Hydrostatic pressure curve

From this relatively simple test, therefore, it is possible to obtain complete flow data on the material as shown in Fig. 5.3. Note that shear rates similar to those experienced in processing equipment can be achieved. Variations in melt temperature and hypostatic pressure also have an effect on the shear and tensile viscosities of the melt. An increase in temperature causes a decrease in viscosity and an increase in hydrostatic pressure causes an increase in viscosity. Topically, for low density polyethlyene an increase in temperature of 40°C causes a vertical shift of the viscosity curve by a factor of about 3. Since the plastic will be subjected to a temperature rise when it is forced through the die, it is usually worthwhile to check (by means of Equation 5.64) whether or not this is signiflcant. Fig. 5.2 shows the effect of temperature on the viscosity of polypropylene. 

Fig. 8.9 ST curves 7hs( obtained from Mossbauer measurements on [Fe(2-pic)3]Cl2-C2H50H at ambient and applied hydrostatic pressures of 600 and 1,300 bar (from [19])...

The influence of pressure has also been used to tune the ST properties of these ID chain compounds. Application of hydrostatic pressure ( 6 kbar) on [Fe(hyptrz)3] (4-chlorophenylsulfonate)2 H20 (hyptrz=4-(3 -hydroxypro-pyl)-l,2,4-triazole) provokes a parallel shift of the ST curves upwards to room temperature (Fig. 5) [41]. The steepness of the ST curves along with the hysteresis width remain practically constant. This lends support to the assertion that cooperative interactions are confined within the Fe(II) triazole chain. Thus a change in external pressure has an effect on the SCO behaviour comparable to a change in internal electrostatic pressure due to anion-cation interactions (e.g. changing the counter-anion). Both lead to considerable shifts in transition temperatures without significant influence on the hysteresis width. Several theoretical models have been developed to predict such SCO behaviour of ID chain compounds under pressure [50-52]. Figure 5 (bottom) also shows the pressure dependence of the LS fraction, yLS, of... 

The profiles of pendant and sessile bubbles and drops are commonly used in determinations of surface and interfacial tensions and of contact angles. Such methods are possible because the interfaces of static fluid particles must be at equilibrium with respect to hydrostatic pressure gradients and increments in normal stress due to surface tension at a curved interface (see Chapter 1). It is simple to show that at any point on the surface... 

With this idea in mind, the horizontal surface in Figure 6.3b can be taken as a reference level at which Ap = 0. Just under the meniscus in the capillary the pressure is less than it would be on the other side of the surface owing to the curvature of the surface. The fact that the pressure is less in the liquid in the capillary just under the curved surface than it is at the reference plane causes the liquid to rise in the capillary until the liquid column generates a compensating hydrostatic pressure. The capillary possesses an axis of symmetry therefore at the bottom of the meniscus the radius of curvature is the same in the two perpendicular planes that include the axis. If we identify this radius of curvature by b, then the Laplace equation applied to the meniscus is Ap = 2y/b. Equating this to the hydrostatic pressure gives... 

When the supercritical fluid has a relatively high solubility in the molten heavy component, the S-L-V curve can have a negative dP/dT slope [64]. The second type of three-phase S-L-V curve shows a temperature minimum [65], In the third type, where the S-L-V curve has a positive dP/dT slope, the supercritical fluid is only slightly soluble in the molten heavy component, and therefore the increase of hydrostatic pressure will raise the melting temperature and a new type of three-phase curve with a temperature minimum and maximum may occur [66]. 

Figure 61 shows the ZFC and FC M(T) curves for the FMM phase II, which show a first-order transition at 7c where the bond-length fluctuations become frozen out to restore the phonon contribution to the thermal conductivity, fig. 62. In the I + II two-phase samples t = 0.973 and t = 0.974, phase II is suppressed and phase fluctuations inhibit phonon formation below Tco or 7c. Tokura et al. (1996) applied hydrostatic pressure to the FM phase II of (Ndo.i25Smo.875)o.5Sro.5Mn03 having / /c they reported the appearance of a CE AFI second phase having a volume fraction that increased with pressure below Too = 7n- Since pressure... 

There are static and dynamic methods. The static methods measure the tension of practically stationary surfaces which have been formed for an appreciable time, and depend on one of two principles. The most accurate depend on the pressure difference set up on the two sides of a curved surface possessing surface tension (Chap. I, 10), and are often only devices for the determination of hydrostatic pressure at a prescribed curvature of the liquid these include the capillary height method, with its numerous variants, the maximum bubble pressure method, the drop-weight method, and the method of sessile drops. The second principle, less accurate, but very often convenient because of its rapidity, is the formation of a film of the liquid and its extension by means of a support caused to adhere to the liquid temporarily methods in this class include the detachment of a ring or plate from the surface of any liquid, and the measurement of the tension of soap solutions by extending a film. 

