Viscosity initial density dependence

Strehlow, T., and Vogel, E., Temperature Dependence and Initial Density Dependence of the Viscosity of Sulfur Hexafluoride, Physica A 161,101,1989,... 

Hendl, S. Vogel, E. (1992). The viscosity of gaseous ethane and its initial density dependence. Fluid Phase Equil, 76,259-272. 

Vogel, E., Bich, E. Nimz, R. (1986). The initial density dependence of the viscosity of organic vapours Benzene and methanol. Physica, A 139,188-207. 

The initial-density dependence r for the viscosity, defined in equation (14.8) - and represented by in equation (5.6) - is shown versus temperature in Figure 14.6b. The... 

Table 14.10. Coefficients for the representation of the viscosity and thermal conductivity of ethane (dilute gas and initial-density dependence).

At present for polyatomic gases, this is possible only for viscosity, since the results for the thermal conductivity are not yet at the stage where they can be used for correlation or prediction purposes. In principle, the best approach to produce the correlation of viscosity at low densities is to analyze the available experimental data in conjunction with theory. Unfortunately, for ethane the available experimental data on the viscosity in the vapor phase at low density are very scarce (Hendl et al 1994), and it has not been possible to take advantage of these data in the development of the initial-density contribution. Thus the theory has been used in a predictive mode to generate the initial-density dependence of the viscosity. This was deemed necessary for ethane, since the vapor phase covers an industrially important and easily accessible region where the need for accurate transport properties is significant. 

In order to separate the initial-density dependence of the viscosity from higher-density terms, the excess viscosity is expressed as... 

Once the excess viscosity data have been generated, the initial density dependence can be evaluated as V and subtracted from the excess to obtain the higher-density contribution, Ah , by use of equation (14.55). ThCTe is no theoretical guidance to the functional form of Ah , but it is customary to express it in terms of power series in the density and in the reciprocal reduced temperature. Thus,... 

The Rainwater-Friend theory that has proved so successful in the representation of the initial-density dependence of the viscosity of pure gases has not been extended to mixtures. It is therefore necessary to make use of the Thome-Enskog equations... 

The consistency (fluidity) of an initial mixture depends on the binder filler weight ratio, all other parameters (binder viscosity, microsphere type, shape, size, density, and mixing conditions) being equal. The mixtures are casting compositions (viscous fluids) at small microsphere concentrations, while they become molding compositions (pastes) at higher concentrations. Thus, the fluidity of a syntactic composition depends primarily on the filler concentration and not on the binder viscosity (Fig. 1)73 ... 

To some extent the way the computation is carried out is governed by the objectives. Usually information about one or more of the following is sought pressure distribution in the lubricant film minimum thickness of the film shape of the film. Items of input into the problem are load, radii of curvature of the boundaries, material properties (such as viscosity and density of the fluid together with their pressure and temperature dependence, elastic constants of the solid boundary material), and speed. A set of assumed initial conditions is used to... 

Qo equation (6.41) of Chapter 6. Moreover, from the correlations for AX and At temperature-dependent initial-density coefficients for the thermal conductivity and the viscosity are deduced and then conqjared with the theoretical predictions presented in Chapter 5. 

Similar convection processes occur in liquids, though at a slower rate according to the viscosity of the liquid. However, it cannot be assumed that convection in a liquid results in the colder component sinking and the warmer one rising. It depends on the liquid and the temperatures concerned. Water achieves its greatest density at approximately 4°C. Hence in a column of water, initially at 4°C, any part to which heat is applied will rise to the top. Alternatively, if any part is cooled below 4°C it, too, will rise to the top and the relatively warmer water will sink to the bottom. The top of a pond or water in a storage vessel always freezes first. 

To achieve the desired cast density for Octol of 1.8g/cc it is necessary that the ratio of HMX TNT be 3 1. However, at this ratio the apparent viscosity, or efflux, is strongly dependent on the polymorphic variety of HMX used and on its particle size distribution. In the initial pilot production of Octol (Ref 3) it was found that for the desired efflux of < 15 sec, 60—70% of the solid HMX must consist of the beta-polymorph having particle diameters in the range of 500—800 microns. Such precise control of particle size was not possible at that time and early Octol casts were made at approximately 50 secs efflux. The economical production of Octol with a satisfactorily short efflux time continues to present a problem in loading shells with this expl (Refs 4, 11 29)... 

