ph-dependent focusing of diffusiophoretic particles, with and without an isoelectric point

Electrolytic diffusiophoresis has been studied extensively and generally induces motion in a single direction, up or down the electrolyte gradient. In this work, we theoretically investigate conditions under which this direction reverses, allowing particles to form a steady-state focusing band. We simulate particle transport in an acid-base reaction front, with the inclusion of a salt alongside the acid. These calculations reveal that for certain salt concentrations, a focusing band forms. Analysis of these results shows that the pH-dependence of a particle's zeta potential allows this phenomenon to occur, and determines when and where the band will form. This model qualitatively captures prior experimental results and highlights the key balance between concentration gradients and zeta-potential dependence. In extension, we study the specific behavior that arises when a particle's zeta potential changes sign within the channel, at an isoelectric point. This analysis reveals interesting similarities to the standard focal response, but has more distinct applications in the area of protein separations. This foundation opens new areas for diffusiophoresis research in acid-base systems and provides novel implications for microfluidic design and biophysical transport processes.