The Electrophoretic Mobility of a Weakly Charged “Soft” Sphere in a Charged Hydrogel: Application of the Lorentz Reciprocal Theorem

The electrophoretic mobility of a dilute, weakly charged “soft” particle in a charged hydrogel modeled as an effective medium is investigated in this work. This is closely related to previous work (Li, F.; Allison, S. A.; Hill, R. J. J. Colloid Interface Sci. 2014, 423, 129–142) but approached in a different way using the Lorentz reciprocal theorem. Under the limiting conditions of the present work, it is possible to avoid numerical solution of differential equations. An analytical equation is derived for the mobility and applied to a number of cases.