We can readily extend our discussion to include a pressure-volume, or P-K curve, which has proved useful for analyzing the water relations of plant organs such as leaves. In particular, the earliest calculations of internal hydrostatic pressure and cellular elastic modulus were based on P-V curves. To obtain such a curve, we can place an excised leaf in a pressure chamber (Fig. 2-10) and increase the air pressure in the chamber until liquid just becomes visible at the cut end of the xylem, which is viewed with a dissecting microscope or a hand-held magnifying lens so that water in individual conducting cells in the xylem can be observed. When the leaf is excised, the... 

Figure 2-15. Relation between the reciprocal of leaf water potential determined with a pressure chamber (Fig. 2-10) and the volume of xylem sap extruded as the air pressure in the chamber is progressively increased. The solid line indicates a typical range for data points for material initially at full turgor (TJ, = 0). The reciprocal of the internal osmotic pressure (1/n1) including the value at full turgor (1 /nj,), the internal hydrostatic pressure (P1), the point of incipient plasmolysis and turgor loss, and the volume of symplastic water (VSympiasm) can all be determined from such a P-V curve.

Fig. 35. Hydrostatic pressure dependence of the bending moment-displacement curves of a notched PP sample...

Figure 14.8 shows stress-strain curves for polycarbonate at 77 K obtained in tension and in uniaxial compression (12), where it can be seen that the yield stress differs in these two tests. In general, for polymers the compressive yield stress is higher than the tensile yield stress, as Figure 14.8 shows for polycarbonate. Also, yield stress increases significantly with hydrostatic pressure on polymers, though the Tresca and von Mises criteria predict that the yield stress measured in uniaxial tension is the same as that measured in compression. The differences observed between the behavior of polymers in uniaxial compression and in uniaxial tension are due to the fact that these materials are mostly van der Waals solids. Therefore it is not surprising that their mechanical properties are subject to hydrostatic pressure effects. It is possible to modify the yield criteria described in the previous section to take into account the pressure dependence. Thus, Xy in Eq. (14.10) can be expressed as a function of hydrostatic pressure P as... 

Figure 26. Curves of hydrostatic pressure P vs. specific volume V at constant moisture content m or relative vapor pressure h, from Barka (26). (Reproduced with permission from Ref l6. Copyright 1972, Syracuse...

Fig. 1. Powder x-ray profiles of solid Ceo at atmospheric pressure (top) and 1.2-GPa hydrostatic pressure (bottom). Dots are experimental points (approximately 70 per point), and the solid curves are least-squares fits to an fee structurewith adjustable lattice constant a. The fitted relative intensities have no physical significance in this simple model. The scattered wave vector Q = 4TTsin6/X, where 0 is the Bragg angle for these profiles wavelength = 0.71 A. Indexing of the strongest peaks is indicated. The high-Q shoulder on the (311) is the weak (222) reflection the low-Q shoulder on the (111), observed to some extent in all our nominally pure Cfio samples, is presently unidentified. The variable intensity of this shoulder has litde eflfect on the lattice constant of a particular sample, so we can safely conclude that it has no effect on the compressibility derived from the present data.

In this model also the decrease of the pore radius due to the formation of an adsorbed layer is incorporated. Flow 1 in Fig. 9.9 is the case of combined Knudsen molecular diffusion in the gas phase and multilayer (surface) flow in the adsorbed phase. In case 2, capillary condensation takes place at the upstream end of the pore (high pressure Pi) but not at the downstream end (P2), and in case 3 the entire capillary is filled with condensate. The crucial point in cases 3 and 4 is that the liquid meniscus with a curved surface not only reduces the vapour pressure (Kelvin equation) but also causes a hydrostatic pressure difference across the meniscus and so causes a capillary suction pressure Pc equal to... 

Guyton has demonstrated, using an isolated limb preparation in which the blood vessels were perfused with fluid of known osmotic pressure and at a given hydrostatic pressure, that a curve as shown in Figure 4 could be recorded. 

When the radius of the capillary tube is appreciable, the meniscus is no longer spherical and also 9> 0°. Then, Equation (329) requires correction in terms of curvatures and it should give better results than those from the rough corrections given in Equations (330)-(332) for almost spherical menisci. Exact treatment of the capillary rise due to the curved meniscus is possible if we can formulate the deviation of the meniscus from the spherical cap. For this purpose, the hydrostatic pressure equation, AP = Apgz (Equation (328)), must be valid at each point on the meniscus, where z is the elevation of that point above the flat liquid surface (see Figure 6.1 in Chapter 6). Now, if we combine the Young-Laplace equation (Equation (325)) with Equation (328), we have... 

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