Electrophoretic mobility of a charged spherical colloidal particle in an uncharged or charged polymer gel medium

A theory is developed of the electrophoretic mobility of a charged spherical colloidal particle in a gel medium due to the long-range hydrodynamic particle-gel interaction by using the Brinkman-Debye-Bueche model and the general mobility expression is derived. On the basis of the obtained general mobility expression, a simple analytic mobility expression for particles with low zeta potential is derived, which is found to be in excellent agreement with the exact mobility equations expressed in terms of exponential integrals derived by Allison et al. for an uncharged gel (J Colloid Interface Sci 313: 328, 2007) and by Li et al. for a charged gel (J Colloid Interface Sci 423: 129, 2014). The relative error is less than 1.6%. An approximate mobility expression for a particle with arbitrary zeta potential in an uncharged gel medium applicable for large κa > 30, where a is the particle radius and κ is the Debye-Hückel parameter, is also derived.