Newtonian hquid

Viscous Hquids are classified based on their rheological behavior characterized by the relationship of shear stress with shear rate. Eor Newtonian Hquids, the viscosity represented by the ratio of shear stress to shear rate is independent of shear rate, whereas non-Newtonian Hquid viscosity changes with shear rate. Non-Newtonian Hquids are further divided into three categories time-independent, time-dependent, and viscoelastic. A detailed discussion of these rheologically complex Hquids is given elsewhere (see Rheological measurements). 

For a Hquid under shear the rate of deformation or shear rate is a function of the shearing stress. The original exposition of this relationship is Newton s law, which states that the ratio of the stress to the shear rate is a constant, ie, the viscosity. Under Newton s law, viscosity is independent of shear rate. This is tme for ideal or Newtonian Hquids, but the viscosities of many Hquids, particularly a number of those of interest to industry, are not independent of shear rate. These non-Newtonian Hquids may be classified according to their viscosity behavior as a function of shear rate. Many exhibit shear thinning, whereas others give shear thickening. Some Hquids at rest appear to behave like soHds until the shear stress exceeds a certain value, called the yield stress, after which they flow readily. 

Viscosity is equal to the slope of the flow curve, Tf = dr/dj. The quantity r/y is the viscosity Tj for a Newtonian Hquid and the apparent viscosity Tj for a non-Newtonian Hquid. The kinematic viscosity is the viscosity coefficient divided by the density, ly = tj/p. The fluidity is the reciprocal of the viscosity, (j) = 1/rj. The common units for viscosity, dyne seconds per square centimeter ((dyn-s)/cm ) or grams per centimeter second ((g/(cm-s)), called poise, which is usually expressed as centipoise (cP), have been replaced by the SI units of pascal seconds, ie, Pa-s and mPa-s, where 1 mPa-s = 1 cP. In the same manner the shear stress units of dynes per square centimeter, dyn/cmhave been replaced by Pascals, where 10 dyn/cm = 1 Pa, and newtons per square meter, where 1 N/m = 1 Pa. Shear rate is AH/AX, or length /time/length, so that values are given as per second (s ) in both systems. The SI units for kinematic viscosity are square centimeters per second, cm /s, ie, Stokes (St), and square millimeters per second, mm /s, ie, centistokes (cSt). Information is available for the official Society of Rheology nomenclature and units for a wide range of rheological parameters (11). 

Polymer melts are frequendy non-Newtonian. In this case the earlier expression given for the shear rate at the capillary wall does not hold. A correction factor (3n + 1)/4n, called the Rabinowitsch correction, must be appHed in such a way that equation 21 appHes, where 7 is the tme shear rate at the wall and nis 2l power law factor (eq. 22) determined from the slope of a log—log plot of the tme shear stress at the wad, T, vs 7. For a Newtonian hquid, n = 1. A tme apparent viscosity, Tj, can be calculated from equation 23. 

Colloidal State. The principal outcome of many of the composition studies has been the delineation of the asphalt system as a colloidal system at ambient or normal service conditions. This particular concept was proposed in 1924 and described the system as an oil medium in which the asphaltene fraction was dispersed. The transition from a coUoid to a Newtonian Hquid is dependent on temperature, hardness, shear rate, chemical nature, etc. At normal service temperatures asphalt is viscoelastic, and viscous at higher temperatures. The disperse phase is a micelle composed of the molecular species that make up the asphaltenes and the higher molecular weight aromatic components of the petrolenes or the maltenes (ie, the nonasphaltene components). Complete peptization of the micelle seems probable if the system contains sufficient aromatic constituents, in relation to the concentration of asphaltenes, to allow the asphaltenes to remain in the dispersed phase. 

The traditional view of emulsion stability (1,2) was concerned with systems of two isotropic, Newtonian Hquids of which one is dispersed in the other in the form of spherical droplets. The stabilization of such a system was achieved by adsorbed amphiphiles, which modify interfacial properties and to some extent the colloidal forces across a thin Hquid film, after the hydrodynamic conditions of the latter had been taken into consideration. However, a large number of emulsions, in fact, contain more than two phases. The importance of the third phase was recognized early (3) and the lUPAC definition of an emulsion included a third phase (4). With this relation in mind, this article deals with two-phase emulsions as an introduction. These systems are useful in discussing the details of formation and destabilization, because of their relative simplicity. The subsequent treatment focuses on three-phase emulsions, outlining three special cases. The presence of the third phase is shown in order to monitor the properties of the emulsion in a significant manner. 

Non-Newtonian Flow For isothermal laminar flow of time-independent non-Newtonian hquids, integration of the Cauchy momentum equations yields the fully developed velocity profile and flow rate-pressure drop relations. For the Bingham plastic flmd described by Eq. (6-3), in a pipe of diameter D and a pressure drop per unit length AP/L, the flow rate is given by... 

Power Consumption of Impellers Power consumption is related to fluid density, fluid viscosity, rotational speed, and impeller diameter by plots of power number (g P/pN Df) versus Reynolds number (DfNp/ l). Typical correlation lines for frequently used impellers operating in newtonian hquids contained in baffled cylindri-calvessels are presented in Fig. 18-17. These cui ves may be used also for operation of the respective impellers in unbaffled tanks when the Reynolds number is 300 or less. When Nr L greater than 300, however, the power consumption is lower in an unbaffled vessel than indicated in Fig. 18-17. For example, for a six-blade disk turbine with Df/D = 3 and D IWj = 5, = 1.2 when Nr = 10. This is only about... 

