Imbibition in geometries with axial variations

Abstract

When surface wetting drives liquids to invade porous media or microstructured materials with uniform channels, the penetration distance is known to increase as the square root of time. We demonstrate, experimentally and theoretically, that shape variations of the channel, in the flow direction, modify this 'diffusive' response. At short times, the shape variations are not significant and the imbibition is still diffusive. However, at long times, different power-law responses occur, and their exponents are uniquely connected to the details of the geometry. Experiments performed with conical tubes clearly show the two theoretical limits. Several extensions of these ideas are described.

Dynamics of elastocapillary rise

“…The channel formed by the two sheets adopts a complex geometry, and the data roughly follows a power law Z m ∝ T 1/13 . This behaviour is consistent with imbibition in a diverging channel having shape h(z) = h 0 + βz n , where the time-dependence of the meniscus position is given by Z m ∝ T 1/(2n+1) (Reyssat et al 2008). Our results are close to n = 6, although any value of n > 1, hence an exponent of 1/(2n + 1) < 1/3, is permissible.…”

Rise in optimized capillary channels

“…As noted in the study conducted by Reyssat et al (2008), capillary geometry can have a significant influence on the wicking dynamics. The design of an optimized shape promoting fast wicking is then of interest regarding the development of passive devices aimed at transporting fluids through capillary effects.…”

“…Erickson, Li & Park (2002) conducted numerical simulations based on the resolution of the Navier-Stokes equation to model capillary-driven flows in diverging-converging and converging-diverging cross-sectional capillaries, showing that these configurations exhibit significantly slower wetting behaviour than straight capillaries. More recently, Reyssat et al (2008) studied imbibition in capillary channels with axial variations and demonstrated that the imbibition dynamics is closely related to the details of the geometry of the capillary channel at long times. Various shapes have also been considered, including stepped capillary tubes (Erickson et al 2002;Polzin & Choueiri 2003;Young 2004), V-shaped open grooves (Romero & Yost 1996;Rye, Mann & Yost 1996;Weislogel & Litcher 1998;Dussaud, Adler & Lips 2003;Warren 2004), assemblies of parallel cylinders (Princen 1969) or corner flows (Higuera, Medina & Linan 2008;Ponomarenko, Quéré & Clanet 2011).…”

The fastest capillary penetration of power-law fluids

“…The manipulated capillary flow in non-uniform porous structures, in terms of the evolution of flow distance to time, deviates from the classical Washburn equation based on uniform tubes (Reyssat et al, 2008(Reyssat et al, , 2009Shou et al, 2014bShou et al, , 2014c. As well, the fastest capillary flow on the basis of Newtonian fluids has been found in the optimally designed tubes and porous systems (Shou and Fan, 2015;Shou et al, 2014bShou et al, , 2014cShou et al, , 2014d.…”