Non-Newtonian fluids behavior

We performed calibration tests for three low-impedance wedge materials, polyetherimide, acrylic (Lucite), and polystyrene. Table 5-4 lists the liquids used for the calibration tests note that all of the liquids have similar densities but vary in viscosity. The calibration results are shown in Fig. 5-40, which reveals that Lucite is the best of the three as a wedge material for measuring viscosity. However, all of the measured viscosities are lower than their expected values. The discrepancies may be attributed to non-Newtonian fluid behavior, surface wetting, and poor sensitivity. 

Dextran can be produced either directly by batch fermentation or indirectly by the use of the enzyme complex dextransucrase mentioned above. Direct production is, of course, the simpler process, but molecular weights of dextrans are varying. The fermentation process is performed in stirred and aerated bioreactors with typical volumes of up to 200 m. Bacterial growth requires amino acids and growth factors. Fermentation is started at 25 - 30 C and a pH of 6.5 - 7.0, dropping to about 4.5 at the end of the production cycle (after about 48 hours) due to formation of lactic acid as a by-product. Maintenance of an adequate dissolved oxygen concentration is problematic due to the non-Newtonian fluid behavior of the nutritional... 

It is customary to account for the non-Newtonian fluid behavior by introducing the so called effective viscosity to define various dimensionless groups. Unlike its constant value for Newtonian liquids, the effective viscosity of non-Newtonian pseudoplastic type fluids depends upon the operating conditions (e.g., gas and liquid velocities) as well as on the geometrical details of the system. Indeed, the lack of a rationed definition of the apparent viscosity or characteristic shear rate appears to be the main impediment in extending the well established predictive correlations for Newtonian media to non-Newtonian media. When we develop correlations for design parameters in bubble columns with non-Newtonian media in an analogous manner to the case of Newtonian media, Newtonian viscosity p is simply replaced by an apparent viscosity for non-Newtonian media. 

If the capillary rheometer is used to compare different polymers, it is not necessary to go through the various correction procedures. However, if one wants to know the absolute values of the viscosity, it is important to apply the various correction factors. The most important corrections are the correction of the shear rate for non-Newtonian fluid behavior (often referred to as Rabinowitsch correction) and the correction of the shear stress for entrance effects (often referred to as Bagley correction). These are the most common corrections applied to capillary rheometers. Other corrections that are sometimes considered are corrections for viscous heating, corrections for the effect of pressure on viscosity, corrections for compressibility, correction for time effects, etc. If many corrections are applied to the data, the whole measurement and data analysis procedure can become very complex and time consuming. 

Non-Newtonian fluid behavior in pastes and fine suspensions can be described by the Bingham model. The fluid remains rigid below a yield stress Tq and then flows when T exceeds Tq. 

As a starting point, consider the behavior of the fluid after extrusion. Immediately after extrusion, the fluid experiences the die swell phenomenon, where the velocity profile flattens. Ultimately, when the fiber solidifies, the velocity profile will be flat (i.e., plug flow). In between, a velocity profile will possibly be first formed and then distorted by solidification at the fiber exterior. Even if the profile becomes fully developed, however, it will not have a parabolic shape but rather will have a blunted form because of the polymer s non-Newtonian fluid behavior. In essence, then, the fiber in the post-extrusion-solidification region will have a velocity profile that can be closely approximated by assuming plug flow (i.e., a constant V across the fiber cross section). 

More recently, Chhabra et al. (1995) have measured drag on straight chains of touching spheres in power-law fluids. They were able to relate the drag on a chain to that of a single sphere by introducing two correction factors, one for the shape and the other for the non-Newtonian fluid behavior. 

Fig. 5 shows the relation of shear stress and shear rate of silver paste with different wt % of thinner. The trend of non-Newtonian behavior is consistent with the results found by Chhabra Richardson, (1999) for the types of time-independent flow behavior. The time-independent non-Newtonian fluid behavior observed is pseudoplasticity or shear-thinning characterized by an apparent viscosity which decreases with increasing shear rate. Evidently, these suspensions exhibit both shear-thinning and shear thickening behavior over different range of shear rate and different wt% of thinner. The viscosity and shear stress relationship with increasing percentage of thinner is plotted in Fig 6. It is clearly observed that both viscosity and shear stress decreases resp>ectively. 

Applications of digital computers in ChE Non-Newtonian fluid behavior (Skelland) Process and control dynamics (Swanson) Process control through instrumentation (Swanson)... 

Illustration of non-Newtonian fluid behavior as well as a Bingham plastic fluid... 

Non-Newtonian Fluids Die Swell and Melt Fracture. Eor many fluids the Newtonian constitutive relation involving only a single, constant viscosity is inappHcable. Either stress depends in a more complex way on strain, or variables other than the instantaneous rate of strain must be taken into account. Such fluids are known coUectively as non-Newtonian and are usually subdivided further on the basis of behavior in simple shear flow. 

