Hquid film

The experimentally observed rates of mass transfer are often proportional to the displacement from equiHbrium and the rate equations for the gas and Hquid films are... 

Expressions similar to equations 6 and 7 may be derived in terms of an overall Hquid-phase driving force. Equation 7 represents an addition of the resistances to mass transfer in the gas and Hquid films. The analogy of this process to the flow of electrical current through two resistances in series has been analyzed (25). 

In situations where the gas film resistance is predominant (gas film-controlled situation), k Pis much smaller than and the tie line is very steep. approachesjy so that the overall gas-phase driving force and the gas-film driving force become approximately equal, whereas the Hquid-film driving force becomes negligible. From equation 7 it also follows that in such cases. The reverse is tme if the Hquid film resistance is controlling. Since the... 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

Lujuid-Pha.se Transfer. It is difficult to measure transfer coefficients separately from the effective interfacial area thus data is usually correlated in a lumped form, eg, as k a or as These parameters are measured for the Hquid film by absorption or desorption of sparingly soluble gases such as O2 or CO2 in water. The Hquid film resistance is completely controlling in such cases, and kjji may be estimated as since x (Fig. 4). This... 

The rate of mass transfer,/, is then assumed to be proportional to the concentration differences existing within each phase, the surface area between the phases,, and a coefficient (the gas or Hquid film mass transfer coefficient, k or respectively) which relates the three. Thus... 

In the case of a less soluble gas such as oxygen, diffusion occurs so slowly through the Hquid film that only a small concentration difference is required to overcome the resistance of the gas film. Thus the Hquid film at the interface is considered to be very close to oxygen saturation and it is not necessary to consider gas film resistance in the calculation (14). 

The diffusion coefficient depends upon the characteristics of the absorption process. Reducing the thickness of the surface films increases the coefficient and correspondingly speeds up the absorption rate. Therefore, agitation of the Hquid increases diffusion through the Hquid film and a higher gas velocity past the Hquid surface could cause more rapid diffusion through the gas film. 

Continuous deaeration occurs when the viscose is warmed and pumped into thin films over cones in a large vacuum tank. The combination of the thinness of the Hquid film and the dismption caused by the boiling of volatile components allows the air to get out quickly. Loss of water and CS2 lower the gamma value and raise the cellulose concentration of the viscose slightly. Older systems use batch deaeration where the air bubbles have to rise through several feet of viscose before they are Hberated. 

If the gas-flow rate is increased, one eventuaHy observes a phase transition for the abovementioned regimes. Coalescence of the gas bubbles becomes important and a regime with both continuous gas and Hquid phases is reestabHshed, this time as a gas-flUed core surrounded by a predominantly Hquid annular film. Under these conditions there is usuaHy some gas dispersed as bubbles in the Hquid and some Hquid dispersed as droplets in the gas. The flow is then annular. Various qualifying adjectives maybe added to further characterize this regime. Thus there are semiannular, pulsing annular, and annular mist regimes. Over a wide variety of flow rates, the annular Hquid film covers the entire pipe waH. For very low Hquid-flow rates, however, there may be insufficient Hquid to wet the entire surface, giving rise to rivulet flow. 

The combined effect of van der Waals and electrostatic forces acting together was considered by Derjaguin and Landau (5) and independently by Vervey and Overbeek (6), and is therefore called DLVO theory. It predicts that the total interaction energy per unit area, also known as the effective interface potential, is given by V(f) = ( ) + dl ( )- absence of externally imposed forces, the equiHbrium thickness of the Hquid film... 

J. A.F. Plateau, who first studied their properties. It is the Plateau borders, rather than the thin Hquid films, which are apparent in the polyhedral foam shown toward the top of Figure 1. Lines formed by the Plateau borders of intersecting films themselves intersect at a vertex here mechanical constraints imply that the only stable vertex is the one made from four borders. The angle between intersecting borders is the tetrahedral angle,... 

Other methods suggested for H2 purification include adsorption and desorption on active carbon and fractional crystalliza tion (qv) of impurities fromhquid hydrogen. Centrifuging at 1—5.1 MPa (10—50 atm) and 64—110 K while keeping the temperature below the dew point of impurities that collect as a hquid film in the centrifuge has also been suggested. Purities over 99% can be obtained by this method (192). 

