Liquid gas interface

It was mentioned previously that when the usual macroscopic boundary conditions are used, no well-defined phase separation can be observed in a Monte Carlo computation. In order to simulate the plane free surface of a liquid, using only a small number of particles, one wants boundary conditions 

In each case the calculations have been for Lennard-Jones particles. Hie results of the various methods are encouragingly similar. Hie surface tension can be calculated from the particle distributions, and the various values agree moderately well with each other and with a perturbation theory result. The density profiles of the interfaces are correspondingly quite similar. 

Abraham et al shows that die oscillations gradually diminish in a very long run. The last result suggests that convergence is quite slow in these calculations, but the reason for that is not yet clear. Current opinion seems to be that the oscillations are not physical, but the final answers on this matter may not yet be in. It is also somewhat unclear how the tendency to layering is connected to the boundary conditions. One suggestion, for example, is that inappropriate cell sizes in the periodic directions parallel to the surfaces could explain the different behaviors of different experiments. 

Evidently some further investigation of these details will be necessary, but the problems seem well on the way to solution. Meanwhile, even the early results are rather satisfying, and it seems certain that Monte Carlo study of free-surface regions will become a valuable tool. New developments of the boundary conditions will be needed, of course, for other types of free surfaces, such as that of liquid liquid phase separations of mixtures. 

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G. L. Gaines, Jr. Insoluble Monolayers at Gas-Liquid Interfaces, Interscience, New York, 1966. 

Mass-Transfer Principles Dilute Systems When material is transferred from one phase to another across an interface that separates the two, the resistance to mass transfer in each phase causes a concentration gradient in each, as shown in Fig. 5-26 for a gas-hquid interface. The concentrations of the diffusing material in the two phases immediately adjacent to the interface generally are unequal, even if expressed in the same units, but usually are assumed to be related to each other by the laws of thermodynamic equihbrium. Thus, it is assumed that the thermodynamic equilibrium is reached at the gas-liquid interface almost immediately when a gas and a hquid are brought into contact. 

For systems in which the solute concentrations in the gas and hquid phases are dilute, the rate of transfer may be expressed by equations which predic t that the rate of mass transfer is proportional to the difference between the bulk concentration and the concentration at the gas-liquid interface. Thus... 

These equations assume that there is no drag force at the gas/liquid interface, such as would be produced by gas flow. For a flat surface inclined at an angle 0 with the horizontal, the preceding equations may be modified by replacing g by g sin 0. For films falhng inside vertical tubes with film thickness up to and including the full pipe radius, see Jackson AlChE1, 231-240 [1955]). 

FK . 15-22 Uqiiid agitation by a disc flat blade turbine in the presence of a gas-liquid interface a) without wall baffles, (h) with wall baffles, and (c) in full vessels without a gas-bqiiid interface (continuous flow) and without baffles. [Couitesy Treyhal, Mass Transfer Operations, 3rd ed., p. 148, McGraw-Hill, NY,... 

FIG. 15-23 Power for agitation impellers immersed in single-phase liquids, baffled vessels with a gas-liquid surface [except curves (c) and (g)]. Curves correspond to (a) marine impellers, (h) flat-blade turbines, w = dj/5, (c) disk flat-blade turbines witb and without a gas-liquid surface, (d) curved-blade turbines, (e) pitcbed-blade turbines, (g) flat-blade turbines, no baffles, no gas-liquid interface, no vortex. 

Liquid-solid interactions due to long-range intermolecular forces are much larger than are gas-solid interactions. This means that it is easier to collect fine particles at a liquid-liquid interface than at a gas-liquid interface. 

Liquid holdup is made up of a dynamic fraction, 0.03 to 0.25, and a stagnant fraction, 0.01 to 0.05. The high end of the stagnant fraction includes the hquid that partially fills the pores of the catalyst. The effective gas/liquid interface is 20 to 50 percent of the geometric surface of the particles, but it can approach 100 percent at high hquid loads with a consequent increase of reaction rate as the amount of wetted surface changes. 

Present research is devoted to investigation of application of luminol reactions in heterogeneous systems. Systems of rapid consecutive reactions usable for the determination of biologically active, toxic anions have been studied. Anions were quantitatively converted into chemiluminescing solid or gaseous products detectable on solid / liquid or gas / liquid interface. Methodology developed made it possible to combine concentration of microcomponents with chemiluminescence detection and to achieve high sensitivity of determination. 

The collection medium for gases can be liquid or solid sorbents, an evacuated flask, or a cryogenic trap. Liquid collection systems take the form of bubblers which are designed to maximize the gas-liquid interface. Each design is an attempt to optimize gas flow rate and collection efficiency. Higher flow rates permit shorter sampling times. However, excessive flow rates cause the collection efficiency to drop below 100%. 

