Analytical solution for diffusiophoretic mobility of soft particles considering finite ion size effect

We present a theoretical study of the diffusiophoretic motion of a core-shell-structured soft particle, consisting of a hard inner core encapsulated by a fluid- and ion-permeable polyelectrolyte layer (PEL), while accounting for the ion steric exclusion effect. The dielectric permittivity of the peripheral soft layer is assumed to differ from that of the surrounding electrolyte, thereby giving rise to the ion partitioning effect. The inner core surface is considered to exhibit velocity slippage. Electrolyte concentration is assumed to be high enough to yield an electric double-layer (EDL) thinner than the PEL thickness and the particle size, so that the surface curvature effects can be ignored, enabling us to model the particle surface as a planar plate. Adopting a flat-plate geometry, a closed-form analytical solution for the diffusiophoretic mobility of the soft particle incorporating the finite ion size effect is derived, which applies to an arbitrarily charged particle. Mobility expressions are also obtained for different asymptotic limits. The joint influence of ion steric and ion partitioning effects in the presence of a hydrophobic core on the particle is analyzed by illustrating the diffusiophoretic mobility as a function of the pertinent electrokinetic parameters. The ion steric effect is significant for cooperative chemiphoretic and electrophoretic components at higher particle charge. The core hydrophobicity and the ion partitioning effect elevate the ion steric effect by enhancing the effective particle charge. For a low-permeable PEL, the influence of the ion steric effect, the ion partitioning effect, and core hydrophobicity becomes negligible.