Electrodynamics of soft multilayered particles dispersions: dielectric permittivity and dynamic mobility

We report a theory for the evaluation of the electrodynamics of dispersions of spherical soft multilayered (bio)particles, with microorganisms and polyelectrolyte multilayers-coated particles as illustrative paradigms. These particles generally consist of a hard (ion-and water-impermeable) core component supporting a succession of step-function or diffuse-like concentric soft (permeable) polymeric layers defined by distinct electrostatic, hydrodynamic and structural properties. The formalism is based on a rigorous numerical resolution of the coupled Navier-Stokes-Brinkman equation, continuity equations for the flow and for the ionic species present in solution, and the non-linear Poisson equation corrected for the multilayered nature of the soft interphase. The frequency-dependent dynamic mobility and dielectric permittivity of such soft particles suspensions are discussed as a function of the key electrohydrodynamic features of the constituting particulate peripheral layers and solution salinity. It is shown that the frequency dependent permittivity is mostly affected by the total charge carried by the overall soft interphase. In contrast, the dynamic mobility is mainly determined by the charge and friction characteristics of the layers located within an electrokinetically-active outer particle region whose extension is defined by the electric double layer thickness and the Brinkman length. Results highlight that under particular electrolyte concentration and layer-to-layer thickness ratio conditions, the dynamic mobility may reflect the physico-chemical and structural properties of the only innermost layers of the soft particle coating.