Gas phase dispersion

Grassman (G7) has proposed a simplified theoretical treatment of heat and mass transfer between two fluid phases, as, for example between a dispersed gas phase and a continuous liquid phase von Bogdandy et al. (V8) measured the rate of absorption of carbon dioxide by water and by decalin, and found that the absorption rate approximated that predicted by Grass-mann in the laminar region but was above the theoretical values in the... 

Mass transfer across the liquid-solid interface in mechanically agitated liquids containing suspended solid particles has been the subject of much research, and the data obtained for these systems are probably to some extent applicable to systems containing, in addition, a dispersed gas phase. Liquid-solid mass transfer in such systems has apparently not been studied separately. Recently published studies include papers by Calderbank and Jones (C3), Barker and Treybal (B5), Harriott (H4), and Marangozis and Johnson (M3, M4). Satterfield and Sherwood (S2) have reviewed this subject with specific reference to applications in slurry-reactor analysis and design. 

Thrust, 4 Trickle-flow, 79 fixed-bed, 90-104 holdup and axial dispersion gas phase, 92-94 liquid phase, 94-102... 

An Eulerian-Eulerian (EE) approach was adopted to simulate the dispersed gas-liquid flow. The EE approach treats both the primary liquid phase and the dispersed gas phase as interpenetrating continua, and solves a set of Navier-Stokes equations for each phase. Velocity inlet and outlet boundary conditions were employed in the liquid phase, whilst the gas phase conditions consisted of a velocity inlet and pressure outlet. Turbulence within the system was account for with the Standard k-e model, implemented on a per-phase basis, similar to the recent work of Bertola et. al.[4]. A more detailed description of the computational setup of the EE method can be found in Pareek et. al.[5]. 

Frohlich, S., Lotz, M., Larson, B., Lilbbert, A., Schilgerl, K., Seekamp, M., Characterization of a Pilot Plant Airlift Tower Loop Bioreactor III. Evaluation of Local Properties of the Dispersed Gas Phase During Yeast Cultivation and in a Model Media, Biotechnol. Bioeng., 38 56 (1991b)... 

Fig. 13 Mean bubble sizes and specific surface areas of the dispersed gas phase in the biphasic system H2/H2O as a function of the hydrogen volume rate...

Membranes play an important role in natural science and for many technical applications. Depending on their purpose, their shape can be very different. For instance, membranes include porous or non-porous films, either supported or non-supported, with two interfaces surrounded by a gas or by a liquid. Important properties of non-porous membranes are their permeability for certain compounds and their stability. In biological cells their main task is to stabilize the cell and to separate the cell plasma from the environment. Furthermore, different cells and cell compartments have to communicate with each other which requires selective permeability of the membranes. For industrial applications membranes are often used for separation of gases, liquids, or ions. Foams and emulsions for instance are macroscopic composite systems consisting of many membranes. They contain the continuous liquid phase surrounded by the dispersed gas phase (foams) or by another liquid (emulsions). Beside these application possibilities membranes give the opportunity to investigate many questions related to basic research, e.g. finite size effects. 

At an axi-symmetric boundary Neuman conditions are used for all the fields, except for the normal velocity component which is zero because the flow direction turns at this point. The assumption of cylindrical axi-symmetry in the computations prevents lateral motion of the dispersed gas phase and leads to an unrealistic radial phase distribution [73, 66[. Krishna and van Baten [73] obtained better agreement with experiments when a 3D model was applied. However, experience showed that it is very difficult to obtain reasonable time averaged radial void profiles even in 3D simulations. 

The limiting steps in the model development are the formulation of closure relations or closure laws determining turbulence effects, interfacial transfer fluxes and the bubble coalescence and breakage processes. When sufliciently dilute dispersions are considered, only particle - fluid interactions are significant and the two-fluid closures can be employed. In these particular cases, only the interaction between each of the dispersed gas phases (d) and the continuous liquid phase (c) is considered parameterizing the last term on the RHS of (8.12) ... 

Several extensions of the two-fluid model have been developed and reported in the literature. Generally, the two-fluid model solve the continuity and momentum equations for the continuous liquid phase and one single dispersed gas phase. In order to describe the local size distribution of the bubbles, the population balance equations for the different size groups are solved. The coalescence and breakage processes are frequently modeled in accordance with the work of Luo and Svendsen [74] and Prince and Blanch [92]. 

The instantaneous volume averaged conservation of mass of the continuous liquid and dispersed gas phases were expressed as ... 

On the other hand, there are two significant differences between macroemulsions and foams (1) The surfactants in the inter-facial film of a foam cannot dissolve in the dispersed (gas) phase, while in a macroemulsion the solubility of the surfactants in the liquid being dispersed is a major factor determining the stability of the emulsion. (2) In macroemulsions, both oil and water can serve as the continuous phase, i.e., both O/W and W/O emulsions are commonly encountered, while in foams, only the liquid acts as the continuous phase. 

