A FLUID MECHANICAL APPROACH TO TURBULENT MIXING AND CHEMICAL REACTION PART II MICROMIXING IN THE LIGHT OF TURBULENCE THEORY

Abstract

The objectives are to identify the key physical processes contributing to mixing on the molecular scale, using information from Fluid Mechanics, and to construct a corresponding mathematical model. The concentration spectrum indicates that molecular diffusion and hence micromixing starts towards the fine scale end of the viscous-convective subrange and becomes dominant in the viscous-diffusive subrange. Such small fluid elements are subject to laminar deformations at rates proportional to (ϵ/v)1/2. Their thickness is related to shear rate and time using a result from the statistical theory of turbulent diffusion, valid in the viscous subrange at short times. One result is that the diffusion field rapidly becomes one-dimensional. Numerical calculation confirms that fluid elements, initially of Kolmogoroffsize, first deform and that diffusion becomes significant only at still smaller scales. The assignment of an initial length scale is therefore not critical. The role of vorticity for small eddies, where en...