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Nonlinear Poisson-Boltzmann equation in spherical symmetry
V I Vishnyakov1, G S Dragan, V M Evtuhov
1Mechnikov Odessa National University, Odessa 65082, Ukraine.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
Summary
The Poisson-Boltzmann equation in spherical symmetry was analyzed for charged grains in plasma. Electrical interactions between grains are limited to distances within eight screening lengths.
Area of Science:
- Plasma Physics
- Physical Chemistry
- Computational Physics
Background:
- The Poisson-Boltzmann equation describes electrostatic interactions in plasmas.
- Understanding potential distribution around charged particles is crucial for plasma behavior.
- Spherical symmetry is a common simplification for modeling charged grains.
Purpose of the Study:
- To analyze solutions to the Poisson-Boltzmann problem in spherical symmetry.
- To investigate the self-consistent potential distribution around a charged grain.
- To determine the range of electrical interactions between charged grains.
Main Methods:
- Analytical solutions of the Poisson-Boltzmann equation.
- Asymptotic analysis of potential distribution.
- Modeling of charged grain interactions in a thermal collisional plasma.
Main Results:
- Qualitative patterns of all possible solutions were presented.
- Asymptotic behavior of the potential was studied.
- It was shown that grain surface curvature can be neglected for large potentials, simplifying the problem to a planar case.
- Electrical interaction between grains is significant only within eight screening lengths.
Conclusions:
- The study provides insights into the electrostatic behavior of charged grains in plasma.
- The findings simplify the analysis of charged grain interactions by allowing the use of planar approximations under certain conditions.
- The range of effective electrical interaction between charged grains is quantitatively defined.
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