(27f) Strong Deformation of the Electric Double Layer during Sedimentation or Electrophoresis of a Charged Particle
Electrokinetic effects arise from the deformation of electric double layers under electric fields or fluid flows. The majority of studies in this venerable field consider weak fields or flows, for which the double layer is only slightly perturbed from equilibrium. Here, we examine the strong deformation of a double layer during sedimentation or electrophoresis of a charged colloid with a fixed surface charge. The former is relevant to particle motion in ultracentrifuges and the latter to electrophoresis in doped nonpolar fluids. Specifically, we invoke the Debye-Huckel approximation to the electrokinetic equations for a particle with a small surface potential (relative to thermal voltage) and also consider the Debye length to be large compared to particle size. In this thick-double-layer regime, the particle appears as a point charge, and the compensating counter-ion charge in the cloud surrounding it obeys an advection-diffusion-screening equation, which encapsulates the effects of advection due to the particle motion; Brownian diffusion of ions; and electrostatic screening of the surface charge by the cloud. For weak advection the cloud is only slight distorted. In contrast, for strong advection the cloud can be completely stripped from the particle: consequently, electrokinetic effects vanish in this strong-advection regime. Thus, for sedimentation, the drag is limits to Stokes law for an uncharged particle. Likewise, the particle velocity for electrophoresis approaches Huckelâs expression.