Tension, hydrostatic

Another process is a penetration of the melt in the refractory s permeable pores. The process of physical penetration without dissolution is governed by capillary forces (surface tension), hydrostatic pressure, viscosity of the melt, and gravity. An illustration of such a process appears in Fig. 1.27, which shows the probability of the penetration of the A1 melt in the pores of the carbon block with and without the application of the current. 

The oscillating jet method is not suitable for the study of liquid-air interfaces whose ages are in the range of tenths of a second, and an alternative method is based on the dependence of the shape of a falling column of liquid on its surface tension. Since the hydrostatic head, and hence the linear velocity, increases with h, the distance away from the nozzle, the cross-sectional area of the column must correspondingly decrease as a material balance requirement. The effect of surface tension is to oppose this shrinkage in cross section. The method is discussed in Refs. 110 and 111. A related method makes use of a falling sheet of liquid [112]. 

In Chapter III, surface free energy and surface stress were treated as equivalent, and both were discussed in terms of the energy to form unit additional surface. It is now desirable to consider an independent, more mechanical definition of surface stress. If a surface is cut by a plane normal to it, then, in order that the atoms on either side of the cut remain in equilibrium, it will be necessary to apply some external force to them. The total such force per unit length is the surface stress, and half the sum of the two surface stresses along mutually perpendicular cuts is equal to the surface tension. (Similarly, one-third of the sum of the three principal stresses in the body of a liquid is equal to its hydrostatic pressure.) In the case of a liquid or isotropic solid the two surface stresses are equal, but for a nonisotropic solid or crystal, this will not be true. In such a case the partial surface stresses or stretching tensions may be denoted as Ti and T2-... 

Another commonly used elastic constant is the Poisson s ratio V, which relates the lateral contraction to longitudinal extension in uniaxial tension. Typical Poisson s ratios are also given in Table 1. Other less commonly used elastic moduH include the shear modulus G, which describes the amount of strain induced by a shear stress, and the bulk modulus K, which is a proportionaHty constant between hydrostatic pressure and the negative of the volume... 

There are four commonly occurring states of stress, shown in Fig. 3.2. The simplest is that of simple tension or compression (as in a tension member loaded by pin joints at its ends or in a pillar supporting a structure in compression). The stress is, of course, the force divided by the section area of the member or pillar. The second common state of stress is that of biaxial tension. If a spherical shell (like a balloon) contains an internal pressure, then the skin of the shell is loaded in two directions, not one, as shown in Fig. 3.2. This state of stress is called biaxial tension (unequal biaxial tension is obviously the state in which the two tensile stresses are unequal). The third common state of stress is that of hydrostatic pressure. This occurs deep in the earth s crust, or deep in the ocean, when a solid is subjected to equal compression on all sides. There is a convention that stresses are positive when they pull, as we have drawn them in earlier figures. Pressure,... 

Fig. 3.2. Common slates of stress, tension, compression, hydrostatic pressure and shear.

Figure 11. Effect of hydrostatic pressure on elongation <5 and area reduction t/) of the Ti-6Al-2.5Mo-2Cr-a H alloys at room temperature tension, a = 0 (dashed line) and 0.15 (solid line).

It should be pointed out that hydrostatic pressure does not produce an effective compression and, therefore, is not considered. If the casing string is suspended at the top of the hole that is filled with fluid, then the only effect of hydrostatic pressure is reduction of casing weight per foot and the string is effectively under tension. 

We conclude that high internal stresses are generated by simple shear of a long incompressible rectangular rubber block, if the end surfaces are stress-free. These internal stresses are due to restraints at the bonded plates. One consequence is that a high hydrostatic tension may be set up in the interior of the sheared block. For example, at an imposed shear strain of 3, the negative pressure in the interior is predicted to be about three times the shear modulus p. This is sufficiently high to cause internal fracture in a soft rubbery solid [5]. 

Pulmonary surfactant decreases surface tension of alveolar fluid. Reduced surface tension leads to a decrease in the collapsing pressure of the alveoli, an increase in pulmonary compliance (less elastic recoil), and a decrease in the work required to inflate the lungs with each breath. Also, pulmonary surfactant promotes the stability of the alveoli. Because the surface tension is reduced, the tendency for small alveoli to empty into larger ones is decreased (see Figure 17.2, panel b). Finally, surfactant inhibits the transudation cf fluid out of the pulmonary capillaries into the alveoli. Excessive surface tension would tend to reduce the hydrostatic pressure in the tissue outside the capillaries. As a result, capillary filtration would be promoted. The movement of water out of the capillaries may result in interstitial edema formation and excess fluid in the alveoli. 

Another well-known phenomenon is the Weissenberg effect, which occurs when a long vertical rod is rotated in a viscoelastic liquid. Again, the shearing generates a tension along the streamlines, which are circles centred on the axis of the rod. The only way in which the liquid can respond is to flow inwards and it therefore climbs up the rod until the hydrostatic head balances the force due to the normal stresses. 

The final factor to be considered here, and known to affect the cavitation threshold, is the temperature. In general, the threshold limit has been found to increase with decrease in temperature. This may in part be due to increases in either the surface tension (a) or viscosity (rj) of the liquid as the temperature decreases, or it may be due to the decreases in the liquid vapour pressure (P ). To best understand how these parameters (a, q, Py) affect the cavitation threshold, let us consider an isolated bubble, of radius Rq, in water at a hydrostatic pressure (Pjj) of 1 atm. 

