Two-Phase Fluid Displacement and Interfacial Instabilities Under Elastic Membranes

Al-Housseiny, Talal T.; Christov, Ivan; Stone, Howard A.

doi:10.1103/physrevlett.111.034502

Cited by 65 publications

(54 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further control strategies were developed by altering the physical apparatus itself; for example, Al-Housseiny et al (2012) constructed a tapered Hele-Shaw cell and showed that a negative gradient in depth could inhibit the normal fingering instability for sufficiently low capillary numbers. Similar results were obtained by replacing the Hele-Shaw plates with elastic membranes, as locally the flow is analogous to that in a tapered cell (Pihler-Puzović et al 2012;Al-Housseiny et al 2013), and so the geometric mechanism for suppressing the instability is the same.…”

Section: Overviewsupporting

confidence: 72%

“…For flow configurations of the type explored in Ducloué et al (2017a) with elastic membranes and/or occlusions, analytical insight may be sought via depth-averaged models based on the lubrication approximation (Al-Housseiny et al 2013;Peng et al 2015).…”

Section: Futurementioning

confidence: 99%

“…These issues are important, since in real applications, such as two-phase flow through a porous medium or a pulmonary tube, the geometry is often complex, involving complicated pathways and compliant walls. One simple control strategy is to taper the Hele-Shaw cell so that the top and bottom plates are no longer parallel (Al-Housseiny et al 2012), while another is to replace the top Hele-Shaw plate with an elastic membrane (Pihler-Puzović et al 2012). A third variation is to vary the depth of the Hele-Shaw cell by including a uniform rectangular occlusion that lies parallel to the direction of flow.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Short, flat-tipped, viscous fingers: novel interfacial patterns in a Hele-Shaw channel with an elastic boundary

McCue

2017

J. Fluid Mech.

View full text Add to dashboard Cite

Injecting a less viscous fluid into a more viscous fluid in a Hele-Shaw cell triggers two-dimensional viscous fingering patterns which are characterised by increasingly long fingers undergoing tip splitting and branching events. These complex structures are considered to be a paradigm for interfacial pattern formation in porous media flow and other related phenomena. Over the past five years, there has been a flurry of interest in manipulating these interfacial fingering patterns by altering the physical components of the Hele-Shaw apparatus. In this Focus on Fluids article, we summarise some of this work, concentrating on a very recent study in which the alterations include replacing one of the two bounding plates with an elastic membrane (Ducloué et al., J. Fluid Mech., vol. 826, 2017, R2). The resulting experimental set-up gives rise to a wide variety of novel interfacial patterns including periodic sideways fingers, dendritic-like patterns and short, flat-tipped viscous fingers that appear to resemble molar teeth. These latter fingers are similar to those observed in the printer's instability and when peeling off a layer of adhesive tape. This delightful work brings together a number of well-studied themes in interfacial fluid mechanics, including how viscous and surface tension forces compete to drive fingering patterns, how interfaces are affected by fluid-solid interactions and, finally, how novel strategies can be implemented to control interfacial instabilities.

show abstract

Section: Overviewsupporting

confidence: 72%

Section: Futurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Short, flat-tipped, viscous fingers: novel interfacial patterns in a Hele-Shaw channel with an elastic boundary

McCue

2017

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…Hosoi & Mahadevan (2004) studied the peeling and busting dynamics of a viscous liquid contained between a rigid surface and an elastic sheet. Taylor-Saffman instability in elastic Hele-Shaw cell configurations was examined by Pihler-Puzović et al (2012) and Al-Housseiny et al (2013), who showed that elasticity delays the onset of the instability. Pihler-Puzović et al (2014) related the patterns of viscous fingering to patterns of wrinkling of the elastic Hele-Shaw Figure 1: Illustration of the configuration and coordinate system.…”

Section: Introductionmentioning

confidence: 99%

Transient dynamics of an elastic Hele-Shaw cell due to external forces with application to impact mitigation

Tulchinsky¹,

Gat²

2016

J. Fluid Mech.

View full text Add to dashboard Cite

We study the transient dynamics of a viscous liquid contained in a narrow gap between a rigid surface and a parallel elastic plate. The elastic plate is deformed due to an externally applied time-varying pressure-field. We model the flow-field via the lubrication approximation, and the plate deformation by the Kirchhoff-Love plate theory. We obtain a self-similarity solution for the case of an external point force acting on the elastic plate. The pressure and deformation field during and after the application of the external force are derived and presented by closed form expressions. We examine a uniform external pressure acting on the elastic plate over a finite region and during a finite time period, similar to the viscous-elastic interaction time-scale. The interaction between elasticity and viscosity is shown to reduce by order of magnitude the pressure within the Hele-Shaw cell compared with the externally applied pressure, thus suggesting such configurations may be used for impact mitigation.

show abstract

“…In the present paper we study the canonical problem, shown schematically in figure 1, which has received much attention in recent years (Jensen et al 2002;Grotberg & Jensen 2004;Michaut 2011;Pihler-Puzović et al 2012Al-Housseiny et al 2013;Lister et al 2013;Hewitt et al 2015). A thin, uniform layer of viscous fluid is contained between a rigid plate and an elastic membrane which forms the upper boundary of the cell.…”

Section: Introductionmentioning

confidence: 99%

Displacement flows under elastic membranes. Part 1. Experiments and direct numerical simulations

et al. 2015

View full text Add to dashboard Cite

The injection of fluid into the narrow, liquid-filled gap between a rigid plate and an elastic membrane drives a displacement flow that is controlled by the competition between elastic and viscous forces. We study such flows using the canonical setup of an elasticwalled Hele-Shaw cell whose upper boundary is formed by an elastic sheet. We investigate both single-and two-phase displacement flows in which the localised injection of fluid at a constant flow rate is accommodated by the inflation of the sheet and the outward propagation of an axisymmetric front beyond which the cell remains approximately undeformed. We perform a direct comparison between quantitative experiments and numerical simulations of two theoretical models. The models couple the Föppl-von Kármán equations, which describe the deformation of the thin elastic membrane, to the equations describing the flow, which we model by (i) the Navier-Stokes equations or (ii) lubrication theory, respectively. We identify the dominant physical effects that control the system's behaviour and critically assess modelling assumptions that were made in previous studies. The insight gained from these studies is then used in Part 2 of this work where we formulate an improved lubrication model and develop an asymptotic description of the key phenomena.

show abstract

Two-Phase Fluid Displacement and Interfacial Instabilities Under Elastic Membranes

Cited by 65 publications

References 21 publications

Short, flat-tipped, viscous fingers: novel interfacial patterns in a Hele-Shaw channel with an elastic boundary

Short, flat-tipped, viscous fingers: novel interfacial patterns in a Hele-Shaw channel with an elastic boundary

Transient dynamics of an elastic Hele-Shaw cell due to external forces with application to impact mitigation

Displacement flows under elastic membranes. Part 1. Experiments and direct numerical simulations

Contact Info

Product

Resources

About