Non-Stokes drag of electrophoresis: a new insight into an old problem

Mobility, the ratio of a charged-particle drift speed in a DC electric field to the magnitude of the field is typically used to quantify electrophoresis. Drag coefficient cannot be measured in a DC field because application of an external force to measure force alters the flow pattern, yielding an apparent drag force that is Stokes-like. The intrinsic electrophoretic drag can be determined, however, by optically trapping a charged particle and placing it in a low-frequency AC field. Using the frequency-dependent phase shift of the particle motion relative to that of the AC field and the magnitude of the particle displacement, this approach yields drag coefficient, effective charge and also a mobility that is the same as that measured using a DC field. The drag coefficient is markedly different from that of the Stokes. Using the drag coefficient and the mobility as input for numerical calculations based on the Planck-Nernst-Poisson equation and the Stokes equation reveals a well-defined transition between an inner and outer flow in the vicinity of the particle. This study provides a new insight into an old problem by providing experimentally measurable quantities, i.e., effective charge, electric force and drag coefficient a microscopic definition.