Diffusiophoresis of a Charged Porous Particle in a Charged Cavity

The quasi-steady diffusiophoresis of a charged porous sphere situated at the center of a charged spherical cavity filled with a liquid solution of a symmetric electrolyte is analyzed. The porous particle can represent a solventpermeable and ion-penetrable polyelectrolyte molecule or floc of nanoparticles in which fixed charges and frictional segments are uniformly distributed, whereas the spherical cavity can denote a charged pore involved in microfluidic or drug-delivery systems. The linearized electrokinetic differential equations governing the ionic concentration, electric potential, and fluid velocity distributions in the system are solved by using a perturbation method with the fixed charge density of the particle and the zeta-potential of the cavity wall as the small perturbation parameters. An expression for the diffusiophoretic (electrophoretic and chemiphoretic) mobility of the confined particle with arbitrary values of a/b, kappa a, and lambda a is obtained in closed form, where a and b are the radii of the particle and cavity, respectively; kappa and lambda are the reciprocals of the Debye screening length and the length characterizing the extent of flow penetration into the porous particle, respectively. The presence of the charged cavity wall significantly affects the diffusiophoretic motion of the particle in typical cases. The diffusio-osmotic (electro-osmotic and chemiosmotic) flow occurring at the cavity wall can substantially alter the particle velocity and even reverse the direction of diffusiophoresis. In general, the particle velocity decreases with an increase in a/b, increases with an increase in kappa a, and decreases with an increase in lambda a, but exceptions exist.