Emulsion turbulent flow

Mixing processes involved in the manufacture of disperse systems, whether suspensions or emulsions, are far more problematic than those employed in the blending of low-viscosity miscible liquids due to the multi-phasic character of the systems and deviations from Newtonian flow behavior. It is not uncommon for both laminar and turbulent flow to occur simultaneously in different regions of the system. In some regions, the flow regime may be in transition, i.e., neither laminar nor turbulent but somewhere in between. The implications of these flow regime variations for scale-up are considerable. Nonetheless, it should be noted that the mixing process is only completed when Brownian motion occurs sufficiently to achieve uniformity on a molecular scale. 

The Froude number, = vP Lg, is similar to it is a measure of the inertial stress to the gravitational force per unit area acting on a fluid. Its inclusion in Eq. (11) is justified when density differences are encountered in the absence of substantive differences in density, e.g., for emulsions more so than for suspensions, the Froude term can be neglected. Dimensionless mixing time is independent of the Reynolds number for both laminar and turbulent flow regimes, as in-... 

Emulsions can be made in different ways. The most common class of processes applies strong flow fields, usually a combination of simple shear flow and of exten-sional flow. Extensional flow is more effective than shear flow in breaking up droplets into smaller ones. Industrial equipment usually operates with turbulent flow, in which inertial forces can be important as well. In addition, for some applications ultrasound is used, which creates, through cavitation, strong local turbulence. 

Polystyrene can be easily prepared by emulsion or suspension techniques. Harkins (1 ), Smith and Ewart(2) and Garden ( ) have described the mechanisms of emulsTon polymerization in batch reactors, and the results have been extended to a series of continuous stirred tank reactors (CSTR)( o Much information on continuous emulsion reactors Ts documented in the patent literature, with such innovations as use of a seed latex (5), use of pulsatile flow to reduce plugging of the tube ( ), and turbulent flow to reduce plugging (7 ). Feldon (8) discusses the tubular polymerization of SBR rubber wTth laminar flow (at Reynolds numbers of 660). There have been recent studies on continuous stirred tank reactors utilizing Smith-Ewart kinetics in a single CSTR ( ) as well as predictions of particle size distribution (10). Continuous tubular reactors have been examined for non-polymeric reactions (1 1 ) and polymeric reactions (12.1 31 The objective of this study was to develop a model for the continuous emulsion polymerization of styrene in a tubular reactor, and to verify the model with experimental data. 

In continuous mechanical emulsification systems based on turbulent flow, the power density Py viz. power dissipated per unit volume of the emulsion) and residence time, L, in the dispersing zone have been found to influence the result of emulsification as measured by the mean droplet size 0(3 2 which is called the Sauter diameter . This dependency is in most cases described by the following expression ... 

Kataoka T and Nishiki T. Dispersed mean drop sizes of (W/0)/W emulsions in a stirred tank. J Chem Eng Jpn 1986 19 408-412. Nishikawa M, Mori F, and Fujieda S. Average drop size in a liquid-liquid phase mixing vessel. J Chem Eng Jpn 1987 20 82-88. Nishikawa M, Mori F, Fujieda S, and Kayama T. Scale-up of liquid-liquid phase mixing vessel. J Chem Eng Jpn 1987 20 454—459. Berkman PD and Calabrese RV. Dispersion of viscous liquids by turbulent flow in a static mixer. AIChE J 1988 34 602-609. Chatzi EG, Gavrielides AD, and Kiparissides C. Generalized model for prediction of the steady-state drop size distributions in batch stirred vessels. Ind Eng Chem Res 1989 28 1704—1711. 

Direct measurement of emulsion viscosity at pipeline conditions is recommended, especially if laminar flow operation is expected. Viscosity is of lesser significance in turbulent flow. 

Emulsion aging rates increase with temperature. Aging rates in turbulent flow appear to become arrested after a certain point, generally being less than the rates observed in laminar flow. Aging rates are suppressed by increased surfactant concentration as a result of the anticoalescence action of the surfactant. 