Any bubble within a liquid is subject to both the crushing force of the hydrostatic pressure (Pjj) and those due to surface tension effects (2a/Rq). In order that the bubble should remain in equilibrium, the supporting forces due to the pressure of gas (P ) and vapour (P ) in the bubble must equal the crushing forces (Eq. 2.19). 

If we neglect, momentarily, any surface tension effects (i. e. 2a/Rq 0) and assume that the liquid contains only a small amount of gas (Pg 0), then we may deduce that expanding bubbles are created in a liquid when the vapour pressure exceeds the atmospheric pressure (P, > Pj ). For water the vapour pressure at 100 °C is 1 atm and hence water, at a hydrostatic pressure of 1 atm, boils as soon as the temperature exceeds 100 °C. At 25 °C the vapour pressure of water is 0.023 atm and thus water will only boil, at 25 °C, if the atmospheric pressure is less than this value. This can readily be achieved by evacuating the system. 

The work done by the (hydrostatic) pressure, Pjj, neglecting surface tension effects, is the product of the pressure and the change in volume and is given by... 

This collapse will be augmented by an increase in the surface tension effect (2cr/R) as the cavity becomes smaller i.e. the total collapse pressure is (Pj( + 2cr/R), but will be opposed by the increase in the pressure within the bubble due to the compression of gas i. e. expanding pressure, By analogy with the empty cavity, the work done by the new hydrostatic pressure (Pj(), minus that of the layer adjacent to the bubble, is equal to the kinetic energy of the liquid. 

When specified, the hydrostatic test liquid shall include a wetting agent to reduce surface tension. This wetting agent should be considered when one or more of the following conditions exists ... 

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... 

At larger Re and for more marked deformation, theoretical approaches have had limited success. There have been no numerical solutions to the full Navier-Stokes equation for steady flow problems in which the shape, as well as the flow, has been an unknown. Savic (S3) suggested a procedure whereby the shape of a drop is determined by a balance of normal stresses at the interface. This approach has been extended by Pruppacher and Pitter (P6) for water drops falling through air and by Wairegi (Wl) for drops and bubbles in liquids. The drop or bubble adopts a shape where surface tension pressure increments, hydrostatic pressures, and hydrodynamic pressures are in balance at every point. Thus... 

To explain this spreading rate behavior, Nikolov et al. [35] postulated that the excess driving force (assuming that capillary and hydrostatic forces balance each other) is a radial surface tension gradient, which can be approximated as... 

Strictly speaking, the pressure Pb inside the rising bubble is the sum of three terms (i) the atmospheric pressure Pq, (ii) the hydrostatic pressure pgH, and (iii) the Laplace pressure 2y/R, originated in the bubble s curvature. H is the depth at which the bubble rises and y is the surface tension of the liquid medium. However, H varying from several millimeters to several centimeters, the surface tension of champagne being of the order of 50 mN m , and bubbles radii varying from several tens to several... 

The equilibrium curvature of a liquid surface or meniscus depends not just on its surface tension but also on its density and the effect of gravity. The variation in curvature of a meniscus surface must be due to hydrostatic pressure differences at different vertical points on the meniscus. If the curvature at a given starting point on a surface is known, the adjacent curvature can be obtained from the Laplace equation and its change in hydrostatic pressure Ahpg. In practice the liquid... 

The first term on the right-hand side is due to the hydrostatic pressure (or suction) acting over the base of the rod and the second term is due to surface tension forces around the perimeter. (It should be noted that O is not equal to the equilibrium contact angle 0 but is determined by the meniscus shape.)... 

In bulk material, the resistivity is independent of crystal orientation because silicon is cubic. However, if the carriers are constrained to travel in a very thin sheet, eg, in an inversion layer, the mobility, and thus the resistivity, become anisotropic (18). Mobility is also sensitive to both hydrostatic pressure and uniaxial tension and compression, which gives rise to a substantial piezoresistive effect. Because of crystal symmetry, however, there is no piezoelectric effect. The resistivity gradually decreases as hydrostatic pressure is increased, and then abrupdy drops several orders of magnitude at ca 11 GPa (160,000 psi), where a phase transformation occurs and silicon becomes a metal (35). The longitudinal piezoresistive coefficient varies with the direction of stress, the impurity concentration, and the temperature. At about 25°C, given stress in a (100) direction and resistivities of a few hundredths of an O-cm, the coefficient values are 500—600 m2/N (50—60 cm2/dyn). 

Let us first consider the synergistic elfect that water has on void stabilization. It is likely that a distribution of air voids occurs at ply interfaces because of pockets, wrinkles, ply ends, and particulate bridging. The pressure inside these voids is not sufficient to prevent their collapse upon subsequent pressurization and compaction. As water vapor diffuses into the voids or when water vapor voids are nucleated, however, there will be an equilibrium water vapor pressure (and therefore partial pressure in the air-water void) at any one temperature that, under constant total volume conditions, will cause the total pressure in the void to rise above that of a pure air void. When the void pressure equals or exceeds the surrounding resin hydrostatic pressure plus the surface tension forces, the void becomes stable and can even grow. Equation 6.5 expresses this relationship... 

Uniaxial tension testing with superposed hydrostatic pressure has been described by Vernon (111) and Surland et al. (103). Such tests provide response and failure measurements in the triaxial compression or tension-compression-compression octants. 

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