Gel electrophoresis in suspensions of charged spherical particles

Gel-electrophoresis, the migration of colloidal particles through a polymer gel in response to an applied electric field, is investigated theoretically in this study. It is a very powerful technique widely used in soft matter science. Both the short range steric effect (due to the direct contact friction between the gel and the migrating particles) and the long range hydrodynamic effect (due to the hydrodynamic force of the gel exerted upon the liquid suspension) are considered with the particle mobility calculated as the product of the predictions from these two approaches separately. Brinkman fluid is assumed to model the polymer gel and Kuwabara's unit cell model is employed to represent the suspension of particles. A pseudo-spectral method is adopted to solve the resulting general electrokinetic equations. We find, among other things, that the deformation of ion clouds surrounding the particles due to the convection flow within the porous gels deters the particle motion significantly, as an induced electric field opposite to the applied electric field is generated, an effect referred to as the polarization effect here. The higher the surface potential of the particle is, the more significant the reduction of mobility due to this polarization effect. Local extrema are observed in the mobility profiles with varying double layer thickness around kappa a = 1, where kappa is the reciprocal of Debye length, and a is the particle radius, as the polarization effect manifests itself there in general. The presence of the gel retards the particle motion in general. The poorer the permeability is, the more severe the reduction. On the other hand, the more concentrated the particle suspension is, the slower the particle motion in general, due to the hindrance effect between neighboring particles. Moreover, the involvement of polarization and overlapping effects of the double layer further complicates the electrophoretic behavior of the particle, which is discussed in detail. Excellent agreement is obtained between the results reported here and the experimental data available in the literature for gold nanoparticles in dilute suspensions. The current study greatly extends the theoretical analysis scope of gel-electrophoresis from previous dilute suspensions only to concentrated ones as well, which are encountered frequently in practical applications in biological and biochemical fields, as well as other fields involving soft matters such as colloids and polymer gels.