John Robert Blake, FIMA, C.Math
Professor of Applied Mathematics

School of Mathematics
The University of Birmingham
Birmingham  B15 2TT
Tel: +44 121 414 6577
Fax: +44 121 414 3389



Graduate of the University of Adelaide (Australia) and University of Cambridge (United Kingdom).  


Main research interests are in the area of applied mathematics and fluid mechanics with a particular emphasis on interdisciplinary research in science, engineering, medicine, sport and the environment.  


Teaching experience has been primarily associated with mathematical techniques during the first two years, while more discipline-specific courses have considered in the latter years of an undergraduate programme.  


Lectures have included Fluid mechanics, Low Reynolds number fluid mechanics, Biological & Physiological fluid mechanics, Dynamics of multi-phase flow and Environmental fluid mechanics.  

bullet Former Head of School and Dean of Faculty at Universities of Wollongong (Australia) and Birmingham (United Kingdom).
bullet Former Member of Executive, University of Birmingham.

Former Director of the UK Higher Education Academy's Mathematics, Statistics & Operational Research Network, a national learning and teaching support network and the U.K. Mathematics Courseware Consortium (MATHWISE).   

1.  Membership of Professional Societies


Australian Mathematical Society


Institute of Mathematics and its Applications


London Mathematical Society

2.  Research Experience and Interests

In Biological and Physiological Fluid Mechanics


  Mechanics of ciliary propulsion
  Muco-ciliary transport +

 Mathematical embryology: the fluid mechanics of nodal cilia +

  Foetal lung physiology
  High frequency ventilation
  Some problems in plant physiology
  Filter feeding
  Bacterial locomotion
  Sperm and ovum transport +
  Ultrasound and Shock Wave Lithotripters

In Low Reynolds Number Fluid Mechanics


  Fundamental singularities and image systems in different boundaries
  Viscous eddies in confined geometries
  Slender body theory +

In Engineering and Industrial Areas


  Dynamics of growth and collapse of cavitation bubbles +
  Acoustic cavitation and sonoluminescence. +
  Heat transfer during hot rolling
  Some aspects of blast furnace operations
  Fluid mechanics of coating technology
  Dynamics of underwater explosions +
  Fluid mechanics of bioreactors

In Environmental Areas


  Sedimentation of industrial slurries
  Pyritic oxidisation in waste rock dumps
  Convection in porous media

In Energy Research


  Two-phase flow in porous media
  Enhanced oil recovery

In Food Research


  Oxygen diffusion in food
  Mixing processes

In Sport


  Behaviour of a golf clubhead

 +~ Areas of current research activity. 

3.  Selected publications

[Citations above 50 are indicated: source Google Scholar]

BLAKE, J.R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46, 199-208.  [101]
BLAKE, J.R. 1971 Infinite models for ciliary propulsion. J. Fluid Mech. 49, 209-222.  [53]

BLAKE, J.R. 1971 A note on the image system for a stokeslet in a no slip boundary. Proc. Camb. Phil. Soc. 70, 303-310.  [229]

BLAKE, J.R. 1972 A model for the microstructure in ciliated micro-organisms. J. Fluid Mech. 55, 1-23. (also published 1985 Physical Society of Japan "Selected Papers in Physics" Series in Biological Fluid Dynamics No. 83, 131-153).  [79]

BLAKE, J.R. and SLEIGH, M. 1974 Mechanics of ciliary locomotion. Biol. Rev. 49, 85-125.  [96]

BLAKE, J.R and CHWANG, A.T. 1974 Fundamental singularities of viscous flow. Part 1: The image systems in the vicinity of a stationary no-slip boundary. J. Eng. Math 8, 23-29.  [71]
BLAKE, J.R. 1975 On the movement of mucus in the lung. J. Biomech. 8, 179-190.  [60]

BLAKE, J.R. and GIBSON, D.C. 1981 Growth and collapse of a vapour cavity near a free surface. J. Fluid Mech. 111, 123-140.  [100]

BLAKE, J.R., TAIB, B.B. and DOHERTY, G. 1986 Transient cavities near boundaries. Part 1. Rigid boundary. J. Fluid Mech. 170, 479-497.  [204]

BLAKE, J.R., TAIB, B.B. and DOHERTY, G. 1987 Transient cavities near boundaries. Part 2. Free surface. J. Fluid Mech. 181, 197-212.  [71]

BLAKE, J.R. and GIBSON, D.C. 1987 Cavitation bubbles near boundaries. Ann. Rev. Fluid Mech. 19, 99-123.   [223]

SLEIGH, M.A., BLAKE, J.R. and LIRON, N. 1988 State of Art: The propulsion of mucus by cilia. Am. Rev. Resp. Disease 137, 726-741 (also published 1989 in Lung Disease: State of the Art, American Lung Assoc. pp. 133-148).   [238]

BLAKE, J.R. 1988 The Kelvin impulse: application to cavitation bubble dynamics. J. Aust. Math. Soc. Ser. B 30, 127-146.

