Diffusiophoresis of a charged porous shell in electrolyte gradients

The diffusiophoresis of a charged spherical porous shell or permeable microcapsule with arbitrary inner and outer radii, fluid permeability, and electric double layer thickness in an ionic solution is analyzed. With the assumption that the imposed electrolyte concentration gradient is relatively weak and the transport system is only perturbed slightly from equilibrium, the electrostatic potential, ionic concentration (electrochemical potential energy), and fluid velocity fields are determined as power-series expansions of the small fixed charge density of the porous shell by solving the relevant linearized electrokinetic equations. An explicit expression for the diffusiophoretic velocity of the porous shell correct to the second order of the fixed charge density results from balancing the exerted electrostatic and hydrodynamic forces. Both the electrophoretic (first-order) and chemiphoretic (second-order) mobilities increase with an increase in the normalized thickness of the porous shell, and these increases are significant when the porous shell is thin. However, the diffusiophoretic velocity of the porous shell, which is the sum of the electrophoretic and chemiphoretic velocities, may not be a monotonic function of its normalized thickness. The variation in the normalized fixed charge density of the porous shell from negative to positive values can lead to more than one reversals in the direction of the diffusiophoretic velocity.