Phase boundary liquid-vapor

Dynamic contact angles are the angles which can be measured if the three-phase boundary (liquid/solid/vapor) is in actual motion. A Wilhelmy plate is used in dynamic contact angle measurements, and this method is also called the tensiometric contact angle method. It has been extensively applied to solid-liquid contact angle determinations in recent years. In practice, a solid substrate is cut as a thin rectangular plate, otherwise a solid material is... 

The mutual attraction through the slit gap affects liquid film stability, and at a certain critical vapor pressure (or film thickness) the two films form a liquid bridge (Fig. 1-1 c) followed by a spontaneous filling up of the slit (assuming the film is in contact with the bulk liquid phase). The liquid-vapor interface moves to the plate boundaries. This phase transition from dilute vapor to a dense liquid is known as capillary condensation and was observed experimentally with the surface force apparatus by Christenson (1994) and Curry and Christenson (1996). Extensive theories for this phenomenon and its critical points are provided by Derjaguin and Chu-raev (1976), Evans et al. (1986), Forcada (1993), and Iwamatsu and Horii (1996). In general, slit-shaped pores fill up at a film thickness of about HI3, or when <) l(H,h)/dh = 0, such that... 

We now use the pressure-temperature map in Figure 4.18 to determine the temperature of our destination. Our condenser maintains 1 atm total pressure, so we plot a path of constant pressure. We move horizontally on the map until we reach the two phase boundary between vapor and liquid, also known as the dew point. One finds in the CRC Handbook of Chemistry and Physics (59th edition, p. D-246) that the dew point of benzene at 10 torr is — 12°C. Thus at 10 torr and — 12°C benzene begins to condense from the air and the partial pressure of benzene falls. The total pressure in the system, however, falls little because the system is predominately (98.7%) air. 

Phase boundary vapor-liquid to liquid-liquid-vapor (LLV) and phase boundary liquid-liquid-vapor to liquid-liquid (LVL). 

Equations (3)-(5) are valid only for ideal, smooth, homogeneous, impermeable, and nondeformable surfaces. Because textile fibers do not have such ideal surfaces, their wetting phenomena are more complicated. In addition, the prediction of wetting phenomena (e.g., spreading) from wetting energetics is difficult because a direct method for determining ysv a term found in Eqs. (3), (4), and (6), is not available. It is more convenient to use the forces in balance at a three-phase (solid, liquid, vapor) boundary as an indication of wettability. 

The lines separating the regions in a phase diagram are called phase boundaries. At any point on a boundary between two regions, the two neighboring phases coexist in dynamic equilibrium. If one of the phases is a vapor, the pressure corresponding to this equilibrium is just the vapor pressure of the substance. Therefore, the liquid-vapor phase boundary shows how the vapor pressure of the liquid varies with temperature. For example, the point at 80.°C and 0.47 atm in the phase diagram for water lies on the phase boundary between liquid and vapor (Fig. 8.10), and so we know that the vapor pressure of water at 80.°C is 0.47 atm. Similarly, the solid-vapor phase boundary shows how the vapor pressure of the solid varies with temperature (see Fig. 8.6). 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

SOLUTION Although the phase diagram in Fig. 8.6 is not to scale, we can find the approximate locations of the points. Point A is at 5 Torr and 70°C so it lies in the vapor region. Increasing the pressure takes the vapor to the liquid-vapor phase boundary, at which point liquid begins to form. At this pressure, liquid and vapor are in equilibrium and the pressure remains constant until all the vapor has condensed. The pressure is increased further to 800 Torr, which takes it to point B, in the liquid region. 

A feature of the phase diagram in Fig. 8.12 is that the liquid-vapor boundary comes to an end at point C. To see what happens at that point, suppose that a vessel like the one shown in Fig. 8.13 contains liquid water and water vapor at 25°C and 24 Torr (the vapor pressure of water at 25°C). The two phases are in equilibrium, and the system lies at point A on the liquid-vapor curve in Fig. 8.12. Now let s raise the temperature, which moves the system from left to right along the phase boundary. At 100.°C, the vapor pressure is 760. Torr and, at 200.°C, it has reached 11.7 kTorr (15.4 atm, point B). The liquid and vapor are still in dynamic equilibrium, but now the vapor is very dense because it is at such a high pressure. 

The normal melting, boiling, and triple points give three points on the phase boundary curves. To construct the curves from knowledge of these three points, use the common features of phase diagrams the vapor-liquid and vapor-solid boundaries of phase diagrams slope upward, the liquid-solid line is nearly vertical, and the vapor-solid line begins at P = 0 and P = 0 atm. 

Most of the discussion of ions in this book will be concerned with large complicated ions in the liquid phase rather than with small simple ions in the vacuum of the mass spectrometer. Organic chemistry is the chemistry of complicated molecules and for this reason the organic chemist will be most interested in the large radicals and ions whose usual habitat is the liquid phase. Perhaps this is why the boundary between physical and organic chemistry has somewhere been defined as the liquid-vapor interface. Certainly it is only in the amicable sense of a preoccupation with his natural habitat that the organic chemist should regard physical chemistry with a fishy eye. 

