Monodisperse system drops

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-... 

For the sedimentation of rarefied monodisperse systems of spherical particles, drops, or bubbles, the mean Sherwood number can be calculated by using formulas (4.6.8) and (4.6.17), where the Peclet number must be determined on the basis of the constrained flow velocity. 

We note that in [421], the cell flow model was used for the investigation of mass and heat transfer in monodisperse systems of spherical drops, bubbles, or solid particles for Re < 250 and 0 < < 0.5. 

Most experimental studies on monodispersed systems were carried out on solid dispersions rather than emulsions, since it is quite tedious to get a monodispersed ei[iulsioii. Experimeiiia] evidence from iiuirowly dispersed emul.sions shows that the viscosity increases as the drop size (average) decreases, often according to an inverse power law such as ... 

The drop size distribution is found to play an important rote as well. In effect, a monodispersed system contains at least a 26% void volume, that may be filled with much smaller droplets, and which could occupy up to 74% of this volume, thus leaving 7% 26% X 26%) void and so on. This means that a... 

The aim of this first section is to describe the rupturing mechanisms and the mechanical conditions that have to be fulfilled to obtain monodisperse emulsions. A simple strategy consists of submitting monodisperse and dilute emulsions to a controlled shear step and of following the kinetic evolution of the droplet diameter. It will be demonstrated that the observed behavior can be generalized to more concentrated systems. The most relevant parameters that govern the final size will be listed. The final drop size is mainly determined by the amplitude of the applied stress and is only slightly affected by the viscosity ratio p. This last parameter influences the distribution width and appears to be relevant to control the final monodispersity. 

For these systems we can presumably apply Eq. (5.11). In (a) we have

protein molecules can fit in the gaps between the drops. Presumably, globular proteins are fairly spherical particles. Equation (5.11) then yields >/rel 40 for volume fraction in (b), its viscosity would be lower. 

Surfactants are either present as impurities that are difficult to remove from the system or are added deliberately to the bulk fluid to manipulate the interfacial flows [24]. Surfactants may also be created at the interface as a result of chemical reaction between the drop fluid and solutes in the bulk fluid [25, 26]. Surfactants usually reduce the surface tension by creating a buffer layer between the bulk fluid and droplet at the interface. Non-uniform distribution of surfactant concentration creates Marangoni stress at the interface and thus can critically alter the interfacial flows. Surfactants are widely used in numerous important scientific and engineering applications. In particular, surfactants can be used to manipulate drops and bubbles in microchannels [2, 25], and to synthesize micron or submicron size monodispersed drops and bubbles for microfluidic applications [27]. 

The theoretical predictions of drop deformation and breakup are limited to infinitely diluted, monodispersed Newtonian systems. However, it is possible to obtain valid relationships between processing parameters and morphology. Thus it was found that in the system PS/HDPE the viscosity ratio, blend composition, screw configuration, temperature, and screw speed significantly influence the blend morphology [Bordereau et al., 1992]. For more detail on the topic see Chapter 9, Compounding Polymer Blends, in this Handbook. 

A better criterion in defining a microemulsion could be its fluidity. In effect, the viscosity of (macro)emulsions and suspensions is known to increase as the fragment size decreases, and thus it is expected that an emulsion with extremely small drop size, an internal phase content greater than 20-30%, and a monodispersed distribution (as expected in a microemulsion) would be quite viscous. However, systems with such a high viscosity have been called gel emulsions or miniemulsions because the authors preferred to elude the label microemulsion in order to avoid confixsion with single-phase microemulsions [5-7]. 

Another complication arises when strong attractive forces operate between the drops or bubbles. This may lead to a finite contact angle, 6, between the intervening film (of reduced tension) and the adjaeent bulk interfaces (21, 24-26). Under those conditions, droplets will spontaneously deform into truncated spheres upon contact and can thus pack to much higher densities. For monodisperse drops, the ideal close-packed density, consistent with minimization of the system s surface free energy, is given (21) by... 

Having described the structural elements of foams approaching the dry-foam limit (O —> 1), it is still a daunting task to describe the structure and properties of the system as a whole. The task is even more difficult for systems in which O Q is exceeded, but the polyhedral regime has not yet been reached. In this case, the drops have exceedingly complex shapes, and linear and tetrahedral Plateau borders, as defined above, are not present. Much can be learned about the qualitative behavior by considering 2-D model systems, in which the drops do not start out as spheres but as parallel circular cylinders, and tetrahedral Plateau borders do not arise. We shall first consider the particularly simple monodisperse case, with a subsequent gradual increase in complexity. 

Figure 6 Disordered, monodisperse 2-D system (0=1) with periodic boimdaries each shade corresponds to drops with a certain number of sides, e.g., the unshaded drops all have 6 sides. (Coiutesy of T. Herdtle and A.M. Kraynik.)...

Ideally, uniform spheres arrange in hexagonal close packing, which is face-centered cubic (fee), at Oq= V2/6 = 0.7405. The role of the circumscribing hexagon in monodisperse 2-D systems is taken over by the rhombic dodecahedron (Fig. 10). As the volume fi-action is raised, each drop flattens against its 12 neighbors. This process has... 

The elastie and yield properties of 2-D systems with the most general type of disorder (ef. Fig. 7) have been simulated by Hutzler et al. (90) for both dry and wet systems. Indeed, as the number of polydisperse drops in the simulation is increased, the jumps in stress assoeiated with individual or cooperative T1 rearrangements beeome less and less noticeable. Instead, the stress increases smoothly with increasing strain until it reaehes a plateau that may be identified with the yield stress. The yield stress was found to increase sharply with increasing volume fraction, very much as in the monodisperse case. Fiuthermore, the shear modulus for the dry system (0=1) was essentially identieal to that for the monodisperse case, as given by Eq. (73) with R y as defined above, replacing R. Its dependence on 0 was very different from that in Eq. (72), however. When expressed in our terms, their results for 1 > O > 0.88 could be fitted to... 

However, the formation of monodisperse aqueous or organic drops in liquid-liquid systems is easily possible by the use of electrostatic fields [81]. Here, the applied voltage and thus the electric field at the capillary tip is the most significant parameter. This again is markedly influenced by the electrode and capillary geometry, as also by the electric properties (conductivity, permittivity, and charge relaxation time) of the liquids. 

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