Comparing laminar flows for efficient reactive mixing

As a chemical reaction occurs, a front is formed at the boundary between reacted and non-reacted regions. We wish to quantify the efficiency of reactive mixing by a variety of shear flows by understanding how fronts evolve over time. A more efficient flow causes the reacted region to grow more quickly. To do this we have performed numerical simulations of chemical reactions in the presence of two-dimensional, laminar shear flow using both the one-dimensional Eikonal approximation, which assumes fronts are thin curves with an inherent burning speed, as well as the two-dimensional advection-reaction-diffusion equation, which captures the dynamics of reactant concentration through both space and time. We find that the key factor in improving mixing efficiency is to maximize the absolute velocity difference in the flow. We have also developed an analytical solution to model these front dynamics and have successfully predicted the final front shape and growth rate for six unique flow profiles.