Exact solution to the linearized Poissonndash;Boltzmann equation in cylindrical coordinates

摘要

For the case of a concentration gradient across a charged membrane, the linearized Poissonndash;Boltzmann equation in cylindrical coordinates, is solved exactly by means of a finite Hankel transform. Although some of the required integrals cannot be analytically evaluated in general, they can be approximated with asymptotic expansions of the modified Bessel functions for large argument. Under these conditions the solution is identical to that obtained with the usual assumption that the electric potential can be separated into one term that depends on only the axial coordinate and a second that depends on both the axial and radial coordinates. Thus this separation, which is much simpler to apply than the transform method presented here, can be applied with confidence under the appropriate conditions.