Irreversible electrokinetic repulsion at zero-Reynolds-number sedimentation

Stokes-flow reversibility is violated in electrolyte solutions by a streaming-potential mechanism, where nonuniform convective currents within Debye layers surrounding charged particles induce electric fields in the electroneutral Ohmic bulk. We demonstrate the irreversibility consequences of this phenomenon for the problem of particle-pair sedimentation, where the two particles experience a repulsive force driven by bulk Maxwell stresses. At small separations the force scales inversely with the third power of separation distance. This singular behavior is associated with the counterrotation of the two torque-free particles, which leads through a lubrication mechanism to an intense electric field in the narrow gap between them. At large separations the force follows an inverse dependence upon the fourth power of separation, now associated with rectilinear particle motion.