Three-phase line

Three boundary lines meet in a single point (shown by a red dot), called a triple point. All three phases are stable simultaneously at this unique combination of temperature and pressure. Notice that, although two phases are stable under any of the conditions specified by the boundary lines, three phases can be simultaneously stable only at a triple point. 

Young s equation is the basis for a quantitative description of wetting phenomena. If a drop of a liquid is placed on a solid surface there are two possibilities the liquid spreads on the surface completely (contact angle 0 = 0°) or a finite contact angle is established.1 In the second case a three-phase contact line — also called wetting line — is formed. At this line three phases are in contact the solid, the liquid, and the vapor (Fig. 7.1). Young s equation relates the contact angle to the interfacial tensions 75, 7l, and 7sl [222,223] ... 

Fig. 9-22. Calculated and observed phase diagrams for PS f4 + PS fl28 (the weight fraction of the latter is 0.05) + CH on the T — ( > plane. Thick solid line, calculated cloud-point curve. Dot-dashed line, calculated shadow curve. Dashed lines, calculated two-phase conjugate coexistence curves for the indicated polymer volume fractions. Thin solid line, three-phase coexistence curve. Unfilled circle, calculated critical point. Filled circles, measured cloud points. Filled triangles, measured polymer volume fractions in three separated phases. 

Figure L Schematic p,T-projections of types of binaiy fluid phase behavior according to the classification of Van Konynenburg and Scott [5,6] —, vapor pressure curve of a pure component - -, critical line —three-phase line ffg , critical point of a pure component o, UCEP =g+ , LCEP f =r+g o, UCEP f-r+g X, DCEP a, TCP (a) Type-III fluid phase behavior (b) DCEP, transition between type-HI and type-IV fluid phase behavior (c) Type-fV fluid phase l havior (d) TCP, transition between type-IV and type-II fluid phase behavior (e) Type-II fluid phase behavior (f) Type-I fluid phase behavior (g) Type-V fluid phase behavior.

Wetting Line - Three-phase Line (Solid/Liquid/Vapour)... 

Suppose that the line tension for a given three-phase line is 1 x 10 dyn. Calculate ff for drops of radius 0.1, 0.01, and 0.001 cm if the value for a large drop is 56. Assume water at 20°C. 

D. Platikanov and M. Nedyalkov, Contact Angles and Line Tension at Microscopic Three Phase Contacts, in Microscopic Aspects of Adhesion and Lubrication, J. M. Georges, ed., Elsevier, Amsterdam, 1982. 

In practice, it may be possible with care to float somewhat larger particles than those corresponding to the theoretical maximum. As illustrated in Fig. XIII-7, if the particle has an irregular shape, it will tend to float such that the three-phase contact occurs at an asperity since the particle would have to be depressed considerably for the line of contact to advance further. The resistance to rounding a sharp edge has been investigated by Mason and co-workers [62]. 

Figure A2.5.31. Calculated TIT, 0 2 phase diagram in the vicmity of the tricritical point for binary mixtures of ethane n = 2) witii a higher hydrocarbon of contmuous n. The system is in a sealed tube at fixed tricritical density and composition. The tricritical point is at the confluence of the four lines. Because of the fixing of the density and the composition, the system does not pass tiirough critical end points if the critical end-point lines were shown, the three-phase region would be larger. An experiment increasing the temperature in a closed tube would be represented by a vertical line on this diagram. Reproduced from [40], figure 8, by pennission of the American Institute of Physics.

Glassification of Phase Boundaries for Binary Systems. Six classes of binary diagrams have been identified. These are shown schematically in Figure 6. Classifications are typically based on pressure—temperature (P T) projections of mixture critical curves and three-phase equiHbria lines (1,5,22,23). Experimental data are usually obtained by a simple synthetic method in which the pressure and temperature of a homogeneous solution of known concentration are manipulated to precipitate a visually observed phase. 