BOULTON-STONE, J. and BLAKE, J.R. 1993 Gas bubbles bursting at a free surface. J. Fluid Mech. 254, 437-466.  [115]

BEST, J.P. and BLAKE, J.R. 1994 An estimate of the Kelvin impulse of a transient cavity. J. Fluid Mech. 261, 75-93.

BLAKE, J.R. and OTTO, S.R. 1996. Ciliary propulsion, chaotic filtration and a 'blinking' stokeslet. J. Eng. Math. 30, 151-168.

BLAKE, J.R., HOOTON, M.C., ROBINSON, P.B. & TONG, R.P. 1997 Collapsing cavities, toroidal bubbles and jet impact. Phil. Trans. Roy. Soc. 355, 537-550.  [50]

TONG, R.P., SCHIFFERS, W.P., SHAW, S.J., BLAKE, J.R. and EMMONY, D.C. 1999 The role of `splashing' in the collapse of a laser generated cavity near a rigid boundary. J. Fluid Mech. 380, 339 - 361.

BLAKE, J.R., KEEN, G.S.,  TONG, R.P. and WILSON, M. 1999 Acoustic cavitation: the fluid dynamics of non-spherical bubbles. Phil. Trans. Roy. Soc. A357, 251 - 267.

BRUJAN, E.A., KEEN, G.S., VOGEL, A. and BLAKE, J.R. 2002 The final stages of collapse of a cavitation bubble near a rigid boundary. Phys. Fluids 14, 85-92.  [66]

ORME, B.A.A., OTTO, S.R. & BLAKE, J.R. 2003 Modelling the motion of particles around choanoflagellates. J. Fluid Mech. 475, 333-355.

PEARSON, A., BLAKE, J.R. & OTTO, S.R. 2004 Jets in bubbles. J. Eng. Math. 48, 391-412.

SZERI, A.J., STOREY, B.D., BLAKE, J.R. & PEARSON, A. 2003 Heat and mass transfer during the violent collapse of non-spherical bubbles. Physics of Fluids 15, 2576-2586.

COX, E., PEARSON, A., BLAKE, J.R. & OTTO, S.R. 2004 Comparison of methods for modelling the behaviour of bubbles produced by marine seismic airguns. Geophysical Prospecting 52, 451-477.

BRUJAN, E.A., PEARSON, A. & BLAKE, J.R. 2005 Pulsating, buoyant bubbles close to a rigid boundary and near the null final Kelvin impulse state. Int. J. Multiphase Flow 31, 302-317.
SMITH, D.J., GAFFNEY, E.A. & BLAKE, J.R. 2007 Discrete cilia modelling with singularity distributions: applications to the embryonic node and the airway surface liquid.  Bull. Math Biol. 69, 1477-1510.
CALVESI, M.L., LINDAU, O., BLAKE, J.R. & SZERI, A.J. 2007 Shape stability and violent collapse of microbubbles in acoustic travelling waves. Physics of Fluids, 19, 047101.
WILSON, M., BLAKE, J.R. & HAESE, P.M. 2008 A potential multipole theory for the hydrodynamics of bubble clouds. IMA J. Applied Math. 73, 556-577, doi 10.1093/imamat/hxm061.
SMITH, D.J., BLAKE, J.R. & GAFFNEY, E.A. 2008 Fluid mechanics of nodal flow due to embryonic primary cilia. J. Royal Society Interface 5, 567-573.
SMITH, D.J., GAFFNEY, E.A. & BLAKE, J.R. 2008 Modelling muco-ciliary clearance. Resp. Physiol. & Neurobiol. 163, 178-199.
SMITH, D.J. and BLAKE, J.R. 2009 Surface accumulation of spermatazoa: a fluid dynamic phenomenon. Math Sci. 34, 74-87.
BLAKE, J.R., TUCK, E.O. and WAKELEY, P.W. 2010 A note on the S-transform and slender body theory in stokes flow. IMA J. Applied Math. 75, 345-355.
WANG, Q.X. and BLAKE, J.R. 2010 Non-spherical bubble dynamics n a compressible fluid. Part 1: Travelling acoustic wave. J. Fluid Mech. 659, 191-224.
SMITH, D.J., SMITH, A.A. and BLAKE, J.R. 2011 Mathematical embryology: the fluid mechanics of nodal cilia. J. Eng. Math.
GAFFNEY, E.A., GADELHA, H., SMITH, D.J., BLAKE, J.R. and KIRKMAN-BROWN, J.C. 2011 Mammalian sperm motility: observation and theory. Ann. Rev. Fluid  43, 501-528.

