Bubble equilibrium

LBE [Lance-bubbling-equilibrium] A steelmaking process in which nitrogen or argon is injected at the base of the furnace and oxygen is introduced at the top. Introduced in the 1970s. See steelmaking. 

Lamination, paper, 18 125 Lamination inks, 14 327-328 Lampblacks, 4 762, 798t manufacture, 4 786-787 Lamproite pipes, 8 519, 520 Lanacordin, molecular formula and structure, 5 98t Lanasol dyes, 9 468, 469 Lance bubbling equilibrium (LBE) process, 23 260... 

The stabihty of colloidal suspensions, emulsions, and foams and their transport properties are determined by the type of disjoining pressure, which acts between particles, droplets, and bubbles. Equilibrium and kinetics of wetting are completely determined also by the shape of the... 

The calculation of single-stage equilibrium separations in multicomponent systems is implemented by a series of FORTRAN IV subroutines described in Chapter 7. These treat bubble and dewpoint calculations, isothermal and adiabatic equilibrium flash vaporizations, and liquid-liquid equilibrium "flash" separations. The treatment of multistage separation operations, which involves many additional considerations, is not considered in this monograph. 

The computer subroutines for calculation of vapor-liquid equilibrium separations, including determination of bubble-point and dew-point temperatures and pressures, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements for these subroutines are given in Appendix J their execution times are strongly dependent on the separations being calculated but can be estimated (CDC 6400) from the times given for the thermodynamic subroutines they call (essentially all computation effort is in these thermodynamic subroutines). 

BUDET calculates the bubble-point temperature or dew-point temperature for a mixture of N components (N < 20) at specified pressure and liquid or vapor composition. The subroutine also furnishes the composition of the incipient vapor or liquid and the vaporization equilibrium ratios. 

For mixtures, the calculation is more complex because it is necessary to determine the bubble point pressure by calculating the partial fugacities of the components in the two phases at equilibrium. 

It is important to remember the significance of the bubble point line, the dew point line, and the two phase region, within which gas and liquid exist in equilibrium. 

The preceding conclusion is easily verified experimentally by arranging two bubbles with a common air connection, as illustrated in Fig. II-2. The arrangement is unstable, and the smaller of the two bubbles will shrink while the other enlarges. Note, however, that the smaller bubble does not shrink indefinitely once its radius equals that of the tube, its radius of curvature will increase as it continues to shrink until the final stage, where mechanical equilibrium is satisfied, and the two radii of curvature are equal as shown by the dotted lines. 

The foregoing is an equilibrium analysis, yet some transient effects are probably important to film resilience. Rayleigh [182] noted that surface freshly formed by some insult to the film would have a greater than equilibrium surface tension (note Fig. 11-15). A recent analysis [222] of the effect of surface elasticity on foam stability relates the nonequilibrium surfactant surface coverage to the foam retention time or time for a bubble to pass through a wet foam. The adsorption process is important in a new means of obtaining a foam by supplying vapor phase surfactants [223]. 

For a given drum pressure and feed composition, the bubble- and dew-point temperatures bracket the temperature range of the equilibrium flash. At the bubble-point temperature, the total vapor pressure exerted by the mixture becomes equal to the confining drum pressure, and it follows that X = 1.0 in the bubble formed. Since yj = KjXi and since the x/s stiU equal the feed concentrations (denoted bv Zi s), calculation of the bubble-point temperature involves a trial-and-error search for the temperature which, at the specified pressure, makes X KjZi = 1.0. If instead the temperature is specified, one can find the bubble-point pressure that satisfies this relationship. 

A third fundamental type of laboratory distillation, which is the most tedious to perform of the three types of laboratory distillations, is equilibrium-flash distillation (EFV), for which no standard test exists. The sample is heated in such a manner that the total vapor produced remains in contact with the total remaining liquid until the desired temperature is reached at a set pressure. The volume percent vaporized at these conditions is recorded. To determine the complete flash curve, a series of runs at a fixed pressure is conducted over a range of temperature sufficient to cover the range of vaporization from 0 to 100 percent. As seen in Fig. 13-84, the component separation achieved by an EFV distillation is much less than by the ASTM or TBP distillation tests. The initial and final EFN- points are the bubble point and the dew point respectively of the sample. If desired, EFN- curves can be established at a series of pressures. 

For bubble caps, Ki is the drop through the slots and Ko is the drop through the riser, reversal, and annular areas. Equations for evaluating these terms for various bubble-cap designs are given by BoUes (in chap. 14 of Smith, Equilibrium Stage Processes, McGraw-HiU, New York, 1963), or may be found in previous editions of this handbook. 

For bubble-cap plates, hydraulic-gradient must be given serious consideration. It is a function of cap size, shape, and density on the plate. Methods for analyzing bubble-cap gradient may be found in the chapter by BoUes (Smith, De.sign of Equilibrium Stage Proce.s.se.s, Chap. 14, McGraw-Hill, New York, 1963) or in previous edition of this handbook. 

FIG. 19-65 Schematic representation of air hubhle-water-solid particle system (a) before, (h) after particle-bubble attachment, and (c) equilibrium force balance. 

Cf, C y, and Cq are the concentrations of the substance in question (which may be a colligend or a surfactant) in the feed stream, bottoms stream, and foamate (collapsed foam) respectively. G, F, and Q are the volumetric flow rates of gas, feed, and foamate respectively, is the surface excess in equilibrium with C y. S is the surface-to-volume ratio for a bubble. For a spherical bubble, S = 6/d, where d is the bubble diameter. For variation in bubble sizes, d should be taken as YLnid fLnidj, where n is the number of bubbles with diameter dj in a representative region of foam. 

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

Figure 6-4 shows the cold feed distillation tower of Figure 6-3. The inlet stream enters the top of the tower. It is heated by the hot gases bubbling up through it as it falls from tray to tray through the downcomers, A flash occurs on each tray so that the liquid is in near-equilibrium with the gas above it at the tower pressure and the temperature of that particular tray.

The bottoms temperature can then be determined by calculating the bubble point of the liquid described by the previous iteration at the clio-sen operating pressure in the tower. This is done by choosing a tempei a-ture, determining equilibrium constants from Chapter 3. Volume I, and computing ... 

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