Coalescence of drops with

Figure 12. Formation of the microemulsion phase as discrete drops in the 1.7 gm/dl-salinity TRS/C12 system views (a), (b), and (c) illustrate coalescence of drops with increasing time during the first five minutes after contact (Bars equal 0.2 mm).

The first term in the right-hand side of equation (11.1) corresponds to the formation rate of drops of volume V due to the coalescence of drops with volumes V — CO and co, and the second term - to the rate of population decrease of drops of volume V at their coalescence with other drops. 

Coalescence of Drops with Fully Retarded Surfaces in a Turbulent Emulsion Flow... 

Consider the coalescence of drops with fiilly retarded (delayed) surfaces (which means they behave as rigid particles) in a developed turbulent flow of a lowconcentrated emulsion. We make the assumption that the size of drops is much smaller than the inner scale of turbulence R Ao), and that drops are non-deformed, and thus incapable of breakage. Under these conditions, and taking into account the hydrodynamic interaction of drops, the factor of mutual diffusion of drops is given by the expression (11.70). To determine the collision frequency of drops with radii Ri and Ri (Ri < Ri), it is necessary to solve the diffusion equation (11.36) with boundary conditions (11.39). Place the origin of a spherical system of coordinates (r, 0,0) into the center of the larger particle of radius i i. If interaction forces between drops are spherically symmetrical, Eq. (11.36) with boundary conditions (11.39) assumes the form... 

Coalescence of Drops with a Mobile Surface in a Turbulent Flow of the Emulsion... 

The assumptions made allow us to consider the coalescence of drops with a mobile surface in the same manner as that of drops with a fully retarded surface. The main difference from the case considered in Section 13.6 is in the form of the hydrodynamic resistance factor. If the drops are placed far apart, the factor of hydrodynamic resistance for the relative motion of drops is determined by the formula (11.71), where each of the factors hi and hi is determined according to Hadamar-Rubczynskis formula... 

From experiments in which both drop breakage and coalescence occurred, Kuri-yama et al. [34] found that drop sizes reached a steady value within an hour, when the initial drop viscosity was low. But with a high drop viscosity, the drop size reduction continued for longer periods of time and the final drop size was higher. Although model, nonreacting, fluids were used for those experiments, the results are relevant to suspension polymerization. In their study of drop coalescence in the suspension polymerization of styrene, Konno et al. [47] found that the Sauter mean diameter increased as the polymer viscosity increased. They also concluded that the stabilizer does not effectively prevent the coalescence of drops with diameters larger than d x-... 

When an impeller is rotated in an agitated tank containing two immiscible Hquids, two processes take place. One consists of breakup of dispersed drops due to shearing near the impeller, and the other is coalescence of drops as they move to low shear zones. The drop size distribution (DSD) is decided when the two competing processes are in balance. During the transition, the DSD curve shifts to the left with time, as shown in Figure 18. Time required to reach the equiHbrium DSD depends on system properties and can sometimes be longer than the process time. 

In the latter case, however, there is also a contribution of the fraction Go of drops with zero concentration. When these drops coalesce with drops in the interval (2a 2a + 2 Aa), drops of the desired concentration are also produced ... 

A further decrease in the surface energy of disperse system may be caused by a decrease in the interfacial area due to the coalescence of drops and bubbles, or by fusion (sintering) of solid particles, as well as by the dissolution of more active smaller particles with the transfer of substance to less active larger particles. 

At low holdups, longitudinal dispersion due to continuous-phase velocity profiles controls the amount of mixing in the countercurrent spray column whereas at higher holdups the velocity profile flattens, and the shed-wake mechanism controls. Above holdups of 0.24, the temperature jump ratio is linearly proportional to the dispersed-to-continuous-phase flow ratio, and all mixing is caused by shed wakes into the bulk water and coalescence of drops. As column size decreases, it approaches the characteristics of a perfect mixer, and the jump ratio approaches unity (as compared with the value of zero for true countercurrent flow). It is interesting to note that changing the inlet temperature of dispersed phase by about 55°F hardly affected the jump ratio, probably due to the balancing effects of reduced viscosities and a decrease of drop diameter. 

