Peter S. Stewart

I am currently a lecturer in Applied Mathematics at the School of Mathematics and Statistics, University of Glasgow. My research focuses on applying continuum mechanics to solve interesting physiological or industrially motivated problems. Before coming to Glasgow, I held Postdoctoral Research Associate positions at the University of Oxford (2011-13) and Northwestern University (2010-2011). I completed my PhD in 2010 from the University of Nottingham, where my thesis was entitled `Flow through flexible walled channels and airways'.

Contact: peter dot stewart at glasgow dot ac dot uk

Research interests

Physiological Modelling and Soft Tissue Mechanics

Applying the methods of fluid and solid mechanics to understand physiologically motivated problems, including:
  • the onset of the Retinal Venous Pulse, as a basis for a non-invasive measure of intracranial pressure;

    Stewart PS, Jensen OE and Foss A, A theoretical model to allow prediction of the CSF pressure from observing the retinal venous pulse, Investigative Ophthalmology and Visual Science 55(10) 6320 (2014)

  • the dynamics of neonatal airway recruitment in Respiratory Distress Syndrome;

    Stewart PS and Jensen, OE, Patterns of recruitment and injury in a heterogeneous airway network model. Journal of The Royal Society Interface, 12, 20150523 (2015)

  • the influence of axonal fibres on the development of cerebral cortex folding;

    Stewart PS, Waters SL, El Sayed T, Vella D, Goriely A, Wrinkling, creasing, and folding in fiber-reinforced soft tissues, Extreme Mechanics Letters, 8, 22-29 (2016)

  • the optimal size of peripheral iridotomoy in uveitis;

    Agraval U, Qi N, Stewart PS, Luo XY, Williams G, Rotchford A, Ramaesh K, Optimum size of iridotomy in uveitis, Clinical and Experimental Ophthalmology 43 (7), 692-696 (2015)

  • the role of the Donnan effect in the swelling of brain tissue.

    Lang GE, Stewart PS, Vella D, Waters SL, Goriely A, Is the Donnan effect sufficient to explain swelling in brain tissue slices? Journal of The Royal Society Interface 11 (96), 20140123 (2014)

Flow in collapsible channels

Fluid flow through a flexible-walled channel or tube can exhibit self-excited oscillations, which can be studied by considering:

  • the global stability in a finite-length flexible-walled channel;

    Stewart PS, Waters SL and Jensen OE, Local and global instabilities of flow in a flexible-walled channel, European Journal of Mechanics B/Fluids, 28, 541-557 (2009)

    Stewart PS, Heil M, Waters SL and Jensen OE, Sloshing and slamming oscillations in a collapsible channel flow, Journal of Fluid Mechanics, 662, 288-319 (2010)

    Stewart PS, Instabilities in flexible channel flow with large external pressure, Journal of Fluid Mechanics, 825, 922-960 (2017)

  • the local stability of Poiseuille flow in a long flexible-walled channel.

    Stewart PS, Waters SL, Billingham J and Jensen OE, Spatially localised growth within global instabilities of flexible channel flows, Proceedings of the Seventh IUTAM Symposium on Laminar-Turbulent Transition (Stockholm 2009)

    Stewart PS, Waters SL and Jensen OE, Local instabilities in a flexible channel: asymmetric flutter driven by a weak critical layer, Physics of Fluids 22, 031902 (2010)

Dynamics and stability of gas-liquid foams

Using fluid mechanics to understand the dynamics and stability of gas-liquid foams, including:

  • fracture of an aqueous foam under an applied driving pressure, which is qualitatively similar to fracture of crystalline atomics solids like metals;

    Stewart PS, Davis SH, Hilgenfeldt S, Viscous Rayleigh--Taylor instability in aqueous foams, Colloids and Surfaces A: Physicochemical and Engineering Aspects 436, 898-905 (2013)

    Stewart PS, Davis SH, Hilgenfeldt S, Microstructural effects in aqueous foam fracture, Journal of Fluid Mechanics 785, 425-461 (2015)

    Stewart PS, Hilgenfeldt S, Cracks and Fingers: Dynamics of ductile fracture in an aqueous foam, Colloids and Surfaces A: Physicochemical and Engineering Aspects (available online)

  • bursting of a rising gas bubble at the surface of an oil-covered water bath, which can enhance oil dispersal;

    Stewart PS, Feng J, Kimpton LS, Griffiths IM, Stone HA, Stability of a bi-layer free film: simultaneous or individual rupture events? Journal of Fluid Mechanics 777, 27-49 (2015)

  • a large scale network model to understand bubble coalescence in metallic foams;

    Stewart PS and Davis SH, Dynamics and stability of metallic foams: Network modeling, Journal of Rheology 56, 543-574 (2012)

    Stewart PS and Davis SH, Self-similar coalescence of clean foams, Journal of Fluid Mechanics 722, 645-664 (2013)

  • the stability of a foam film draining under gravity.

    MJ Davis, PS Stewart and SH Davis, Local effects of gravity on foams, Journal of Fluid Mechanics 737, 1-18 (2013)

Industrial modelling

Using the methods of continuum mechanics to improve industrial protocols, including:

  • tailoring the efficency of membrane filtration;

    Griffiths IM, Kumar A, Stewart PS, A combined network model for membrane fouling, Journal of Colloid and Interface Science 432, 10-18 (2014)

    Griffiths IM, Kumar A, Stewart PS, Designing asymmetric multilayered membrane filters with improved performance, Journal of Membrane Science 511, 108-118 (2016)

  • using fluid flow to enhance chiral separation;

    Hermans TM, Bishop KJM, Stewart PS, Davis SH, Grzybowski BA, Vortex flows impart chirality-specific lift forces, Nature communications 6, 5640 (2015)

  • transforming a chemical oscillator from the temporal domain to the spatial domain.

    Hermans TM, Stewart PS, Grzybowski BA, pH Oscillator Stretched in Space but Frozen in Time, The Journal of Physical Chemistry Letters 6 (5), 760-766 (2015)

Hydrodynamic stability theory

Study of fundamental hydrodynamic instabilities, including:

  • the role of non-normal growth in the instability of current sheets.

    MacTaggart D, Stewart PS, Optimal energy growth in current sheets, submitted

Current PhD students

Danyang Wang (2014-), The energetics of self-excited oscillations in collapsible channel flow

Ahmed Mostafa Abdelhady Ismaeel (2015-), Mathematical modelling of cancer treatment by photothermal ablation

Roxanna Barry (2016-), Discrete-to-continuum modelling of cells to tissues


(2014/15, 2015/16, 2016/17) 5M Advanced Numerical Methods

(2016/17) 2B Linear Algebra (semester 1)

(2014/15, 2015/16) 4H Fluid Mechanics (semester 1)

Applying the methods of fluid mechanics to practical problems, including the theory of flight (see photos above)

(2013/14) 3H Dynamical Systems (semester 2)