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Fluid flow in fields of resistance

Published online by Cambridge University Press:  17 April 2009

J.R. Blake
J.R. Blake
Affiliation:
CSIRO, Division of Mathematics and Statistics, Canberra, ACT.
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Abstract

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The velocity profiles in volumes of either passive resistance or active transport are calculated for both linear and non-linear resistive models. These include fluid flows containing particles in a channel or pipe subject to either a steady or oscillatory pressure gradient, cilia induced transport, and laminar flow in a non-linear resistive shear layer. Resistive elements tend to substantially reduce the inertial phase lag component in oscillatory flows. Only small concentrations of particles are needed to reduce the flow field to the Darcy approximation. An ‘active porous media’ model for a cilia sublayer predicts accurate voleoity profiles for dense concentrations of cilia (for example, on Opaline, and in the lung).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 1 , August 1975 , pp. 129 - 145
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Blake, John, “A model for the micro-structure in ciliated organisms”, J. Fluid Mech. 55 (1972), 1–23.CrossRefGoogle Scholar
[2]Blake, J.R. and Sleigh, M.A., “Hydro-mechanical aspects of ciliary propulsion”, Proc. Symp. Mech. Swimming and Flying (to appear).Google Scholar
[3]Brinkman, H.C., “A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles”, Appl. Sci. Res. A1 (1949), 27–34.CrossRefGoogle Scholar
[4]Chow, Chuen-Yen and Lai, Ying-Chung, “Alternating flow in trachea”, Resp. Physiol. 16 (1972), 22–32.Google ScholarPubMed
[5]Cowan, I.R., “Mass, heat and momentum exchange between stands of plants and their atmospheric environment”, Quart. J. Roy. Met. Soc. 94 (1968), 523–544CrossRefGoogle Scholar
[6]Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G. (edited by), Higher transcendental functions, Volume II (based, in part, on notes left by Harry Bateman. McGraw-Hill, New York, Toronto, London, 1953).Google Scholar
[7]Happel, John, Brenner, Howard, Lower Reynolds number hydro dynamics with special applications to particulate media (Prentice-Hall, Englewood Cliffs, N.J., 1965).Google Scholar
[8]Inoue, E., “On the turbulent structure of airflow within crop canopies”, J. Met. Soc. Japan 41 (1963), 317–325.CrossRefGoogle Scholar
[9]Jones, A.S., “Wall shear in pulsatile flow”, Bull. Math. Biophys. 34 (1972), 79–86.CrossRefGoogle ScholarPubMed
[10]Murphy, George M., Ordinary differential equations and their solutions (Van Nostrand Reinhold, London, New York, Cincinati, Toronto, Melbourne, 1960).Google Scholar
[11]Saffman, P.G., “On the boundary conditions at the surface of a porous medium”, Studies in Appl. Math. 50 (1951), 93–101.CrossRefGoogle Scholar
[12]Womersley, J.R., “Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known”, J. Physiol. 127 (1955), 553–563.CrossRefGoogle ScholarPubMed