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

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 (epsilon/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 Kolmogoroff size, 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 energy dissipation and laminar deformations occur, is discussed. Vortices provide the mechanism to form laminar structures by engulfing the fluid in their immediate environment. The frequency of vortex formation is determined. Diffusion and reaction occur within deforming laminated structures temporarily trapped inside stretching vortices. At the end of vortex activity, as the fluid has returned temporarily to isotropy, a new burst of vorticity creates a further generation of vortices out of old vortex material and its surroundings. This description applies to liquid mixing, for which Sc >> 1 i.e. diffusion is much slower than momentum transfer. Mixing, brought about by these periodic processes, ends when the concentration is uniform at the molecular scale.