4.  Research Funding


Australian Research Grants Committee


National Health and Medical Research Council


Australian Atomic Energy Commission


University of Wollongong Research Grants Committee


University of Wollongong/CSIRO Collaborative Research Scheme


Australian Research Council


United Kingdom Admiralty Research Establishment, Dunfermline


Science and Engineering Research Council Mathematics Committee


Biotechnology and Biological Sciences Research Council


Defence Evaluation and Research Agency, Fort Halstead, Winfrith, HASLAR


Engineering and Physical Sciences Research Council Mathematics Programme




QinetiQ Ltd, Centre for Marine Technology

5.  Research Students



G.R. Fulford "Slender body theory near an interface at very low Reynolds Numbers"
B.B. Taib "Boundary integral methods applied to cavitation bubble dynamics"
D. Yuen "Heat transfer analysis of sheet rolling"
J.P. Best "The dynamics of underwater explosions"


United Kingdom
J.M. Boulton-Stone "Application of boundary integral methods to rising and bursting bubbles"
P.B. Robinson "Numerical modelling of bubble interactions"
M.C. Hooton "Underwater explosion bubbles"
J.E. Hall "Oxygen diffusion in food"
G.S. Keen "Modelling cell damage in bioreactors"
C.G. Round "Mathematical modelling of acoustic cavitation and sonoluminescence"
G. Jia "Cavitation on a hydrofoil"
M. Wilson "Mathematical modelling of bubble-vortex interactions"
M. Pettitt "Prey capture and ingestion in choanoflagellates"
B. Orme "Biological mixing and chaos"
A Pearson "Hydrodynamics of jet impact in a collapsing bubble"
E. Cox "The source signature due to the close interaction of marine seismic airguns"

D. Smith "Models of muco-ciliary transport in the lung"
S. Brown "Dynamics of large oscillating bubbles"
T. Collings "Acoustic cavitation and sonochemistry"

P. Wakeley "Optimisation and properties of gamete transport"

G. Curtiss "Cavitation bubble interaction with multiphase flow"

I. Ogilvy "Fluid dynamics of underwater explosions"



S. Nicholls "Mathematical models of a muscle/tendon complex in a human joint"
A. Ahmed "Filter Feeding"

Subiarto "Water coning in oil reservoirs"

M. Grammatika "Transport phenomena associated with complex fluids in micro-fluidic devices"

Current Ph.D. students


J.Ndam "Fluid mechanics of a detached retina" (University of Jos, Nigeria)

T. Johnson "Modelling mechanics of sperm motility"

A. Smith "Fluid mechanics of nodal cilia"

6.  Research Fellows & Assistants

Dr P Cerone
Dr P Vann
Dr A Kucera
Dr R Paull
Mr D Jamieson
Dr BP Huynh
Dr T Tran-Cong
Dr P Harris
Dr J Norris
Dr S Shaw
Dr JM Boulton-Stone
Dr GS Keen
Dr RP Tong
Dr A Pearson
Dr PM Haese
Dr M Calvisi
Dr DJ Smith

7.  Editorial Activities


Editor: The Mathematical Scientist 

bullet Former Associate Editor, Theoretical and Computational Fluid Dynamics, IMA Journal of Applied Mathematics

Invited Editor:  Special issue of Phil. Trans. Roy. Soc. (1999) on "Acoustic cavitation and sonoluminescence" 357, 199-369. 

8.  Teaching Experience

Taught a range of courses at the Australian National University, Canberra and University of Wollongong, New South Wales, Australia.  
Recent lectures at the University of Birmingham include:


Calculus for First Year Students,


Research Frontiers in Applied Mathematics,


Biological and Physiological Fluid Mechanics,


Viscous Fluid Dynamics and its Applications,


History of Twentieth Century Fluid Mechanics - Prandtl, von Karman & Taylor.

9.  External Examiner


University of Bath, School of Mathematical Sciences  (1992-1995)


University of Exeter, Department of Mathematics  (1993-1996)


University of Pertanian, Malaysia, Department of Mathematics  (1994)


University of Bristol, Department of Mathematics  (1996-1998 )


University of Manchester, Department of Mathematics  (1997-1999 )


University of Nottingham  (1999-2002)


University of Bristol, Engineering Mathematics  (2000-2003)


These pages were last updated on 10/03/2011