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On the control and suppression of the Rayleigh-Taylor instability using electric fields
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Cimpeanu, Radu, Papageorgiou, Demetrios and Petropoulos, Peter (2014) On the control and suppression of the Rayleigh-Taylor instability using electric fields. Physics of Fluids, 26 . 022105. doi:10.1063/1.4865674 ISSN 1070-6631.
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Official URL: https://doi.org/10.1063/1.4865674
Abstract
It is shown theoretically that an electric field can be used to control and suppress the classical Rayleigh-Taylor instability found in stratified flows when a heavy fluid lies above lighter fluid. Dielectric fluids of arbitrary viscosities and densities are considered and a theory is presented to show that a horizontal electric field (acting in the plane of the undisturbed liquid-liquid surface), causes growth rates and critical stability wavenumbers to be reduced thus shifting the instability to longer wavelengths. This facilitates complete stabilization in a given finite domain above a critical value of the electric field strength. Direct numerical simulations based on the Navier-Stokes equations coupled to the electrostatic fields are carried out and the linear theory is used to critically evaluate the codes before computing into the fully nonlinear stage. Excellent agreement is found between theory and simulations, both in unstable cases that compare growth rates and in stable cases that compare frequencies of oscillation and damping rates. Computations in the fully nonlinear regime supporting finger formation and roll-up show that a weak electric field slows down finger growth and that there exists a critical value of the field strength, for a given system, above which complete stabilization can take place. The effectiveness of the stabilization is lost if the initial amplitude is large enough or if the field is switched on too late. We also present a numerical experiment that utilizes a simple on-off protocol for the electric field to produce sustained time periodic interfacial oscillations. It is suggested that such phenomena can be useful in inducing mixing. A physical centimeter-sized model consisting of stratified water and olive oil layers is shown to be within the realm of the stabilization mechanism for field strengths that are approximately 2 × 104 V/m.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Navier-Stokes equations, Fluid mechanics -- Mathematical models, Viscous flow -- Mathematical models, Electrohydrodynamics | ||||||||||||
| Journal or Publication Title: | Physics of Fluids | ||||||||||||
| Publisher: | American Institute of Physics | ||||||||||||
| ISSN: | 1070-6631 | ||||||||||||
| Official Date: | 19 February 2014 | ||||||||||||
| Dates: |
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| Volume: | 26 | ||||||||||||
| Article Number: | 022105 | ||||||||||||
| DOI: | 10.1063/1.4865674 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Reuse Statement (publisher, data, author rights): | This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| Date of first compliant deposit: | 28 October 2019 | ||||||||||||
| Date of first compliant Open Access: | 30 October 2019 | ||||||||||||
| RIOXX Funder/Project Grant: |
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