Theoretical modeling of transient reaction-diffusion dynamics in electrokinetic Y-shaped microreactors

We perform a theoretical study on transient reaction-diffusion kinetics in an electrokinetic Y-shaped microreactor. The flow is assumed to be both steady and fully developed. The governing equations are solved in dimensionless form utilizing a 3D finite-volume-based numerical algorithm, assuming a second-order irreversible reaction between the components. Analytical solutions are also obtained for cross-stream diffusion without reaction under a uniform velocity distribution. It is shown that the well-known butterfly-shaped form of the product concentration profile is not immediately created and it is established only after the system is sufficiently close to its steady-state. Furthermore, the inclination of the concentration peak toward the component of lower diffusivity or inlet concentration is less significant at the earlier stages of the production. Finally, it is demonstrated that the short-term influence of the parameters affecting the advection of mass on the total efficiency, defined as the ratio of the total production to the amount of the limiting reactant within the device, is quite the opposite of that at the steady-state.