The critical point of a material is the temperature and pressure conditions at which the liqiud state ceases to exist. As a liquid is heated, it becomes less dense and starts to form a vapor phase. The vapors being formed becomes more dense, with continued heating the liquid and vapor densities become closer to each other until the critical temperature point is reached. At this same point, the liquid-line or phase boundary disappears. This critical point was first discovered and reported in 1822 by Baron Charles Cagniard de la Tour. 

Cracking of PS because of capillary forces can be circumvented if one avoids crossing the liquid-vapor boundary in the phase diagram of the solvent. This is the case for supercritical drying [Ca4] or freeze drying [Ami], as shown in the inset of Fig. 6.12. 

B) A critical point specifies the conditions (temperature and pressure) at which the liquid state of the matter ceases to exist. As a liquid is heated, its density decreases while the pressure and density of the vapor being formed increases. The liquid and vapor densities become closer and closer to each other until the critical temperature is reached where the two densities are equal and the liquid-gas line or phase boundary disappears. At extremely high temperatures and pressures, the liquid and gaseous phases become indistinguishable. In water, the critical point occurs at around 647K (374°C or 705°F) and 22.064 MPa (3200 PSIA). 

Fig. 6. Qualitative pressure—temperature diagrams depicting critical curves for the six types of phase behaviors for binary systems, where Ca or C corresponds to pure component critical point G, vapor L-, liquid U, upper critical end point and U, lower critical end point. Dashed curves are critical lines or phase boundaries (5). (a) Class I, the Ar—Kr system (b) Class II, the C02—C8H18 system (c) Class III, where the dashed lines A, B, C, and D correspond to the H2-CO, CH4-H2S, He-H2, and He-CH4 system, respectively (d) Class IV, the CH4 C6H16 system (e) Class V, the C2H6 C2H5OH...

Comparison of Release Data with Proposed Model. A summary of the cesium release data obtained with helium as carrier gas is shown in Figure 5, where the percentage of cesium remaining is plotted vs, heating time on semilogarithmic coordinates. In all of the experiments the flow rate was maintained at 300 cc./min. and the temperature at 730° = = 5°K. The geometric parameters are indicated on each curve. Since only about 5% of the sodium was vaporized in each experiment, the assumption of a stationary liquid-phase boundary is justified. 

Figure 7.1 Schematic phase diagram of water (not to scale), showing phase boundaries (heavy solid lines), triple point (triangle), critical point (circle-x), and a representative point (circle, dotted lines) at 25°C on the liquid-vapor coexistence curve.

Figure 7.5 Phase diagram of elemental sulfur, showing the stable solid phases a-sulfur (orthorhombic red sulfur ) and /3-sulfur (monoclinic yellow sulfur ) and equilibrium phase boundaries (solid lines) as well as the metastable phase boundary (dashed line) that connects a-sulfur to liquid and vapor phases.

Figure 13.28. Vapor-liquid equilibria of some azeotropic and partially miscible liquids, (a) Effect of pressure on vapor-liquid equilibria of a typical homogeneous azeotropic mixture, acetone and water, (b) Uncommon behavior of the partially miscible system of methylethylketone and water whose two-phase boundary does not extend byond the y = x line, (c) x-y diagram of a partially miscible system represented by the Margules equation with the given parameters and vapor pressures Pj = 3, = 1 atm the broken line is not physically significant but is...

An interesting class of exact self-similar solutions (H2) can be deduced for the case where the newly formed phase density is a function of temperature only. The method involves a transformation to Lagrangian coordinates, based upon the principle of conservation of mass within the new phase. A similarity variable akin to that employed by Zener (Z2) is then introduced which immobilizes the moving boundary in the transformed space. A particular case which has been studied in detail is that of a column of liquid, initially at the saturation temperature T , in contact with a flat, horizontal plate whose temperature is suddenly increased to a large value, Tw T . Suppose that the density of nucleation sites is so great that individual bubbles coalesce immediately upon formation into a continuous vapor film of uniform thickness, which increases with time. Eventually the liquid-vapor interface becomes severely distorted, in part due to Taylor instability but the vapor film growth, before such effects become important, can be treated as a one-dimensional problem. This problem is closely related to reactor safety problems associated with fast power transients. The assumptions made are ... 

Let s see how this simple expression applies to the phase diagrams we have been considering. When two phases are in equilibrium, such as liquid water and water vapor, we set p = 2 and obtain f = 3 — 2=1. One degree of freedom means that we can vary either the pressure or the temperature. To preserve the equilibrium when we vary the pressure, we have to adjust the temperature by an appropriate amount to preserve the equilibrium when we vary the temperature, the pressure must change appropriately. That is, the pressures and temperatures at which two phases are present in a one-component system are not independent of each other, and the relation between them is represented by a line on the phase diagram. As the temperature is changed, the pressure changes as indicated by the phase boundary. 

The process of pressure distillation through a homogeneous membrane is based first on the common fact that the vapor pressure of any liquid can be increased by compressing it or decreased by placing it under suction, and second on the equally common fact that only pure water vapor escapes from water into vapor or air, leaving nonvolatile salts behind the phase boundary. In operating the processes of vaporization—heat transfer and diffusion across an extremely thin gap—no new phenomena or new properties of materials are required. However, the novel combination of capillary surfaces, pressure, and extremely short paths for heat and diffusion offers an opportunity for improvements in film properties and methods of construction not known before. 

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