A Model for Diffusiophoretic Particle Transport in Acid-Base Reaction Fronts

Diffusiophoresis is a fundamental transport mechanism, describing the tendency of micro-scale particles to move along the concentration gradients of chemical species in their environment. Diffusiophoresis plays a key role in many biological, reaction engineering and separations processes involving colloidal suspensions. These processes are abundant, and therefore, a fundamental understanding of diffusiophoresis is of great importance. It was recently shown in experiment, that diffusiophoretic particles are able to focus on the steady-state reaction front of a channel with acid and salt added on one side, and base added in the other. While this discovery provides an interesting insight into the diffusiophoretic process, there is currently little theoretical understanding of how this occurs. In order to better explore this phenomena, we have created a mathematical model describing the situation. This setup can be modeled by the steady Poisson-Nernst-Planck equation, solved for each individual species in the environment, in addition to special case boundary conditions regarding the location of the reaction front, and properties of the profiles at this point. The resulting concentration profiles are used to determine diffusiophoretic velocities that would be observed by particles added to the system, corroborating experimental results. In addition, a transient system can be considered in order to add depth to our understanding of the phenomena as a whole, beyond what was observed in experiment. It was shown that the location of focusing is highly dependent on added salt concentration, and so the transient system will provide insight into the propagation of the reaction front up until steady state is reached. This system can be solved numerically, and analytically in certain limits, in order to better explain this observation from first principles. Using this model, we can provide insight into the underlying principles governing this phenomena, and establish predictions about its applications in similar setups. The model is able to reasonably capture experimental results, and provide scalable insight into the process as whole.