Wicking of a liquid bridge connected to a moving porous surface
We study the coupled problem of a liquid bridge connected to a porous surface and an impermeable surface, where the gap between the surfaces is an externally controlled function of time. The relative motion between the surfaces influences the pressure distribution and geometry of the liquid bridge, thus affecting the shape of liquid penetration into the porous material. Utilizing the lubrication approximation and Darcy's phenomenological law, we obtain an implicit integral relation between the relative motion between the surfaces and the shape of liquid penetration. A method to control the shape of liquid penetration is suggested and illustrated for the case of conical penetration shapes with an arbitrary cone opening angle. We obtain explicit analytic expressions for the case of constant relative speed of the surfaces as well as for the relative motion between the surfaces required to create conical penetration shapes. Our theoretical results are compared with experiments and reasonable agreement between the analytical and experimental data is observed.
© 2012 Cambridge University Press. Received 10 January 2012; revised 19 March 2012; accepted 2 May 2012; first published online 12 June 2012. We thank Dr S. Paikoff of the Defense Threat Reduction Agency (DTRA) which supported this project.
Published - Gat2012p19035J_Fluid_Mech.pdf