Emulsions are usually prepared by the application of mechanical energy produced by a wide range of agitation techniques. These disrupt droplets by the application of either shear forces in laminar flow or inertial forces in turbulent flow. Emulsifying devices ranging from simple hand mixers and stirrers to the use of propeller or turbine mixers, static mixers, colloid mills, homogenizers, and ultrasonic devices have been used. 

Nevertheless, caution must be taken in selecting an effective spray jet operating strategy and design. The violent action of the cleanout jets can develop turbulent flows sufficient to reform emulsions. 

Now, consider the parametric method. As was already mentioned, the underlying assumption is that the distribution belongs to a certain class. The choice of the distribution class can be made on the basis of general considerations about the kind of distribution that is likely to be formed in a specific physical process. For example, for a turbulent flow of emulsion in a pipe, the distribution can be described with sufficient accuracy by a logarithmic normal distribution or a gamma-distribution. Consider these two cases successively. 

The use of turbulent emulsion flow regime to facilitate integration of drops is justifled by the substantial increase of collision frequency that is achieved in a turbulent flow as compared to the collision frequency during the sedimentation of drops in a quiescent liquid or in a laminar flow. Particles suspended in the liquid are entrained by turbulent pulsations and move chaotically inside the volume in a pattern similar to Brownian motion. Therefore this pulsation motion of particles can be characterized by the effective factor of turbulent diffusion Dj, and the problem reduces to the determination of collision frequency of particles in the framework of the diffusion problem, as it was first done by Smoluchowsld for Brownian motion [18]. A similar approach was first proposed and realized in [19] for the problem of coagulation of non-interacting particles. The result was that the obtained frequency of collisions turned out to be much greater than the frequency found in experiments on turbulent flow of emulsion in pipes and agitators [20, 21]. 

Consider now motion of small particJes in turbulent flow of liquid. Assume that the volume concentration of particJes is small enough, so it is possible to neglect their influence on the flow of hquid. The large-scale pulsations transfer a particJe together with layers of hquid adjoining to it. Small-scale pulsations with A R, where R is particle radius, cannot involve the particJe in their motions -the particle behaves in this respect as a stationary body. Pulsations of intermediate scales do not completely involve the particle in their motion. Consider the case most interesting for apphcations, when respective densities of particle p and external liquid are only slightly different from one another, and radius of the particle is much less than inner scale of turbulence, that is R A . Thus, for water-oil emulsion pjp 1.1-1.5. Let Uq be the velocity of hquid at the particle s location, and Ui the velocity of particJe relative to hquid. At full entrainment of particle by the hquid, the same force would ad on the particle as on... 

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... 

For Browrtian diffusion of small particles, the influence of hydrodynamic interaction on the collision frequency was studied in works [28, 29], which also mention the decrease in the collision frequency by a factor of 1.5-2. This decrease is not as large as in the case of turbulent coagulation. There are two reasons why the effect of hydrodynamic interaction on the collision frequency of particles differs so substantially in the cases of turbulent flow and Brownian motion. First, the particle size is different in these two cases (the characteristic size of particles participating in Brownian motion is smaller than that of particles in a turbulent emulsion flow). Second, the hydrodynamic force behaves differently (the factor of Browrtian diffusion is inversely proportional to the first power of the hydrodynamic resistance factor h, and the factor of turbulent diffusion - to the second power of h). 

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

The diffusion model of turbulent coagulation is applicable to homogeneous and isotropic turbulent flow. A developed turbulent flow of emulsion in a pipe, in the vicinity of the flow core, can be considered as isotropic. However, the turbulent motion of liquid in a stirrer is neither homogeneous nor isotropic. Therefore the applicability of diffusion model to process of coagulation in agitator is not established with certainty. 

Coalescence of Conducting Emulsion Drops in a Turbulent Flow 451... 

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