Viscosity expressions

The viscosity is determined by measuring the time it takes for a crude to flow through a capillary tube of a given length at a precise temperature. This is called the kinematic viscosity, expressed in mm /s. It is defined by the standards, NF T 60-100 or ASTM D 445. Viscosity can also be determined by measuring the time it takes for the oil to flow through a calibrated orifice standard ASTM D 88. It is expressed in Saybolt seconds (SSU). 

The reduced viscosity expresses the specific viscosity per unit of solute concentration. 

When reviewing the subject of plastic melt flow, the subject of viscosity is involved. Basically viscosity is the property of the resistance of flow exhibited within a body of material. Ordinary viscosity is the internal friction or resistance of a plastic to flow. It is the constant ratio of shearing stress to the rate of shear. Shearing is the motion of a fluid, layer by layer, like a deck of cards. When plastics flow through straight tubes or channels they are sheared and the viscosity expresses their resistance. 

Cheremisinoff and Davis (1979) relaxed these two assumptions by using a correlation developed by Cohen and Hanratty (1968) for the interfacial shear stress, using von Karman s and Deissler s eddy viscosity expressions for solving the liquid-phase momentum equations while still using the hydraulic diameter concept for the gas phase. They assumed, however, that the velocity profile is a function only of the radius, r, or the normal distance from the wall, y, and that the shear stress is constant, t = tw. ... 

For the liquid phase, Cheremisinoff and Davis (1979) solved the momentum equation using von Karman s and Deissler s eddy viscosity expressions. 

Vsc Dynamic viscosity of the material in centistokes (cS). Obtained when the absolute viscosity, expressed as centipoise, is divided by the specific gravity of the material. 

It appears that the formal theories are not sufficiently sensitive to structure to be of much help in dealing with linear viscoelastic response Williams analysis is the most complete theory available, and yet even here a dimensional analysis is required to find a form for the pair correlation function. Moreover, molecular weight dependence in the resulting viscosity expression [Eq. (6.11)] is much too weak to represent behavior even at moderate concentrations. Williams suggests that the combination of variables in Eq. (6.11) may furnish theoretical support correlations of the form tj0 = f c rjj) at moderate concentrations (cf. Section 5). However the weakness of the predicted dependence compared to experiment and the somewhat arbitrary nature of the dimensional analysis makes the suggestion rather questionable. 

Unlike Williams, Chikahisa attempts to deal directly with entangling systems. The result is a viscosity expression which is not far from that observed experimentally, but the form is unfortunately more dependent on a series of intermediate assumptions about the nature of the friction forces than on the basic transport theory itself. Although not implausible, the assumptions are nevertheless arbitrary and lacking in theoretical justification. 

Using the viscosity versus temperature table evaluated from the Chapman-Enskog expression in the previous problem, determine a best fit for the S parameter in the form of a Sutherland viscosity expression. Assume reference values of 7o = 273 K and i o = 1.716 x 10-5 N-s/m2. 

Tn GPC the product [77] M has been widely accepted as a universal calibration parameter, where [77] is the intrinsic viscosity and M is the molecular weight. This product is defined by the Einstein-Simha viscosity expression (I) as... 

It can be shown following the arguments of Newman et al. (3), that only the number-average molecular weight and hydrodynamic radius are valid when the Einstein-Simha viscosity expression is applied to whole polymers. Higher moments require a polydispersity factor. Thus,... 

By use of both the appropriate value for in Equation 2 and the Mark-Houwink viscosity expression, one may write... 

C. Similarity Between the Viscosity Expressions of Kadanoff and Swift and Those of Geszti... 

The numerical constants in these expressions are appropriate to intrinsic viscosities expressed in dl-g-1, but with AtM in ml g-1. These are the units most commonly employed at present. 

Intrinsic viscosity is the most useful of the various viscosity expressions because it can be related to molecular weight by the Mark-Houwink-Sakurada equation ... 

Because much work was done with viscosity expressed in poise in sensory assessment of viscosity, the same tradition will be continued in Chapter 7 on sensory assessment of viscosity. 

By comparison of the dynamic viscosity expressions without and with internal viscosity [see Eqs. (3.1.15) and (3.3.16), respectively], we see that in the former case the sum tends to zero for large co, unlike in the latter we conclude that in the presence of internal viscosity the dynamic viscosity deviates from what is commonly regarded as a general law. The reason lies in the fact that with internal viscosity the intramolecular tension contains a contribution depending on x h,t), unlike the other models where it depends on the elastic force only, that is, on x h,t). 

Thb is an empirical measurement of "paste viscosity, expressing the time (in seconds) for 50 ml. of hot gelatinized 4.7% starch paste to flow through a standard orifice. 

Let us start with Eq. (1.8). The average quantity vf) appearing in the intrinsic viscosity expression (1.12) is obtained from... 

In order to derive an intrinsic viscosity expression for random chain molecules in the presence of hydrodynamical interactions we must evaluate the eigen-value A k) of the tensor G k) in accordance with Eq. (4.8). We find... 

Viscosity (Expressed in Centipoises) of Ethylene Glycol-Methanol-Water Mixtures as a Function of Temperature11... 

Under conditions of low pressure, the viscosity expression of the multicomponent mixture is much more complex. It is usual to use two simple methods which were developed by Wilke as well as Heming and Zipperer. 

The viscosity expression of Richert and Bassler (1990) (see Chapter 3) suggests the presence of a logarithmic relaxation time which varies as 1/F. A relation between experimental glass transition temperatures and quenching rates has been obtained on this basis which is given by. 

Then the apparent viscosity expression that covers the entire range of Darcy velocity is... 

Here, j = 1 for the aqueous phase, 2 for the oleic phase, and 3 for the microemulsion phase. The a parameters are determined by matching laboratory microemulsion viscosities at several compositions. In the absence of surfactant and polymer, aqueous and oleic phase viscosities reduce to pure water and oil viscosities ( a and 1 0), respectively. When polymer is present, is replaced by polymer viscosity ( Jp). Figure 7.28 shows an example of microemulsion viscosity expressed in the preceding equation, where a = (2, 3, 0, 0.9, 0.7), a = 1 cP, and j o = 5 cP. 

Beside these two examples, there is the general fact that if a pressure-driven dilfusivity expressed in m -Pa-sec is multiplied by a viscosity expressed in Pa-sec, the product has dimensions (length). Thus for several decades, the ideas have been accepted that... 

Figure 2. Effect of molecular weight on reduced bulk viscosity expressed as a master curve for fractionally precipitated samples of (BAB)X which contain 50 wt % polystyrene and MA = 13,500. T = 463°K.

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