Electrophoresis of an arbitrarily oriented toroid in an unbounded electrolyte solution

The electrophoresis of a non-conducting rigid toroid in an unbounded Newtonian electrolyte solution having an arbitrary orientation is modeled theoretically under the condition of low surface potential. In particular, the influence of the orientation angle, defined as the angle between the applied electric field and the center line of the toroid, on its electrophoretic behavior as the thickness of double layer varies is investigated. The results of numerical simulation reveal that both the thickness of double layer and the orientation angle can influence appreciably the mobility of the toroid. In general, for a fixed orientation, the mobility of the toroid increases with decreasing double layer thickness, and for a fixed double layer thickness, the scaled electrophoresis mobility increases with increasing orientation angle. If the double layer is infinitely thin, then the present result reduces to that predicted by Smoluchowski, that is, the scaled electrophoretic mobility of the toroid is unity, and is not influenced by its shape. On the other hand, if it is infinitely thick, then the present result follows the same trend as that predicted by Henry, that is, the electrophoretic mobility of the toroid depends highly on its form effect, and the thicker the double layer the smaller that mobility. If the thickness of double layer is comparable to the radius of a toroid, the variation in the orientation angle can lead to as much as 40% difference in the mobility.