AC electrokinetics of concentrated suspensions of soft particles

In this work, we show how the cell model traditionally used for the evaluation of the electrokinetic properties of concentrated suspensions can be modified to include the case of soft particles, that is, particles consisting of a rigid core and a polyelectrolyte membrane. The Navier-Stokes and Poisson's equations have been modified to account for the presence of extra friction and a volume-distributed charge in the membrane. In addition to the boundary conditions on the particle and the cell boundary, it is necessary to define conditions on the polymer-electrolyte solution interface. The frequency dependence of the dynamic mobility and electric permittivity of suspensions of soft particles with arbitrary solids concentration is computed. It is shown that the dynamic mobility of these systems is larger than that corresponding to hard particles with the same charge. For the permittivity, the same trends are observed: the R-relaxation amplitude increases upon coating. It is found that friction plays an important role in determining the mobility, while the permittivity is more affected by the concentration of solids. The model also predicts that the charges on the core and in the membrane are very important parameters, although their effects differ on the mobility and the permittivity. While the former depends mainly on the membrane charge, the latter is responsive to both charges at comparable extents.