Electrokinetic phenomena in a dilute suspension of spherical colloidal particles in a salt-free medium

Electrokinetic phenomena are considered in a dilute suspension of spherical colloidal particles in a salt-free medium containing counter-ions only. Simple derivation is given for the electrophoretic mobility of the particles. Expressions for the electrical conductivity and the sedimentation potential are also obtained. An Onsager relation is found to hold between electrophoretic mobility and sedimentation potential. It is shown that if the particle charge Q is lower than a certain critical value, then the electrophoretic mobility and the electrical conductivity due to counter-ions increase linearly with increasing Q. If Q is higher than the critical value, then these quantities become constant independent of Q because of counter-ion condensation effects. The sedimentation potential, however, is not subject to the counter-ion condensation effects, since these effects upon the electrical conductivity and the concentration of the counter-ions cancel out with each other.