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.

Download: PDF

Submission history

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

Unique-IP document downloads: 10 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus