Shear electroconvective instability in electrodialysis channel under extreme depletion and its scaling laws

Liu, Wei; Zhou, Yueting; Shi, Pengpeng

doi:10.1103/physreve.101.043105

Cited by 21 publications

(15 citation statements)

References 34 publications

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“…EC patterns have also been observed in liquid crystals when induced by an alternating current [23,25]. In charge-neutral electrokinetic (EK) systems, electroconvection is triggered by the electro-osmotic slip of the electrolyte in the electric double layer at membrane surfaces [19,20,[26][27][28][29][30][31][32][33][34][35][36]. In non-equilibrium EHD systems [18,[37][38][39][40][41][42][43][44], poorly conductive and leaky dielectric fluid acquires unipolar charge injection at the interface in response to the electric field.…”

Section: Introductionmentioning

confidence: 99%

Sparse nonlinear models of chaotic electroconvection

2021

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Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modelling convection has given rise to the development of chaos theory and the reduced-order modelling of multiphysics systems; however, these models have been limited to relatively simple thermal convection phenomena. In this work, we develop a reduced-order model for chaotic electroconvection at high electric Rayleigh number. The chaos in this system is related to the standard Lorenz model obtained from Rayleigh–Benard convection, although our system is driven by a more complex three-way coupling between the fluid, the charge density, and the electric field. Coherent structures are extracted from temporally and spatially resolved charge density fields via proper orthogonal decomposition (POD). A nonlinear model is then developed for the chaotic time evolution of these coherent structures using the sparse identification of nonlinear dynamics (SINDy) algorithm, constrained to preserve the symmetries observed in the original system. The resulting model exhibits the dominant chaotic dynamics of the original high-dimensional system, capturing the essential nonlinear interactions with a simple reduced-order model.

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Section: Introductionmentioning

confidence: 99%

Sparse nonlinear models of chaotic electroconvection

2021

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“…Other instabilities including the electroconvective instability in channels have been investigated; see, e.g. Liu et al, 32 and references therein. Despite the intensive investigation yielding detailed information and the reasonable success, little is known about the non‐electroneutral phenomenon near the charged surface.…”

Section: Introductionmentioning

confidence: 99%

Near‐ and far‐field expansions for stationary solutions of Poisson‐Nernst‐Planck equations

Lyu

Lee

Lin

2021

Math Methods in App Sciences

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This work is concerned with the stationary Poisson‐Nernst‐Planck equation with a large parameter which describes a huge number of ions occupying an electrolytic region. First, we focus on the model with a single specie of positive charges in one‐dimensional bounded domains due to the assumption that these ions are transported in the same direction along a tubular‐like mircodomain. We show that the solution asymptotically blows up in a thin region attached to the boundary and establishes the refined “near‐field” and “far‐field” expansions for the solutions with respect to the parameter. Moreover, we obtain the boundary concentration phenomenon of the net charge density, which mathematically confirms the physical description that the non‐neutral phenomenon occurs near the charged surface. In addition, we revisit a charge‐conserving Poisson‐Boltzmann model for monovalent binary ions and establish a novel comparison for these two models.

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“…To simulate desalination with intensive currents, it is necessary to consider the entire desalination channel formed by the AEM and CEM. Liu et al [14] numerically investigated such a system taking into account electroconvective instability and showed that the operation of the system in this mode leads to a decrease in the mass transfer rate and the formation of a peak on the current-voltage characteristic of the system Numerical modeling of the mass transfer process in the membrane system until complete desalination of the electrolyte solution was carried out in the article [15]. For this purpose, a 1D model of the desalination of the quiescent electrolyte layer between AEM and CEM under the action of an electric field was built.…”

Section: Introductionmentioning

confidence: 99%

“…The above-mentioned studies [14][15][16] were carried out for the potentiostatic and potentiodynamic modes, when the potential drop in the system is set, while experimental research and operation of membrane systems generally occurs in galvanostatic (or galvanodynamic) modes [17]. The objective of this work is a theoretical analysis of the basic regularities of the space-charge breakdown on the basis of a mathematical model of the desalination process in the galvanostatic mode.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of the Phenomenon of Space-Charge Breakdown in the Galvanostatic Mode in the Section of the Electromembrane Desalination Channel

Uzdenova

Уртенов

2021

Membranes

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One of the ways to increase the efficiency of the desalination process in membrane systems is to use intensive current modes. Recently, the phenomenon of space-charge breakdown was theoretically described for desalination under intensive current modes. The space-charge breakdown is a decrease in the magnitude and size of the extended space charge regions (SCRs) of opposite signs, formed at the cation- and anion-exchange membranes in the desalination channel, when they approach each other. Therefore, this phenomenon negatively affects the intensity of electroconvection and the efficiency of mass transfer in membrane systems. We report the results of the first theoretical analysis of the space-charge breakdown in the galvanostatic electric mode, which is generally used in the research and operation of membrane systems. For this purpose, a one-dimensional model of the ion transfer of the electrolyte solution in the section of the desalination channel at the direct current is developed. The regularities of changes in the extended SCRs in the galvanostatic mode are determined. A relation is obtained for the onset time of the space-charge breakdown, which makes it possible to determine the parameters of the effective operation of the membrane system.

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Shear electroconvective instability in electrodialysis channel under extreme depletion and its scaling laws

Cited by 21 publications

References 34 publications

Sparse nonlinear models of chaotic electroconvection

Sparse nonlinear models of chaotic electroconvection

Near‐ and far‐field expansions for stationary solutions of Poisson‐Nernst‐Planck equations

Mathematical Modeling of the Phenomenon of Space-Charge Breakdown in the Galvanostatic Mode in the Section of the Electromembrane Desalination Channel

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