Fluid Mechanical Mixing—Lamellar Description

It is not obvious how one should apply the mathematical apparatus of fluid mechanics to mixing. With facilities for massive computation one is tempted to solve the Navier—Stokes equation for particular boundary and initial conditions and for laminar motion of fluid volumes in a particular flow field. However, the result of such a time-consuming computation is as specific as a single physical experiment, and many such experiments lead only to empirical generalizations. With highly developed statistical theories of turbulence, one is also tempted to add the concepts of time-averaged concentration intensity and concentration scale and seek revelations from further manipulation of the equations of change using distributions of values of the averaged quantities. Unfortunately, in a structured continuum where mechanical mixing, interdiffusion of chemical species, and chemical reaction, can occur at differential space and time scales which range from the molecular scales of a solution phase to the macroscopic scales of a mixing device, spatial averaging is also required.