Electrophoresis of soft particles with partially penetrable polymer layer: impact of location of slip plane and hydrodynamic slip length

The present article deals with the theoretical development of the electrophoresis of core-shell structured soft particles in which the inner rigid core is decorated with a fluid and ion-permeable polymeric shell layer. Note that such a particle resembles several biocolloids (e.g., bacteria, virus, humic acid), functionalized nanoparticles, and environmental entities, to name a few. For such a structured particle, the conventional \(\zeta\)-potential concept loses its meaning, and an extensive theory is required to analyze the electrohydrodynamics of the particle considering the penetration of ionized liquid across the shell layer. Note that the dielectric permittivity of the shell layer is often lower than that of the bulk aqueous medium, which induces the ion partitioning effect. Besides, in several practical situations, the hydrodynamic slipping may occur along the slipping plane. In addition, the slipping plane may not always be located along the surface of the inner core due to grafting of a polymeric shell layer along its surface, and thus, it may be assumed to be located somewhere within the surface polymeric layer. The slipping plane separates two regions with different Brinkman parameters. The region outside the slipping plane the Brinkmann screening length takes a finite value, which allows fluid flow across this region. In the region inside the slipping plane, the Brinkman parameter may practically be equal to infinity, but electrolyte ions still can penetrate this region. Considering all the physical aspects indicated above, we have proposed a simple model to study the electrophoresis of soft particles within the flat-plate regime. Based on the weak charge limit, we adopt the Debye-Hückel linearization to simplify the governing equations, and the explicit form of electrophoretic mobility is derived. Several closed-form analytic expressions are further deduced from the general mobility expressions valid under various limiting situations. We have illustrated our findings graphically to highlight the impact of pertinent parameters on the electrophoretic mobility of such a particle. In addition, we have further provided an estimate of the parametric range in which the particle may attain a zero mobility. Overall, the analytical results presented in this study will be helpful to the experimentalists to analyze their findings.

Graphical Abstract