Dr Richard John Clarke



  • Senior Lecturer

Richard undertook both his undergraduate Masters degree (MMath. 1996-2000) and PhD (2002-2005) within the School of Mathematical Sciences at The University of Nottingham in the UK. His doctoral thesis, entitled Hydrodynamics of the Atomic Force Microscope, examined the influence of fluid dynamics in the atomic force microscope and other similar microscopic devices.

He then went on to study the small-scale fluid flows generated by swimming micro-organisms, such as motile bacteria, during a David Crighton Fellowship within the Department of Applied Mathematics and Theoretical Physics at The University of Cambridge. This was followed by a two year Australian Research Council Associate Researcher position within the School of Mathematics at The University of Adelaide (2006-2008) developing theory for describing viscous flow through suddenly-stopped curved pipes, before joining the Department of Engineering Science at The University of Auckland as a lecturer in April 2008, and senior lecturer in 2011.


PhD in Mathematical Sciences, University of Nottingham
MMath in Mathematical Sciences, University of Nottingham

PGCert in Academic Practice


Part IV Project Coordinator

Professional Memberships


Research | Current

My research is heavily focussed on microhydrodynamics and modelling mechanics within microscopic systems. Such systems typically combine viscous flows, elastic deformations, and stochastic external forcing (e.g. Brownian effects), hence they require a multiphysics, and interdisciplinary, approach. I also have interests in rotating flows, in particular how they can destabilise.

Microelectromechanical Systems (MEMS):

Micromechanical devices are  widespread within  the Physical and Life Sciences. Many operate in a non-vacuum environment and, as such, hydrodynamics and Brownian effects can significantly affect their operation. For example, many such microdevices rely upon the resonant response of a microcantilever. This can be degraded by fluid damping, thereby compromising the  performance of  the device. Our models aim to predict the full stochastic elastohydrodynamics within such devices, which help the community to calibrate their apparatus, as well as potentially exploit new modes of operation. This work has applications to Atomic Force Microscopy, as well as Microsensing and Microrheology.

Microorganism Suspensions:

The motility of microswimmers  in suspension, both natural (e.g. microorganisms) and artificial,  is important in a great number of different circumstances. These include the formation of resilient biofilms, chemical transport within bioreactors, digestion, assisted reproduction, and the marine food chain. Microswimmers  generate long-ranged flows, which affect the motion of their neighbours. This leads to hydrodynamic coupling between individuals, which can result in complex collective motion (sometimes referred to as 'slow turbulence'). This is a phenomenon that has been associated with increased transport within the suspension, as well as complex bulk material properties of the suspending solution. The goal of our research in this area is to derive effective macroscopic (continuum-level) models for suspensions of microswimmers, which are able to reproduce many of the crucial features predicted by current, computationally-expensive microscopic  simulations. This has potential applications in areas where classical colloidal science is considered important  (i.e.  suspensions of passive particles), including biochemistry and the pharmaceutical industry.

Microvessel Mechanics:

The interior walls of microvessels (endothelium) are lined with a brush-like deformable structure known as the Endothelial Glycocalyx Layer (EGL). This layer is hypothesised to fulfil a number of functions, ranging from protecting the vessel wall from excessive fluid shear, to assisting in the body's inflammatory response. Measuring the EGL in-vivo is extremely difficult, as is preserving its structure in-vitro. We therefore use computational models to examine some of the current unanswered hypotheses surrounding the EGL. For example, the impact upon fluid shear stress of the layer becoming redistributed to the gaps between cells, an effect which has been observed in experiments. Also, restoring of an EGL that is crushed by a passing cell.

We have also begun to examine the microvessels within the Lymphatic Capillary System. In particular, modelling how the lymphatic capillaries increase their carrying capacity to accommodate greater volumes of lymph fluid (a mechanism which breaks down in conditions such as lymphedema).

Hydrodynamic Stability

I also have research interests in better understanding unsteady separation.  In a physiological setting, this can occur in large blood vessels, leading to an ejection of fluid into the core of the vessel lumen.  This, in turn, has implications for the fluid shear stress exerted upon arterial walls, known to be linked to diseases such as atherosclerosis. Some fundamental aspects of unsteady separation still remain incompletely understood, with no  generally-accepted and consistent theoretical framework with which to describe the mechanism. In a recent Marsden-funded project, we have used a convenient toroidal flow regime to examine the details of the flow physics both experimentally, and computationally.

