Biological Fluid Dynamics - MAT00039H

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  • Department: Mathematics
  • Module co-ordinator: Prof. Martin Bees
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2017-18

Module will run

Occurrence Teaching cycle
A Spring Term 2017-18

Module aims

  • To review essential fluid dynamics from previous courses.
  • To introduce several important concepts in the mathematical study of fluids applied to biological systems.
  • To explore aspects of blood flow (or other physiological systems), the propulsion of individual swimming microorganisms, and instabilities generated by many swimming microorganisms (bioconvection).
  • To apply and develop knowledge of complex analysis, differential equations and asymptotic methods to facilitate investigation of solution behaviour.

Module learning outcomes

At the end of the module you should be able to:

  • Understand and discuss in detail the range of applications of Fluid Dynamics in Biology
  • Set up models for a range of biological systems involving fluids, employing the Navier-Stokes equations with appropriate boundary conditions
  • Define non-dimensional parameters for particular models, and employ a range of appropriate mathematical tools based upon their values to establish solutions
  • Derive the equations of motion of pulse propagation in large arteries, and apply linear wave theory
  • Use Riemann invariants and the method of characteristics to predict shock formation in large arteries, and employ Womersleys theory for the velocity pulse prole
  • Apply low Reynolds number theory to the motion of blood cells through capillaries
  • Calculate the swimming velocity of a wavy sheet and relate this to swimming by ciliates
  • Use resistive force theory to analyse the swimming of bacteria and spermatozoa
  • Establish governing equations for gyrotactic and phototactic bioconvection and describe the onset of pattern formation using linear stability analysis
  • Discuss all of the above theories, identifying their strengths and weaknesses


Task Length % of module mark
University - closed examination
Biological Fluid Dynamics
2 hours 100

Special assessment rules



Task Length % of module mark
University - closed examination
Biological Fluid Dynamics
2 hours 100

Module feedback

Information currently unavailable

Indicative reading

D. J. Acheson, Elementary Fluid Dynamics, Oxford University Press, 1990.

T. J. Pedley, The Fluid Mechanics of Large Blood Vessels, 446pp, C.U.P., 1980.

J. Lighthill, Flagellar hydrodynamics, SIAM Review, 18, pp. 161-230, 1976.

S. Childress, Mechanics of swimming and flying, Cambridge Studies in Mathematical Biology (2), C.U.P., 1981.

T. J. Pedley and J. O. Kessler, Hydrodynamic phenomena in suspensions of swimming micro-organisms, Annu. Rev. Fluid Mech., 24, 1992.

N. A. Hill and T. J. Pedley, Bioconvection, Fluid Dynamics Research, 37, pp. 1-20, 2005.

C. R. Williams and M. A. Bees. Photo-gyrotactic bioconvection. Journal of Fluid Mechanics, J. Fluid Mech. 100, 1-46, 2011.

C. R. Williams and M. A. Bees. A tale of three taxes: photo-gyro-gravitactic bioconvection. J. Experimental Biol. 214:2398-2408, 2011.

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.