Expression for hydrodynamic resistance factor of drops with mobile interface will be given in section 13.7, in which the coalescence of drops in emulsion will be considered. 

Turbulent coalescence of drops was studied in works [22, 32]. In [22], an expression for the flux] R, R2) was derived in the assumption that particle 1 (i.e. the large particle) is fixed. The obtained flux does not obey the condition of symmetry with respect to particle sizes. 

Coagulation of drops with only molecular force of attraction Fa is referred to as fast. In the above-introduced notations, this case corresponds to the zero value of parameter Sr. Denote the appropriate diffusion flux as J. The influence of hydro-dynamic and molecular forces on coalescence frequency can be determined by comparing flux with Jq and neglecting the interaction forces. The last flux can be obtained from (13.82) at F = 0, h = ho and Dj = Dtq. ... 

Consider first the coalescence of drops under the action of a molecular attraction force in the absence of electrostatic repulsion (Sr =0). Dependence of coalescence frequency on ratio of drop radii k for various values of viscosity ratio p, and with the electromagnetic retardation neglected (y = 0), is shown in Fig. 13.25. The coalescence frequency increases with relative size of drops and with decrease of their relative viscosity. This can be explained by fall of viscous... 

Droplets in motion in a turbulent flow of gas in a pipe are subject to breakage and coagulation (coalescence). These processes occur simultaneously and as a result a dynamic balance is established between them, determined by some distribution of drops with average radius i av-... 

The behavior of emulsions is considered in Section V in connection with the process of oil dehydration. Actual problems of drop integration in emulsions are discussed. It is shown that this process occurs most effectively if the emulsion is subjected to an electric field. In this context, the behavior of conducting drops in emulsions, the interaction of drops in an electric field, and the coalescence of drops in emulsions are examined in detail. In terms of applications, processes of emulsion separation in settling tanks, electro dehydrators, and electric filters are considered. 

Separation processes of gas-liquid (gas-condensate) mixtures are considered in Section VI. The following processes are described formation of a liquid phase in a gas flow within a pipe coalescence of drops in a turbulent gas flow, condensation of liquid in throttles, heat-exchangers, and turboexpanders the phenomena related to surface tension efficiency of division of the gas-liquid mixtures in gas separators separation efficiency of gasseparators equipped with spray-catcher nozzles of various designs - louver, centrifugal, string, and mesh nozzles absorbtive extraction of moisture and heavy hydrocarbons from gas prevention of hydrate formation in natural gas. 

The physical importance of these results is related to the fact that the coalescence of drops at the early highly dynamic stages of emulsion production is expected to be sensitive to the degree of saturation of the newly created interfaces with surfactant, and correspondingly, to the relaxation time of surfactant adsorption. The surfactant transport is especially important when the emulsion is prepared from nonpre-equilibrated liquid phases. In such cases one can observe dynamic phenomena like the cyclic dimpling (59, 60) and osmotic swelling (61), which bring about additional stabilization of the emulsions (see also Refs 1 and 62). 

Chapter 5 considers the stabiUty of fluid interfaces, a subject pertinent both to the formation of emulsions and aerosols and to thdr destruction by coalescence of drops. The closely related topic of wave motion is also diseussed, along with its implications for mass transfer. In both cases, boundary eonditions applicable at an interface are derived—a significant matter because it is through boundary conditions that interfacial phenomena influence solutions to the governing equations of flow and transport in fluid systems. 

Coalescence of drops or bubbles is a phenomenon of fundamental importance to the understanding of dispersed fluid systems such as foams and emidsions. As two drops or bubbles approach, a film forms between thran. It drains, and if coalescence occurs, ultimately breaks. We are concerned here with this last step, which involves film instability. 

In the foregoing example, the deterministic event is the chemical reaction in the drops while the random events are those of drop entry into and exit from the reactor, and coalescence-redispersion within the reactor. The interval of quiescence, therefore, represents the period in which none of the following processes occur (i) addition of drops with the feed, (ii) loss of... 

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