Journal
JOURNAL OF COLLOID AND INTERFACE SCIENCE
Volume 320, Issue 1, Pages 259-263Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcis.2008.01.009
Keywords
capillary rise; capillary tube; analytic solution; liquid penetration; porous medium; imbibition; Lucas-Washburn equation; Washburn equation; Lambert W function
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We derive an analytic solution for the capillary rise of liquids in a cylindrical tube or a porous medium in terms of height h as a function of time t. The implicit t (h) solution by Washburn is the basis for these calculations and the Lambert W function is used for its mathematical rearrangement. The original equation is derived out of the 1D momentum conservation equation and features viscous and gravity terms. Thus our h(t) solution, as it includes the gravity term (hydrostatic pressure), enables the calculation of the liquid rise behavior for longer times than the classical Lucas-Washburn equation. Based on the new equation several parameters like the steady state time and the validity of the Lucas-Washburn equation are examined. The results are also discussed in dimensionless form. (C) 2008 Elsevier Inc. All rights reserved.
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