Dispersion-coalescence equilibrium

Turbulent Dispersion Coalescence. After the dispersed phase leaves the motionless mixer, it will tend to coalesce to an equilibrium drop or bubble size characteristic of the shear field in the downstream piece of pipe. This coalescence is not just a phenomenon of the downstream tailpipe but is a process happening in parallel with dispersion. It is not as well understood. We do know that just like dispersion, coalescence is affected by volume concentration and is promoted by turbulence. Coalescence is strongly affected by surface chemistry effects. The role of many chemicals added to stabilize dispersions is to slow down the coalescence rate. 

Church and Shinnar (1961) described the interrelationship between suspension, dispersion, and coalescence. Figure 12-25 shows drop size as a function of agitator speed in a turbulent process vessel. A stable region exists in the center area bounded by three lines representing dispersion, coalescence, and suspension phenomena. Consider constant impeller speed. If a large drop exists above the upper dispersion line, it will continue to break up until the dispersion line is reached. Breakage can result in some drops whose size lies below the lower coalescence line. These drops will continue to coalesce until the coalescence line is reached. Inside the bounded region, equilibrium is established between dispersion and coalescence. 

The archetypal, stagewise extraction device is the mixer-settler. This consists essentially of a well-mixed agitated vessel, in which the two liquid phases are mixed and brought into intimate contact to form a two phase dispersion, which then flows into the settler for the mechanical separation of the two liquid phases by continuous decantation. The settler, in its most basic form, consists of a large empty tank, provided with weirs to allow the separated phases to discharge. The dispersion entering the settler from the mixer forms an emulsion band, from which the dispersed phase droplets coalesce into the two separate liquid phases. The mixer must adequately disperse the two phases, and the hydrodynamic conditions within the mixer are usually such that a close approach to equilibrium is obtained within the mixer. The settler therefore contributes little mass transfer function to the overall extraction device. 

Mixer-settlers have been the more common type of equipment and, with the development of hydrometallurgy over the past 20 years, designs have improved considerably. To select the appropriate equipment, a clear understanding of the chemical and physical aspects of the process is required. Also the economics must be considered relative to the type of equipment to suit particular conditions of given throughput, solution and solvent type, kinetics and equilibrium, dispersion and coalescence, solvent losses, number of stages, available areas, and corrosion. 

The types of equipment used, which range from stirred tanks and mixer-settlers to centrifugal contactors and various types of columns, affect both capital and operating costs [9]. In the decision to build a plant, the choice of the most suitable contactor for the specific situation is most important. In some systems, because of the chemistry and mass transfer rates involved, several alternative designs of contacting equipment are available. In the selection of a contactor, one must consider the capacity and stage requirements solvent type and residence time phase flow ratio physical properties direction of mass transfer phase dispersion and coalescence holdup kinetics equilibrium presence of solids overall performance and maintenance as a function of contactor complexity. This may appear very complicated, but with some experience, the choice is relatively simple. 

An analogy may be drawn between the phase behavior of weakly attractive monodisperse dispersions and that of conventional molecular systems provided coalescence and Ostwald ripening do not occur. The similarity arises from the common form of the pair potential, whose dominant feature in both cases is the presence of a shallow minimum. The equilibrium statistical mechanics of such systems have been extensively explored. As previously explained, the primary difficulty in predicting equilibrium phase behavior lies in the many-body interactions intrinsic to any condensed phase. Fortunately, the synthesis of several methods (integral equation approaches, perturbation theories, virial expansions, and computer simulations) now provides accurate predictions of thermodynamic properties and phase behavior of dense molecular fluids or colloidal fluids [1]. 

Coalescence and Phase Separation. Coalescence between adjacent drops and between drops and contactor internals is important for two reasons. It usually plays a part in combination wilh breakup, in determining Ihe equilibrium drop size in a dispersion, and it can therefore affect holdup and flooding in a countercurrent extraction column. Secondly, it is an essential step in the disengagement of the phases and the control of entrainment after extraction has been completed. 

The rate of foam drainage is determined not only by the hydrodynamic characteristics of the foam (border shape and size, liquid phase viscosity, pressure gradient, mobility of the Iiquid/air interface, etc.) but also by the rate of internal foam (foam films and borders) collapse and the breakdown of the foam column. The decrease in the average foam dispersity (respectively the volume) leads the liberation of excess liquid which delays the establishment of hydrostatic equilibrium. However, liquid drainage causes an increase in the capillary and disjoining pressure, both of which accelerate further bubble coalescence and foam column breakdown. 

Let us consider the simplest model of a real foam built up of different by size bubbles but having equilibrium films. If the diffusion expansion of bubbles runs slowly, then the real (aggregative) stability with respect to coalescence will be preserved but the column height and dispersity will decrease as a result of gas diffusion transfer between bubbles in the foam and from the upper bubbles to the surrounding medium (if the foam is open). 

It is because of the subdivision of matter in colloidal systems that they have special properties. The large surface-to-volume ratio of the particles dispersed in a liquid medium results in a tendency for particles to associate to reduce their surface area, so reducing their contact with the medium. Emulsions and aerosols are thermodynamically unstable two-phase systems which only reach equilibrium when the globules have coalesced to form one macro-phase, for which the surface area is at a minimum. Many pharmaceutical problems revolve around the stabilisation of colloidal systems. 

The ability to predict drop size is critical to determining both the interfadal area for mass transfer and the state of dispersion of the system. In dilute systems and in moderately concentrated systems where coalescence can be neglected, the following equation describes the maximum equilibrium (i.e., after a long time) drop diameter of an inviscid or low viscosity dispersed phase ... 

The structure of Immiscible blends Is seldom at equilibrium. In principle, the coarser the dispersion the less stable It Is. There are two aspects of stability Involved the coalescence In a static system and deformability due to flow. As discussed above the critical parameter for blend deformability Is the total strain In shear y = ty, or In extension, e = te. Provided t Is large enough In steady state the strains and deformations can be quite substantial one starts a test with one material and ends with another. This means that neither the steady state shearing nor elongatlonal flow can be used for characterization of materials with deformable structure. For these systems the only suitable method Is a low strain dynamic oscillatory test. The test Is simple and rapid, and a method of data evaluation leading to unambiguous determination of the state of miscibility is discussed in a later chapter. 

Pawlowski [432] derived a simulation model for calculating droplet size distributions upon dispersion in the I/L system and tested it on equilibrium distributions [55, 244] and on the time sequence of distributions in the case of suppressed coalescence [392]. In total 6 material systems with 34 distributions in 7 test arrangements were taken into consideration. The volume fraction of the dispersed phase was ipy = 0.001 to 0.20. 

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