On the derivation of the Smoluchowski result of electrophoretic mobility

Abstract

One of the most enduring, broadly applicable and widely used theoretical results of electrokinetic theory is the Smoluchowski expression for the electrophoretic mobility. It is a limiting form that holds for any solid particle of arbitrary shape in an electrolyte of any composition provided the thickness of the electrical double layer is “infinitely” thin compared to the particle size and the particle has uniform surface potential. The familiar derivation of this result that is a simplified version of the original Smoluchowski analysis in 1903, considers the motion of the electrolyte adjacent to a planar surface. The theory is deceptively simple but as a result much of the interesting physic..