MODELING DIFFUSIOPHORESIS IN MULTI-ION SOLUTE GRADIENTS

Abstract

Current analytical and numerical models of diffusiophoresis are largely focused on particle motion in symmetric charge 𝑍:𝑍 solutions of a single electrolyte at steady state, where 𝑍 denotes the ion valence. While these models provide a foundation for understanding diffusiophoretic motion, they fail to capture the complexity of many real-world systems that involve diffusiophoretic motion of particles within multi-electrolyte rather than single electrolyte solutions. A system of two electrolytes with a shared ion is the simplest multi-ion case, and therefore provides the foundation for understanding diffusiophoresis within larger and more complex multi-ion systems. As such, we developed a diffusiophoretic model for a multi-ion solution composed of two distinct cations with a shared anion. This model was then used to extend the work of Jesse Ault, a recent MAE graduate student, by applying multi-ion diffusiophoresis to the dead-end pore geometry. Our particular model assumed the pore to be populated with the 𝐾𝐶𝑙 electrolyte while a bulk fluid containing 𝑁𝑎𝐶𝑙 and colloidal particles flowed past its entrance. The resulting numerical solution provided by our model captured the one-dimensional concentration profiles of the ions along the length of pore for various times as 𝑁𝑎𝐶𝑙 entered the pore as a result of the concentration gradient between the bulk fluid and the pore. The numerical solution was then plotted for two distinct initial conditions. From varying the relative diffusivity of 𝐶𝑙− to 𝑁𝑎+, it was determined that for the three-ion case in the presence of a 𝐶𝑙− concentration gradient between the bulk fluid and the pore the concentration profiles of 𝐾+ and 𝑁𝑎+will change. This indicates that an anion concentration gradient between the pore and the bulk fluid produces the separation of charge necessary to produce an electric field that then affects the concentration profiles of 𝐾+ and 𝑁𝑎+ through electrostatic interactions. Additionally, the numerical solution for the first initial condition for our model was plotted against the solution provided for by a similar numerical model for three-ion diffusiophoresis developed by Wyss [17]. From comparing the concentration profiles produced by varying the relative diffusivity of 𝐶𝑙− to 𝑁𝑎+, it was determined that by using an ambipolar diffusion coefficient, as with Wyss’ model, instead of including an electrostatic term when developing a model for the concentration profiles of the three-ions, the resulting concentration profiles of the ions are dependent solely upon the diffusivity of two-ions, which ignores the electrostatic interactions occurring between the three-ions. This additionally treats each electrolyte as independent from one another and therefore treats the shared anions as distinct ions, when in fact they are the same. As such, this means some of the complex behaviors exhibited in the case of three-ion diffusiophoresis are obscured in Wyss’ model and require accounting for the electrostatic interactions of the three ions to describe the resulting behaviors more accurately.