  This paper presents a new theory of turbulent mixing in stirred reactors. The
degree of homogeneity of a mixed fluid may be characterized by the Kolmogorov
micro-scale. The smaller its value, the better homogeneity. The micro-scale
scales inversely with the fourth root of the energy dissipation rate in the
stirring process. The higher this rate, the smaller lambda, and the better the
homogeneity in the reactor. This is true for Newtonian fluids. In non-Newtonian
fluids the situation is different. For instance, in shear-thickening fluids it
is plausible that high shear rates thicken the fluid and might strangle the
mixing. The internal interactions between different fluid-mechanical and
colloidal variables are subtle, namely due to the (until recently) very limited
understanding of turbulence. Starting from a qualitatively new turbulence
theory for inviscid fluids [Baumert, 2013], giving e.g. the Karman constant as
$(2\pi)^{-1/2} = 0.40$ [the super-pipe in Princeton gave 0.40 p/m 0.02, Bailey
et al., 2014], we generalize this approach to the case of viscous fluids and
derive equations which in the steady state exhibit two solutions. One solution
branch describes a state of good mixing, the other a state of strangled
turbulence. The physical system cannot be in two different steady states at the
same time. But it is physically admissible to switch between the two steady
states by non-stationary transitions, maybe in a chaotic fashion.
