Diffusiophoretic and diffusioosmotic velocities for mixtures of valence-asymmetric electrolytes

Diffusiophoresis and diffusioosmosis are electrokinetic phenomena where relative motion is induced between a charged surface and a surrounding electrolyte due to a concentration gradient of ions. In the literature, a relative velocity between a surface and the electrolyte has been derived for a valence-symmetric (z:z) electrolyte. In this article, we reformulate the governing equations in a convenient form based on a systematic generalization of the nonlinear Poisson-Boltzmann equations in the limit of a thin double layer, which allows us to derive results for diffusiophoretic and diffusioosmotic velocities for a mixture of electrolytes with a general combination of cation and anion valences. We find that the relative motion depends significantly on ion valences. We also provide analytical approximations for the diffusiophoretic and diffusioosmotic velocities and discuss their accuracy and applicability. Further, we tabulate diffusiphoretic velocities for some common cases, which highlights the importance of asymmetry in cation and anion valences. Finally, we discuss the validity of our assumptions and the importance of effects such as finite ion size, dielectric decrement, and surface conduction for typical experimental conditions.