Asymptotic formulae for the interaction force and torque between two charged parallel cylinders

The electrostatic interactions between charged particles immersed in an ionic solution play an important role for the stability of colloidal dispersions. The distribution of the electrostatic potential in the continuous phase obeys the nonlinear Poisson-Boltzmann equation. This study aims to calculate the asymptotic expressions for the interaction force and torque between two parallel charged cylinders at large distances between them. The exact formulae obtained are expressed in terms of the modified Bessel function of the second kind. From the general physical principles two theorems about the interaction energy and the stability of the quasi-equilibrium states for multipole-multipole interactions are proved.