Carbon dioxide gas diluted with nitrogen is passed continuously across the surface of an agitated aqueous lime solution. Clouds of crystals first appear just beneath the gas-liquid interface, although soon disperse into the bulk liquid phase. This indicates that crystallization occurs predominantly at the gas-liquid interface due to the localized high supersaturation produced by the mass transfer limited chemical reaction. The transient mean size of crystals obtained as a function of agitation rate is shown in Figure 8.16. 

Figure 8.29 The gas-liquid interface in the early stages of the precipitation process at 450rpm. LHS CFD model Mq (a t = 0.1s c t=l s e 10s ), RHS Experimental (h 1 = 0 d t= 1 min f. l = 3miiis). (After Wachi and Jones, 199Ur, Al-Rashed and Jones, 1999)...

Hikita, H. and Ishikawa, H., 1969. Physical absorption in agitated vessels with a flat gas-liquid interface. Bulletin of the UniversityOsaka Prefect, A18, 427-437. 

Stressed, such as heat-affected zones near welds, in areas of high acid-gas concentration, or at a hot gas-liquid interface. Therefore, stress-relieving all equipment after manufacturing is necessary to reduce corrosion, and special metallurgy in specific areas such as the still overhead or the reboiler tubes may be required. 

Molar transformation of oxygen is proportional to the concentration gradient of oxygen at the gas-liquid interface and oxygen dissolved in the bulk liquid phase ... 

Because the interface region is thin, the flux across a thin film will be at steady state. Therefore, the transfer rate to the gas-liquid interface is equal to its transfer rate through the liquid-side film. Thus,... 

The gaseous components must be transferred from the bulk gaseous phase to the bulk liquid phase. The components are transferred to the gas-liquid interface by convection and diffusion in the gas and from the interface by diffusion and convection in the liquid. 

The absorbed products are transferred across the gas-liquid interface by convective and diffusive transport. 

In a later publication, Kolbel et al. (K16) have proposed a less empirical model based on the assumption that the rate-determining steps for a slurry process are the catalytic reaction and the mass transfer across the gas-liquid interface. When used for the hydrogenation of carbon monoxide to methane, the process rate is expressed as moles carbon monoxide consumed per hour and per cubic meter of slurry ... 

Farkas and Sherwood (FI, S5) have interpreted several sets of experimental data using a theoretical model in which account is taken of mass transfer across the gas-liquid interface, of mass transfer from the liquid to the catalyst particles, and of the catalytic reaction. The rates of these elementary process steps must be identical in the stationary state, and may, for the catalytic hydrogenation of a-methylstyrene, be expressed by ... 

Such a model should take into account at least the following phenomena Mass transfer across gas-liquid interface, mass transfer to exterior particle surface, catalytic reaction, flow and axial mixing of gas phase, and flow and axial mixing of liquid phase. 

The experimental and theoretical work reported in the literature will be reviewed for each of the five major types of ga s-liquid-particle operation under the headings Mass transfer across gas-liquid interface mass transfer across liquid-solid interface holdup and axial dispersion of gas phase holdup and axial dispersion of liquid phase heat transfer reaction kinetics. 

Calderbank et al. (C6) studied the Fischer-Tropsch reaction in slurry reactors of 2- and 10-in. diameters, at pressures of 11 and 22 atm, and at a temperature of 265°C. It was assumed that the liquid-film diffusion of hydrogen from the gas-liquid interface is a rate-determining step, whereas the mass transfer of hydrogen from the bulk liquid to the catalyst was believed to be rapid because of the high ratio between catalyst exterior surface area and bubble surface area. The experimental data were not in complete agreement with a theoretical model based on these assumptions. 

Morris (M9) has recently reviewed a number of studies of mass transfer across the gas-liquid interface in mechanically agitated systems containing suspended solid particles. These studies [Hixon and Gaden (H7), Eckenfelder... 

The mass-transfer rates obtainable across the gas-liquid interface are of nearly the same magnitude in the different operations. Bubble-column slurries exhibit rather higher transfer rates than conventional packed columns... 

Equilibrium exists at the gas-liquid interface and the concentration is constant at c . 

The following assumptions were made (1) The gas bubbles are evenly distributed throughout the liquid phase and have constant radius and composition (2) the concentration of the gas-liquid interface is constant and equal to C (3) no gross variations occur in liquid composition throughout the vessel and (4) the gas is sparingly soluble, and, in the case of a chemical reaction, it is removed by a first-order irreversible reaction with respect to the dissolving gas. 

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