Viscosity-Pressure Relationship

Polyalkylene glycols for use in engineering and lubrication applications are usually homopolymers of propylene oxide or random copolymers. The relative proportions of ethylene oxide and propylene oxide have significant effects on several properties, e.g. pour point, water solubility and pressure-viscosity relationship. 

The underlying solution technique used In this paper Is the Newton-Raphson scheme, refined by Houpert and Hamrock [3], which Incorporates lubricant compressibility, the Roelands pressure-viscosity relationship, an Improved elastic calculation and variable mesh spacing. 

Some selected chemical and physical properties of naphthalene are given in Table 1. Selected values from the vapor pressure—temperature relationship for naphthalene are Hsted in Table 2, as are selected viscosity—temperature relationships for Hquid naphthalene. Naphthalene forms a2eotropes with several compounds some of these mixtures are Hsted in Table 3. 

Two new LDPE resins are proposed to be processed on a similar extruder as described in the example in Section 1.5.1. The extruder here is configured with a downstream gear pump such that the discharge pressure for the extruder is targeted at 7 MPa. The resin manufacturer has provided viscosity data in the form of a viscosity relationship ... 

Woodman, A. L., W. J. Murbach, and M. H. Kaufman, Vapor Pressure and Viscosity Relationships fora Homologous Series of a, a -Dinitriles. J. Phys. Chem., 1960 64, 658-660. 

T 8 — Molecular weight-intrinsic viscosity relationship and molecular weight distribution of low pressure polyethylenes. J. Polymer Sci. 24,333 (1957). 

The effect of osmotic pressure in macromolecular ultraflltra-tlon has not been analyzed in detail although many similarities between this process and reverse osmosis may be drawn. An excellent review of reverse osmosis research has been given by Gill et al. (1971). It is generally found, however, that the simple linear osmotic pressure-concentration relationship used in reverse osmosis studies cannot be applied to ultrafiltration where the concentration dependency of macromolecular solutions is more complex. It is also reasonable to assume that variable viscosity effects may be more pronounced In macromolecular ultra-filtration as opposed to reverse osmosis. Similarly, because of the relatively low diffuslvlty of macromolecules conqiared to typical reverse osmosis solutes (by a factor of 100), concentration polarization effects are more severe in ultrafiltration. 

Viscosity-pressure behaviour The relationship between viscosity and pressure, the pressure viscosity coefficient, is an important parameter for lubrication performance. Higher values are obtained for polymers with a high degree of propylene oxide units. 

It is assumed that a Poiseuille type pressure-flow relationship is valid for the individual vessels, whereby the apparent blood viscosity can be diameter dependent (Fahraeus-Lindqvist effect). The symmetric conductance tensor is depen-... 

Data for a typical mineral lubricant is used in the calculation, and the lubricant properties are viscosity, Tio = 0.96x10" Ns/mm, pressure-viscosity coefficient, a = 0.01820 mm /N, and index in the Roelands viscosity-pressure relationship is 0.67. 

Fiber dimensions have been studied for hemodialysis. When blood is circulated through the fiber lumen (m vivo), a significant reduction in apparent blood viscosity may occur if the flow-path diameter is below 100 p.m (11). Therefore, current dialy2ers use fibers with internal diameters of 180—250 p.m to obtain the maximum surface area within a safe range (see Dialysis). The relationship between the fiber cross section and the blood cells is shown in Figure 5. In many industrial appUcations, where the bore fluid is dialy2ed under elevated pressure (>200 kPa or 2 atm), fibers may burst at points of imperfection. Failure of this nature is especially likely for asymmetric fibers that display a large number of macro voids within the walls. 

Table 2. Selected Values of Vapor Pressure—Temperature and Viscosity—Temperature Relationship s for Naphthalene ...

The results of [91] supply ample evidence in support of this qualitative picture. The authors determined the baric viscosity factor b = [0 In j/(0P)-1] T (where t] is viscosity, P is pressure) for impact-resistant polystyrene filled with antimony trioxide. The viscosity piezocoefficient is known to be related to the free volume. A very simple formula for this relationship has been proposed in [92] in this form ... 

The uncertainty of calculating the Poiseuille number from the measurements must be taken into account. The viscosity-pressure relationship of certain liquids (e.g., isopropanol, carbon tetrachloride) must be kept in mind to obtain the revised theoretical flow rate. The effect of evaporation from the collection dish during the mass flow rate measurement must be taken into consideration. The effect of evaporation of collected water into the room air may not be negligible, and due to the extremely low mass flow rates through the micro-channel this effect can become significant. 

This integrated version of Equation (3.15) requires viscosity to be constant as well as density, but this assumption is not strictly necessary. See Problem 3.15. Write separate equations for the pressure drop in the large and small reactors and take their ratio. The physical properties cancel to give the following, general relationship ... 

The relationship between film thickness of hexadecane with the addition of cholesteryl LCs and rolling speed under different pressures is shown in Fig. 25 [50], where the straight line is the theoretic film thickness calculated from the Hamrock-Dowson formula based on the bulk viscosity under the pressure of 0.174 GPa. It can be seen that for all lubricants, when speed is high, it is in the EHL regime and a speed index 4> about 0.67 is produced. When the rolling speed decreases and the film thickness falls to about 30 nm, the static adsorption film and ordered fluid film cannot be negligible, and the gradient reduces to less than 0.67 and the transition from EHL to TFL occurs. For pure hexadecane, due to the weak interaction between hexadecane molecules and metal surfaces, the static and ordered films are very thin. EHL... 

In order to set up the relationship among the pressure, speed, and viscosity of lubricants without polar additives, Luo et al. [19] define the fluid factor L as ... 

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