Effect of counterions on the Rayleigh-Plateau instability of a charged cylinder.

The effect of counterions on the instability of a charged cylinder is investigated. Both axisymmetric and asymmetric perturbations are considered. The analysis shows that the Rayleigh-Plateau instability is modified for a charged cylinder in the presence of counterions. For the axisymmetric instability, the counterions have a stabilizing effect at low values of kappa, the inverse Debye layer thickness. However, the effect is destabilizing at higher values of kappa . The asymmetric modes which are stable for an uncharged cylinder are rendered unstable at high values of kappa . The analysis should be important in pearling instability of charged cylindrical vesicles. The expression for the correlation time of thermally induced shape fluctuations of charged cylindrical vesicles is also derived.