Explicit analytical solutions for liquid infiltration into capillary tubes: dynamic and constant contact angle

Journal of Colloid and Interface Science
Markus Hilpert

Abstract

We derive new analytical solutions for liquid infiltration into a gas-filled capillary tube, whose inlet is connected to a liquid reservoir held at a constant pressure. We generalize the Lucas-Washburn theory to account for a model for dynamic contact angle that assumes the nonequilibrium Young force to depend linearly on the velocity of the gas-liquid interface. Like Lucas and Washburn, we neglect inertial forces. Using the Lambert function, we derive explicit analytical solutions for the interface position, velocity, and acceleration as a function of time. Consistent with previous work, which used more general models for dynamic contact angle, we can distinguish between five infiltration scenarios: horizontal infiltration, upward infiltration (capillary rise), as well as steady-state, accelerating, and decelerating downward infiltration. We determine the mutually exclusive conditions for the different infiltration scenarios to occur in terms of the nondimensional parameters that define the problem. Moreover, we develop 2D and 3D diagrams that show which parameter combination results in which infiltration scenario. Our analytical solutions are also valid in the limit where the dynamic contact angle becomes constant. For a cons...Continue Reading

References

Oct 14, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·E Schaffer, P Z Wong
Aug 19, 2007·Journal of Colloid and Interface Science·R Chebbi
Jan 19, 2008·Langmuir : the ACS Journal of Surfaces and Colloids·Becky LaviJoerg Bachmann
Feb 8, 2008·Journal of Colloid and Interface Science·N Fries, M Dreyer

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Citations

Apr 11, 2012·Journal of Colloid and Interface Science·Xavier ClotetJordi Ortín
Apr 20, 2010·Journal of Colloid and Interface Science·Markus Hilpert

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