Condensed Matter


Solution to the Poisson Boltzmann Equation Involving Various Spherical Geometries

Authors: Rajib Chakraborty

The distribution of free charges within fluids or plasma is often modeled using linearized Poisson-Boltzmann equation (PBE). However, this author has recently shown that the usual boundary conditions (BC), namely the Dirichlet condition and the Neumann condition cannot be used to solve the PBE due to some physical reasons. This author has used the BC of `mixed' type to obtain the physical solution to the 1-D PBE and derived the charged density distribution $\rho_e$ within {\it rectangular} and {\it cylindrical} geometries before. Here the 1-D formulae of $\rho_e$ (i) within, (ii) between and (iii) outside {\it spherical} geometries has been derived. The result shows that the electric field is high at the surface of small objects, immersed in electrolyte solution. These formulae could be very useful in explaining similar physical situations that are found in nature or made in the laboratories.

Comments: 6 Pages.

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Submission history

[v1] 2019-05-13 12:04:56

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