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Related Concept Videos

The Electrical Double Layer01:30

The Electrical Double Layer

In the region where two bulk phases meet, an intricate electric charge distribution arises due to charge transfer, ion adsorption, molecular orientation, and charge distortion. This complex distribution is commonly referred to as the electrical double layer.When a solid electrode interfaces with ions in an electrolyte solution, the speed of electron transfer dictates the rates of oxidation and reduction. The electrode acquires a charge through the escape of atoms into the solution as cations or...
Electric Field of Parallel Conducting Plates01:16

Electric Field of Parallel Conducting Plates

Gauss' law relates the electric flux through a closed surface to the net charge enclosed by that surface. Gauss's law can be applied to find the electric field and the charge enclosed in a region depending on its charge distribution.
Consider a cross-section of a thin, infinite conducting plate having a positive charge. For such a large thin plate, as the thickness of the plate tends to zero, the positive charges lie on the plate's two large faces. Without an external electric field, the...
Electric Field of a Charged Disk01:23

Electric Field of a Charged Disk

The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
The system's symmetry is in the cylindrical directions across the plane of the charge. As a result, the electric fields created by various surface charge elements nullify each other in the direction parallel to the surface. Thereby, the resulting electric field is perpendicular to the plane. Since the disk is...
Equipotential Surfaces and Conductors01:16

Equipotential Surfaces and Conductors

For a conductor in which all charges are at rest, the conductor's surface is equipotential. The electric field is always perpendicular to equipotential surfaces. Therefore, in a conductor with static charges, the electric field just outside the conductor is always perpendicular to the conductor's surface. Any tangential component of the electric field will cause charges to move inside the conductor, which will violate the electrostatic nature of the system. In an electrostatic situation, if a...
Electric Field Inside a Conductor01:20

Electric Field Inside a Conductor

When a conductor is placed in an external electric field, the free charges in the conductor redistribute and very quickly reach electrostatic equilibrium. The resulting charge distribution and its electric field have many interesting properties, which can be investigated with the help of Gauss's law.
Suppose a piece of metal is placed near a positive charge. The free electrons in the metal are attracted to the external positive charge and migrate freely toward that region. This region then has...
Electric Field at the Surface of a Conductor01:26

Electric Field at the Surface of a Conductor

Consider a conductor in electrostatic equilibrium. The net electric field inside a conductor vanishes, and extra charges on the conductor reside on its outer surface, regardless of where they originate.
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Related Experiment Video

Updated: Jun 14, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Effective zero-thickness model for a conductive membrane driven by an electric field.

Falko Ziebert1, Martin Z Bazant, David Lacoste

  • 1Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI, 10 rue Vauquelin, F-75231 Paris, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary

A new theoretical model describes conductive membranes in electric fields. This model predicts membrane instability and fluid flow, simplifying analysis and aligning with experimental results.

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Area of Science:

  • Physics
  • Materials Science
  • Electrochemistry

Background:

  • Conductive membranes are crucial in various electrochemical and fluidic systems.
  • Understanding their behavior in electric fields is essential for device optimization.
  • Existing models often lack generality or simplicity for complex analyses.

Purpose of the Study:

  • To develop a simplified yet general theoretical model for conductive membranes in static electric fields.
  • To investigate charge accumulation, elastic property changes, and potential instabilities.
  • To analyze associated fluid flow patterns and compare with experimental data.

Main Methods:

  • A zero-thickness membrane model was constructed using a Robin-type boundary condition for electric potential.
  • Theoretical analysis was performed to derive corrections to elastic moduli due to capacitive effects and currents.
  • Fluid flow surrounding the membrane was calculated and compared to induced charge electro-osmosis (ICEO) phenomena.

Main Results:

  • The model predicts corrections to elastic moduli, leading to potential undulation instability.
  • Fluid flow patterns were characterized and found similar to ICEO.
  • The model effectively describes nonequilibrium steady states of the membrane and surrounding fluid.

Conclusions:

  • The developed zero-thickness model offers a simpler and more general approach compared to previous methods.
  • The theoretical predictions show good agreement with recent experimental findings on supported membranes.
  • This framework advances the understanding of conductive membrane behavior under electric field influence.