Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 

 

Asymptotic analysis of Stokes flow in a tortuous vessel


Author: R. S. Chadwick
Journal: Quart. Appl. Math. 43 (1985), 325-336
MSC: Primary 92A06; Secondary 76D07, 76Z05, 92A09
DOI: https://doi.org/10.1090/qam/814231
MathSciNet review: 814231
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Abstract: Steady slow viscous flow is considered inside a vessel with circular cross section. The centerline curvature is specified as a function of arc length. The Stokes equations are written in orthogonal curvilinear coordinates. The primary small parameter is the slenderness ratio $ \epsilon $, which is the ratio of vessel radius to vessel length or wavelength. The product of centerline curvature and vessel length is assumed to be of order unity. A transverse drift appears at $ O\left( {{\epsilon ^2}} \right)$ that is proportional to the rate of change of curvature. Contours of axial velocity show a primary peak shifted toward the inside wall and a secondary peak grows toward the outside wall as curvature is increased. The flux ratio or relative hydrodynamic conductance is calculated to $ O\left( {{\epsilon ^4}} \right)$ and includes the effect of variable curvature. The present calculations tend to indicate that the sinusoidal mode of buckled micro-vessel could offer substantially more resistance to flow than the helical buckled mode.


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DOI: https://doi.org/10.1090/qam/814231
Article copyright: © Copyright 1985 American Mathematical Society


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