Mathematics & statistics Continuum mechanics & industrial mathematics

Research in the Continuum Mechanics and Industrial Mathematics (CMIM) group focuses on the mathematical description of processes that are of key importance to many industrial companies.

Our research focuses on both the development of accurate mathematical theories of physical materials and the use of these theories in the mathematical modelling of industrial processes – from the flow of the tiny amount of liquid that is contained in the display in your mobile phone to how ultrasound waves travel through engineering structures to detect cracks.

This research is extremely multidisciplinary, with group members having expertise in continuum theories, material science, fluid dynamics and mathematical modelling in general, and collaborations with physicists, engineers, chemists and many industrial companies.

We have key groups in liquid crystal theory, fluid dynamics and non-destructive testing, with international links to similar research groups around the world.

If you're interested in collaborating with us or wish to enquire about postgraduate or postdoctoral research positions then please contact one of our group members.

Our researchers

Our research activities

Liquid crystals

Liquid crystal materials are ubiquitous in our world – they make up the walls of every cell in our body and are contained in almost all electronic device displays, from mobile phones and televisions to washing machines and car dashboards.

The group has a long history in the development of theories of liquid crystal materials started by Professor Frank Leslie who, with Professor Jerry Ericksen, developed the key theory of how liquid crystals flow – the Ericksen-Leslie theory.

Over the last forty years we have grown from strength to strength and our group’s interests have widened considerably. Current research interests include:

  • flow induced switching and defects in nematic liquid crystals
  • chevrons and flow effects in smectic liquid crystals
  • structure and flow effects due to external electric and magnetic fields
  • phase transitions, ferroelectric properties and cholesteric ordering in both nematic and smectic liquid crystals
  • statistical mechanics and continuum theories of liquid crystal phases

Because of the technological interest in liquid crystals we have worked with a number of industry partners on this research, including Hewlett-Packard, Dow Corning, Sharp, Merck. We also work with academic groups at Bristol, Exeter, Oxford, Nottingham Trent, Manchester, Sheffield and Southampton.

We've also established valuable international links, with collaborators based in institutions including Gothenburg (Sweden), Stuttgart (Germany), Virginia Tech (USA), Kent State (USA) and Pavia (Italy).

Droplet evaporation

Droplet evaporation plays a crucial role in many practical applications such as ink-jet printing, nano-wire fabrication, spray cooling and thin film coating.

As a result, the evaporation of a fluid droplet on a solid substrate has been the subject of extensive theoretical and experimental investigation by many research groups in recent years.

In collaboration with expert experimentalists at the University of Edinburgh, members of this group have made substantial advances on the study of droplet evaporation, aspects of which led to the joint award of the IoP Printing and Graphics Science Group Prize in 2009.

Thin-film flow

There are many situations, in contexts ranging from biology to geology via industry and medicine, in which thin films of fluid play a key role.

A judicious combination of asymptotic and numerical methods can bring new insight into a wide range of practically important problems of this kind.

This can include the flow of sheets and rivulets of both Newtonian and non-Newtonian fluids driven by physical effects including: gravity, surface tension, thermoviscosity, centripetal forces, externally applied jets of air, coating and rimming flow on a rotating horizontal cylinder.

Current projects include collaborations with Princeton and Oxford on microfluidics, Oxford on spin coating, Paris on rivulets, and Edinburgh on droplet evaporation.

The 2012 special issue of the Journal of Engineering Mathematics (volume 73, part 1) was guest-edited by two members of our research group and contains some excellent recent papers of various different aspects of thin-film flow. 

Complex fluids

Closely related to the work on liquid crystals, we're also working on various aspects of the flow of complex fluids, some of it motivated by geophysical applications.

A particular theme of our analytical work is the investigation of time-dependent rheological effects (thixotropy and antithixotropy) on various classical flow problems such as the Stokes oscillatory flow problem and slowly-varying lubrication flows.

We're also currently engaged in an exciting collaboration with the University of Edinburgh on the evaporation of nanofluids (fluids containing a suspension of very small metal particles).

We also have a longstanding partnership with the University of São Paulo, Brazil. We're looking at developing numerical methods for free surface flows described by various rheological models (including the Oldroyd B, Phan-Thien-Tanner, Pompom and Ericksen-Leslie models), as well as on the development of a universal convection-diffusion methodology.

Non-destructive testing

A number of our projects within the group concern the modelling of non-destructive measurement and testing.

In particular, we've strong working 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. 

Medical product design

Mathematical modelling is being carried out as part of collaborative projects with Biomedical Engineering, Strathclyde Institute of Pharmacology & Biomedical Sciences, Chemistry and Mechanical & Aerospace Engineering. Projects include:

  • the development of a fluorescent capillary-fill device (used for pregnancy testing)
  • drug-eluting stents and an artificial lung
  • the modelling of biomedical systems such as red blood cell membranes and hypoplastic left heart syndrome
  • the development of an in-field blood testing device

Flows in porous & complex media

Current research in this area includes the modelling of flow and transport processes in porous media, in particular convection in chemically reactive geothermal systems.

We also have 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

Non-linear waves

We have an interest in the propagation of nonlinear waves in dispersive media. Topics under investigation include:

  • the stability properties of periodic and solitary wave solutions to some new evolution equations that occur in plasma physics
  • the internal dynamics of soliton interactions
  • the derivation of new equations having multi-loop soliton solutions, and their properties

Applied numerical analysis

In the area of applied numerical analysis, our work continues on iterative methods for large systems.

There's particular reference to the Navier-Stokes equations and on Volterra-type integral equations, principally arising from science and technology.