Electrokinetic Control of Viscous Fingering

Mirzadeh, Mohammad; Bazant, Martin Z.

doi:10.1103/physrevlett.119.174501

Cited by 51 publications

(51 citation statements)

References 54 publications

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“…Indeed, a simple analysis of this mechanism leads to the generalized stability condition 33 , as follows. In a Hele-Shaw cell, the depth-averaged hydraulic velocity is related to the pressure gradient, G = −∇ p , via u h = K h G , where K h = h 2 /12 μ is the hydraulic conductivity and h is the gap thickness.…”

Section: Resultsmentioning

confidence: 99%

Active control of viscous fingering using electric fields

et al. 2019

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Viscous fingering is a widely observed phenomenon, in which finger-like instabilities occur at the interface of two fluids, whenever a less viscous phase displaces a more viscous phase. This instability is notoriously difficult to control, especially for given viscosity ratio and geometry. Here we demonstrate experimentally the active control of viscous fingering of two given liquids, for given geometry and flow rate in a Hele-Shaw cell. The control is realized by taking advantage of electro-osmotic flows along the surfaces confining the fluid, via applying an external electric field. Depending on the direction of electric field, the induced secondary electro-osmotic flows either assist or oppose the hydraulic flow, effectively reducing or increasing the flow resistance, leading to the control of interface stability. The mechanism of apparent “electrokinetic thinning/thickening” is proposed to explain the experimental observations. Theoretical predictions of linear stability are confirmed experimentally for a broad range of immiscible electrolyte displacements.

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Section: Resultsmentioning

confidence: 99%

Active control of viscous fingering using electric fields

et al. 2019

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“…The immiscible fluids are separated by a sharp interface, which becomes increasingly unstable as it expands, forming distinct viscous fingering patterns characterised by their branching and tip-splitting morphology. describe these processes (Ben-Jacob & Garik 1990;Liang 1986;Li et al 2004;Mirzadeh & Bazant 2017).…”

Section: Introductionmentioning

confidence: 99%

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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“…Here, we focus on morphological stability analysis in which linear stability analysis is used to analyze morphological instabilities of interfaces formed between different phases observed in various diverse phenomena such as electrodeposition [2,[9][10][11][12][13][14][15], solidification [1][2][3]9] and morphogenesis [3,16]. Some particular examples of morphological stability analysis include the Saffman-Taylor instability (viscous fingering) [17][18][19][20], viscous fingering coupled with electrokinetic effects [21], the Mullins-Sekerka instability of a spherical particle during diffusion-controlled or thermally controlled growth [22] and of a planar interface during solidification of a dilute binary alloy [23,24], and control of phase separation using electro-autocatalysis or electro-autoinhibition in driven open electrochemical systems [25,26].…”

Section: Introductionmentioning

confidence: 99%

Linear Stability Analysis of Transient Electrodeposition in Charged Porous Media: Suppression of Dendritic Growth by Surface Conduction

Khoo

Zhao

Bazant

2019

J. Electrochem. Soc.

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We study the linear stability of transient electrodeposition in a charged random porous medium, whose pore surface charges can be of any sign, flanked by a pair of planar metal electrodes. Discretization of the linear stability problem results in a generalized eigenvalue problem for the dispersion relation that is solved numerically, which agrees well with the analytical approximation obtained from a boundary layer analysis valid at high wavenumbers. Under galvanostatic conditions in which an overlimiting current is applied, in the classical case of zero surface charges, the electric field at the cathode diverges at Sand's time due to electrolyte depletion. The same phenomenon happens for positive charges but earlier than Sand's time. However, negative charges allow the system to sustain an overlimiting current via surface conduction past Sand's time, keeping the electric field bounded. Therefore, at Sand's time, negative charges greatly reduce surface instabilities and suppress dendritic growth, while zero and positive charges magnify them. We compare theoretical predictions for overall surface stabilization with published experimental data for copper electrodeposition in cellulose nitrate membranes and demonstrate good agreement between theory and experiment. We also apply the stability analysis to how crystal grain size varies with duty cycle during pulse electroplating.

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Electrokinetic Control of Viscous Fingering

Cited by 51 publications

References 54 publications

Active control of viscous fingering using electric fields

Active control of viscous fingering using electric fields

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

Linear Stability Analysis of Transient Electrodeposition in Charged Porous Media: Suppression of Dendritic Growth by Surface Conduction

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