Liquid dispersion effects

Gas-Liquid Dispersion This involves physical dispersion of gas bubbles by the impeller, and the effect of gas flow on the impeller. 

To illustrate, consider the hmiting case in which the feed stream and the two liquid takeoff streams of Fig. 22-45 are each zero, thus resulting in batch operation. At steady state the rate of adsorbed carty-up will equal the rate of downward dispersion, or afV = DAdC/dh. Here a is the surface area of a bubble,/is the frequency of bubble formation. D is the dispersion (effective diffusion) coefficient based on the column cross-sectional area A, and C is the concentration at height h within the column. 

No exact theoretical analysis has as yet been possible because of the large number of variables involved and the complex mechanisms governing the transfer mechanism in a gas-liquid dispersion. The following section analyzes in a qualitative manner some of the effects produced by the mixing impeller in the disperser. It will serve to show some of the interrelationships involved as well as to illustrate the difficulties in the path of arriving at an exact mechanism. 

The overall set of partial differential equations that can be considered as a mathematical characterization of the processing system of gas-liquid dispersions should include such environmental parameters as composition, temperature, and velocity, in addition to the equations of bubble-size and residence-time distributions that describe the dependence of bubble nucleation and growth on the bubble environmental factors. A simultaneous solution of this set of differential equations with the appropriate initial and boundary conditions is needed to evaluate the behavior of the system. Subject to the Curie principle, this set of equations should include the possibilities of coupling effects among the various fluxes involved. In dispersions, the possibilities of couplings between fluxes that differ from each other by an odd tensorial rank exist. (An example is the coupling effect between diffusion of surfactants and the hydrodynamics of bubble velocity as treated in Section III.) As yet no analytical solution of the complete set of equations has been found because of the mathematical difficulties involved. To simplify matters, the pertinent transfer equation is usually solved independently, with some simplifying assumptions. 

In this section, a general formulation will be given for the effect of bubble residence-time and bubble-size distributions on simultaneous and thermodynamically coupled heat- and mass-transfer in a multicomponent gas-liquid dispersion consisting of a large number of spherical bubbles. Here one can... 

To evaluate the effects of operating variables on the capacity of the gas-liquid disperser one can make the following substitutions ... 

K. Rietema, Segregation in Liquid-Liquid Dispersions and Its Effect on Chemical Reactions... 

An attempt has been made by Tsouris and Tavlarides[5611 to improve previous models for breakup and coalescence of droplets in turbulent dispersions based on existing frameworks and recent advances. In both the breakup and coalescence models, two-step mecha-nisms were considered. A droplet breakup function was introduced as a product of droplet-eddy collision frequency and breakup efficiency that reflect the energetics of turbulent liquid-liquid dispersions. Similarly, a coalescencefunction was defined as a product of droplet-droplet collision frequency and coalescence efficiency. The existing coalescence efficiency model was modified to account for the effects of film drainage on droplets with partially mobile interfaces. A probability density function for secondary droplets was also proposed on the basis of the energy requirements for the formation of secondary droplets. These models eliminated several inconsistencies in previous studies, and are applicable to dense dispersions. 

Contributing to Ajj are, in addition to the solvent structural effects explicitly considered, contributions from dielectric saturation, from the liquid structure effects one has even in simple fluids, from solvent-mediated dispersion interactions of the ions, from charge-polarizability interactions of the ions, and so on. It is difficult to tell a-priori which effects are dominant or how big they are. However the collection of A 5 coefficients has characteristics that are consistent with the first named effect being dominant. 

In liquids the effects of longitudinal dispersion are small, even at low Reynolds Numbers. 

---