Mixing and fast chemical reaction—VI: Extension of the reaction zone

Work reported earlier[1, 3] as well as here indicates that mixing at the molecular scale (micromixing) takes place by molecular diffusion in fluid elements, which are simultaneously undergoing laminar deformations. Whereas simple shear was considered before, the present analysis describes diffusion and reaction in regions deformed by extensional flow. After outlining various simple types of extension, results in the literature[4,7] are quoted, which were obtained from observations on the diffusion of heat spots in turbulent air. These indicated stretching motions in two directions with a corresponding shrinkage in the third. Direct application of these findings to diffusion in the direction of shrinkage leads to predictions of th product distribution from competitive, consecutive reactions. Without fitting any parameters, these predictions agree quite well with the distributions of two dyestuffs produced by two diazo coupling reactions. Insufficient fluid mechanical information is available to enablea more accurate comparison; matters requiring further study are listed.