Liquid film, thickness

In Taylor flow, a thin film is observed near the gas bubble which prohibits the contact between gas and solid. This phenomenon is similar to the role of lubricating viscous fluid in bearing for preventing the solid-solid contact. The spherical region at the front has a constant radius r with the Laplace pressure difference across the interface AP = la jr for small thickness of the film (6 r). The curvature in the axial direction vanishes for the flat film region, and the Laplace 

Detailed analysis of N-S equation by Bretherton in the transition region results in the expression of film thickness as 

Marangoni effects may be responsible for the difference between theory and experiment in the low capillary number regime, where surface tension effect is dominant. The presence of impurities may lead to gradient of these impurities in the gas-liquid interface. The surfactants 

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The carbon dioxide volume content was varied from 0.8 to 100 vol.-% the gas velocity changes from 0.1 to 42.9 mm s [5]. The residence time varied from 0.1 to 9.7 min 64 single streams of a liquid film thickness of 65 pm were used at a total volume flow of 50 ml h . The ratio of carbon dioxide to sodium hydroxide was fixed at 0.4. 

Measurement of liquid film thickness. A variety of techniques have been used to measure the time variation of local film thickness and the data on wave structure that can be deduced therefrom (Dukler and Taitel, 1991a) ... 

Figure 3.32 Measurement of liquid film thickness by Moire fringes (a) experimental setup and (ft) Moire pattern with liquid films of varying thicknesses. (From Kheshgi and Scriven, 1983. Copyright 1983 by Elsevier Science Ltd., Kidlington, UK. Reprinted with permission.)...

Figure 3.33 Measurement of liquid film thickness by means of a wall optical sensor as used by Ohba et al. (1984). (From Del-ha ye, 1986. Copyright 1986 by Hemisphere Publishing Corp., New York. Reprinted with permission.)... 

Quandt (1962) measured the values of (CfICm - 1) at various axial positions of an air-water mixture flow in a 0.25-in. X 3-in. channel and converted the raw data to the exchange mass flux, pLV(, as shown in Figure 5-23. He also measured the film velocity Vf by injecting a pulse of dye into the liquid film and recording its transport time between two photocells. Such measured data are shown in Figure 5.24. By using the measured values for Vf, the liquid film thickness t may be calculated as... 

Since the liquid film thickness is zero at dryout, Bennett et al. (1967a) suggested that the mass balance on the wall for a small length increment, AZ, upstream of the dryout, be in the form... 

In a high-quality two-phase flow in a straight tube, the surface roughness increases the liquid entrainment and thus reduces the liquid film thickness and brings about a low CHF. 

Considering a section of a vertical pipe through the base of a gas slug where the liquid film thickness is constant, and calling the gas volume fraction at this point Ro and the true point gas flow Qo, we find from Eq. (46) that... 

Entrainment studies have been relatively few, as pointed out earlier. Anderson and Mantzouranis (A3) used the results of measurements of entrainment (which was small in their work) to correct their calculated liquid film thickness, and thus obtained somewhat better agreement with experimental values. Wicks and Dukler (W2) measured entrainment in horizontal flow, and obtained a correlation for the amount of entrainment in terms of the Lockhart and Martinelli parameter, X. The entrainment parameter, R, of Wicks and Dukler is given by... 

The third term of Equation 2.80 accounts for resistance to mass transfer in liquid phase. An obvious way of reducing this term is to reduce the liquid film thickness d. This causes a reduction in k and an increase in the term k1/(1 + k )2- However, using thinly coated column packings increases the probability of adsorption of solute molecules on the surface of support material, which might result in peaks tailing. 

Al. Adomi, N., Casagrande, I., Cravarolo, L., Hassid, A., and Silvestri, M., Experimental Data on Two-phase Adiabatic Flow Liquid Film Thickness, Phase and Velocity Distribution, Pressure Drops in Vertical Gas-Liquid Flow . Centro Informazioni Studi Esperienze, Milan, Report R-35, March 1961. 

In compact geometries the heat transfer coefficient depends on the two-phase flow pattern (51-67). For low condensation rates, the heat transfer is gravity controlled, and the heat transfer coefficient depends on the liquid film thickness. For higher condensation rates, the heat transfer coefficient depends on the vapor shear effect, and for small passages the liquid-vapor interaction leads to high heat transfer coefficients. 

Figure 7 further shows that, as gaseous C02 moves up the absorber, phase equilibrium is achieved at the vapor-liquid interface. C02 then diffuses through the liquid film while reacting with the amines before it reaches the bulk liquid. Each reaction is constrained by chemical equilibrium but does not necessarily reach chemical equilibrium, depending primarily on the residence time (or liquid film thickness and liquid holdup for the bulk liquid) and temperature. Certainly kinetic rate expressions and the kinetic parameters need to be established for the kinetics-controlled reactions. While concentration-based kinetic rate expressions are often reported in the literature, activity-based kinetic rate expressions should be used in order to guarantee model consistency with the chemical equilibrium model for the aqueous phase solution chemistry. 

A foam is a colloidal dispersion in which a gas is dispersed in a continuous liquid phase. The dispersed phase is sometimes referred to as the internal (disperse) phase, and the continuous phase as the external phase. Despite the fact that the bubbles in persistent foams are polyhedral and not spherical, it is nevertheless conventional to refer to the diameters of gas bubbles in foams as if they were spherical. In practical occurrences of foams, the bubble sizes usually exceed the classical size limit given above, as may the thin liquid film thicknesses. In fact, foam bubbles usually have diameters greater than 10 pm and may be larger than 1000 pm. Foam stability is not necessarily a function of drop size, although there may be an optimum size for an individual foam type. It is common but almost always inappropriate to characterize a foam in terms of a given bubble size since there is inevitably a size distribution. This is usually represented by a histogram of sizes, or, if there are sufficient data, a distribution function. 

The simulator used was a DISMOL, described previously by Batistella and Maciel (2). All explanations of the equations used, the solution methods, and the routine of solution are described in Batistella and Maciel (5). DISMOL is a simulator that permits changes in feed composition, feed temperaturethe evaporation rate, as well as feed flow rate. The effective rate of surface evaporation is obtained from the kinetic theory of gases. The liquid film thickness is obtained by mass balance and geometry of the evaporator. The temperature in the liquid obeys the Fourier-Kirchhoff equation. The solution of the velocity profile requires knowledge of the viscosity and the liquid film thickness over the evaporator. The solution for the temperature and the concentration profiles requires knowledge of the velocity profiles, which determine the convective heat and mass fluxes. 

Mass transfer coefficients and specific contact area are calculated with the correlations of Onda et al. [60]. In order to determine the liquid film thickness, the diffusion coefficient for SO2 is used. 

In this model, the temporal change of the molar quantity of the element calcium is due to the temporal change of the molar quantity on the fluidized-bed material. With a constant liquid film thickness, this problem reduces to the temporal change of the wetted surface ... 

Equations (3),(4) are supplemented by the conjugate boundary conditions (velocity and shear stress continuity) at the interface. The numerical solution of the hydrodynamic equations yields the liquid film thickness as well as velocity profiles in each phase. They are used for the description of mass and heat transfer. 

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