Diffusiophoretic motion of an isolated charged porous sphere

Diffusiophoretic motion, the migration of a colloidal particle in response to an externally applied solute concentration gradient, is investigated theoretically in this study for an isolated charged porous sphere suspended in an unbounded medium of electrolyte solution. The porous sphere is treated as a Brinkman medium with a uniformly distributed fixed charge density. The resulted general electrokinetic equations adopting the full nonlinear Poisson equation are solved numerically with a pseudo-spectral method based on Chebyshev polynomials. In particular, the convection contribution of the ion flux is taken into account properly as well. Key parameters of electrokinetic interest are examined for their respective effect on the particle motion. The particle mobility is much smaller in general than the analytical prediction neglecting the convection-induced double layer polarization effect, which is by far the most important factor in determining the porous particle motion. A less charged particle may actually move faster than a highly charged one due to this effect. Visual demonstration of the polarization is provided. Formation of a separate axisymmetric vortex flow is be responsible for the observation that a particle may reverse its direction of motion across a threshold permeability. This implies that a porous polyelectrolyte (like a protein or a DNA) assuming a random coil conformation may tango back and forth as it makes gyrations in diffusiophoretic motion.