The three-dimensional problem of a charged spherical particle immersed in an ionic solution is solved asymptotically. The small parameter used is δ/a, where δ is the Debye screening distance and a the radius of the particle. The solutions to the Poisson-Boltzmann equation are obtained inside the double layer and outside the double layer. They are matched together asymptotically to obtain a solution whose error is of order δ2/ a2 smaller than the expression kept. A uniform solution valid in all the regions is also obtained. Comparison with numerical solution to the problem, which is usually tedious, shows excellent agreement.
ASJC Scopus subject areas
- General Physics and Astronomy
- Physical and Theoretical Chemistry