Self-similar and disordered front propagation in a radial Hele-Shaw channel with time-varying cell depthCitation formats

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Self-similar and disordered front propagation in a radial Hele-Shaw channel with time-varying cell depth. / Vaquero-Stainer, Christian; Heil, Matthias; Juel, Anne; Pihler-Puzovic, Draga.

In: Physical Review Fluids, 06.06.2019.

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@article{8a2abd67ae37469cb9f28dc5089fc147,
title = "Self-similar and disordered front propagation in a radial Hele-Shaw channel with time-varying cell depth",
abstract = "The displacement of a viscous fluid by an air bubble in the narrow gap between two parallel plates can readily drive complex interfacial pattern formation known as viscous fingering. We focus on a modified system suggested recently by [1], in which the onset of the fingering instability is delayed by introducing a time-dependent (power-law) plate separation. We perform a complete linear stability analysis of a depth-averaged theoretical model to show that the plate separation delays the onset of non-axisymmetric instabilities, in qualitative agreement with the predictions obtained from a simplified analysis by [1]. We then employ direct numerical simulations to show that in the parameter regime where the axisymmetrically expanding air bubble is unstable to nonaxisymmetric perturbations, the interface can evolve in a self-similar fashion such that the interface shape at a given time is simply a rescaled version of the shape at an earlier time. These novel, self-similar solutions are linearly stable but they only develop if the initially circular interface is subjected to unimodal perturbations. Conversely, the application of non-unimodal perturbations (e.g. via the superposition of multiple linearly unstable modes) leads to the development of complex, constantly evolving finger patterns similar to those that are typically observed in constant-width Hele-Shaw cells.",
author = "Christian Vaquero-Stainer and Matthias Heil and Anne Juel and Draga Pihler-Puzovic",
year = "2019",
month = jun,
day = "6",
doi = "10.1103/PhysRevFluids.4.064002",
language = "English",
journal = "Physical Review Fluids",
issn = "2469-990X",
publisher = "American Physical Society",

}

RIS

TY - JOUR

T1 - Self-similar and disordered front propagation in a radial Hele-Shaw channel with time-varying cell depth

AU - Vaquero-Stainer, Christian

AU - Heil, Matthias

AU - Juel, Anne

AU - Pihler-Puzovic, Draga

PY - 2019/6/6

Y1 - 2019/6/6

N2 - The displacement of a viscous fluid by an air bubble in the narrow gap between two parallel plates can readily drive complex interfacial pattern formation known as viscous fingering. We focus on a modified system suggested recently by [1], in which the onset of the fingering instability is delayed by introducing a time-dependent (power-law) plate separation. We perform a complete linear stability analysis of a depth-averaged theoretical model to show that the plate separation delays the onset of non-axisymmetric instabilities, in qualitative agreement with the predictions obtained from a simplified analysis by [1]. We then employ direct numerical simulations to show that in the parameter regime where the axisymmetrically expanding air bubble is unstable to nonaxisymmetric perturbations, the interface can evolve in a self-similar fashion such that the interface shape at a given time is simply a rescaled version of the shape at an earlier time. These novel, self-similar solutions are linearly stable but they only develop if the initially circular interface is subjected to unimodal perturbations. Conversely, the application of non-unimodal perturbations (e.g. via the superposition of multiple linearly unstable modes) leads to the development of complex, constantly evolving finger patterns similar to those that are typically observed in constant-width Hele-Shaw cells.

AB - The displacement of a viscous fluid by an air bubble in the narrow gap between two parallel plates can readily drive complex interfacial pattern formation known as viscous fingering. We focus on a modified system suggested recently by [1], in which the onset of the fingering instability is delayed by introducing a time-dependent (power-law) plate separation. We perform a complete linear stability analysis of a depth-averaged theoretical model to show that the plate separation delays the onset of non-axisymmetric instabilities, in qualitative agreement with the predictions obtained from a simplified analysis by [1]. We then employ direct numerical simulations to show that in the parameter regime where the axisymmetrically expanding air bubble is unstable to nonaxisymmetric perturbations, the interface can evolve in a self-similar fashion such that the interface shape at a given time is simply a rescaled version of the shape at an earlier time. These novel, self-similar solutions are linearly stable but they only develop if the initially circular interface is subjected to unimodal perturbations. Conversely, the application of non-unimodal perturbations (e.g. via the superposition of multiple linearly unstable modes) leads to the development of complex, constantly evolving finger patterns similar to those that are typically observed in constant-width Hele-Shaw cells.

U2 - 10.1103/PhysRevFluids.4.064002

DO - 10.1103/PhysRevFluids.4.064002

M3 - Article

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

ER -