a rivulet of perfectly wetting fluid to split?: Wilson SK and Duffy BR
Phys. Fluids, 2005, 17, 078104.
Steady flow of a nematic liquid crystal in a slowly varying channel: QuintansCarou J, Duffy BR, Mottram NJ and Wilson SK
Mol. Cryst. Liq. Cryst., 2005, 438, 1801-1813.
Unidirectional flow of a thin rivulet on a vertical substrate subject to a prescribed uniform shear stress at its free surface: Wilson SK and Duffy BR
Phys. Fluids, 2005, 17, 108105.
A rivulet of perfectly wetting fluid draining steadily down a slowly varying substrate: Wilson SK and Duffy BR
IMA J. Appl. Math., 2005, 70, 293-322.
A rivulet of perfectly wetting fluid with temperature-dependent viscosity draining down a uniformly heated or cooled slowly varying substrate: Duffy BR and Wilson SK
Phys Fluids, 2003, 15 (10), 3236-3239.
Similarity solutions for slender rivulets with thermocapillarity: Holland D, Wilson SK and Duffy BR
Q. J. Mech. Appl. Math., 2003, 56 (3), 411-439.
A slender rivulet of a power-law fluid driven by either gravity or a constant shear stress at the free surface: Wilson SK, Duffy BR and Hunt R
Q. J. Mech. Appl. Math., 2002, 55, 385-408.
Lectures on topics in thin-film flow: Wilson SK and Duffy BR
University of Strathclyde Mathematics Research Report, 2002, #16
On the critical solutions in coating and rimming flow on a uniformly rotating horizontal cylinder: Wilson SK, Hunt R and Duffy BR
Q. J. Mech. Appl. Math., 2002, 55, 357-383.
On the gravity-driven draining of a rivulet of a viscoplastic material down a slowly varying substrate: Wilson SK, Duffy BR and Ross AB
Phys. Fluids, 2002, 14, 555-571.
On the gravity-driven draining of a rivulet of fluid with temperature-dependent viscosity down a uniformly heated or cooled substrate: Wilson SK and Duffy BR
J. Eng. Math., 2002, 42, 359-372.
The linear stability of a drop of fluid during spin coating or subject to a jet of air: McKinley IS and Wilson SK
Phys. Fluids, 2002, 14, 133-142.
Similarity solutions for slender dry patches with thermocapillarity: Holland D, Wilson SK and Duffy BR
J. Eng. Math., 2002, 44, 369-394.
On a slender dry patch in a liquid film draining under gravity down an inclined plane: Wilson SK, Duffy BR and Davis SH
Eur. J. Appl. Math., 2001, 12, 233-252.
The linear stability of a ridge of fluid subject to a jet of air: McKinley IS and Wilson SK
Phys Fluids, 2001, 13(4), 872-883.
Thermocapillary effects on a thin viscous rivulet draining steadily down a uniformly heated or cooled slowly varying substrate: Holland D, Duffy BR and Wilson SK
J. Fluid Mech., 2001, 441, 195-221.
Thin-film flow of a viscoplastic material round a large horizontal stationary or rotating cylinder: Ross AB, Wilson SK and Duffy BR
J. Fluid Mech., 2001, 430, 309-333.
The rate of spreading in spin coating: Wilson SK, Hunt R and Duffy BR
J. Fluid Mech., 2000, 413, 65-88.
The unsteady expansion and contraction of a long two-dimensional vapour bubble between superheated or subcooled parallel plates: Wilson SK, Davis SH and Bankoff SG
J. Fluid Mech., 1999, 391, 1-27.
Thin-film and curtain flows on the outside of a rotating horizontal cylinder: Duffy BR and Wilson SK
J. Fluid Mech., 1999, 394, 29-49.
A third-order differential equation arising in thin-film flows and relevant to Tanner's law: Duffy BR and Wilson SK
Appl. Math. Lett., 1997, 10, 63-68.

Vacancies & Studentships

Industrial Mathematics

Reference No.: SKW/BRD1

Supervisors:

Date Advertised: 6th February 2007

Please contact Professor Stephen Wilson for further information.

There are lots of exciting potential projects available involving constructing and analysing mathematical models for a diverse collection of "real world" problems.

New problems are always coming up (especially ones related to medical and/or biological applications), but specific problems of current interest which would make good PhD projects include:

flow in helical channels
flow of complex fluids
dynamics of towed pipelines
mathematical modelling of the human placenta
mathematical modelling of atherosclerosis
mathemtical modelling of a scraped-surface heat exchanger
and many more!

Rivulet Flows

Reference No.: SKW/BRD2

Supervisors:

Date Advertised: 23rd January 2008

Please contact Professor Stephen Wilson for further information.

Rivulets of fluid occur in may different practical situations ranging from small trickles of rain on a car windscreen to mile-long lava flows.

Enormous progress can be made by exploiting the slenderness and/ot thinness of many rivulets to obtain tractable problems whose solutions can be obtained an analysed using a combination of analytical and simple numerical methods.

There are many fascinating aspects of rivulet flow which would make good PhD projects, including:

rivulet meandering
rivulet flow on a rotating cylinder
high-speed rivulet flow
rivulet flow of a porous substrate
rivulet flow of complex fluids
a rivulet in a confined geometry (i.e. a Hele Shaw cell)
a dry patch in a liquid film (a sort of "negative" rivulet!)
rivulets with thermal effects
an evaporating rivulet
rivulet stability and splitting.

Droplet Spreading

Reference No.: SKW/BRD3

Supervisors:

Date Advertised: 23rd January 2008

Please contact Professor Stephen Wilson for further information.

The spreading of a liquid droplet on a substrate is a fundamental fluid mechanics problem arising in a wide variety of physical contexts ranging from the domestic to the industrial and the geophysical.

In recent years new developments in a number of technological applications involving droplet evaporation, notably cooling, desalination, DNA mapping and gene expression analysis, coating and patterning, have helped to inspire renewed interest in this fascinating problem.

There are numerous aspects of droplet spreading which would make challenging and exciting research projects, including:

the dynamics of droplet evaporation
the dynamics of droplets of nanofluids
the dynamics of droplets of liquid crystal
sliding droplets
bouncing droplets
thermal waves in evaporating droplets
droplet spreading driven by surface diffusion
droplets with various thermal effects.

Modelling Rain-Wind Induced Vibration

Reference No.: SKW/BRD4

Supervisors:

Date Advertised: 20th November 2008

Please contact Professor Stephen Wilson for further information.

Rain-wind induced vibration (RWIV) is a fluid structure interaction that occurs on inclined cables, due to the interaction between the unsteady aerodynamic field and rain-water "rivulets" on the cable surface.

However, the underlying physical mechanism of the oscillation is still not well understood, due to limitations in measurement techniques in experiments.

The aim of the proposed project is to use a combination of analytical and numerical techniques to:

formulate and analyse the governing equations for thin film on a circular cable,
develop analytical models for a non-fully wetted cylinder, an
investigate the fully coupled problem for thin film and external flow.

The project is in collaboration with colleagues on Mechanical Engineering who will
help to keep us focused on the physical realities of RWIV.