Stability of viscous fingering in lifted Hele-Shaw cells with a hole

Kanhurkar, Sachin D.; Patankar, V.S.; Islam, Tanveer ul; Gandhi, Prasanna S.; Bhattacharya, Amitabh

doi:10.1103/physrevfluids.4.094003

Cited by 16 publications

(23 citation statements)

References 27 publications

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“…We note that, as already indicated in the introduction, the situation here is very different from that considered by Kanhurkar et al (2019), who conducted the plate-lifting experiment with a small hole in the upper plate, allowing for equalisation of pressure in the air bubble with atmospheric pressure. Air can flow through the hole, so the volume of the bubble is no longer constant as the lifting proceeds; this affects the pressure distribution throughout the viscous fluid annulus.…”

Section: Destabilising Effect Of Trapped Air Bubblementioning

confidence: 93%

“…An interesting variant on the three-layer lifting problem has been explored by Kanhurkar et al (2019), who introduced a small hole in the upper plate, which could be opened during the lifting phase; this must have caused a bubble to expand from air passing through the hole from the atmosphere during the subsequent evolution. The pressure in this bubble is equal to the atmospheric pressure; this makes this situation very different from that studied in the present paper, for which the pressure in the bubble is less than atmospheric during the lifting phase by an amount given by (3.2) below; this has a strong effect on the stability characteristics, for reasons that will be evident in the sketch of figure 10(b).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spreading or contraction of viscous drops between plates: single, multiple or annular drops

Moffatt¹,

Guest²,

Huppert

2021

J. Fluid Mech.

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The behaviour of a viscous drop squeezed between two horizontal planes (a squeezed Hele-Shaw cell) is treated by both theory and experiment. When the squeezing force $F$ is constant and surface tension is neglected, the theory predicts ultimate growth of the radius $a\sim t^{1/8}$ with time $t$. This theory is first reviewed and found to be in excellent agreement with experiment. Surface tension at the drop boundary reduces the interior pressure, and this effect is included in the analysis, although it is negligibly small in the squeezing experiments. An initially elliptic drop tends to become circular as $t$ increases. More generally, the circular evolution is found to be stable under small perturbations. If, on the other hand, the force is reversed ($F<0$), so that the plates are drawn apart (the ‘contraction’, or ‘lifting plate’, problem), the boundary of the drop is subject to a fingering instability on a scale determined by surface tension. The effect of a trapped air bubble at the centre of the drop is then considered. The annular evolution of the drop under constant squeezing is still found to follow a ‘one-eighth’ power law, but this is unstable, the instability originating at the boundary of the air bubble, i.e. the inner boundary of the annulus. The air bubble is realised experimentally in two ways: first by simply starting with the drop in the form of an annulus, as nearly circular as possible; and second by forcing four initially separate drops to expand and merge, a process that involves the resolution of ‘contact singularities’ by surface tension. If the plates are drawn apart, the evolution is still subject to the fingering instability driven from the outer boundary of the annulus. This instability is realised experimentally by levering the plates apart at one corner: fingering develops at the outer boundary and spreads rapidly to the interior as the levering is slowly increased. At a later stage, before ultimate rupture of the film and complete separation of the plates, fingering spreads also from the boundary of any interior trapped air bubble, and small cavitation bubbles appear in the very low-pressure region, far from the point of leverage. This exotic behaviour is discussed in the light of the foregoing theoretical analysis.

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Section: Destabilising Effect Of Trapped Air Bubblementioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Spreading or contraction of viscous drops between plates: single, multiple or annular drops

Moffatt¹,

Guest²,

Huppert

2021

J. Fluid Mech.

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“…Linear stability analysis of viscous fingering with Newtonian fluids in ULHSC 22 showed that at a given radius ratio(ratio of the initial outer radius of fluid film and the initial inner radius of fluid film, in our case initial inner radius of the fluid film is taken as source hole radius), stability of the fluid film interface is governed by the non-dimensional number Ca/(h * ) 3 where Ca…”

Section: Stability Graphmentioning

confidence: 99%

“…Theoretical development in literature 22 presents linear stability analysis for Newtonian non-volatile fluid on ULHSC. The analytical expression for the dimensionless growth rate of the inner interface (ω * in ) in terms of non-dimensional parameters capillary number(Ca), aspect ratio(h * ), wavenumber(n), and radius ratio(γ) is given as…”

Section: Validation Of Stability Graph and Capturing The Effect Of Vo...mentioning

confidence: 99%

Viscous fingering in volatile fluid towards spontaneous evolution of well-ordered 3D patterns

Rakshe

Gandhi

2022

Preprint

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Mimicking nature using artificial technologies has always been a quest/fascination of scientists and researchers of all era. This paper characterizes viscous fingering instability-based, lithography-less, spontaneous, and scalable process for fabricating 3D patterns like a nature-inspired honeycomb structure with ultra-high aspect ratio walls. Rich experimental data on volatile fluids shaping in uniport and multiport lifted Hele-Shaw cells (ULHSC and MLHSC) obtained through extensive experiments is represented on a non-dimensional phase plot. The phase plot with five orders of magnitude variation of non-dimensional numbers on each axis demarcates the regions of several newly observed phenomena: ‘No retention’, ’Bridge breaking’, and ‘wall formation’ with ‘stable’ and ‘unstable’ evolution. A new non-dimensional ratio of the velocity of evaporating static interface vs. lifting velocity is proposed for the same. This work establishes a solid foundation with valuable insights for scalable manufacturing of devices useful for application in biomedical and other domains.

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“…Examples of passive control methods include manipulating the Hele-Shaw cell geometry ( Al-Housseiny and Stone, 2013 ; Bongrand and Tsai, 2018 ; Anjos et al., 2018 ; Morrow et al., 2019 ; Dias and Miranda, 2013a , 2013b ), using elasto-visco-plastic materials ( Eslami and Taghavi, 2017 ) and elastic-walled cells ( Pihler-Puzovic et al., 2012 , 2018 ; Al-Housseiny et al., 2013 ), employing large gap widths in Hele-Shaw cells ( Honda et al., 2006 ; Kollner et al., 2015 ; Maes et al., 2010 ; Islam and Gandhi, 2016 ), and modifying the wettability ( Trojer et al., 2015 ; Holtzman and Segre, 2015 ; Anjos et al., 2021 ). Active manipulation methods are achieved by adjusting the flow rate ( Li et al., 2009 ; Coutinho and Miranda, 2020 ; Dias et al., 2012 ; Arun et al., 2020 ), or gap thickness ( Zheng et al., 2015 ; Vaquero-Stainer et al., 2019 ) over time, or multiport lifted Hele-Shaw cells ( Kanhurkar et al., 2019 ) and harnessing electro-osmotic flows generated through applying electric fields ( Gao et al., 2019 ; Mirzadeh and Bazant, 2017 ; Anjos et al., 2022 ). Although both types of methods can achieve interfacial control, active methods are preferable in applications due to their simple operation.…”

Section: Introductionmentioning

confidence: 99%

Active control of electro-visco-fingering in Hele-Shaw cells using Maxwell stress

Li¹,

Huang²,

Zhao³

2022

iScience

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Stability of viscous fingering in lifted Hele-Shaw cells with a hole

Cited by 16 publications

References 27 publications

Spreading or contraction of viscous drops between plates: single, multiple or annular drops

Spreading or contraction of viscous drops between plates: single, multiple or annular drops

Viscous fingering in volatile fluid towards spontaneous evolution of well-ordered 3D patterns

Active control of electro-visco-fingering in Hele-Shaw cells using Maxwell stress

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