A kinetic study for the polymerization of styrene, initiated with n BuLi, was designed to explore the Trommsdorff effect on rate constants of initiation and propagation and polystyryl anion association. Initiator association, initiation rate and propagation rates are essentially independent of solution viscosity, Polystyryl anion association is dependent on media viscosity. Temperature dependency correlates as an Arrhenius relationship. Observations were restricted to viscosities less than 200 centipoise. Population density distribution analysis indicates that rate constants are also independent of degree of polymerization, which is consistent with Flory s principle of equal reactivity. 

Yarin and Weiss[357] also determined the number and size of secondary droplets, as well as the total ejected mass during splashing. Their experimental observations by means of a computer-aided charge-coupled-device camera and video printer showed that the dependence of the critical impact velocity, at which splashing initiates, on the physical properties (density, viscosity, and surface tension) and the frequency of the droplet train is universal, and the threshold velocity may be estimated by ... 

Background on Spin Casting. As early as 1958, Emslie, et al. (A) proposed a theoretical treatment of spin casting for nonvolatile Newtonian fluids. This theory predicted that films formed on a flat rotating disc would have radial thickness uniformity. They predicted that the final film thickness would depend on spin speed (w) and viscosity (ij) as well as other variables such as liquid density and initial film thickness. The dependence of thickness on u> and ij was also recognized by many of the other authors reviewed in this paper, and their proposed relationships are compared in Table I. Acrivos, et al. (5) extended the Emslie treatment to the general case of non-Newtonian fluids, a category into which most polymers fall. Acrivos predicted that non-Newtonian fluids would yield films with non-uniform radial thickness. 

Equation (228) is the normalized density correlation function in the Fourier frequency plane and has the same structure as Eq. (210), which is the density correlation function in the Laplace frequency plane. i/ (z) in Eq. (228) is the memory function in the Fourier frequency plane and can be identified as the dynamical longitudinal frequency. Equation (228) provides the expression of the density correlation function in terms of the longitudinal viscosity. On the other hand, t]l itself is dependent on the density correlation function [Eq. (229)]. Thus the density correlation function should be calculated self-consistently. To make the analysis simpler, the frequency and the time are scaled by (cu2)1 2 and (cu2)-1 2, respectively. As the initial guess for rjh the coupling constant X is considered to be weak. Thus rjt in zeroth order is... 

Division of the total tensile strain under conditions of F = const into several components 25,6R,69) produced interesting results (see Fig. 8). It has been found that the behavior of molten low-density polyethylene (Fig. 8a) is qualitatively different from polyisobutylene (Fig. 8 b) the extension of which was performed under temperature conditions where the high-elasticity modulus, relaxation time, and initial Newtonian viscosity practically coincided (in the linear range) in the compared polymers. Flow curves in the investigated range of strain velocities were also very close to one another (Fig. 21). It can be seen from the comparison of dependencies given in Fig. 8a,... 

The initiation step could also be positively affected by the above-mentioned transport properties, as the efficiency factor f assumes higher values with respect to conventional liquid solvents due to the diminished solvent cage effect One further advantage is constituted by the tunability of the compressibility-dependent properties such as density, dielectric constant, heat capacity, and viscosity, all of which offer additional possibilities to modify the performances of the polymerization process. This aspect could be particularly relevant in the case of copolymerization reactions, where the reactivity ratios of the two monomers, and ultimately the final composition of the copolymer, could be controlled by modifying the pressure of the reaction system. 

Eq. (8) shows the dependency of the critical thickness with mass m, radius rp, and velocity v0 of the inert particles coated with plastic and with the viscosity of the material that coats the sand fi. For the experimental conditions (total mass of sand, 30 g mass of plastic in the feed, 1 g sand particle diameter, between 0.6 and 1.2 mm sand density 2600 kg m-3, average velocity of the particles in the annular zones, 0.25ms-1 [7], the critical thickness predicted by Eq. (8) is 250 p,m. In this calculation, the viscosity of the plastic has been taken at its fusion temperature, 16 poises, because it is in the initial step of fusion when the stickiness of the plastic is maximum point. 

We should note that the Navier-Stokes equation holds only for Newtonian fluids and incompressible flows. Yet this equation, together with the equation of continuity and with proper initial and boundary conditions, provides all the equations needed to solve (analytically or numerically) any laminar, isothermal flow problem. Solution of these equations yields the pressure and velocity fields that, in turn, give the stress and rate of strain fields and the flow rate. If the flow is nonisothermal, then simultaneously with the foregoing equations, we must solve the thermal energy equation, which is discussed later in this chapter. In this case, if the temperature differences are significant, we must also account for the temperature dependence of the viscosity, density, and thermal conductivity. 

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