Rotating Hele-Shaw cell with a time-dependent angular velocity

Anjos, Pedro H. A.; Alvarez, V. M. Martinez; Dias, Eduardo O.; Miranda, José A.

doi:10.1103/physrevfluids.2.124003

Cited by 13 publications

(7 citation statements)

References 44 publications

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“…For that scenario, both the lifting and centrifugal configurations produce fingers which appear to be distinct from traditional Saffman-Taylor fingers. These problems with the complementary geometry have been studied through a combination of experimental, analytical, and numerical techniques (Alvarez-Lacalle et al 2004;Anjos et al 2017;Carrillo et al 1996Carrillo et al , 1999Chen et al 2005;Gadêlha & Miranda 2004;Lindner et al 2005;Nase et al 2011;Shelley et al 1997), but will not be pursued here.…”

Section: Governing Equationsmentioning

confidence: 99%

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Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

2019

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Viscous fingering experiments in Hele-Shaw cells lead to striking pattern formations which have been the subject of intense focus among the physics and applied mathematics community for many years. In recent times, much attention has been devoted to devising strategies for controlling such patterns and reducing the growth of the interfacial fingers. We continue this research by reporting on numerical simulations, based on the level set method, of a generalised Hele-Shaw model for which the geometry of the Hele-Shaw cell is altered. First, we investigate how imposing constant and time-dependent injection rates in a Hele-Shaw cell that is either standard, tapered or rotating can be used to reduce the development of viscous fingering when an inviscid fluid is injected into a viscous fluid over a finite time period. We perform a series of numerical experiments comparing the effectiveness of each strategy to determine how these non-standard Hele-Shaw configurations influence the morphological features of the inviscid-viscous fluid interface. Surprisingly, a converging or diverging taper of the plates leads to reduced metrics of viscous fingering at the final time when compared to the standard parallel configuration, especially with carefully chosen injection rates; for the rotating plate case, the effect is even more dramatic, with sufficiently large rotation rates completely stabilising the interface. Next, we illustrate how the number of non-splitting fingers can be controlled by injecting the inviscid fluid at a time-dependent rate while increasing the gap between the plates. Our simulations compare well with previous experimental results for various injection rates and geometric configurations. We demonstrate how the number of non-splitting fingers agrees with that predicted from linear stability theory up to some finger number; for larger values of our control parameter, the fully nonlinear dynamics of the problem lead to slightly fewer fingers than this linear prediction. † Email address for correspondence: scott.mccue@qut.edu.au arXiv:1901.00288v4 [physics.flu-dyn] 7 Jul 2019 , (5.3)

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Section: Governing Equationsmentioning

confidence: 99%

“…1999; Alvarez-Lacalle, Ortın & Casademunt 2004; Gadêlha & Miranda 2004; Chen, Chen & Miranda 2005; Lindner, Derks & Shelley 2005; Dias & Miranda 2010; Nase, Derks & Lindner 2011; Anjos et al. 2017), but will not be pursued here.…”

Section: Mathematical Modelmentioning

confidence: 99%

Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

2019

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“…Recent studies in isotropic environments have identified the viscosity ratio as an important control parameter that governs not only the onset of the instability, [46][47][48][49][50] but also the global features of the patterns introducing a second length scale, the radius of a central region of complete outer-fluid displacement that grows concomitantly with the fingers. 49,[51][52][53] This central region becomes increasingly larger, and therefore the relative length of the fingers increasingly smaller, as the viscosity ratio between the two fluids increases. Here we show that a morphology transition from dense-branching to dendritic growth can occur over a large range of viscosity ratios.…”

Section: Introductionmentioning

confidence: 99%

Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments

et al. 2021

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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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Rotating Hele-Shaw cell with a time-dependent angular velocity

Cited by 13 publications

References 44 publications

Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments

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

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