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Deterministic and stochastic bifurcations in two-dimensional electroconvective flows

Published online by Cambridge University Press:  12 July 2021

Zhe Feng Open the ORCID record for Zhe Feng [Opens in a new window] ,
Mengqi Zhang Open the ORCID record for Mengqi Zhang [Opens in a new window] ,
Pedro A. Vazquez Open the ORCID record for Pedro A. Vazquez [Opens in a new window]  and
Chang Shu Open the ORCID record for Chang Shu [Opens in a new window]
Zhe Feng
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575Republic of Singapore
Mengqi Zhang*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575Republic of Singapore
Pedro A. Vazquez
Affiliation:
Departamento de Física Aplicada III, Universidad de Sevilla, ESI, Camino de los Descubrimientos s/n, 41092Sevilla, Spain
Chang Shu
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575Republic of Singapore
*
†Email address for correspondence: [email protected]
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Abstract

We investigate deterministic and stochastic bifurcations in electroconvecitve flows of a dielectric liquid confined between two parallel plates subjected to a strong unipolar injection by direct numerical simulations. A long-standing discrepancy of linear instability criteria between the experiment and theory exists in this flow. We here test the hypothesis that the discrepancy may be related to the inhomogeneity in ion-exchange membranes used in experiments, contrasted by the homogeneous ion injection assumed in theoretical and numerical analyses. To study this effect, we consider stochastic boundary conditions around linear criticality and first bifurcations in this flow. For a complete presentation of flow bifurcations, deterministic bifurcation analysis (without stochasticity) is first performed to investigate primary bifurcations in this flow by progressively increasing the strength of electric field. Lyapunov spectrum and dimension are calculated and probed to characterise the chaotic motion therein. Our results confirm the high dimensionality of chaos in electroconvective flows and reveal for the first time that its chaos is extensive in a range of finite-sized systems. We then conduct stochastic bifurcation analyses by considering random perturbations in the boundary conditions of charge density and electric potential. Owing to the subcritical nature of electroconvective flows, the linear instability criteria under stochastic boundaries are closer to the experimental values than former theoretical and numerical results (assuming the homogeneous charge injection) for different levels of stochasticity, which confirms the hypothesis aforementioned. Furthermore, stochasticity can also enhance the efficiency of ionic transport.

JFM classification

Complex Fluids: Dielectrics Nonlinear Dynamical Systems: Bifurcation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 922 , 10 September 2021 , A20
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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