Wicking flow in irregular capillaries

Understanding capillary flow in porous media (wicking) is critical for predicting and improving the performance of absorbent structures. Capillary flow in straight circular tubes has long been known to be quite well described by the Lucas-Washburn equation. Experimental wicking results with beds of glass beads led us to investigate a minor modification of this equation to describe more complex systems. These results, as well as the mathematical treatment, are presented to describe capillary flow as a function of time in tubes irregularly shaped along their primary axis. The cross-section of the model tubes remains circular. Variations of the diameter that are periodic along the length of the tube are the focus of the study, and a sinusoidal description is argued to be sufficiently general to describe most systems. The variables used to describe the system can be divided into two groups. Fluid and surface chemistry are defined by the viscosity (eta), surface tension (gamma), contact angle (theta), and density (rho). In the sinusoidal case, the capillary itself is described by D-cap, the diameter at the largest portion of the tube which determines the limiting capillary pressure, D-vis, the diameter of the throat which dominates the viscous drag, and lambda, 'wavelength' of the fluctuations. The conclusions are: (1) as long as the wavelength of the fluctuation in diameter for the capillary is small relative to the length of travel, the actual value of this wavelength does not matter in the time derivative of the flow. This is typically the case for porous media in which the flow path dimensions fluctuate in the range of microns, and the wicking distances are measured in centimeters. (2) As a result of this simplification, a two-parameter equation can be written which yields the time t for the fluid front to reach a given distance L, analogous to the Lucas-Washburn equation: ln(1 - L/L-eq) + L/L-eq = - (CDcaprhog2)-D-2/32etaL(eq) The term L-eq defines the equilibrium height and is a function of gamma, theta, rho, and D-cap. The rate is determined in addition by eta and D-vis (= C x D-cap). (C) 2002 Published by Elsevier Science B.V.