Abstract
Micromixing takes place by unsteady diffusion, often accompanied by chemical reaction, within deforming laminated structures, which are embedded within energy dissipating vortices. Several quantities characterizing micromixing (Kolmogorov velocity microscale, Batchelor concentration microscale, rate and duration of vortex deformation, etc.) depend upon the rate of energy dissipation in a given turbulent fluid. This energy dissipation had previously been treated as spatially uniform, although in many mixers (e.g. stirred tanks) this is not so. The earlier micromixing model is thus extended here to apply to inhomogeneous turbulence, characterized by the spatial distributions of velocity and energy dissipation. It is assumed that turbulent dispersion is negligible compared to the convection of fluid undergoing mixing and that the macroscopic concentration field is known or calculable. A description of micromixing in inhomogeneous turbulence is first derived and then reduced to the governing dimensionless groups. As an application of these general principles, the product distribution from rapid, consecutive, competitive reactions occurring in the decaying energy field downstream from a turbulence generating grid is calculated for typical flow rates, mesh sizes and solution viscosities.
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