Capillary Imbibition into Converging Tubes: Beating Washburn’s Law and the Optimal Imbibition of Liquids

Gorce, Jean-Baptiste; Hewitt, Ian; Vella, Dominic

doi:10.1021/acs.langmuir.5b04495

Cited by 58 publications

(60 citation statements)

References 23 publications

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“…When the pore size, or the channel gap, varies along the direction of the capillary flow, the scaling exponent β in the form of h ∼ t β deviates from 1/2, being a function of the shape of the gap (Reyssat et al 2008;Gorce, Hewitt & Vella 2016). For capillary flows occurring against gravity in open geometries imposing no length scale, the curvature of the advancing liquid front may change with height, as has been observed in sharp vertical corners (Ponomarenko, Qu & Clanet 2011;Weislogel 2012) and walls decorated with short pillars with rounded edges (Obara & Okumura 2012).…”

Section: Introductionmentioning

confidence: 99%

Capillary rise of non-aqueous liquids in cellulose sponges

Kim

2017

J. Fluid Mech.

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A cellulose sponge is a mundane porous medium composed of numerous microporous cellulose sheets surrounding macroscale voids. Here, we quantify the capillary rise dynamics of non-aqueous liquids in a sponge using a combination of experiment and theory. Although the classical law of Washburn is obeyed in the early stages, the wet front propagation is no longer diffusive in the late stages and follows a power law, $h\sim t^{1/4}$, with $h$ and $t$ being the capillary rise height and time respectively. The transition of the power law is a consequence of the peculiar heterogeneous pore structure of cellulose sponges. The permeability and driving pressure change at the rise height above which the macro voids can no longer be filled completely due to significant effects of gravity. We rationalize the $t^{1/4}$ law by considering liquid flows along the corners of macro voids driven by capillary pressure of microscale wall pores.

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Section: Introductionmentioning

confidence: 99%

Capillary rise of non-aqueous liquids in cellulose sponges

Kim

2017

J. Fluid Mech.

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“…In this respect, the present problem is closely related to the dynamics governed by thin film dissipation such as the imbibition of textured surfaces. [33][34][35][36][37][38] In this sense, our problem is quasi two-dimensional, although the geometry of the Hele-Shaw cell is often associated with a purely two-dimensional problem. ρ in depends on its kinematic viscosity ν in only slightly (see the details for Methods).…”

Section: Introductionmentioning

confidence: 99%

Scaling crossover in thin-film drag dynamics of fluid drops in the Hele-Shaw cell

Yahashi

Kimoto

Okumura

2016

Sci Rep

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We study both experimentally and theoretically the descending motion due to gravity of a fluid drop surrounded by another immiscible fluid in a confined space between two parallel plates, i.e., in the Hele-Shaw cell. As a result, we show a new scaling regime of a nonlinear drag friction in viscous liquid that replaces the well-known Stokes’ drag friction through a clear collapse of experimental data thanks to the scaling law. In the novel regime, the dissipation in the liquid thin film formed between the drop and cell walls governs the dynamics. The crossover of this scaling regime to another scaling regime in which the dissipation inside the droplet is dominant is clearly demonstrated and a phase diagram separating these scaling regimes is presented.

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“…3): in many previous works, the existence of such thin films is not considered. In this respect, the present problem is closely related to the dynamics governed by thin film dissipation such as the imbibition of textured surfaces [19][20][21][22][23][24], as further discussed in Sec. V. In this sense, our problem is quasi two-dimensional, although the geometry of the Hele-Shaw cell is often associated with a purely two-dimensional problem.…”

Section: Drag Friction Acting On a Bubblementioning

confidence: 99%

Viscous dynamics of drops and bubbles in Hele-Shaw cells: Drainage, drag friction, coalescence, and bursting

Okumura

2018

Advances in Colloid and Interface Science

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In this review article, we discuss recent studies on drops and bubbles in Hele-Shaw cells, focusing on how scaling laws exhibit crossovers from the three-dimensional counterparts and focusing on topics in which viscosity plays an important role. By virtue of progresses in analytical theory and high-speed imaging, dynamics of drops and bubbles have actively been studied with the aid of scaling arguments. However, compared with three-dimensional problems, studies on the corresponding problems in Hele-Shaw cells are still limited. This review demonstrates that the effect of confinement in the Hele-Shaw cell introduces new physics allowing different scaling regimes to appear. For this purpose, we discuss various examples that are potentially important for industrial applications handling drops and bubbles in confined spaces by showing agreement between experiments and scaling theories. As a result, this review provides a collection of problems in hydrodynamics that may be analytically solved or that may be worth studying numerically in the near future.

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Capillary Imbibition into Converging Tubes: Beating Washburn’s Law and the Optimal Imbibition of Liquids

Cited by 58 publications

References 23 publications

Capillary rise of non-aqueous liquids in cellulose sponges

Capillary rise of non-aqueous liquids in cellulose sponges

Scaling crossover in thin-film drag dynamics of fluid drops in the Hele-Shaw cell

Viscous dynamics of drops and bubbles in Hele-Shaw cells: Drainage, drag friction, coalescence, and bursting

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