Gas-liquid interfacial tension

From the above equations it is also apparent that in horizontal two-phase flow, all irreversibilities appear as wall friction, provided gas-liquid interfacial tension effects are neglected. 

One concerned with the measurement of gas-liquid interfacial tension should consult the useful reviews of methods prepared by Harkins [in Chap. 9 of Weissberger, Techniques of Organic Chemstry, 2d ed., vol. 1, part 2, Interscience, New York, 1949), Schwartz and coauthors [Surface Acttve Agents, vol. 1, Interscience, New York, 1949, pp. 263-271 Surface Active Agents and Detergents, vol. 2, Interscience, New York, 1958, pp. 389-391, 417-418], and by Adamson [Physical Chemistry of Surfaces, Interscience, New York, I960]. 

Increase in the bubble velocity Vs favors bed contraction. At Vsup = 0 = gq, Vs represents the rise velocity of bubble in a stagnant liquid. Since the rise velocity of a single bubble increases with gas-liquid interfacial tension, it follows that any decrease in surface tension favors expansion. This effect of surface tension has been observed by, among others, Dakshinamurty et al. (1971) and Kim et al. (1975). 

The gas bubbles in food foams are separated by sheets of the continuous phase, composed of two films of proteins adsorbed on the interface between a pair of gas bubbles, with a thin layer of liquid in between. The volume of the gas bubbles may make up 99% of the total foam volume. The contents of protein in foamed products are 0.1-10% and of the order of 1 mg/m2 interface. The system is stabilized by lowering the gas-liquid interfacial tension and formation of rupture-resistant, elastic protein film surrounding the bubbles, as well as by the viscosity of the liquid phase. The foams, if not fixed by heat setting of the protein network, may be destabilized by drainage of the liquid from the intersheet space, due to gravity, pressure, or evaporation, by diffusion of the gas from the smaller to the larger bubbles, or by coalescence of the bubbles resulting from rupture of the protein films. 

In the above expression, the first term on the right represents the work of liquid displacement by gas, the second term represents the work of creating the surface area between the gas and the liquid, and the last term represents the work of creating the interface between the gas and the solid, a is the gas-liquid interfacial tension, and and are the inter facial tensions between... 

Bubbles are a rather spectacular embodiment of the forces produced by surface tension. Their spherical shape is a testimony to the isotropic nature of the gas/liquid interfacial tension. Of all the forces involved in shaping and making bubbles, surface tension is preeminent, and this dominant position is reinforced by the appearance of the surface tension to the third power in the exponential in the rate expression for bubble nucleation as shown in Eq. (6). In this review, the author has chosen to emphasize a property of gas bubbles that has been noted in the past, but whose implications have not been fully worked out that the surface tension is a function of the bubble size. This is not true for cavitation or boiling in unary liquids. 

Gravitational force favors the separation of gas from liquid in a disperse system, causing the bubbles to rise to the hquid surface and the liquid contained in the bubble walls to drain downward to the main body of the liquid. Interfacial tension favors the coalescence and ultimate disappearance of bubbles indeed, it is the cause of bubble destruction upon the rupture of the laminae. 

Decreased liquid-liquid interfacial tension (when compared with a gas-liquid system) results in higher liquid-liquid interfacial areas, which favor solid-particle droplet collisions. 

Viscosity and density of the component phases can be measured with confidence by conventional methods, as can the interfacial tension between a pure liquid and a gas. The interfacial tension of a system involving a solution or micellar dispersion becomes less satisfactory, because the interfacial free energy depends on the concentration of solute at the interface. Dynamic methods and even some of the so-called static methods involve the creation of new surfaces. Since the establishment of equilibrium between this surface and the solute in the body of the solution requires a finite amount of time, the value measured will be in error if the measurement is made more rapidly than the solute can diffuse to the fresh surface. Eckenfelder and Barnhart (Am. Inst. Chem. Engrs., 42d national meeting, Repr. 30, Atlanta, 1960) found that measurements of the surface tension of sodium lauryl sulfate solutions by maximum bubble pressure were higher than those by DuNuoy tensiometer by 40 to 90 percent, the larger factor corresponding to a concentration of about 100 ppm, and the smaller to a concentration of 2500 ppm of sulfate. 

Specifically, pore condensation represents a confinement-induced shifted gas-liquid-phase transition [20], This means that condensation takes place at a pressure, P, less than the saturation pressure, of the fluid [2,4,5], The x = P/P0 value, where pore condensation takes place, depends on the liquid-interfacial tension, the strength of the attractive interactions between the fluid and pore walls, the pore geometry, and the pore size [20],... 

The efficiency of surfactant adsorption is determined as a function of minimum bulk surfactant concentration, C that produces saturation adsorption (rmax) at the liquid-gas or liquid-liquid interface. This minimum concentration is defined as p C20 which is (— log C2o) reducing the surface or interfacial tension by 20 dyne cm-1 (n = 20 dyne cm-1). With Qo, r lies between 84 and 99.9% of rmax. The larger the pC2o (smaller the C), the more efficient the surfactant is in adsorbing at the interface and reducing the surface tension at liquid-gas or interfacial tension at liquid-liquid interfaces. The pC20 values for several surfactants can be found in Chapter 2 of [2]. 

Gas holdup is an important hydrodynamic parameter in stirred reactors, because it determines the gas-liquid interfacial area and hence the mass transfer rate. Several studies on gas holdup in agitated gas-liquid systems have been reported, and a number of correlations have been proposed. These are summarized in Table VIII. For a slurry system, only a few studies have been reported (Kurten and Zehner, 1979 Wiedmann et al, 1980). In general, the gas holdup depends on superficial gas velocity, power consumption, surface tension and viscosity of liquids, and the solid concentration. The dependence of gas holdup on gas velocity, power consumption, and surface tension of the liquid can be described as... 

At a fluid interface (gas liquid or liquid liquid) interfacial tension can be measured, and adsorption leads to lowering of y (Figure 10.4). The extent by which y is decreased is called the surface pressure, defined as... 

System variables. Viscosity, density and thermal conductivity of the liquid, interfacial tension, diffusion coefficients, chemical reaction rate constants Operating variables. Impeller speed, gas flow rate, liquid volume, pressure Equipment variables. Impeller type and diameter, geometry of the equipment. 

In order to overcome the coupling of power dissipation and mass transfer, we need to consider a different mechanism for gas-liquid contacting. If we turn to laminar flow, an external structure should be used to create or maintain the surface area. For example, in a falling-film reactor the gas /liquid interfacial area is roughly equal to the wall area. In capillaries at moderate velocities, the predominant flow pattern is called Taylor [29] flow, see Fig. 6.3. In Taylor flow, the gas bubbles are too large to retain their spherical shape and are stretched to fit inside the channel. Surface tension pushes the bubble towards the channel wall, and only a thin film remains between the bubble and the wall. 

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