Capillary flow in a noncircular tube

The 1‐D axial, laminar, Newtonian flow through a tube of uniform, but noncircular, cross‐section is analyzed. The tube boundary is r = R[1 + εf(θ)], in which R is a reference radius, ε is a small parameter, and the function f(θ) of the polar angle is general, albeit subject to minimal constraints en...

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Bibliographic Details
Published in:	AIChE journal Vol. 46; no. 4; pp. 695 - 706
Main Authors:	Turian, Raffi M., Kessler, Frederick D.
Format:	Journal Article
Language:	English
Published:	Hoboken Wiley Subscription Services, Inc., A Wiley Company 01-04-2000 Wiley Subscription Services American Institute of Chemical Engineers
Subjects:	Exact sciences and technology Flows through porous media Fluid dynamics Fundamental areas of phenomenology (including applications) Nonhomogeneous flows Physics Packed beds Porous medium flow Poiseuille flow Friction factor Velocity distribution Permeability Capillar porosity Non circular cross section Analytical solution
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Summary:	The 1‐D axial, laminar, Newtonian flow through a tube of uniform, but noncircular, cross‐section is analyzed. The tube boundary is r = R[1 + εf(θ)], in which R is a reference radius, ε is a small parameter, and the function f(θ) of the polar angle is general, albeit subject to minimal constraints ensuring single‐valuedness and quadrant symmetry. All results are determined as asymptotic expansions complete to terms O(ε2), which include the velocity distribution, average velocity, volume flow rate, ratio of flow rates in the noncircular to that in a circular pipe of the same cross‐sectional area, the friction factor‐Reynolds number dependence, the permeability of packed beds comprising noncircular capillaries, kinetic‐energy and momentum‐flux correction factors, the capillary penetration rate under the influence of the capillary pressure and the equilibrium value of the capillary rise. Expressions are derived in terms of the general boundary function f(θ) and, for special cases, when f(θ) = sin2kθ (k = 1, 2, 3) and f(θ) = sin2kθ with k a positive integer. The results provide quantitative measures of the effect of tube shape on flow properties and on imbibition and drainage from noncircular capillaries.
Bibliography:	ArticleID:AIC690460405 ark:/67375/WNG-8S5BHF7J-C istex:7C82443DF993A74C4519A35234897C55EDF90569
ISSN:	0001-1541 1547-5905
DOI:	10.1002/aic.690460405