Research

The fast and flexible: dynamic buckling

In this project our team studied dynamic buckling in rings of elastic material, and in doing so developed a new, dynamic take on a classic surface tension demonstration.

There is a demonstration of surface tension commonly used in outreach, where a loop of string is placed on a soap film, where it is held and floats freely.  The part of the soap film inside the string circle is then broken, and the soap film remaining outside of the string circle pulls it taut.  In doing so, it demonstrates that the soap film acts to minimise its surface area.

If the soap film outside the loop is broken instead, and the inner soap film remains intact, it will pull the loop radially inward.  Depending on the geometry of the loop, it can buckle in one of the two ways shown to the left.  Our ultimate goal in the project was to learn about the number of oscillations in the loop during this buckling process, and it turned out to depend on the inertia in an interesting an non-trivial way.  You can learn more about this system in 

Dynamic buckling of an elastic ring in a soap film, F. Box, O. Kodio, D. O'Kiely, V. Cantelli, A. Goriely & D. Vella, Phys. Rev. Letters (2020)

or in the video to the left, created by Finn Box.  It has also been featured by Fuck Yeah Fluid Dynamics.

Dynamic wrinkling of floating elastic sheets

Thin elastic sheets cannot sustain compressive loads, and buckle under confinement. For a thin elastic sheet floating at a liquid interface, indenting the sheet vertically creates an azimuthal confinement by drawing material radially inward. This gives rise to a distintive wrinkling pattern, with wrinkles aligned radially like the spokes on a bicycle wheel. The equilibrium wavelength of these wrinkles is determined by a balance between the bending stiffness of the sheet, which favours long-wavelength deformations, and factors such as liquid buoyancy, which favour short-wavelength deformations.

If the indentation is fast, dynamic effects come into play, and the behaviour is significantly different. This research project formed a major component of my postdoc with Dominic Vella in OCIAM at the University of Oxford.  The primary experimentalist on this project was Finn Box, now at the University of Manchester.



Read about our research in more detail in:

Dynamics of wrinkling in ultrathin elastic sheets, F. Box, D. O'Kiely, O. Kodio, A. A. Castrejón-Pita & D. Vella, Proc. Nat Acad. Sci (2019)

Impact on floating thin elastic sheets, D. O'Kiely, F. Box, O. Kodio, J. Whiteley & D. Vella, Phys. Rev. Fluids (2020)

Mathematical models for glass manufacture

There are a number of glass manufacture processes where a sheet or thread of viscous glass is elongated to create a very thin screen or very slender fibre.  Challenges arise in these manufacture processes which can be aided by mathematical modelling.  From a mathematics point of view, the long thin geometry of these sheets and threads corresponds to a small aspect ratio which can be exploited to derive very simplified models.  For example, highly complex three-dimensional systems can be accurately described with one- or two-dimensional equations.


During my PhD I developed mathematical models for the redraw process, used to manufacture very thin (<100 μm) glass sheets. In the redraw process, a prefabricated glass block is fed into a furnace where it is reheated and stretched, making it thinner and also causing the edges to neck in. This stretching process gives rise to a final product that is thicker at the edges than in the centre, and these "thick edges" are highly undesirable. We developed mathematical models to describe the redraw process and hence identify the source of the thick edges, as well as a method to reduce or eliminate them.  My PhD was supervised by Ian Griffiths, Chris Breward and Peter Howell at the University of Oxford and was in collaboration with glass-manufacture company Schott AG.  Read about our research in more detail in:

Edge behaviour in the glass sheet redraw processD. O'Kiely, C. J. W. Breward, I. M. Griffiths, P. D. Howell & U. Lange, Journal of Fluid Mechanics (2016)

Glass sheet redraw through a long heater zone, D. O'Kiely, C. J. W. Breward, I. M. Griffiths, P. D. Howell & U. Lange, IMA Journal of Applied Mathematics (2018)

This research has also been featured in the IMA magazine Mathematics Today and in the LMS newsletter.


More recently, I worked with Niall Hanevy to develop a new mathematical model of fibre drawing.  Niall carried out this research as a student on our Mathematical Modelling MSc, and is now completing a PhD at Aston University.  In the fibre drawing process, a thread of molten glass or uncured polymer is stretched out to create a fibre for use e.g. in telecommunications.  Our work showed that previous mathematical models of this process  needed to be modified to accurately describe the behaviour of a viscous thread beyond leading order, and is published in:

Asymptotic analysis for fiber drawing processes, N. Hanevy & D. O'Kiely, SIAM Journal on Applied Mathematics (2023)

Out-of-plane buckling in glass manufacture

In addition to the thickness variations described above, glass sheets undergoing redraw may also buckle out of plane, forming ripples that render the final product unusable. These ripples form due to localized regions of lateral compression that occur when the sheet is stretched along its length. We investigated the growth of ripples due to compression in a glass sheet, and the feedback between the out-of-plane deformation and the consequent change in stresses.

Read about glass buckling in more detail in:

Out-of-plane buckling in two-dimensional glass drawing, D. O'Kiely, C. J. W. Breward, I. M. Griffiths, P. D. Howell & U. Lange, Journal of Fluid Mechanics (2019)

or read about models for three-dimensional buckling in my thesis


Read about our research:

Mathematical modelling of chemical agent removal by reaction with an immiscible cleanser, M. Dalwadi, D. O'Kiely, S. Thomson, T. Khaleque & C. Hall (2017)

Mathematical models for decontamination

Spill a nasty chemical onto a smooth surface, and a careful choice of cleaning materials are required to wipe it up properly.  Spill a nasty chemical onto a porous surface, such as untreated concrete, and the situation is significantly more difficult to deal with.  A cleansing agent must "chase" the contaminant into the porous material, and react there to neutralise it.   The success of this procedure is dependent on the correct choice of neutralising agent, and is difficult to study experimentally.  A mathematical modelling challenge on this topic was therefore proposed at the 100th European Study Group with Industry.


Our modelling team developed a mathematical model for the neutralization reaction between a contaminant and a neutralizing agent inside porous medium.  We studied the effect of parameters such as chemical reaction rate and diffusion coefficients on the time taken to neutralize the contaminant.    We found that increasing the speed of chemical reaction has limited benefit, but that the efficiency with which neutralizing agent and neutral product are transported to and from the reaction front is pivotal.


More recently, Sarah Murphy has been carrying out research on this topic as part of her PhD in our SFI Centre for Research Training in Foundations of Data Science - stay tuned for our publication, which is currently under review.