Diffusiophoresis in gradients of mixtures of colloidal and molecular-sized ions

Ambipolar diffusion has been traditionally considered for the joint diffusion of molecular-sized ions: the ambipolar diffusion coefficient is a function of the diffusivities of the cation and anion, due to their interaction via the electric field. The diffusiophoretic motion of colloidal particles with a surface charge in these ion gradients is well understood. Recent experimental work observed that diffusiophoresis also occurs in gradients of colloidal-sized ions, with molecular-sized counterions. This present work derives a ‘revised’ ambipolar diffusion coefficient for this case, and for the diffusiophoretic motion of another (‘second’) type of charged colloidal particle in the gradient. The solution methodology, of forming simultaneous equations for the colloidal particle's diffusiophoretic velocity and the electric potential gradient, is new, as well as extendable to mixtures of any number of colloidal and molecular ions. The dependence of the derived coefficients on the particles' properties is characterised and explained. The revised ambipolar diffusion coefficient resembles the molecular equation, with the colloidal ion's contributions determined by diffusiophoretic effects. Compared to the molecular version, the chemiphoretic contribution to the diffusiophoretic mobility of a second type of colloidal particle is unchanged, whilst the electrophoretic component is altered: itself a combination of electrophoretic and chemiphoretic effects on the first type of colloidal particle. A diffusiophoresis experiment is reanalysed in light of these new expressions.