Nonlinear dispersion analysis using dynamic traveling wave model in chemical kinetics

The Thomas equation, which controls ion exchange as well as chemical kinetics and advection processes in chemical systems, has its coefficients expanded as functions of time in this work. The goal of this modification is to produce simulations of advection and kinetic processes that are more precise and lifelike. In order to examine the nonlinear distribution and interaction features, the dynamic traveling wave solution of the time-dependent variable coefficient Thomas equation has been successfully achieved. The physical properties of the constants and functions in the wave model presented with certain initial and boundary conditions have been examined. Constants and functions are designed to be as close to reality as possible in order to improve our understanding of the distribution of ions over time in the chemical process. With this design, the newly introduced dynamic traveling wave model is better adapted to the ion exchange process. The coefficient functions that have a direct effect on the stability of the physical mechanism are analyzed under which conditions the system will remain stable. It is envisaged that ion exchange processes in water treatment plants can be optimized by using the wave model introduced for the first time in this study. The gradual damping of ion motions in the chemical process and the trend towards equilibrium over time were investigated using the proposed model.