Liquid films, free

Mass transfer controlled by diffusion in the gas phase (ammonia in water) has been studied by Anderson et al. (A5) for horizontal annular flow. In spite of the obvious analogy of this case with countercurrent wetted-wall towers, gas velocities in the cocurrent case exceed these used in any reported wetted-wall-tower investigations. In cocurrent annular flow, smooth liquid films free of ripples are not attainable, and entrainment and deposition of liquid droplets presents an additional transfer mechanism. By measuring solute concentrations of liquid in the film and in entrained drops, as well as flow rates, and by assuming absorption equilibrium between droplets and gas, Anderson et al. were able to separate the two contributing mechanisms of transfer. The agreement of their entrainment values (based on the assumption of transfer equilibrium in the droplets) with those of Wicks and Dukler (W2) was taken as supporting evidence for this supposition. 

Sindayihebura, D. and Bolle, L., Ultrasonic atomization of liquid stability analysis of the viscous liquid film free surface, Atomiz. Spray, 8, 217-233, 1998. 

Gumerman and Homsy [554] have extended this analysis by taking into account the effects of wall and film drainages. Williams and Davis [555] have shown that the nonlinear effects (in the case of a surfactant-free thin liquid films) may have a significant effect on file rupture time. The nonlinear stability of evaporating/condensing thin liquid films, free from surfactant, is discussed in Refs. 556-558. The authors show that the evaporation and the condensation lead to destabilization of the film. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

There are two procedures for doing this. The first makes use of a metal probe coated with an emitter such as polonium or Am (around 1 mCi) and placed above the surface. The resulting air ionization makes the gap between the probe and the liquid sufficiently conducting that the potential difference can be measured by means of a high-impedance dc voltmeter that serves as a null indicator in a standard potentiometer circuit. A submerged reference electrode may be a silver-silver chloride electrode. One generally compares the potential of the film-covered surface with that of the film-free one [83, 84]. 

The value so obtained will differ from that of the bulk liquid, y, by a thickness-dependent term P(e). For a nonvolatile liquid film, the free energy F (per unit area) will then be expressed as [1] ... 

The shape of a droplet or of the front end of a film can be determined from the surface energies and interaction forces between the interfaces. These also determine the equilibrium thickness of a liquid film that completely wets a surface. The calculation is done by minimization of the free energy of the total system. In a two-dimensional case the free energy of a cylindrical droplet can be expressed as [5] ... 

However, on rigid substrates, the growth of dry zones is accompanied by a rim of excess liquid with width X (Fig. 10). As the dewetting proceeds, X increases. For short times and < K, the growth of dry patches is controlled only by surface tension forces and the dewetting speed is constant. A constant dewetting speed of 8 mm-s has been measured when a liquid film of tricresyl phosphate (TCP) dewets on Teflon PFA, a hard fluoropoly-mer of low surface free energy (p. = 250 MPa, 7 = 20 mJ-m ). 

The temperature of a liquid metal stream discharged from the delivery tube prior to primary breakup can be calculated by integrating the energy equation in time. The cooling rate can be estimated from a cylinder cooling relation for the liquid jet-ligament breakup mechanism (with free-fall atomizers), or from a laminar flat plate boundary layer relation for the liquid film-sheet breakup mechanism (with close-coupled atomizers). 

An entirely different approach to equilibrium adsorption is to assume that adsorbed layers behave like liquid films, and that the adsorbed molecules are free to move over the surface. It is then possible to apply the equations of classical thermodynamics. The properties which determine the free energy of the film are pressure and temperature, the number of molecules contained and the area available to the film. The Gibbs free energy G may be written as ... 

The disjoining pressure vs. thickness isotherms of thin liquid films (TFB) were measured between hexadecane droplets stabilized by 0.1 wt% of -casein. The profiles obey classical electrostatic behavior. Figure 2.20a shows the experimentally obtained rt(/i) isotherm (dots) and the best fit using electrostatic standard equations. The Debye length was calculated from the electrolyte concentration using Eq. (2.11). The only free parameter was the surface potential, which was found to be —30 mV. It agrees fairly well with the surface potential deduced from electrophoretic measurements for jS-casein-covered particles (—30 to —36 mV). 

J. Lyklema and T. Van VUet Polymer-Stabilized Free Liquid Films. Faraday Disc. Chem. Soc. 65, 26 (1978). 

Of course, both of the two coefficients, C and Klo are some combination of the processes considered when equation (8.87) through (8.102) were developed, and are a function of liquid film coefficient across both the bubbles and the free surface, bubble and water surface interfacial area, hydrostatic pressure, the mole ratio of gas in the bubbles, and equilibrium with the atmosphere. These two coefficients, however, can be valuable in the design of an aeration system, as long as (1) the arrangement of diffusers in the water body or tank is similar to the application and (2) the depth of the test is the same as the application. Significant deviations from these two criteria will cause errors in the application of the tests to the field. 

The thicknesses of free soap films and liquid films adsorbed on surfaces (Figs. 1.26d and 1.26e), which can be measured using optical techniques such as reflected intensity, total internal reflection spectroscopy, or ellipsometry as functions of salt concentration or vapor pressure, can provide information on the long-range repulsive forces stabilizing thick wetting films. We see an example of this in Chapter 11. 

Liquid crystals stabilize in several ways. The lamellar structure 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 liquid crystalline phase, coalescence takes place over a thin liquid 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 liquid crystal present, coalescence takes place over a thick film and the slope of the van der Waals potential is small. In addition, the liquid crystal is highly viscous, and two droplets separated by a viscous film of liquid crystal with only a small compressive force exhibit stability against coalescence. Finally, the network of liquid crystalline leaflets (30) hinders the free mobility of the emulsion droplets. 

Lyklema and Vliet8 determined the equilibrium thickness to of free liquid films stabilized by poly(vinyl alcohol) (PVA) adsorbed at the air-water interface. They estimated to at different applied hydrostatic pressures by measuring the intensities of light reflected from the surface of the film to that of the silvery film. The to values obtained increased with rising hydrostatic pressure and were extrapolated to zero pressure to obtain to for a free film. The extrapolated to should correspond to twice the thickness of the adsorbed PVA layer, but it far exceeded twice the latter determined by ellipsometry. The great difference was interpreted in terms of the presence of long dangling tails which are probably not to be seen by ellipsometry. 

The cosine cannot exceed one. Then we might ask What happens, if 7s — 7sl — 7l > 0 or 7S - 7Si is higher than 7// Does this not violate Young s equation No, it does not because in thermodynamic equilibrium 7s — Ysl — 1l can never become positive. This is easy to see. If we could create a situation with 7s > 7SL + 7l, then the Gibbs free energy of the system could decrease by forming a continuous liquid film on the solid surface. Vapor would condense onto the solid until such a film is formed and the free solid surface would be replaced to a solid-liquid interface plus a liquid surface. 

Transports of HTO vapour and H20 vapour to and from surfaces are controlled similarly by eddy diffusion in the free air and molecular diffusion across the viscous boundary layer near the surface. There is also a liquid phase boundary layer, and diffusion through this is a limiting resistance to the transport of sparingly soluble gases such as H2 or HT. For HTO, the liquid film resistance is negligible (Slinn et al., 1978). When the concentration gradients are in opposite directions, transport of HTO to a water surface can proceed simultaneously with evaporation of H20. 

Also at the liquid film-air interface (z = h), the shear stress-free boundary condition is generally applicable ... 

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