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Capillary flow in a noncircular tube
Author(s) -
Turian Raffi M.,
Kessler Frederick D.
Publication year - 2000
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690460405
Subject(s) - laminar flow , capillary action , mechanics , reynolds number , newtonian fluid , capillary number , volumetric flow rate , thermodynamics , physics , chemistry , geometry , materials science , mathematics , turbulence
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 + ε f (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(ε 2 ), 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) = sin 2k θ (k = 1, 2, 3) and f (θ) = sin 2 kθ 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.