The ionic boundary layer relaxation in the problem of proton exchange

Abstract

The article is devoted to the study of the behavior of proton exchange reaction products in a benzoic acid melt during its interaction with a lithium niobate crystal. During protonation, positively charged lithium ions and negatively charged benzoate ions got into the acid. After recombination, these ions formed lithium benzoate molecules. The diffusion and recombination processes were described using the equations of continuum mechanics: the Navier-Stokes equation for an incompressible fluid, the equations of electrostatics, and transport equations. The numerical solution of this system of equations shows that near the interphase, benzoate ions form a stationary boundary layer supported by the flux of ions from the side of the crystal. Lithium ions, due to greater mobility, filled the entire computational region. Due to differences in ion concentration distributions within the boundary layer, an electric field formed. However, the emerging inhomogeneities were not sufficient for the occurrence of large-scale convective transfer, therefore all fields were uniform along the interphase. The study simulates a situation in which, at a certain moment of time, the conditions promoting proton exchange cease to be met, and the indicated flow of ions from the crystal ceases, as a result of which a gradual disappearance of the boundary layer is observed. The article provides time evolutions of the concentration profiles of ions and lithium benzoate molecules and of the electric potential during this relaxation. The ions, like the electric field, disappear over time, while the lithium benzoate molecules tend to uniformly fill the entire region. The influence of the intensity of the initial ion flow on relaxation processes is shown.