For non-Newtonian fluids the correlations in Figure 35 can be used with generally acceptable accuracy when the process fluid viscosity is replaced by the apparent viscosity. For non-Newtonian fluids having power law behavior, the apparent viscosity can be obtained from shear rate estimated by... 

The main use of these clays is to control, or adjust, viscosity in nonaqueous systems. Organoclays can be dispersed in nonaqueous fluids to modify the viscosity of the fluid so that the fluid exhibits non-Newtonian thixotropic behavior. Important segments of this area are drilling fluids, greases (79,80), lubricants, and oil-based paints. The most used commercial products in this area are dimethyl di (hydrogen a ted tallow) alkylammonium chloride [61789-80-8] dimethyl (hydrogen a ted tallow)aLkylbenzylammonium chloride [61789-72-8] and methyldi(hydrogenated tallow)aLkylbenzylammonium chloride [68391-01-5]. 

Eig. 7. Viscoelastic behavior of encapsulant materials (a) Newtonian fluid (b) non-Newtonian fluid. 

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 viscosity of a fluid arises from the internal friction of the fluid, and it manifests itself externally as the resistance of the fluid to flow. With respect to viscosity there are two broad classes of fluids Newtonian and non-Newtonian. Newtonian fluids have a constant viscosity regardless of strain rate. Low-molecular-weight pure liquids are examples of Newtonian fluids. Non-Newtonian fluids do not have a constant viscosity and will either thicken or thin when strain is applied. Polymers, colloidal suspensions, and emulsions are examples of non-Newtonian fluids [1]. To date, researchers have treated ionic liquids as Newtonian fluids, and no data indicating that there are non-Newtonian ionic liquids have so far been published. However, no research effort has yet been specifically directed towards investigation of potential non-Newtonian behavior in these systems. 

The flow of plastics is compared to that of water in Fig. 8-5 to show their different behaviors. The volume of a so-called Newtonian fluid, such as water, when pushed through an opening is directly proportional to the pressure applied (the straight dotted line), the flow rate of a non-Newtonian fluid such as plastics when pushed through an opening increases more rapidly than the applied pressure (the solid curved line). Different plastics generally have their own flow and rheological rates so that their non-Newtonian curves are different. 

Certain polymeric systems can become more viscous on shearing ( shear thickening ) due to shear-introduced organization. These systems become more resistant to flow as the crystals form so that the introduction of the shear increases their viscosity. Figure 6.5 shows the viscosity versus strain rate relationship for Newtonian and non-Newtonian fluids, highlighting the differences in their behaviors. 

In order to understand the nature and mechanisms of foam flow in the reservoir, some investigators have examined the generation of foam in glass bead packs (12). Porous micromodels have also been used to represent actual porous rock in which the flow behavior of bubble-films or lamellae have been observed (13,14). Furthermore, since foaming agents often exhibit pseudo-plastic behavior in a flow situation, the flow of non-Newtonian fluid in porous media has been examined from a mathematical standpoint. However, representation of such flow in mathematical models has been reported to be still inadequate (15). Theoretical approaches, with the goal of computing the mobility of foam in a porous medium modelled by a bead or sand pack, have been attempted as well (16,17). 

It is also evident that this phenomenological approach to transport processes leads to the conclusion that fluids should behave in the fashion that we have called Newtonian, which does not account for the occurrence of non-Newtonian behavior, which is quite common. This is because the phenomenological laws inherently assume that the molecular transport coefficients depend only upon the thermodyamic state of the material (i.e., temperature, pressure, and density) but not upon its dynamic state, i.e., the state of stress or deformation. This assumption is not valid for fluids of complex structure, e.g., non-Newtonian fluids, as we shall illustrate in subsequent chapters. 

This classification of material behavior is summarized in Table 3-1 (in which the subscripts have been omitted for simplicity). Since we are concerned with fluids, we will concentrate primarily on the flow behavior of Newtonian and non-Newtonian fluids. However, we will also illustrate some of the unique characteristics of viscoelastic fluids, such as the ability of solutions of certain high polymers to flow through pipes in turbulent flow with much less energy expenditure than the solvent alone. 

The typical viscous behavior for many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels) is illustrated by the curves labeled structural in Figs. 3-5 and 3-6. These fluids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. In some materials this can be attributed to a reversible structure or network that forms in the rest or equilibrium state. When the material is sheared, the structure breaks down, resulting in a shear-dependent (shear thinning) behavior. Some real examples of this type of behavior are shown in Fig. 3-7. These show that structural viscosity behavior is exhibited by fluids as diverse as polymer solutions, blood, latex emulsions, and mud (sediment). Equations (i.e., models) that represent this type of behavior are described below. 

Differentiate between Newtonian and non-Newtonian fluids, and know which behavior is appropriate for a certain type of material in the fluid state. 

---