Breakage droplet

Changes in the natures of individual phases of or phase separation within a formulation are reasons to discontinue use of a product. Phase separation may result from emulsion breakage, clearly an acute instability. More often it appears more subtly as bleeding—the formation of visible droplets of an emulsion s internal phase in the continuum of the semisolid. This problem is the result of slow rearrangement and contraction of internal structure. Eventually, here and there, globules of what is often clear liquid internal phase are squeezed out of the matrix. Warm storage temperatures can induce or accelerate structural crenulation such as this thus,... 

Dense ammonium nitrate crystals are formed by spraying droplets of molten ammonium nitrate solution (>99.6%) down a short tower. The spray produces spherical particles known as prills . These crystals are non-absorbent and used in conjunction with nitroglycerine. An absorbent form of ammonium nitrate can be obtained by spraying a hot, 95% solution of ammonium nitrate down a high tower. The resultant spheres are carefully dried and cooled to prevent breakage during handling. These absorbent spheres are used with fuel oil. 

Tavlarides presents a sophisticated model for representing coalescence and breakage of droplets in liquid-liquid dispersions. The model relies on the population balance equation and still requires the adjustment of 6 parameters. The solution of such equations is difficult and requires the use of Monte-Carlo methods... 

M. M. Attarakih, H.-J. Bart and N. M. Faqir, Solution of the droplet breakage equation for interacting liquid-liquid dispersions ... 

M. Simon, S. A. Schmidt, H.-J. Bart, The Droplet Populance Model -Estimation of Breakage and Coalescence. Chem. Ing. Techn,... 

In those liquid-fluid systems under consideration, interfacial tension is reduced at elevated pressures which favors creation of new interfacial area by droplet breakage. In addition, the rapid dissolution of the supercritical fluid in the liquid drops leads to a reduction in viscosity and thus to a generally positive mass transfer behaviour in the high-pressure spray extraction. 

Different methods [120] such as volume variation, internal phase droplet size variation, viscosity variation, density variation, tracer method, Karl-Fischer method, and electrical conductivity have been employed in the measurement of emulsion swelling. The data obtained tends to be as varied as the methods used [120]. One major drawback is that none of the above methods is capable of determining both emulsion swelling and membrane breakage in the same experiment. Further, osmotic swelling cannot be differentiated from entrainment swelling. 

Furthermore, the assumption is made that the motion of the centers of mass of daughter droplets to be formed (binary breakage) is similar to the relative motion of two lumps of fluid in a turbulent flow field as described by Batchelor (B6). Thus, for the inertial subrange eddies... 

The population balance approach is employed for the description of droplet dynamics in various flow fields. A significant advantage of the method is that a vehicle is provided to include the details of the breakage and coalescence processes in terms of the physical parameters and conditions of operation. A predictive multidimensional particle distribution theory is at hand which, in the case of well-defined droplet processes, can be employed for a priori prediction of the form and the magnitude of the particle size distribution. The physical parameters which affect the form... 

Conceptually, the framework of the theory permits description of interphase heat and mass transfer with reaction occurring in either or both phases. In theory one can use this approach to study the affects of partial mixing of the dispersed phase on extent of reaction for non-first-order reactions which occur in the droplets. Analyses can be made for mass-transfer-controlled reactions and selectivity for complex reactions. Difficulties in the solution of the resulting integro-diflferential equations have restricted applications at present to partial solutions. For example, the effects of partial droplet mixing on extent of reaction were studied for uniform drops. Mass transfer from nonuniform drops for various reactor geometries was studied for dispersions with drop breakage only or drop coalescence only. 

The population balance equation is employed to describe the temporal and steady-state behavior of the droplet size distribution for physically equilibrated liquid-liquid dispersions undergoing breakage and/or coalescence. These analyses also permit evaluation of the various proposed coalescence and breakage functions described in Sections III,B and C. When the dispersion is spatially homogeneous it becomes convenient to describe particle interaction on a total number basis as opposed to number concentration. To be consistent with the notation employed by previous investigators, the number concentration is replaced as n i,t)d i = NA( i t)dXi, where N is the total number of particles per unit volume of the dispersion, and A(xj t) dXi is the fraction of drops in increment X, to X( + dxi- For spatially homogeneous dispersions such as in a well-mixed vessel, continuous flow of dispersions, no density changes, and isothermal conditions Eq. (102) becomes... 

