Use of stream functions for the computation of currents in thin circuits determination of the impedances

Bandelier, B.; Daveau, Christian; Ashtiani, Payam; Rais, A.; Rioux‐Damidau, F.

doi:10.1109/20.877558

Cited by 7 publications

(3 citation statements)

References 5 publications

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“…Apparently, the first to introduce the stream function for modeling electric current was G. Taylor et al They used the mathematical analogy between the flow of fluid and that of electric current to solve problems of fluid mechanics. Later on, a rather large number of studies have applied stream functions for simulation of electric current density distribution in different media: in semiconductors, in superconductors, in thin circuits, on the earth’s surface, and in electromagnetic devices and other systems. In membrane electrochemistry this method was applied only by Pismensky et al The aim of this paper is to show how the advantages of the stream function approach can be used in modeling transient ion transfer at an electrically heterogeneous surface.…”

Section: Introductionmentioning

confidence: 99%

Chronopotentiometric Response of an Electrically Heterogeneous Permselective Surface: 3D Modeling of Transition Time and Experiment

et al. 2016

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Understanding of the current density distribution over an electrically heterogeneous surface and its effect on ion transport represents an important issue in electrochemistry, composite materials, geophysics, and some other domains. We report an approach for three-dimensional (3D) modeling (with cylindrical symmetry) of transient ion transfer across a surface composed of conductive and nonconductive areas. In the model formulation and solution we use the electrical current stream function. It allows setting the integral boundary condition for electric current at a heterogeneous surface without any restrictions on the local current density distribution. A very good agreement is found between the numerical solution and the experimental transition time determined from chronopotentiograms. The use of a specially designed membrane allows computation without fitted parameters. We show that the application of specific simplifications for the current density distribution over the surface (uniform distribution throughout all the surface or its conductive area, neglect of tangential current density) results in essential deviations from experimental transition time.

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Section: Introductionmentioning

confidence: 99%

Chronopotentiometric Response of an Electrically Heterogeneous Permselective Surface: 3D Modeling of Transition Time and Experiment

et al. 2016

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“…They used the mathematical analogy between the flow of fluid and that of electric current. Later on, this approach was applied for simulation of electric current density distribution in semiconductors [307], in superconductors [308], in thin circuits [309], on the earth's surface [310], in electromagnetic devices [311] and other systems. In membrane systems, this method was applied by Pismensky et al [312] and Mareev et al [303].…”

Section: The Use Of Electric Current Stream Function Comparison Withmentioning

confidence: 99%

Modelling of Ion Transport in Electromembrane Systems: Impacts of Membrane Bulk and Surface Heterogeneity

et al. 2018

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Artificial charged membranes, similar to the biological membranes, are self-assembled nanostructured materials constructed from macromolecules. The mutual interactions of parts of macromolecules leads to phase separation and appearance of microheterogeneities within the membrane bulk. On the other hand, these interactions also cause spontaneous microheterogeneity on the membrane surface, to which macroheterogeneous structures can be added at the stage of membrane fabrication. Membrane bulk and surface heterogeneity affect essentially the properties and membrane performance in the applications in the field of separation (water desalination, salt concentration, food processing and other), energy production (fuel cells, reverse electrodialysis), chlorine-alkaline electrolysis, medicine and other. We review the models describing ion transport in ion-exchange membranes and electromembrane systems with an emphasis on the role of micro-and macroheterogeneities in and on the membranes. Irreversible thermodynamics approach, "solution-diffusion" and "pore-flow" models, the multiphase models built within the effective-medium approach are examined as the tools for describing ion transport in the membranes. 2D and 3D models involving or not convective transport in electrodialysis cells are presented and analysed. Some examples are given when specially designed surface heterogeneity on the membrane surface results in enhancement of ion transport in intensive current electrodialysis.Recently, Svoboda et al. [13] developed a specific scanning cell for the analysis of heterogeneous IEM structure by micro-computed tomography, which provides volume reconstruction of the studied material. The unique working principle of the cell allows one to scan membranes not only in their dry state but also in fully swollen state. The micro-computed tomography showed that there are profound changes in the structure of the IEM associated with their transition from the dry state into the swollen one. This study applied to the heterogeneous cation-exchange membrane (CEM) coming from Mega a.s., Czech Republic showed that swelling of the membrane is caused by the swelling of the ion-exchange resin. Its volume increased nearly three times after exposure to deionized water, while the overall membrane volume increased by 50%. If the membrane contained approximately 28%vol. of the resin in the dry state, this content increased to 52%vol. after swelling.Micro-computed tomography not only allows one to analyse volumetric composition of the membrane bulk but also to quantify the composition of the surface. By using two different methods, Vobecka et al. [14] evaluated the fraction of the conductive area (e.g., the ion-exchange resin) on the surface of an AEM and CEM in the swollen state. The obtained results showed that the volume fraction of the conductive domains does not correspond to the surface fraction of these domains and thus the volume composition is not reflected on their surface. For example, the volume fraction of the conductive domains for the st...

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“…The use of stream function for the characterization of surface current densities has been widely employed [1]. The BEM has been proved to be an excellent tool in the solution of electromagnetic problems [2,3]; and the incorporation of the stream function into a numerical computational technique, such us BEM, has also been already considered for the solution of electromagnetic inverse problems [4].…”

Section: Introductionmentioning

confidence: 99%

A Divergence-Free Bem Method to Model Quasi-Static Currents: Application to Mri Coil Design

Sánchez¹,

Barrio‐García²,

Angulo³

et al. 2010

PIER B

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The modeling of quasi-static optimization problems often involves divergence-free surface current densities. In this paper, a novel technique to implement these currents by using the boundary element method framework is presented. A locally-based characterization of the current density is employed, to render a fully geometry-independent formulation, so that it can be applied to arbitrary shapes. To illustrate the versatility of this approach, we employ it for the design of gradient coils for MRI, providing a solid mathematical framework for this type of problem.

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Use of stream functions for the computation of currents in thin circuits determination of the impedances

Cited by 7 publications

References 5 publications

Chronopotentiometric Response of an Electrically Heterogeneous Permselective Surface: 3D Modeling of Transition Time and Experiment

Chronopotentiometric Response of an Electrically Heterogeneous Permselective Surface: 3D Modeling of Transition Time and Experiment

Modelling of Ion Transport in Electromembrane Systems: Impacts of Membrane Bulk and Surface Heterogeneity

A Divergence-Free Bem Method to Model Quasi-Static Currents: Application to Mri Coil Design

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