Boosting CO₂-driven diffusiophoresis of colloidal suspensions by permeation

When carbon dioxide dissolves into an aqueous colloidal suspension, the resulting transient pH gradients drive diffusiophoresis of the suspended particles. We investigate the effects of CO₂ permeation on the extent of particle motion in a model system consisting of a suspension-filled pore in a gas-permeable polymer. Pure CO₂ is applied to both ends of the pore and the outer surface of the polymer is either sealed (preventing steady leakage of CO₂) or open to the atmosphere, in which case a steady CO₂ (and pH) distribution is established. For both cases, we compute the transient CO₂ distributions (in the water and polymer) and the diffusiophoretic migration of suspended particles. For the second (open) case, we also determine the steady particle distribution. Loss of CO₂ into the surrounding material increases the magnitude and duration of the pH gradient and therefore boosts the migration of the particles. We evaluate the effects of the thickness of the polymer around the pore and the permeability of the polymer to CO₂ (the product of the solubility and diffusivity of CO₂ in the polymer). An optimal diffusivity maximizes the displacement of the particles. The numerical predictions are consistent with experiments in poly(dimethylsiloxane) blocks with varying thicknesses.