Non-Newtonian fluids defined

The generalized approach of Metzner and Reed AIChE /., 1, 434 [1955]) for time-independent non-Newtonian fluids defines a modified Reynolds number as... 

Reynolds number, dimensionless A1rc. , modified Reynolds number for non-newtonian fluids, defined by Eq, (5.50)... 

For a solid particle settling in a non-Newtonian fluid, defining... 

All fluids for which the viscosity varies with shear rate are non-Newtonian fluids. For uou-Newtouiau fluids the viscosity, defined as the ratio of shear stress to shear rate, is often called the apparent viscosity to emphasize the distiuc tiou from Newtonian behavior. Purely viscous, time-independent fluids, for which the apparent viscosity may be expressed as a function of shear rate, are called generalized Newtonian fluids. 

The term viscosity has no meaning for a non-Newtonian fluid unless it is related to a particular shear rate y. An apparent viscosity fia can be defined as follows (using the negative sign convention for stress) ... 

No methods appear to be available for the precise prediction of pressure drop when a non-Newtonian fluid is being heated or cooled, but Vaughn (V2) has shown that the procedure recommended most recently by McAdams (M4, p. 149) for Newtonian fluids is slightly conservative when applied to pressure-drop data on the heating of non-Newtonian solutions in laminar flow. McAdams has suggested evaluation of the fluid properties at a film temperature [Pg.116]

Based on the control volume approach and using the three-dimensional finite element formulations for heat conduction with convection and momentum balance for non-Newtonian fluids presented earlier, Turng and Kim [10] and [17] developed a three-dimensional mold filling simulation using 4-noded tetrahedral elements. The nodal control volumes are defined by surfaces that connect element centroids and sides as schematically depicted in Fig. 9.33. 

The former vanishes when the velocity of the moving plate is zero, and the latter vanishes in the absence of a pressure gradient, (a) Explain on physical and mathematical grounds why the solution of the same flow problem with a non-Newtonian fluid, for example, a Power Law model fluid, no longer leads to the same type of expressions, (b) It is possible to define a superposition correction factor as follows... 

The ambiguity of definition of Re encountered in the concentric annulus case is compounded here because of the fact that no viscosity is definable for non-Newtonian fluids. Thus, in the literature one encounters a bewildering array of definitions of Re-like parameters. We now present friction factor results for the non-Newtonian constitutive relations used above that are common and consistent. Many others are possible. 

In the case of fluids without yield stress, viscous and viscoelastic fluids can be distinguished. The properties of viscoelastic fluids lie between those of elastic solids and those of Newtonian fluids. There are some viscous fluids whose viscosity does not change in relation to the stress (Newtonian fluids) and some whose shear viscosity T] depends on the shear rate y (non-Newtonian fluids). If the viscosity increases when a deformation is imposed, we define the material as a shear-thickening (dilatant) fluid. If viscosity decreases, we define it as a shear-thinning fluid. 

In solutions, the most important physical factors that influence the solubility of ingredients are type of fluid, mixing equipment, and mixing operations. Generalized Newtonian fluids are ideal fluids for which the ratio of the shear rate to the shear stress is constant at a particular time. Unfortunately, in practice, usually liquid dosage forms and their ingredients are non-Newtonian fluids in which the ratio of the shear rate to the shear stress varies. As a result, non-Newtonian fluids may not have a well-defined viscosity [32],... 

Viscosity, is the internal friction of a fluid or its tendency to resist flow. It is denoted by the symbol t] for Newtonian fluids, whose viscosity does not depend on the shear rate, and for non-Newtonian fluids to indicate shear rate dependence by Depending on the flow system and choice of shear rate and shear stress, there are several equations to calculate. Here, it is defined by the equation ... 

To further illustrate the differences in the swallowing processes of Newtonian and non-Newtonian fluids, tcv was coined to represent the time to swallow a critical volume and was defined as the number of seconds needed to transport the first 1.0 mL of fluid into the esophagus. The greater the fcv value, the safer is the swallow, as the muscles in the pharynx have more time to close off entryway to the air passages before food arrives. The parameter tcv may be useful for characterizing the severity of deglutition in a particular patient. It may also be used as a benchmark for any improvement or deterioration in the patient. Because it would be difficult to obtain... 

The stress in viscoelastic liquids at steady-state conditions is defined, in simple shear flow, by the shear rate and two normal stress differences. Chapter 13 reviews the evolution of both the normal stress differences and the viscosity with increasing shear rate for different geometries. Semiquantitative approaches are used in which the critical shear rate at which the viscosity starts to drop in non-Newtonian fluids is estimated. The effects of shear rate, concentration, and temperature on die swell are qualitatively analyzed, and some basic aspects of the elongational flow are discussed. This process is useful to understand, at least qualitatively, the rheological fundamentals of polymer processing. 

To proceed formulating the momentum equation we need a relation defining the total stress tensor in terms of the known dependent variables, a constitutive relationship. In contrast to solids, a fluid tends to deform when subjected to a shear stress. Proper constitutive laws have therefore traditionally been obtained by establishing the stress-strain relationships (e.g., [11] [12] [13] [89] [184] [104]), relating the total stress tensor T to the rate of deformation (sometimes called rate of strain, i.e., giving the name of this relation) of a fluid element. However, the resistance to deformation is a property of the fluid. For some fluids, Newtonian fluids, the viscosity is independent both of time and the rate of deformation. For non-Newtonian fluids, on the other hand the viscosity may be a function of the prehistory of the flow (i.e., a function both of time and the rate of deformation). 

Next, you will consider flow in a pipe where the fluid is a non-Newtonian fluid, in particular a polymer melt. Take the viscosity as a Garreau function, Eq. (9.14). The parameters used here are rjo = 0.492, A = 0.1 and n = 0.8. The problem is defined by... 

From this equation a Reynolds number Nr, for non-newtonian fluids can be defined, on the assumption that for laminar flow... 

The definition of the Reynolds number for a non-Newtonian fluid is not uniquely defined as the viscosity is a function of the shear rate, that is, vm. Several approaches have been used to obtain an expression for Re in non-Newtonian fluids. One approach is to define a mean vis-... 

The transition from laminar to turbulent flow in a non-Newtonian fluid depends on the rheological model used to describe it. The concepts of a critical friction factor or critical Reynolds number have been used to define the boundary. For a power law fluid the critical friction factor fCT is given by (96)... 

Agitation in the bioreactor is promoted mainly by the top baffle. In the Newtonian fluid, a well-defined zone of 16 cm, having small loops, was observed. In non-Newtonian fluids, these loops were occasionally observed. In this case, the top baffle improves the flow in the bioreactor in a manner similar to the helical flow promoter proposed by Wu and Merchuk [17]. 

The viscosity is defined as the shear force per unit area necessary to achieve a velocity gradient of unity. Equation 5.2 applies to the majority of fluids, and they are generally known as Newtonian fluids, or fluids that display Newtonian behaviour. There are exceptions, and some fluids (usually liquids) do not conform to Equation 5.2, and these are generally classified as non-Newtonian fluids although within this grouping there is a sub classification with distinctly different "viscosity" behaviour for the fluids within the different groups. 

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