Pour point ranges from 213 K (—80°F) for some kerosene-type jet fuels to 319 K (115°F) for waxy No. 6 fuel oils. Cloud point (which is not measured on opaque fuels) is typically 3 to 8 K higher than pour point unless the pour has been depressed by additives. Typical petroleum fuels are practically newtonian hquids between the cloud point and the boiling point and at pressures below 6.9 MPa (1000 psia). 

The existence of solid particles suspended in the hquid caused an increase in the hquid mixing time. In contrast, aeration caused a decrease in the hquid mixing time for water, but an increase for non-Newtonian hquids [14]. 

When estimating the stirrer power requirements for non-Newtonian liquids, correlations of the power number versus the Reynolds number (Re see Figure 7.8) for Newtonian hquids are very useful. In fact, Figure 7.8 for Newtonian liquids can be used at least for the laminar range, if appropriate values of the apparent viscosity are used in calculating the Reynolds number. Experimental data for various non-Newtonian fluids with the six-blade turbine for the range of (Re) below 10 were correlated by the following empirical Equation 12.1 [1] ... 

For Newtonian and non-Newtonian liquids, the shear stress at the wall is given by Eq. (13.54). The shear rate at the wall for Newtonian hquids can be expressed in terms of the volumetric flow, making = 1 in Eqs. (13.57) and (13.58). In this case, this quantity can be written as... 

A method for predicting pressure drop and volume fraction for non-Newtonian fluids in annular flow has been proposed by Eisen-berg and Weinberger AIChE J., 25, 240-245 [1979]). Das, Biswas, and Matra Can. J. Chem. Eng., 70, 431-437 [1993]) studied holdup in both horizontal and vertical gas/hquid flow with non-Newtonian hquids. Farooqi and Richardson Trans. Inst. Chem. Engp., 60, 292-305, 323-333 [1982]) developed correlations for holdup and pressure drop for gas/non-Newtonian liquid horizontal flow. They used a modified Lockhart-Martinelli parameter for non-Newtonian... 

Park [74] studied the efficiency of the ELM with non-Newtonian hquids in the removal of Zn, Pb, Ni and Cd from a simulated industrial wastewater using the Taylor-vortex column. The author adapted the shrinking core mathematical model of Liu and Liu [86] for quantitative description of the mass-transfer kinetics of the process [74]. The LM was prepared by the dissolution of 5 g dm of polyisobutylene in Soltrol 220 (see above). After complete dissolution of the polymer, the membrane phase... 

The ELMs could be apphed if the concentrations of precious metals in the wastewater range from 0.1 to 10,000 mg dm [90]. The apphcation of the ELMs based on non-Newtonian hquids and the Taylor-vortex column carry a lot of promise for industrial apphcations in the near future. Several commercial applications have been reported for ELM pertraction. Passivating is an operation commonly used in the galvanization industry to improve the resistance of metal parts to corrosion [87]. Metal parts are submerged into the passivating bath and become coated with Cr and/or Co to provide a protective layer against corrosion [87]. 

Theoretical Treatment The theoretical treatment of two-phase flow was reviewed by Cox and Mason [1971], Leal [1980], and Barthes-Biesel [1988]. As indicated before, dispersions of one Newtonian hquid in another result in systems that are characterized by elasticity and relaxation times, e.g., viz. Eq 7.57. 

Nearly a decade later, Oldroyd [1953, 1955] proposed a constitutive model similar to that of Frohlich and Sack, vahd at small deformations. The model considered low concentration of monodispersed drops of one Newtonian hquid in another. The interfacial tension and the viscoelastic properties of the interfacial film were incorporated by means of convected derivatives. The model provided the following relation for the complex modulus ... 

Anchors, helical ribbons and screws, are generally used for high viscosity and non-Newtonian hquids. The anchor and ribbon types are arranged with a close clearance at the vessel wall, whereas the helical screw has a smaller diameter and is often used inside a draft tube to promote liquid motion through out the vessel. Helical ribbons or interrupted ribbons are often used in horizontally-moimted cylindrical vessels. A variation of the simple helix mixer is the helicone (Figure 8.27), which has the additional advantage that... 

Three problems with outcome of blow molding axe related to rheology, including sharkskin, die swell, and parison dimensions (sag). These can be related to the influence of the above mechanisms of lubrication. Sharkskin is a surface roughness introduced by slip-stick effect between melt resin and metal surface. Melts are non-Newtonian hquids and shear rate is expressed usually by a power law ... 

S.3.2 The rheological behavior of polyesters in the presence of surfactants. Methods of measuring the rheological ch u acteristics were chosen to suit the features of the systems investigated. Unsaturated polyesters in the form of monomers in solution u e Newtonian hquids since flow does not cause changes in their structure and their viscosity does not depend on voltage shift. 

M.D. Giavedoru, F.A. Saita, The axisymmetric and plane cases of a gas phase steadily displacing a Newtonian hquid - a simultaneous solution of the governing equations. Physics of Lduids,... 

Einstein [63-65] was the pioneer in the study of the viscosity of dilute suspensions of neutrally buoyant rigid spheres without Brownian motion in a Newtonian hquid. He proposed the following relationship between the relative viscosity of the suspension and the volume fraction of the suspended particles... 

Polyethylene is a semicrystalline, thermoplastic material classified as a synthetic organic polymer. Depending on manufacturing process conditions, polyethylene melts between approximately 110-135°C to form a non-Newtonian hquid that may be molded into a wide variety of shapes utilizing various fabrication techniques. One of the first questions many scientists and engineers ask when beginning a career in the polyethylene industry is How can such a simple polymer, represented by the formula -(CH -CH ) -, result in such a complex business The answer lies in the enormous variety of molecular structures that are possible in the polymerization and, more importantly, copolymerization of ethylene with a wide variety of other 1-olefins. 

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