Fluids, Theologically complex

Realistic mixing problems are inherently difficult owing to the complexity of the flow fields, to the fact that the fluids themselves are Theologically complex, and to the coupling of length scales. For this very reason, mixing problems have been attacked traditionally on a case-by-case basis. Modeling becomes intractable if one wants to incorporate all details at once. Nevertheless it appears important to focus on common features and to take a broad view. 

Nienow, A. W. and Elson, T.P., Aspects of mixing in Theologically complex fluids, Chemical Engineering Research and Design, 66, pp. 5-15 (1988). 

Schulman ZP (1975) Convective heat mass transfer in Theologically complex fluids, Energiya, Moscow... 

Mixing of dense suspensions and Theologically complex opaque fluids... 

Under one-dimensional shear, many Theologically stable fluids of complex structure (whose rheological characteristics are time-independent) have a flow curve other than Newtonian. If the flow curve is curvilinear but still passes through the origin in the plane 7, r, then the corresponding fluids are said to be nonlinearly viscous (often they are said to be purely viscous, anomalously viscous, or sometimes non-Newtonian). 

Savins, J. G. and Wallick, G. C., Velocity profiles, discharge rates, pressures, and torques for a Theologically complex fluid in a helical flow, A/ChE J. 

Chhabra, R. P. and D. De Kee, Fluid particles in theologically complex media. Transport Processes in Bubbles, Drops and Particles, Hemisphere, New York, 1991, Chap. 2. 

Non-Newtonian fluids are Theologically complex fluids that exhibit one... 

Polymer melts and solutions, on the other hand, are Theologically more complex fluids and, even under simple radiating flows in the entrance region, would need more stress components to sustain them thus there are larger entrance pressure drops. Additionally, the entrance flow patterns with polymer melts and solutions are typically more complex.6... 

The laminar mixing action can only be analyzed if the exact flow patterns are known. This can be done reasonably well for simple rectangular flow channels in an extruder screw. However, when mixing sections are incorporated into the extruder screw, the flow patterns generally become quite complex. In one respect, this is desirable because complex velocity profiles tend to Improve the mixing effectiveness. However, on the other hand, the mathematical description of the velocity profiles can become very involved. This is particularly true when the minor fluid component has flow properties that are different from the major fluid components, i.e., when the fluid mixture is Theologically non-homogeneous. 

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