The model assumes that drop coalescence is followed by immediate redispersion into two drops sized according to a uniform distribution. By assuming that the coalescence frequency is independent of drop size, the solution of the resulting form of Eq. (107) is exponential for the equilibrium drop volume distribution. Comparison of the distribution to experimental data is favorable. The analysis is useful in that a functional form for the distribution is obtained. The attendant simplifications necessary for solution, however, do not permit more rational forms of the interaction frequency of droplet pairs in order to account for the physical processes which lead to droplet coalescence and breakage as discussed in Section III. A similar work was presented by Inone et al. (II). 

It is encouraging that substantial progress has been made in analyzing the hydrodynamics of droplet interactions in dispersions from fundamental considerations. Effects of flow field, viscosity, holdup fraction, and interfacial surface tension are somewhat delineated. With appropriate models of coalescence and breakage functions coupled with the drop population balance equations, a priori prediction of dynamics and steady behavior of liquid-liquid dispersions should be possible. Presently, one universal model is not available. The droplet interaction processes (and... 

Valentas and Amundson (V3) studied the performance of continuous flow dispersed phase reactors as affected by droplet breakage processes and size distribution of the droplets. Various reaction cases with and without mass transfer were studied for both completely mixed or completely segregated dispersed phase. Droplet size distribution is shown to have a considerable effect on the efliciency of a segregated reaction system. They indicated that polydispersed drop populations require a larger reactor volume to obtain the same conversion as a monodispersed system for zero-order (or mass-transfer-controlled) reactions in higher conversion regions. As the dispersed phase becomes completely mixed, the distribution of droplet sizes becomes less important. These interactions are un-... 

The work discussed in this section clearly delineates the role of droplet size distribution and coalescence and breakage phenomena in mass transfer with reaction. The population balance equations are shown to be applicable to these problems. However, as the models attempt to be more inclusive, meaningful solutions through these formulations become more elusive. For example, no work exists employing the population balance equations which accounts for the simultaneous affects of coalescence and breakage and size distribution on solute depletion in the dispersed phase when mass transfer accompanied by second-order reaction occurs in a continuous-flow vessel. Nevertheless, the population balance equation approach provides a rational framework to permit analysis of the importance of these individual phenomena. 

It is observed, even in the partial solution to the problem, that realistic models of the droplet coalescence and breakage processes as discussed in Section V,D,2 have yet to be employed. A parallel development has occurred. The work is currently at the point where the realistic model of the droplet dynamics can be applied to the pertinent problems of extent of reaction and solute depletion in dispersions. The success of this effort would permit the researcher and designer to predict dispersed-phase reactor performance from fundamental properties of the dispersion, operation conditions of the vessel, and knowledge of the intrinsic kinetics. 

Zeitlin and Tavlarides (Z2-5) developed a simulation model which attempts to account for the macroflow patterns of the dispersed phase in a turbine-agitated vessel, the droplet mixing via breakage or coalescence, and nonuniform drop size on mass transfer or reaction in dispersions. 

Batch, semibatch, or continuous-flow operation can be simulated. The continuous phase is assumed well mixed. Particle movement was either random or followed the flow direction of the sum of the local average fluid velocity and the particle gross terminal velocity. The probability of droplet breakup is assigned based on droplet size. Binary breakage was assumed to form two randomly sized particles whose masses equal the parent drop. The probability of coalescence exists when two drops enter the same grid location. Particles are added and removed to simulate flow. 

The drops behave as segregated entities between flow and coalescence-redispersion simulation. The coalescence and breakage frequencies can be varied with vessel position. The computational time was related to coalescence frequency data available in the literature. Figure 15 shows the steady-state dimensionless droplet number size distribution as a function of rotational speed for continuous-flow operation. As expected the model predicts smaller droplet sizes and less variation of the size distribution with increase in rotational speed. Figure 16 is a comparison of the droplet number size distribution with drop size data of Schindler and Treybal (Sll). 

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