Minimal Reaction-Diffusion Model of Micromixing during Stopped-Flow Experiments

The reaction-diffusion equation was used to simulate kinetic curves measured in a stopped-flow instrument in order to understand the origin of micromixing effects. The partial differential equations were solved both by numeric means and by a more analytical approach using Fourier series. A fully analytical solution was obtained for the diffusion only case (when no reaction occurs). Comparisons with the results of numerical calculations showed that very reasonable analytical approximations were obtained for the diffusion-reaction case. The simulations could readily reproduce the saturation of the pseudo-first-order rate constants with an increase in the concentration of excess reagent, a phenomenon first observed about 30 years ago. From the results, it can be concluded that further improvement of the performance of stopped-flow instruments is not possible by simply reducing the dead time; the efficiency of the mixing is the primary limiting factor.