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (soHd line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, C , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are CO2—/ -hexane and CO2—benzene. More compHcated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (Hquid—Hquid) immiscihility lines, and even three-phase (Hquid—Hquid—gas) immiscihility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include CO2—hexadecane and CO2—H2O Class IV, CO2—nitrobenzene Class V, ethane—/ -propanol and Class VI, H2O—/ -butanol. 

The KTTS depends upon an absolute 2ero and one fixed point through which a straight line is projected. Because they are not ideally linear, practicable interpolation thermometers require additional fixed points to describe their individual characteristics. Thus a suitable number of fixed points, ie, temperatures at which pure substances in nature can exist in two- or three-phase equiUbrium, together with specification of an interpolation instmment and appropriate algorithms, define a temperature scale. The temperature values of the fixed points are assigned values based on adjustments of data obtained by thermodynamic measurements such as gas thermometry. 

Fig. 15. A typical powder pattern with three phases Calcite (—), Aragonite and Brucite ( ). The lines below the peaks are the powder lines...

Roll-up. The principal means by which oily soil is removed is probably roU-up. The appHcable theory is simply the theory of wetting. In briefest outline, a droplet of oily soil attached to the substrate forms at equiUbrium a definite contact angle at the oil-sohd-air boundary line. This contact angle (Fig. 4) is the result of the interaction of interfacial forces in the three phase boundaries of the system. These interfacial forces, expressed in mN/m(= dyn/cm), or interfacial free energy values expressed in mj/m (erg/cm s) are conveniently designated 1SA iSlj subscripts relate to the Hquid-air,... 

When the primary of a three-phase two-winding transformer, having its secondary wound for a three-phase open delta, is connected across an unbalanced supply system, a residual voltage across the open delta will appear. This is the principle on which this transformer is based (Figure 15.4(a)). As discussed in Section 21.2.2, and illustrated in Figure 21.7, the phasor sum of all the three line to ground voltages in a three-phase balanced system is zero, i.e. 

Nominal voltage ratio e.g. 6.6 kV/110 V for two phase or three phase transformers and -transformers 4 times this for line to neutral... 

A distribution network 33 kV, three-phase 50 Hz feeding an industrial belt with a number of medium-sized factories some with non-linear loads and some with static drives and some with both. It was observed that while the lines were apparently running reasonably loaded, the active power supplied was much below the capacity of the network. Accordingly, a harmonic study of the network was conducted and it was found that despite localized p.f. control by most factories, the p.f. of the network itself was well below the optimum level and the voltage was also distorted by more than was permissible. To improve this network to an acceptable level, we have considered the following load conditions, as were revealed through the analysis. 

A three-phase fault somewhere in the bus system, without reactive compensation and ignoring the line impedance, can reach a level of... 

The other place where the constitution is not fully defined is where there is a horizontal line on the phase diagram. The lead-tin diagram has one line like this - it runs across the diagram at 183°C and connects (Sn) of 2.5 wt% lead, L of 38.1% lead and (Pb) of 81% lead. Just above 183°C an alloy of tin -i- 38.1% lead is single-phase liquid (Fig. 3.5). Just below 183°C it is two-phase, (Sn) -i- (Pb). At 183°C we have a three-phase mixture of L -I- (Sn) -I- (Pb) but we can t of course say from the phase diagram what the relative weights of the three phases are. 

The cloudiness of ordinary ice cubes is caused by thousands of tiny air bubbles. Air dissolves in water, and tap water at 10°C can - and usually does - contain 0.0030 wt% of air. In order to follow what this air does when we make an ice cube, we need to look at the phase diagram for the HjO-air system (Fig. 4.9). As we cool our liquid solution of water -i- air the first change takes place at about -0.002°C when the composition line hits the liquidus line. At this temperature ice crystals will begin to form and, as the temperature is lowered still further, they will grow. By the time we reach the eutectic three-phase horizontal at -0.0024°C we will have 20 wt% ice (called primary ice) in our two-phase mixture, leaving 80 wt% liquid (Fig. 4.9). This liquid will contain the maximum possible amount of dissolved air (0.0038 wt%). As latent heat of freezing is removed at -0.0024°C the three-phase eutectic reaction of... 

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