Dr David Leppinen BMath (Hons) PhD

Dr David Leppinen

School of Mathematics
Senior Lecturer

Contact details

School of Mathematics
Watson Building
University of Birmingham
B15 2TT

Dr David Leppinen is a Senior Lecturer in Applied Mathematics.

He has extensive experience applying mathematics to examine industrial processes. His research has been recognized with a patent for the design of a dissolved air flotation and has been exhibited at the Royal Society’s Summer Science Festival and on the BBC News 24 Science Review.

David is currently interested in studying the dynamics of free surface flows, particularly the compressible and incompressible dynamics of bubbles and droplets.


  • PhD in Mathematics, University of Cambridge, 1997
  • BMath (Hons) in Applied Mathematics with Engineering Electives, University of Waterloo, Canada, 1993


David Leppinen graduated with an Honours BMath (Co-operative) degree in Applied Mathematics with Engineering Electives from the University of Waterloo, Canada (1993). He went on to study for a PhD in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge, where he combined experimental, analytical and numerical techniques to study problems in single and double diffusive convection.

David continued his PostDoctoral training at DAMTP studying aspects of Dissolved Air Flotation (culminating in a successful patent application), droplet pinch-off and the Rayleigh-Taylor instability culminating in promotion to Deputy Director of the GK Batchelor Fluid Dynamics Laboratory.

He joined the School of Mathematics at the University of Birmingham as a lecturer in January 2005. His research has continued to focus on the dynamics of bubbles and droplets, including the important bio-medical application of decompression sickness. Recent interest has extended to using skills in numerical analysis to examine the dynamics of fuel cells.

He won the Educational Leadership award at the University of Birmingham in the 2019/2020 academic session.


Semester 1

LH/LM Mathematical Finance

Semester 2

LC Vectors, Geometry and Linear Algebra

Postgraduate supervision

Dr Leppinen has been involved in supervising PhD students in the areas of 

  • Hydraulics of Estuaries
  • Bubble dynamics
  • Applications of Ferrite Devices
  • Dynamics of Fuel Cells

For a full list of available Doctoral Research opportunities, please visit our Doctoral Research programme listings.


Dr Leppinen’s strengths involve using numerical and asymptotic techniques to examine problems of practical industrial relevance. His experimental background provides a firm physical understanding of a wide range of industrial and geophysical fluid flows.

Dr Leppinen is an expert in using the Boundary Integral technique to examine the influence of surface tension on inviscid fluid flows. He is also interested in employing high order finite difference and finite volume techniques to examine buoyancy generated flows.

Other activities

In the past, David has held the following positions:

  • MSci Director
  • Student Experience Officer
  • Welfare Tutor
  • Senior Tutor
  • Head of Education
  • Director of PGT Studies


Recent publications


Wang, Q, Liu, W, Leppinen, D & Walmsley, D 2019, 'Microbubble dynamics in a viscous compressible liquid near a rigid boundary', IMA Journal of Applied Mathematics, vol. 84, no. 4, pp. 696–711. https://doi.org/10.1093/imamat/hxz009

Wang, SP, Wang, Q, Leppinen, D, Zhang, AM & Liu, YL 2018, 'Acoustic bubble dynamics in a microvessel surrounded by elastic material', Physics of Fluids, vol. 30, no. 1, 012104. https://doi.org/10.1063/1.5005534

Vyas, N, Sammons, R, Walmsley, A, Wang, Q, Dehghani, H & Leppinen, D 2017, 'Imaging and Analysis of Individual Cavitation Microbubbles around Dental Ultrasonic', Ultrasonics, vol. 81, pp. 66–72. https://doi.org/10.1016/j.ultras.2017.05.015

Vyas, N, Pecheva, E, Dehghani, H, Sammons, R, Wang, Q, Leppinen, D & Walmsley, A 2016, 'High speed imaging of cavitation around dental ultrasonic scaling tips', PLoS ONE, vol. 11, no. 3, e0149804. https://doi.org/10.1371/journal.pone.0149804

Blake, J, Leppinen, D & Wang, Q 2015, 'Cavitation and bubble dynamics: the Kelvin impulse and its applications', Interface Focus, vol. 5, no. 5, 20150017. https://doi.org/10.1098/rsfs.2015.0017

Curtiss, GA, Leppinen, DM, Wang, Q & Blake, J 2013, 'Ultrasonic cavitation near a tissue layer', Journal of Fluid Mechanics, vol. 730, pp. 245-272. https://doi.org/10.1017/jfm.2013.341

Pearson, A, Otto, SR, Leppinen, D & Blake, J 2011, 'Laser generated cavitation bubbles in a fluid layer of finite depth', Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications & Algorithms.

Zhang, Y, Leppinen, D & Dalziel, SB 2009, 'A new nozzle for dissolved air flotation', Water Science & Technology: Water Supply, vol. 9, no. 6, pp. 611-. https://doi.org/10.2166/ws.2009.229


Leppinen, D, Wang, Q & Blake, J 2013, Pulsating bubbles near boundaries. in Bubble Dynamics and Shock Waves. Springer, pp. 33-65. https://doi.org/10.1007/978-3-642-34297-4_2


Leppinen, D, Curtiss, GA, Wang, Q & Blake, J 2011, 'Bubble behaviou near a two fluid interface', WIMRC 3rd International Cavitation Forum 2011, 1/01/11.

Leppinen, D, Curtiss, GA, Wang, Q & Blake, J 2011, 'The interaction of ultrasonic bubbles with tissue layer', WIMRC 3rd International Cavitation Forum 2011, 1/01/11.

Conference contribution

Curtiss, GA, Leppinen, DM, Wang, QX & Blake, JR 2011, Bubble behavior near a two fluid interface. in Integral Methods in Science and Engineering: Computational and Analytic Aspects. Integral Methods in Science and Engineering: Computational and Analytic Aspects, pp. 147-158, 11th International Conference on Integral Methods in Science and Engineering, IMSE 2010, Brighton, United Kingdom, 12/07/10. https://doi.org/10.1007/978-0-8176-8238-5-14


Leppinen, D, Curtiss, GA, Wang, Q & Blake, J 2011, 'The interaction of ultrasonically driven bubbles with a tissue layer', Paper presented at British Appl. Maths. Colloquium 2011, 1/01/11.

Curtiss, GA, Leppinen, D & Blake, J 2010, 'Bubble behaviour near a two fluid interface', Paper presented at British Appl. Maths. Colloquium 2010, 14/07/10.

Curtiss, GA, Blake, J, Leppinen, D & Wang, Q 2008, 'The motion of toroidal cavitation bubbles near a two fluid interface', Paper presented at British Appl. Maths. Colloquium 2008, 1/01/08.

View all publications in research portal