Newtonian fluids behavior

The only two product physical properties needed are density and viscosity. Generally, parenterals, as the most solution-type products, will follow Newtonian fluid behavior and may also be considered incompressible. Therefore, point densities and viscosities can be used satisfactorily. 

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... 

Unfortunately, the Reynolds-Nusselt dimensional analysis studies are not directly applicable to polymer melt and rubber processing for two important reasons. First, they are based on Newtonian fluid behavior, and second, they do not include viscous dissipation heating. 

The molecular theory of extensional viscosity of polymer melts is again based oti the standard tube model. It considers the linear viscoelastic factors such as reptation, tube length fluctuations, and thermal constraint release, as well as the nonlinear viscoelastic factors such as segment orientations, elastic contractimi along the tube, and convective constraint release (Marrucci and lannirubertok 2004). Thus, it predicts the extensional stress-strain curve of monodispersed linear polymers, as illustrated in Fig. 7.12. At the first stage, the extensional viscosity of polymer melts exhibits the Newtonian-fluid behavior, following Trouton s ratio... 

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. 

Assuming Newtonian fluid behavior (constant viscosity), the no-slip assumption (v = 0 at the die wall), and fully developed flow, a parabolic velocity distribution can be derived for the material flowing down the capillary ... 

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). 

From Figure 16.3, it can be observed that the viscosity of the solution increased linearly with the increase of shear rate, showing a Newtonian fluid behavior for PI-3 in the analyzed regime. The viscosity measured at a shear rate of 100 s increased from 0.074 to 4.17 Pa s as the concentration of PI-3 increased from 12 up to 25 wt%. 

In contrast to simple elastic solids and viscous liquids, the situation with polymeric fluids is somewhat more complicated. Polymer melts (and most adhesives are composed of polymers) display elements of both Newtonian fluid behavior and elastic solid behavior, depending on the temperature and the rate at which deformation takes place. One therefore characterizes polymers as viscoelastic materials. Furthermore, if either the total strain or the rate of strain is low, the behavior may be described as one of linear or infinitesimal viscoelasticity. In such a case, the stress-deformation relationship (the constitutive equation) involves not just a single time-independent constant but a set of constants called the relaxation spectrum,(2) and this, too, may be determined from a single stress relaxation experiment, or an experiment involving small-amplitude oscillatory motion. 

The present paper will use the very fast and accurate method of calculating the pressure and film thickness in eiastohydrodynamic lubricated conjunctions developed by Houpert and Hamrock (1986) and investigate the effects of a complete operating range of load, speed and materials parameters. The performance parameters to be studied are the details of the pressure spike including the amplitude, width and location of the spike, the mass flow rate, the center of pressure the minimum film thickness. Formulas will be developed to describe the performance parameters as a function of the operating parameters. The results to be presented are only applicable for idealized situations of smooth surfaces, Newtonian fluid behavior, isothermal and fully flooded lubrication conditions. 

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... 

This is a two-parameter model in which n describes the degree of deviation from Newtonian behavior, m, which has the units of Pa-s , is called the consistency. For n = 1 and m = IX, this model predicts Newtonian fluid behavior. For n < 1, the fluid is pseudoplastic while for n > 1 the fluid is dilatant. The Ellis model is a three-parameter model and is defined as... 

A.8 Efficiencies of Mixers and Striation Thickness Reduction. Calculate the shear and extension rates required to reduce the striation thickness 1000 times in 10 s in the three mixers—pure shear, uniaxial extensional, and simple shear—and then prove Eq. 6.81 assuming Newtonian fluid behavior. 

Most structured fluids do not obey a simple linear relationship between applied stress and flow (Newtonian fluid behavior). Most of these materials have viscosities, which decrease with increasing stress. Such an observation is known as shear thinning which becomes progressively significant as the volume concentration of solid particles increases. 

The ratio of the fluid relaxation time to the timescale for flow If defines a dimensionless group termed the Deborah number, De = /tf. This group has been used in the literature to characterize deviations from Newtonian flow behavior in polymers [6]. Specifically, in flows such as simple steady shear flow where a single flow time tf = y can be defined, it has been observed that for De 1, a Newtonian fluid behavior is observed, whereas for De 1, a non-Newtonian fluid response is observed. However, in flows where multiple timescales can be identified, for example, shear flow between eccentric cylinders, the Deborah number is clearly not unique. In this case, it is generally more useful to discuss the effect of flow on polymer liquids in terms of the relative rates of deformation of material lines and material relaxation. In a steady flow, this effect can be captured by a second dimensionless group termed the Weissenberg number, Wi = k A, where k is a characteristic deformation rate and A is a characteristic fluid relaxation time. For polymer liquids, A is typically taken to be the longest relaxation time Ap, and for steady shear flow, k = y, which leads to Wi = y Ap. 

Wi therefore characterizes the relative intensity of fluid relaxation and shear-induced molecular alignment. Thus, for Wi 1, relaxation outcompetes shear-induced orientation and disentanglement, so shear has little effect on polymer structure and a Newtonian fluid behavior is observed. However, for Wi 1, polymer molecules are... 

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