Liquid-liquid reactors are similar to gas-liquid reactors. In the former case, the dispersed phase is in the form of droplets as against bubbles in the latter. The motion of bubbles and drops can be described using a unified approach. A spray column (or a drop column) is the equivalent of a bubble column but with one difference. The dispersed gas phase is always lighter than the continuous liquid phase (p < Pl)- However, the dispersed liquid phase in spray columns may be lighter or heavier than the continuous immiscible liquid phase. Nevertheless, spray columns can be easily described similar to bubble columns. Furthermore, packed bubble columns and sectionalized bubble columns can be considered equivalent to packed extraction columns and plate extraction columns. External-loop and internal-loop reactors are also possible (for equivalent gas-liquid reactors, refer to Section 11.4.2.1.4). 

Aqueous liquid-organic liquid (in the presence of a dispersed gas phase)... 

As can be seen, a utilization factor close to unity can be achieved if the reaction is mainly occuring in the bulk of the liquid phase. From a practical point of view, it means that homogeneous catalytic reactions are performed in reactors with continuous liquid phase and dispersed gas phase. 

Both the aerosol sprays and the aerosol foam products originally tended to contain chlorofluorocarbons (CFCs) like Freon as the pressurized propellant phase (which in foam applications becomes the dispersed gas phase). With increasing environmental awareness and concerns, formulation practices have changed in... 

Like other colloidal systems, foams may be formed either by dispersion or condensation processes. In the former process, the incipient dispersed gas phase is present as a bulk or condensed phase. Small volumes of the future dispersed phase are introduced into the liquid by agitation or converted into gas by some mechanism such as heating, or pressure reduction. In the case of condensation, the gas phase is introduced at the molecular level and allowed to condense within the liquid to form bubbles. 

Figure 7.5 Five steps of Taylor (slug) flow generation. Dispersed gas phase is introduced through side channel while wetting continuous phase is introduced through main channel.

Continuous liquid/disperse gas-phase contactors (Type B)... 

Experimentally it was found that the mass spectra of analytes showed much less dependence on background electrolytes (such as sodium) when nanospray was used for the electrostatic dispersion. Gas-phase ions are produced from charged droplets only when the droplets are very small. This holds both for lEM and CRM. Therefore, if one starts with relatively small initial droplets as generated with nanospray, much less solvent evaporation will be required to reach the final droplet size required for the generation of gas-phase ions. Therefore, in the presence of impurities such as sodium salts the concentration increase of the salt will be much smaller with nanospray. 

The consistent difference in prevailing between 0.1 and 19.4 MPa for d > 2 mm is due to the significant increase in gas density (as large as a 200-fold increase with pressure from 0.1 to 19.4 MPa). The density effect is accounted for in Fan-Tsuchiya equation in terms of Ap/pi or in Tomiyama s equation in terms of both Ap/pi and Eo. As can be seen from the equations and figure, the density differenee between the eontinu-ous liquid phase and the dispersed gas phase plays an important role in determining bubble rise velocity, especially for large bubbles. 

If the dispersed gas phase is assumed to be incompressible, a similar conservation equation can be written for the gas phase as ... 

Reactions between components of a gas and a liquid, the kinetics of which were discussed in Chapter 6, are carried out in a variety of equipment, often having confusing names. The variety stems from a number of conditions that have to be fulfilled simultaneously efficient contact between gas and liquid — and eventually a solid catalyst, limitation of pressure drop, ease of removal of heat, and low cost of construction and operation. Depending on whether the main mass transfer resistance is located in the gas or in the liquid, multiphase reactors or absorbers are operated either with a dispersed gas phase and continuous liquid phase or vice versa. Whether cocurrent or countercurrent flow of gas and liquid is used depends on the availability of driving forces for mass and heat transfer and reaction. 

The model species, total mass, momentum, and energy continuity equations are similar to those presented in Section 13.7 on fluidized bed reactors. Constant values of the gas and liquid phase densities, viscosities, and diffusivities were assumed, as well as constant values of the interphase mass transfer coefficient and the reaction rate coefficient. The interphase momentum transfer was modelled in terms of the Eotvos number as in Clift et al. [1978]. The Reynolds-Averaged Navier-Stokes approach was taken and a standard Computational Fluid Dynamics solver was used. In the continuous liquid phase, turbulence, that is, fluctuations in the flow field at the micro-scale, was accounted for using a standard single phase k-e model (see Chapter 12). Its applicability has been considered in detail by Sokolichin and Eigenberger [1999]. No turbulence model was used for the dispersed gas phase. Meso-scale fluctuations around the statistically stationary state occur and were explicitly calculated. This requires a transient simulation and sufficiently fine spatial and temporal grids. 

Eularian-Eularian two-fluid model. In this model, both gas (vapor) and liquid phases are considered as a system to be concerned aiming to obtain the transport information of each phase. Model assumptions are made that both phases (the continuous liquid phase and the dispersed gas phase) are considered as two interpenetrating continua, so that the Eularian method (expressed by volume average Navier-Stokes equation) can be applied to both phases. The model equations for phase 9 are as follows ... 

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