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Electrified cone formation in perfectly conducting viscous liquids: Self-similar growth irrespective of Reynolds number

Albertson, Theodore G. and Troian, Sandra M. (2019) Electrified cone formation in perfectly conducting viscous liquids: Self-similar growth irrespective of Reynolds number. Physics of Fluids, 31 (10). Art. No. 102103. ISSN 1070-6631. https://resolver.caltech.edu/CaltechAUTHORS:20191014-142854756

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Abstract

Above a critical field strength, the free surface of an electrified, perfectly conducting viscous liquid, such as a liquid metal, is known to develop an accelerating protrusion resembling a cusp with a conic tip. Field self-enhancement from tip sharpening is reported to generate divergent power law growth in finite time of the forces acting in that region. Previous studies have established that tip sharpening proceeds via a self-similar process in two distinguished limits—the Stokes regime and the inviscid regime. Using finite element simulations to track the shape and forces acting at the tip of an electrified protrusion in a perfectly conducting Newtonian liquid, we demonstrate that the conic tip always undergoes self-similar growth irrespective of the Reynolds number. The blowup exponents at the conic apex for all terms in the Navier-Stokes equation and the normal stress boundary condition at the moving interface reveal the dominant forces at play as the Reynolds number increases. Rescaling of the tip shape by the power law representing the divergence in capillary stress at the apex yields an excellent collapse onto a universal cone shape with an interior half-angle dependent on the Maxwell stress. The rapid acceleration of the liquid interface also generates a thin interfacial boundary layer characterized by a significant rate of strain. Additional details of the modeled flow, applicable to cone growth in systems such as liquid metal ion sources, help dispel prevailing misconceptions that dynamic cones resemble conventional Taylor cones or that viscous stresses at a finite Reynolds number can be neglected.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1063/1.5123742DOIArticle
https://arxiv.org/abs/1908.04377arXivDiscussion Paper
ORCID:
AuthorORCID
Troian, Sandra M.0000-0003-1224-6377
Additional Information:© 2019 Published under license by AIP Publishing. Submitted: 8 August 2019; Accepted: 18 September 2019; Published Online: 14 October 2019. The authors gratefully acknowledge financial support from a 2014 NASA Space Technology Research Fellowship (T.G.A.) and the NASA/Jet Propulsion Laboratory (JPL) President’s and Director’s Fund (S.M.T.). T.G.A. also wishes to thank Andy Ylitalo (2016 Caltech Summer Undergraduate Research Fellow) for assistance with the numerical simulations during early stages of this work and fellow office mate Chengzhe Zhou for helpful and interesting discussions about electrified liquid behavior.
Funders:
Funding AgencyGrant Number
NASA Space Technology Research FellowshipUNSPECIFIED
JPL President and Director's FundUNSPECIFIED
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Issue or Number:10
Record Number:CaltechAUTHORS:20191014-142854756
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191014-142854756
Official Citation:Electrified cone formation in perfectly conducting viscous liquids: Self-similar growth irrespective of Reynolds number. Theodore G. Albertson and Sandra M. Troian. Physics of Fluids 31:10. https://doi.org/10.1063/1.5123742
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99260
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Oct 2019 21:37
Last Modified:05 Oct 2020 16:57

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