Modelling finger propagation in elasto-rigid channels

Fontana, João V.; Juel, Anne; Bergemann, Nico; Heil, Matthias; Hazel, Andrew L.

doi:10.1017/jfm.2021.219

Cited by 9 publications

(25 citation statements)

References 64 publications

(181 reference statements)

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“…2017 a , b ; Fontana et al. 2021). Those latter considerations are of primary importance for numerous biological flows (Heil & Hazel 2011), in particular in collapsed lungs (Grotberg 1994; Grotberg & Jensen 2004; Heil, Hazel & Smith 2008).…”

Section: Introductionmentioning

confidence: 99%

Intermittent air invasion in pervaporating compliant microchannels

Keiser

Marmottant²,

Dollet³

2022

J. Fluid Mech.

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We explore air invasion in a dead-end compliant water-filled microchannel containing a constriction. The phenomenon is driven by the pervaporation of the liquid present in the channel through the surrounding medium. The penetration is intermittent, jerky and characterised by a stop-and-go dynamics as the bubble escapes the constriction. We demonstrate that this sequence of arrest and jump of the bubble is due to an elasto-capillary coupling between the air–liquid interface and the elastic medium. When the interface enters the constriction, its curvature increases strongly, leading to a depressurisation within the liquid-filled channel that drives a compression of the channel. As the interface is forced to leave the constriction at a given threshold pressure, due to the ongoing loss of liquid content by pervaporation, the pressure is suddenly released, which gives rise to a rapid propagation of the air bubble away from the constriction, and a restoration of the rest shape of the channel. Combining macroscopic observations and confocal imaging, we present a comprehensive experimental study of this phenomenon. In particular, the effect of the channel geometry on the time of arrest in the constriction and the jump length is investigated. Our novel microfluidic design succeeds in mimicking the role of inter-vessel pits in plants, which transiently stop the propagation of air embolisms during long and severe droughts. It is expected to serve as a building block for further biomimetic studies in more complex leaf-like architectures, in order to recover this universal phenomenon of intermittent propagation reported in real leaves.

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Section: Introductionmentioning

confidence: 99%

Intermittent air invasion in pervaporating compliant microchannels

Keiser

Marmottant²,

Dollet³

2022

J. Fluid Mech.

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“…A modelling framework for fluid–structure interaction flows was proposed by Fontana et al. (2021), based on a depth-averaged model to describe the propagation of an air finger into a collapsed elasto-rigid channel. They showed that the presence of the elastic wall can lead to interaction between solution branches that are isolated in the rigid channel, thus altering their stability and potentially leading to complex dynamics at higher levels of initial collapse.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we enable the simulation of intricate interfacial patterns by extending the depth-averaged model introduced by Fontana et al. (2021) to include an artificial disjoining pressure to prevent self-intersection of the interface. We investigate systematically the transition to feathered modes across a range of levels of collapse.…”

Section: Introductionmentioning

confidence: 99%

“…Fontana et al. (2021) also demonstrated that a thin-film model is fundamental to capturing experimental results both qualitatively and quantitatively. In this paper, we refine their thin-film model to improve the prediction of finger speed as a function of injection flow rate, but we also find that the dynamics is not sensitive to the exact choice of thin-film model.…”

Section: Introductionmentioning

confidence: 99%

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Peeling fingers in an elastic Hele-Shaw channel

Fontana,

Cuttle,

Pihler-Puzović

et al. 2024

J. Fluid Mech.

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Using experiments and a depth-averaged numerical model, we study instabilities of two-phase flows in a Hele-Shaw channel with an elastic upper boundary and a non-uniform cross-section prescribed by initial collapse. Experimentally, we find increasingly complex and unsteady modes of air-finger propagation as the dimensionless bubble speed $Ca$ and level of collapse are increased, including pointed fingers, indented fingers and the feathered modes first identified by Cuttle et al. (J. Fluid Mech., vol. 886, 2020, A20). By introducing a measure of the viscous contribution to finger propagation, we identify a $Ca$ threshold beyond which viscous forces are superseded by elastic effects. Quantitative prediction of this transition between ‘viscous’ and ‘elastic’ reopening regimes across levels of collapse establishes the fidelity of the numerical model. In the viscous regime, we recover the non-monotonic dependence on $Ca$ of the finger pressure, which is characteristic of benchtop models of airway reopening. To explore the elastic regime numerically, we extend the depth-averaged model introduced by Fontana et al. (J. Fluid Mech., vol. 916, 2021, A27) to include an artificial disjoining pressure that prevents the unphysical self-intersection of the interface. Using time simulations, we capture for the first time the majority of experimental finger dynamics, including feathered modes. We show that these disordered states evolve continually, with no evidence of convergence to steady or periodic states. We find that the steady bifurcation structure satisfactorily predicts the bubble pressure as a function of $Ca$ , but that it does not provide sufficient information to predict the transition to unsteady dynamics that appears strongly nonlinear.

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“…Since this experiment, numerous studies have been performed to generate further insight into how the taper angle influences viscous fingering [2,3,14,73,86,99]. Other popular physical alterations to the Hele-Shaw cell include uniformly separating the plates in time [43,44,83,100,122,133,143], rotating the entire Hele-Shaw cell at a given angular velocity [5,17,43,119], or replacing one of the plates with an elastic membrane [1,32,48,85,89,[108][109][110][111]. All of these configurations have been shown to produce patterns distinct from traditional Saffman-Taylor fingering.…”

Section: Introductionmentioning

confidence: 99%

A Review of One-Phase Hele-Shaw Flows and a Level-Set Method for Nonstandard Configurations

et al. 2021

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The classical model for studying one-phase Hele-Shaw flows is based on a highly nonlinear moving boundary problem with the fluid velocity related to pressure gradients via a Darcy-type law. In a standard configuration with the Hele-Shaw cell made up of two flat stationary plates, the pressure is harmonic. Therefore, conformal mapping techniques and boundary integral methods can be readily applied to study the key interfacial dynamics, including the Saffman–Taylor instability and viscous fingering patterns. As well as providing a brief review of these key issues, we present a flexible numerical scheme for studying both the standard and nonstandard Hele-Shaw flows. Our method consists of using a modified finite-difference stencil in conjunction with the level-set method to solve the governing equation for pressure on complicated domains and track the location of the moving boundary. Simulations show that our method is capable of reproducing the distinctive morphological features of the Saffman–Taylor instability on a uniform computational grid. By making straightforward adjustments, we show how our scheme can easily be adapted to solve for a wide variety of nonstandard configurations, including cases where the gap between the plates is linearly tapered, the plates are separated in time, and the entire Hele-Shaw cell is rotated at a given angular velocity.

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Modelling finger propagation in elasto-rigid channels

Abstract: Abstract

Cited by 9 publications

References 64 publications

Intermittent air invasion in pervaporating compliant microchannels

Intermittent air invasion in pervaporating compliant microchannels

Peeling fingers in an elastic Hele-Shaw channel

A Review of One-Phase Hele-Shaw Flows and a Level-Set Method for Nonstandard Configurations

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