Research groups

Fluid Dynamics


FRDF (2017-2019) [Principal Investigator]: Cleaning NZ's Waterways

FRDF (2012-2014) [Associate Investigator] Understanding fluid flow through and within aquaculture pens. Faculty Research Development Fund

Marsden Fast Start, (2010-2013) [Principal Investigator] A Novel approach for probing unsteady boundary layer separation

FRDF (2010-2012): [Co-Principal Investigator] Quantifying elastohydrodynamic effects in Atomic Force Microscopy: Faculty Research Development Fund

Research Capex (2014): [Associate Investigator] Enhancements to the laser diagnostic facilities within the Faculty of Engineering

Teaching | Current

  • ENGSCI111 - Mathematical Modelling 1
  • ENGSCI311 - Mathematical Modelling 3
  • ENGSCI344 - Modelling and Simulation in Computational Mechanics
  • ENGSCI711 - Advanced Mathematical Modelling
  • ENGSCI740 - Advanced Continuum Mechanics

Postgraduate supervision

Current Students

Tharanga Don (PhD) -  Modelling Lymphatic Flow (http://www.engineering.auckland.ac.nz/people/tjay723)

Tet Chuan Lee (PhD) - Modelling the Endothelial Glycocalyx Layer (http://www.engineering.auckland.ac.nz/people/tlee114)

Michael Gravatt (PhD) - Modelling the collective behaviour of swimming microorganisms (http://www.engineering.auckland.ac.nz/people/mgra163)

Past Students

Pavel Sumets (PhD, 2013-2016) - Modelling the Microvasculature (http://www.des.auckland.ac.nz/uoa/home/about/ourstaff/our-doctoral-candidates/pavel-sumetc)

Tet Chuan Lee (ME, 2012-2013) - Near Wall Microfluidics in the Microcirculation


Departmental Course Coordinator Part IV Projects

Departmental Seminar Convenor

Areas of expertise

Fluid Dynamics, Microfluidics, Microorganism Swimming, Collective Dynamics, Hydrodynamic Stability, Biological Fluid Dynamics

Committees/Professional groups/Services

Member of Faculty of Engineering Teaching and Learning Quality Committee

Panel of Independent Chairs for Doctoral Examinations

Editorial Board: Applied Mathematical Modelling (https://www.journals.elsevier.com/applied-mathematical-modelling/)

Selected publications and creative works (Research Outputs)

  • Muller, A., Clarke, R., & Ho, H. (2017). Fast blood-flow simulation for large arterial trees containing thousands of vessels. Computer methods in biomechanics and biomedical engineering, 20 (2), 160-170.
    URL: http://hdl.handle.net/2292/31961
    Other University of Auckland co-authors: Harvey Ho
  • Clarke, R. J. (2017). Microorganisms and their response to stimuli. In S. M. Becker (Ed.) Modeling of microscale transport in biological processes (pp. 171-206). Elsevier. 10.1016/B978-0-12-804595-4.00007-9
  • McDowell, A., Zarrouk, S. J., & Clarke, R. (2016). Modelling viscous fingering during reinjection in geothermal reservoirs. Geothermics, 64, 220-234. 10.1016/j.geothermics.2016.06.003
    Other University of Auckland co-authors: Sadiq Zarrouk
  • Lee, T. C., Long, D. S., & Clarke, R. J. (2016). Effect of endothelial glycocalyx layer redistribution upon microvessel poroelastohydrodynamics. Journal of Fluid Mechanics, 798, 812-852. 10.1017/jfm.2016.337
    Other University of Auckland co-authors: Tet Chuan Lee
  • Sumets, P., Cater, J., Long, D., & Clarke, R. J. (2015). A boundary-integral representation for biphasic mixture theory, with application to the post-capillary glycocalyx. Proceedings of the Royal Society London A, 471 (2179).10.1098/rspa.2014.0955
    Other University of Auckland co-authors: John Cater
  • Clarke, R. J., Bachtiar, V., Lee, T. C., Cater, J. E., & Minton, J. (2015). Response of a fluid-immersed microcantilever close to a deformable body. Journal of Applied Physics, 117 (9), 094501-1-094501-12. 10.1063/1.4913602
    URL: http://hdl.handle.net/2292/26036
    Other University of Auckland co-authors: John Cater, Tet Chuan Lee
  • Clarke, R. J. (2015). Transport in the Microbiome. In S. Becker, A. Kuznetsov (Eds.) Heat Transfer and Fluid Flow in Biological Processes (pp. 157-187). Springer. 10.1016/B978-0-12-408077-5.00006-7
  • Levy, B., Friedrich, H., Cater, J. E., Clarke, R. J., & Denier, J. P. (2014). The impact of twine/mesh ratio on the flow dynamics through a porous cylinder. Experiments in Fluids, 55 (10).10.1007/s00348-014-1829-y
    URL: http://hdl.handle.net/2292/23301
    Other University of Auckland co-authors: Heide Friedrich, John Cater


Contact details

Primary location

Level 3, Room 311
New Zealand

Web links