(26e) Defining Mixing

When we speak of mixing as the control of segregation, we target process objectives such as a fixed drop size distribution, nano-sized crystals, repeatable mixing patterns such as those observed in Corian countertop and plastic wood decking materials, and design of reactors for highly repeatable performance to maximize selectivity and minimize byproduct formation. The equipment used for mixing operations ranges from the traditional stirred tank and turbulent pipe to more targeted static mixers and rotor-stator or in-line mixers, and a range of industry specific equipment, such as twin screw extruders, which have evolved for specialized applications. We still do not have a simple, mathematically rigorous definition of mixing, beyond the assertion that mixing reduces both the scale and intensity of segregation.

In this talk, the mathematics and statistics used in population studies are applied to mixing. The results allow us to relate the various definitions of mixing to eachother, and to place them in the context of turbulence and chaos theory. We are particularly interested in definitions which work in the limits, and which can be applied to both experimental and computational data.