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

Abstract

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.

Kinetic detection of osmium(VI) ester intermediates during the OsO4‐mediated aqueous dihydroxylation of chloroethylenes

“…Kinetic studies were performed on an Applied Photophysics SX-20 Stopped-flow spectrophotometer (fast complexation reactions) and Perkin-Elmer Lambda 25 spectrophotometer equipped with thermostated cell block (slow redox processes). The dead time of the stopped-flow instrument was experimentally determined to be 1.0 ms. [33][34][35] Kinetic curves were evaluated, and rate constants were fitted by the respective built-in softwares of the instruments. Each point presented is the average of at least seven runs in the complexation study, while the same averaging was done for at least three runs in the redox study.…”