Multi-ion diffusiophoresis

The movement of charged particles occurs in a salt concentration gradient by the mechanism of diffusiophoresis. Current analytical models for diffusiophoresis have been developed for a gradient generated by a symmetric Z:Z electrolyte at steady state. Recently, our lab has reported diffusioosmotic flows due to dissolving calcium carbonate (CaCO₃) which generates three ions (Ca²⁺, HCO3-, and OH^-), and this fluid motion cannot be described by current analytical models. In this communication, we derive an expression for the diffusioosmotic flow in a gradient involving multiple ions of different valences, assuming infinitesimally thin double layers. We also solve numerically the time-dependent concentration profiles for the three-ion case and find that the concentration profile of HCO3- is non-monotonic in solution. Finally, we examine quantitatively the assumption of electroneutrality in solution, finding that electroneutrality is a good approximation even for the multi-ion case, indicating that our electric field derived from the ion migration equation is quite accurate.