Chaotic Mixing & Chemical Reactions
"Predicting the progress of diffusively limited chemical reactions in the presence of chaotic advection" P.E. Arratia & J.P. Gollub (to appear in PRL 2006). For a pre-print of the manuscript, please click here (Adobe PDF).
*Also, please read a commentary on this work to appear in Physics Today (2006). For a pre-print of the commentary, please click here. (Adobe PDF)
ABSTRACT: In these experiments, we investigate the effects of chaotic advection and diffusion on fast chemical reactions in two-dimensional fluid flows. We do so by using experimentally measured stretching fields and fluorescent monitoring of the local concentration. Flow symmetry, Reynolds number, and mean path length affect the spatial distribution and time dependence of the reaction product. A single parameter , lN where l is the mean Lyapunov exponent and N is the number of mixing cycles, can be used to predict the time-dependent total product for flows having different dynamical features.
Below are 2 sample movies that use distinct magnetic array configurations. Note that we are tracking the product concentration. Regions in red and blue represent high and low product concentration, respectively.
Movie 1 displays a regular array configuration (see below) at Re=56.
Movie 2 displays a random array configuration (see below) at Re=56.
Movies of the progress of the chemical reaction, in a regular array, is shown below.