Biochemical Engineering Fundamentals, Part 1 - Bailey J., Ollis D. 1989

Transport phenomena in biotechnological systems
Non-Newtonian fluids
Mathematical models of non-Newtonian fluids and corresponding parameters

Special cases of the general Ostwald–de Waele equation, or the power law for fluids, include dilatant, Newtonian, and pseudoplastic behavior:

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In some cases, flow occurs only when the shear stress exceeds a certain threshold value т₀. For Bingham plastic fluids, the equation applies:

For a finite т₀ and n < 1, the curve corresponding to Equation (8.93) takes the same form as the curve corresponding to the Casson equation [Equation (8.94)]:

In the subsequent study of Mass transfer coefficients, power consumption, mixing, etc., we will refer to microbial Suspensions or other liquid (gas-liquid) systems as (apparently) pseudoplastic, Newtonian, etc., and present equations relating the parameters of the corresponding model to the parameters of the system under study. The description of fluid flow types in Fig. 8.12 refers to their behavior under steady shear. Under transient conditions, arising, for example, from a step change in shear rate, A change in apparent viscosity η_v over time is often observed; transient states in such a system can only be described by a more structured model (in a sense analogous to the Structured models of Cell growth kinetics discussed in Ch. 7). Apparently, such transient states more accurately describe mixing with turbine impellers and turbulent mixing in non-Newtonian systems. The Development of more structured models, however, is a rather difficult task; in general, this area of mechanics is relatively poorly understood. Here, we limit ourselves to the remark that our understanding of the factors responsible for non-Newtonian behavior, and their mathematical description, are significantly inferior to the theoretical developments of other problems discussed in the previous sections of this chapter.

Non-Newtonian behavior can be characteristic of at least Two Types of systems: 1) suspensions of small particles and 2) solutions of high-molecular-weight compounds. Obviously, the boundary between these two types of systems becomes blurred if the diameter of polymer molecules exceeds 50—100 A or if the particle size decreases to less than a micrometer.