Density of electric field energy around two surface-charged spheres surrounded by electrolyte I. The spheres are separated from each other

István P. Sugár; István P. Sugár

doi:10.3934/biophy.2022008

AIMS Biophysics

2022, Volume 9, Issue 2: 86-95. doi: 10.3934/biophy.2022008

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Density of electric field energy around two surface-charged spheres surrounded by electrolyte I. The spheres are separated from each other

István P. Sugár ^,

Department of Neurology, Icahn School of Medicine at Mount Sinai, New York, NY 10029

Received: 20 January 2022 Revised: 16 March 2022 Accepted: 21 March 2022 Published: 24 March 2022

Based on the generalized version of Newton's Shell Theorem the electric field energy density, u_F around two separated surface-charged spheres surrounded by electrolyte is calculated. According to the calculations when the surfaces of the charged spheres are farther from each other than four times of the Debye length the field energy density around one of the charged sphere is basically independent from the presence of the other sphere. In this case at low electrolyte ion concentration u_F = 0 within the spheres and outside the sphere u_F decreases with increasing distance from the surface of the sphere, while at high electrolyte ion concentration u_F fast decreases with increasing inner and outer distance from the surface of the sphere. When the charged sheres are close to each other their electric interaction affects the field energy density especially where the surfaces of the spheres are close to each other. Also to model electrophoresis analytical equations are derived for the interaction energy between and the density of electric field energy around a charged flat surface and a charged sphere surrounded by neutral electrolyte.
- Screened Poisson Equation,
- Debye length,
- density of electric field energy
Citation: István P. Sugár. Density of electric field energy around two surface-charged spheres surrounded by electrolyte I. The spheres are separated from each other[J]. AIMS Biophysics, 2022, 9(2): 86-95. doi: 10.3934/biophy.2022008

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Abstract

Based on the generalized version of Newton's Shell Theorem the electric field energy density, u_F around two separated surface-charged spheres surrounded by electrolyte is calculated. According to the calculations when the surfaces of the charged spheres are farther from each other than four times of the Debye length the field energy density around one of the charged sphere is basically independent from the presence of the other sphere. In this case at low electrolyte ion concentration u_F = 0 within the spheres and outside the sphere u_F decreases with increasing distance from the surface of the sphere, while at high electrolyte ion concentration u_F fast decreases with increasing inner and outer distance from the surface of the sphere. When the charged sheres are close to each other their electric interaction affects the field energy density especially where the surfaces of the spheres are close to each other. Also to model electrophoresis analytical equations are derived for the interaction energy between and the density of electric field energy around a charged flat surface and a charged sphere surrounded by neutral electrolyte.

Acknowledgments

The author is very thankful for Chinmoy Kumar Ghose.

Conflict of interest

The author declares no conflict of interest.

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