Analytical solution for diffusiophoretic mobility of a pH-dependent soft particle with a hydrophobic inner core incorporating the ion partitioning effect

An analytical investigation is conducted on the diffusiophoresis of a pH-regulated soft particle consisting of a hydrophobic solid core enveloped by a peripheral polyelectrolyte layer (PEL). The PEL is assumed to contain dissociable acidic and basic functional groups, and the immobile charge density of the soft layer depends on the solution pH. The dielectric permittivity of the PEL is assumed to be different from that of the electrolyte, inducing the ion partitioning effect. The electrolyte concentration is considered to be sufficiently high to ensure a thin Debye layer, allowing the outer edge of the soft particle to be approximated as a planar interface. Consequently, a flat-plate framework is employed to analyze the flow. A closed-form analytical expression for the diffusiophoretic mobility is derived, applicable to an arbitrary immobile charge density of the PEL, under a thin Debye layer assumption. Exact mobility solutions are further obtained for a weakly charged soft particle and a low-permeable soft layer. The diffusiophoretic mobility retains a positive value for the entire pH range when the flow is governed purely by chemiphoresis. For a non-negligible electrophoretic component, the diffusiophoretic mobility is negative for a pH lower than the isoelectric point (IEP), and it acquires a positive value as pH exceeds IEP. The influence of the core surface wettability is significant when the difference between pH and the IEP is considerable. The ion partitioning effect enhances the diffusiophoretic mobility when electrophoretic and chemiphoretic components act cooperatively, whereas it attenuates the mobility when these components act in opposition.