Dr Richard John Clarke


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Associate Professor


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 examined the influence of fluid dynamics in scanning force microscopy. 

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 Mathematical Sciences at the University of Adelaide (2006-2008) developing theory for describing boundary layer separation in rotating flows, before joining the Department of Engineering Science at the University of Auckland in April 2008.  


PhD in Mathematical Sciences, University of Nottingham

MMath in Mathematical Sciences, University of Nottingham

PGCert in Academic Practice


Associate Dean - Postgraduate Research

Part IV Project Coordinator

Professional Memberships


Research | Current

My research is heavily focussed on mathematical and computational modelling in health research. The systems of interest typically combine viscous flows, elastic deformations, and stochastic external forcing (e.g. Brownian effects), hence they require a multiphysics, and interdisciplinary, approach. 

Biological Flows

This research falls into two main areas:

i) Physiological Fluid Dynamics

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).

ii) Microbe 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.

Microfluidic Systems:

Microfluidic systems are typically multiphysics environments, governed not only by fluid dynamics, but often also elastodynamics and chemistry. Our models aim to predict the full  electro-, poroelasto- hydrodynamics, within such devices, as well as the transport of species within these devices. This work has applications to  Microscopy, as well as Lab-on-Chip type technologies, and has been the subject of collaborative projects with researchers in the Faculties of Science and Health Sciences.


Research groups

Fluid Dynamics


HRC Programme 2021 [Associate Investigator]: Translating treatments for lymphatic dysfunction associated with organ failure

​HRC Explorer (2019-2021) [Associate Investigator] Rebalancing fluid distribution in critical illness

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

  • ENGSCI211 - Mathematical Modelling 2
  • ENGSCI343 - Mathematical and Computational Modelling in Mechanics
  • ENGSCI711 - Advanced Mathematical Modelling
  • ENGSCI740 - Advanced Continuum Mechanics

Postgraduate supervision

Current Students

Alec Baumann (PhD) - Macroscopic Mathematical Modeling of Microorganism Suspensions

Henri Gaudin (PhD) - Modelling Molecular Filtration through the EGLDasha Shieff (ME) - Optimising the Shape of Microswimmers

Sherine Valiyaveetil Ali (PhD) - Learning based control for soft robotic esophageal simulator

Past Students

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

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

Dr Tet Chuan Lee (PhD, 2014-2018) - Modelling the Endothelial Glycocalyx Layer (http://www.engineering.auckland.ac.nz/people/tlee114)

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

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


Associate Dean - Postgraduate Research

Course Coordinator Part IV Projects

Areas of expertise

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

Committees/Professional groups/Services

Member of the University of Auckland Board of Graduate Studies

Member of the University of Auckland Senate

Member of Faculty of Engineering Postgraduate Committee

Member of Faculty Academic Programmes Committee

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/)

Editorial Board: Journal of Engineering Mathematics (https://www.springer.com/journal/10665)

Selected publications and creative works (Research Outputs)

As of 29 October 2020 there will be no automatic updating of 'selected publications and creative works' from Research Outputs. Please continue to keep your Research Outputs profile up to date.
  • Adiputro, A. S., Zarrouk, S. J., Clarke, R. J., Harcouet-Menou, V., & Bos, S. (2020). Geothermal wells with water hammer during injection fall-off test: Numerical pressure transient analysis. GEOTHERMICS, 8710.1016/j.geothermics.2020.101838
    Other University of Auckland co-authors: Sadiq Zarrouk
  • Lee, T. C., Suresh, V., & Clarke, R. J. (2020). Influence of endothelial glycocalyx layer microstructure upon its role as a mechanotransducer. Journal of Fluid Mechanics, 89310.1017/jfm.2020.249
    Other University of Auckland co-authors: Vinod Suresh
  • Baker, N., Clarke, R., & Ho, H. (2020). A coupled 1D and transmission line model for arterial flow simulation. International Journal for Numerical Methods in Biomedical Engineering10.1002/cnm.3327
    Other University of Auckland co-authors: Harvey Ho
  • Franiatte, S., Clarke, R., & Ho, H. (2019). A computational model for hepatotoxicity by coupling drug transport and acetaminophen metabolism equations. International journal for numerical methods in biomedical engineering, 35 (9)10.1002/cnm.3234
    Other University of Auckland co-authors: Harvey Ho
  • Barléon N, Clarke, R. J., & Ho, H. (2018). Novel methods for segment-specific blood flow simulation for the liver. Computer Methods in Biomechanics and Biomedical Engineering, 21 (15), 780-783. 10.1080/10255842.2018.1520224
    Other University of Auckland co-authors: Harvey Ho
  • Bilton, M. A., Thambyah, A., & Clarke, R. J. (2018). How changes in interconnectivity affect the bulk properties of articular cartilage: a fibre network study. Biomechancis and Modeling in Mechanobiology, 17 (5), 1297-1315. 10.1007/s10237-018-1027-6
    Other University of Auckland co-authors: Ashvin Thambyah
  • Holloway, C. R., Cupples, G., Smith, D. J., Green, J. E. F., Clarke, R. J., & Dyson, R. J. (2018). Influences of transversely isotropic rheology and translational diffusion on the stability of activesuspensions. Royal Society Open Science, 5 (8).10.1098/rsos.180456
  • Gravatt, M., Suresh, V., Clark, A., & Clarke, R. (2018). Importance of irrotational components of swimming flows on the stability of a suspension of weakly-squirming microorganisms. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 83 (4), 720-742. 10.1093/imamat/hxy020
    Other University of Auckland co-authors: Vinod Suresh, Alys Clark


Contact details

Primary office location

Level 3, Room 311
New Zealand

Web links