Ceramic, Metal, and Liquid Membranes. The discussion so far implies that membrane materials are organic polymers and, in fact, the vast majority of membranes used commercially are polymer based. However, interest in membranes formed from less conventional materials has increased. Ceramic membranes, a special class of microporous membranes, are being used in ultrafHtration and microfiltration appHcations, for which solvent resistance and thermal stabHity are required. Dense metal membranes, particularly palladium membranes, are being considered for the separation of hydrogen from gas mixtures, and supported or emulsified Hquid films are being developed for coupled and facHitated transport processes. 

Emulsified oil contains a Hquid film so that it will not separate by gravity without first breaking the emulsion. This is achieved by adding surfactants, emulsion breaking polymers or coagulants. After the emulsion is broken, the conventional technologies described above are appHcable. 

Based on this low surface tension feature and the commonly observed insolubiUty of defoamers, two related antifoam mechanisms have been introduced (29) (/) The agent dispersed in the form of fine drops enters the Hquid film between bubbles and spreads as a duplex film. The tensions created by this Spreading lead to the mpture of the original Hquid film. (2) A droplet of the agent enters the Hquid film between bubbles, but rather than spreading produces a mixed monolayer on the surface. This monolayer, if of less coherence than the original film-stabilizing monolayer, causes destabilization of the film. 

The traditional view of emulsion stability (1,2) was concerned with systems of two isotropic, Newtonian Hquids of which one is dispersed in the other in the form of spherical droplets. The stabilization of such a system was achieved by adsorbed amphiphiles, which modify interfacial properties and to some extent the colloidal forces across a thin Hquid film, after the hydrodynamic conditions of the latter had been taken into consideration. However, a large number of emulsions, in fact, contain more than two phases. The importance of the third phase was recognized early (3) and the lUPAC definition of an emulsion included a third phase (4). With this relation in mind, this article deals with two-phase emulsions as an introduction. These systems are useful in discussing the details of formation and destabilization, because of their relative simplicity. The subsequent treatment focuses on three-phase emulsions, outlining three special cases. The presence of the third phase is shown in order to monitor the properties of the emulsion in a significant manner. 

Before determining the degree of stabiUty of an emulsion and the reason for this stabiUty, the mechanisms of its destabilization should be considered. When an emulsion starts to separate, an oil layer appears on top, and an aqueous layer appears on the bottom. This separation is the final state of the destabilization of the emulsion the initial two processes are called flocculation and coalescence (Fig. 5). In flocculation, two droplets become attached to each other but are stiU separated by a thin film of the Hquid. When more droplets are added, an aggregate is formed, ia which the iadividual droplets cluster but retain the thin Hquid films between them, as ia Figure 5a. The emulsifier molecules remain at the surface of the iadividual droplets duiing this process, as iadicated ia Figure 6. 

In the coalescence step, the thin Hquid film between the droplets is destabilized, and a large droplet is formed. Hence, the coalesciag emulsion is characterized by a wide size distribution of the droplets, but no clusters are present (Fig. 5b). FiaaHy, the droplets achieve such a size that they are recognized by the naked eye as a separate phase. A fully separated emulsion consists of an oil layer and an aqueous layer. 

Liquid crystals stabilize in several ways. The lamellar stmcture leads to a strong reduction of the van der Waals forces during the coalescence step. The mathematical treatment of this problem is fairly complex (28). A diagram of the van der Waals potential (Fig. 15) illustrates the phenomenon (29). Without the Hquid crystalline phase, coalescence takes place over a thin Hquid film in a distance range, where the slope of the van der Waals potential is steep, ie, there is a large van der Waals force. With the Hquid crystal present, coalescence takes place over a thick film and the slope of the van der Waals potential is small. In addition, the Hquid crystal is highly viscous, and two droplets separated by a viscous film of Hquid crystal with only a small compressive force exhibit stabiHty against coalescence. Finally, the network of Hquid crystalline leaflets (30) hinders the free mobiHty of the emulsion droplets. 

Thomas and Rice [/. Appl. Mech., 40, 321-325 (1973)] applied the hydrogen-bubble technique for velocity measurements in thin hquid films. DureUi and Norgard [Exp. Mech., 12,169-177 (1972)] compare the flow birefringence and hydrogen-bubble techniques. 

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