Biaxiality in a liquid crystal splay-bend transition (AMS)
The Continuum Mechanics Teaching and Research Group contains researchers looking at a variety of continuum modelling, material science and fluid dynamics problems.
Liquid Crystals
A principal activity within the group is the mathematical modelling of macroscopic effects in thermotropic liquid crystals.
Current interests in this area include:
- modelling of flow induced switching in weakly anchored nematic cells
- modelling of chevrons and flow effects in smectic liquid crystals
- modelling of defect motion in nematic liquid crystals
- modelling of effects associated with the application of external electric and magnetic fields
The Continuum Mechanics Group have produced posters providing some background into our research.
There are many industrial collaborators connected to this research including Hewlett-Packard, Dow Corning as well as academic groups at Bristol, Exeter, Oxford, Nottingham Trent, Manchester, Sheffield and Southampton. In this area the group also enjoys valuable international links, especially with Gothenburg (Sweden), Virgina Tech (USA), Kent State (USA), Pavia (Italy) and Calabria (Italy).
Physical foundations
Other research activity within the group examines the physical foundations of continuum modelling through the use of spatial weighting functions and the projection operator formalism of statistical mechanics, and currently considers
- flow of fluids at boundaries of porous bodies
- relationship between statistical mechanics and deterministic continuum mechanics, with particular regard to space-time scales
the latter in collaboration with Visiting Professor Bedeaux (Leiden).
Mathematical Modelling in the Earth Sciences
Current research in this area includes the modelling of flow and transport processes in porous media, including convection in chemically reactive goethermal systems and the propagation of vaporisation and salinisation fronts in water-vapour systems; the latter is being carried out in collaboration with the Numerical Analysis group.
A second direction is mathematical modelling of environmental flow and sediment transport processes, with reference both to modern deposits such as those from
tsunamis and to ancient seafloor deposits (turbidites).
Nonlinear waves
There is also active interest in the propagation of nonlinear waves in dispersive media, and topics under investigation include:
- stability properties of periodic and solitary wave solutions to some new evolution equations that occur in plasma physics
- internal dynamics of soliton interactions
- derivation of new equations having multi-loop soliton solutions, and their properties
There is continued interest in fluid mechanics in general, and currently mainly concerning the application of thin film theory of viscous fluids to coating flows. This in collaboration with the Industrial Mathematics Group.
Oscillations in a fractal ultrasonic transducer (Dr Tony Mulholland)
Research within the Industrial Mathematics Teaching and Research Group arises largely in response to problems arising from an industrial setting.
Numerical Methods for Rheological Flows and CFD
- Numerical methods for (free surface) rheological models e.g. Oldroyd B, Phan-Thien-Tanner (PTT), Pompom, Ericksen-Leslie, etc.
- Development of a universal convection-diffusion methodology
This work is being carried out in collaboration with our Brazil link (Sao Carlos, University of São Paulo).
Medical Product Design
- Fluorescent capillary-fill device (principal application-pregnancy testing)
- Drug eluting stents
- Artificial lung
- Red blood cell membranes
- Hypoplastic left heart syndrome
For the most part this is in collaboration with the Departments of Bioengineering or Physiology and Pharmacology.
Non-destructive testing
A number of projects within the group concern the modelling of non-destructive measurement and testing.
In particular there are strong links with the Centre for Ultrasonic Engineering (CUE) which designs, manufactures and tests ultrasonic transducers for use in biomedical diagnosis and therapeutic treatment, and in non-destructive testing and sonar.
Thin Fluid Films
There is an on-going collaborative work with Professors S Davis and G Bankoff (North-western University) on the role of the microlayer in subcooled nucleate boiling and on the existence and stability of dry patches in flowing fluid layers.
There is also substantial collaborative work on the dynamics of thin fluid films in a variety of industrially relevant problems.
Specifically, the flow of sheets and rivulets of both Newtonian and non-Newtonian fluids driven by a variety of different physical effects including gravity, surface tension, surface-tension-gradients, centripetal forces and externally applied jets of air (the later two relevant to the industrial spin coating and and air-knife coating processes respectively) has been investigated.
Flows in Complex Media
Penetrative convection in fluid layers and hydrodynamic stability is being studied as are flows in saturated porous media, the latter with application to the geophysical problem of patterned ground formation.
The Group also has expertise in the Mathematical modelling and simulation of wave processes in heterogeneous and fractal media, in particular:
- reaction-diffusion wave propagation in excitable media
- heat transfer in fractal deposits
- mass transfer of condensing salts in combustion chambers
Applied Numerical Analysis
In the area of applied numerical analysis, work continues on iterative methods for large systems with particular reference to the Navier-Stokes equations and on Volterra-type integral equations, principally arising from science and technology.
Teaching and Research Group members