Random force correlation function for a charged particle in an electrolyte solution

Abstract

The equations governing the motion of a charged particle and of the electrolytic ions in its neighborhood are formulated. The equations are linearized with respect to the disturbance caused by the motion of the particle, and an approximation is introduced which excludes the consideration of a particle radius that is large compared to the thickness of the diffuse double layer. The coupling between the hydrodynamic and the electrostatic aspects of the problem is accounted for in first approximation only. The result is applicable to a high frequency oscillation such as may be caused by an ultrasonic field. The frequency range discussed in particular is that which is relevant to the rapidly changing velocity in Brownian motion. It is found that in this range of frequencies the electrostatic force on the particle may, in extreme cases, be about 20% of the hydrodynamic resistance, but in most cases the effect will be of the order of only a few percent.