Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Slow viscous flow inside a torus--the resistance of small tortuous blood vessels

Author: R. S. Chadwick
Journal: Quart. Appl. Math. 43 (1985), 317-323
MSC: Primary 92A06; Secondary 76D07, 76Z05, 92A09
DOI: https://doi.org/10.1090/qam/814230
MathSciNet review: 814230
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Abstract: The hydrodynamic resistance of a buckled microvessel in the form of a tightly would helix is approximated by studing the Stokes flow inside a torus. The unidirectional flow is driven by a constant tangential pressure gradient. The solution is obtained by an eigenfunction expansion in toroidal coordinates. The ratio of volume flow carried by the torus to that carried by a straight tube is computed as a function of the vessel radius: coil radius ratio. An asymptotic expansion for this flux ratio is also obtained. The results show that the resistance of a moderately curved vessel is slightly less than the resistance of a straight one, whereas the resistance of a greatly curved vessel is at most $ 3\% $ greater than the straight one.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/qam/814230
Article copyright: © Copyright 1985 American Mathematical Society

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