Dynamics of non-wetting drops confined in a Hele-Shaw cell

Keiser, Ludovic; Jaafar, Khalil; Bico, José; Reyssat, Étienne

doi:10.1017/jfm.2018.240

Cited by 24 publications

(25 citation statements)

References 54 publications

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“…Note here that, in the singly confined regime, in which a rising bubble is not affected by side walls, R T scales as r as announced in Eq. (17); this corresponds to the straight line observed for small in Fig. 5(b).…”

Section: Bubble-shape Crossoversupporting

confidence: 79%

“…In the singly and doubly confined cases, L is significantly larger and smaller than 2r, respectively. The singly confined case corresponds to experiments using Hele-Shaw cells [13,[15][16][17]. In summary, in this paper, we distinguish the following two cases as illustrated in Figs.…”

Section: Methodsmentioning

confidence: 87%

“…In 2018, another scaling regime closely related to the one found in Ref. [15] was shown, and possible effects of long-range intermolecular interactions were discussed [17] (The role of the lubricating film and molecular interactions were discussed in the different context of oil droplets surrounded by water in microchannels in Ref. [18]).…”

Section: Introductionmentioning

confidence: 90%

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Rising bubble in a cell with a high aspect ratio cross-section filled with a viscous fluid and its connection to viscous fingering

Murano

Okumura

2020

Phys. Rev. Research

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We investigate, both experimentally and theoretically, the velocity and shape of bubbles that rise in a vertical cell with a rectangular cross-section due to buoyancy. The shorter length of the cross-section is comparable to, and the longer length is larger than, the capillary length. This geometry allows us to confine the bubble in two lateral directions, where the bubble is strongly confined by the front and back walls of the cell, and weakly confined by the side walls. Due to this double confinement, one lateral dimension of the bubble is comparable to, but the other lateral and vertical dimensions are larger than, the capillary length. This combination of length scales results in the distinct behavior described in the present study. Our focus here is on the dynamics in the viscous regime, in which buoyancy acts as the driving force for the vertical motion, which is opposed by viscous drag. We have successfully established simple laws for the velocity and shape of the doubly confined bubbles, which lead to a scaling law for the viscous drag acting on the bubble. It is shown that the downward flow around the bubble is essential to the dynamics in this regime. Confocal imaging on submillimeter scales reveals velocity profiles consistent with the present theory. We explore how this doubly confined regime exhibits crossover to previously known scaling laws, and present a corresponding phase diagram. By using a simple velocity transformation, we show the behavior of rising bubbles in the present study corresponds to, and leads to a deeper understanding of, certain types of viscous fingering.

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Section: Bubble-shape Crossoversupporting

confidence: 79%

Section: Methodsmentioning

confidence: 87%

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Rising bubble in a cell with a high aspect ratio cross-section filled with a viscous fluid and its connection to viscous fingering

Murano

Okumura

2020

Phys. Rev. Research

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“…The experimental data are plotted against the theoretical equation ( that for low Ca ranges, the dissipation in the thin film (Keiser et al 2018) and in the dynamic meniscus (Reyssat 2014) have to be taken into account.…”

Section: Experimental Results For Drop Velocitymentioning

confidence: 99%

“…Eri &Okumura (2011) andYahashi et al (2016) studied experimentally such configurations, trying to build up the scaling laws for the viscous drag friction of the Hele-Shaw droplets. Recently, Keiser et al (2018) conducted experiments to study a sedimenting Hele-Shaw droplet, focusing on its velocity as a function of confinement, viscosity contrast and the lubrication capacity of the carrier phase.…”

Section: Introductionmentioning

confidence: 99%

Film thickness distribution in gravity-driven pancake-shaped droplets rising in a Hele-Shaw cell

et al. 2019

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We study here experimentally, numerically and using a lubrication approach; the shape, velocity and lubrication film thickness distribution of a droplet rising in a vertical Hele-Shaw cell. The droplet is surrounded by a stationary immiscible fluid and moves purely due to buoyancy. A low density difference between the two mediums helps to operate in a regime with capillary number Ca lying between 0.03 − 0.35, where Ca = µ o U d /γ is built with the surrounding oil viscosity µ o , the droplet velocity U d and surface tension γ. The experimental data shows that in this regime the droplet velocity is not influenced by the thickness of the thin lubricating film and the dynamic meniscus. For iso-viscous cases, experimental and three-dimensional numerical results of the film thickness distribution agree well with each other. The mean film thickness is well captured by the Aussillous & Quéré (2000) model with fitting parameters. The droplet also exhibits the "catamaran" shape that has been identified experimentally for a pressure-driven counterpart (Huerre et al. 2015). This pattern has been rationalized using a two-dimensional lubrication equation. In particular, we show that this peculiar film thickness distribution is intrinsically related to the anisotropy of the fluxes induced by the droplet's motion.

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Bifurcations of drops and bubbles propagating in variable-depth Hele-Shaw channels

Thompson

2021

J Eng Math

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The steady propagation of air bubbles through a Hele-Shaw channel with either a rectangular or partially occluded cross section is known to exhibit solution multiplicity for steadily propagating bubbles, along with complicated transient behaviour where the bubble may visit several edge states or even change topology several times, before typically reaching its final propagation mode. Many of these phenomena can be observed both in experimental realisations and in numerical simulations based on simple Darcy models of flow and bubble propagation in a Hele-Shaw cell. In this paper, we investigate the corresponding problem for the propagation of a viscous drop (with viscosity $$\nu $$ ν relative to the surrounding fluid) using a Darcy model. We explore the effect of drop viscosity on the steady solution structure for drops in rectangular channels or with imposed height variations. Under the Darcy model in a uniform channel, steady solutions for bubbles map directly on to those for drops with any internal viscosity $$\nu \ne 1$$ ν ≠ 1 . Hence, the solution multiplicity predicted for bubbles also occurs for drops, although for $$\nu >1$$ ν > 1 , the interface shape is reversed with inflection points appearing at the rear rather than the front of the drop. The equivalence between bubbles and drops breaks down for transient behaviour, at the introduction of any height variation, for multiple bodies of different viscosity ratios and for more detailed models which produce a more complicated flow in the interior of the drop. We show that the introduction of topography variations affects bubbles and drops differently, with very viscous drops preferentially moving towards more constricted regions of the channel. Both bubbles and drops can undergo transient behaviour which involves breakup into two almost equal bodies, which then symmetry break before either recombining or separating indefinitely.

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Dynamics of non-wetting drops confined in a Hele-Shaw cell

Cited by 24 publications

References 54 publications

Rising bubble in a cell with a high aspect ratio cross-section filled with a viscous fluid and its connection to viscous fingering

Rising bubble in a cell with a high aspect ratio cross-section filled with a viscous fluid and its connection to viscous fingering

Film thickness distribution in gravity-driven pancake-shaped droplets rising in a Hele-Shaw cell

Bifurcations of drops and bubbles propagating in variable-depth Hele-Shaw channels

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