Analytical study on diffusiophoresis of soft particles: Role of surface-charge-mobility-dependent hydrophobic core

This paper theoretically analyzes the diffusiophoretic motion of a soft particle comprising a surface charge-dependent hydrophobic rigid core coated with a polyelectrolyte layer. The surface hydrophobicity of the inner core is considered to depend on the lateral mobility of the surface charge ions. A modified slip boundary condition is employed at the inner core interface to account for the hydrodynamic frictional and tangential electric forces on the flow due to the mobile adsorbed ions. The dielectric permittivity of the porous layer is assumed to be lower than the background electrolyte's permittivity constant, yielding the ion partitioning effect. The electrolyte concentration is considered sufficiently high so that the electric double layer around the particle becomes very thin compared to the porous layer thickness, and the inner core surface can be regarded as a flat plate. Considering the particle to be weakly charged, for which the Debye-Hückel approximation can be applied, a closed-form general diffusiophoretic mobility expression is derived, valid to a thin Debye layer. Analytic expressions for the electrophoretic and chemiphoretic components are also reported separately. Asymptotic mobility solutions are further deduced for various limiting situations. Results show that the lateral mobility of the surface charge ions significantly influences the diffusiophoretic motion of the particle, and the impact is extensive for a highly hydrophobic surface. Additionally, the ion partitioning effect strengthens the influence of the surface charge mobility on the flow by augmenting the effective charge of the particle. The contribution of the surface charge-dependent hydrophobic inner core and the ion partitioning effect is substantial for a highly permeable porous layer and insignificant for a thinner hydrodynamic screening length.