Droplet clustering

Many of the mesoscale techniques have grown out of the polymer SCF mean field computation of microphase diagrams. Mesoscale calculations are able to predict microscopic features such as the formation of capsules, rods, droplets, mazes, cells, coils, shells, rod clusters, and droplet clusters. With enough work, an entire phase diagram can be mapped out. In order to predict these features, the simulation must incorporate shape, dynamics, shear, and interactions between beads. 

Before determining the degree of stabiUty of an emulsion and the reason for this stabiUty, the mechanisms of its destabilization should be considered. When an emulsion starts to separate, an oil layer appears on top, and an aqueous layer appears on the bottom. This separation is the final state of the destabilization of the emulsion the initial two processes are called flocculation and coalescence (Fig. 5). In flocculation, two droplets become attached to each other but are stiU separated by a thin film of the Hquid. When more droplets are added, an aggregate is formed, ia which the iadividual droplets cluster but retain the thin Hquid films between them, as ia Figure 5a. The emulsifier molecules remain at the surface of the iadividual droplets duiing this process, as iadicated ia Figure 6. 

After venting of the elongated bubble, the region of liquid droplets begins. The vapor phase occupies most of the channel core. The distinctive feature of this region is the periodic dryout and wetting phenomenon. The duration of the two-phase period, i.e., the presence of a vapor phase and micro-droplet clusters on the heated wall, affects the wall temperature and heat transfer in micro-channels. As the heat flux increases, while other experimental conditions remain unchanged, the duration of the two-phase period decreases, and CHF is closer. 

Lagues et al. [17] found that the percolation theory for hard spheres could be used to describe dramatic increases in electrical conductivity in reverse microemulsions as the volume fraction of water was increased. They also showed how certain scaling theoretical tools were applicable to the analysis of such percolation phenomena. Cazabat et al. [18] also examined percolation in reverse microemulsions with increasing disperse phase volume fraction. They reasoned the percolation came about as a result of formation of clusters of reverse microemulsion droplets. They envisioned increased transport as arising from a transformation of linear droplet clusters to tubular microstructures, to form wormlike reverse microemulsion tubules. 

Pulsation in a spray is generated by hydrodynamic instabilities and waves on liquid surfaces, even for continuous supply of liquid and air to the atomizer. Dense clusters of droplets are projected into spray chamber at frequencies very similar to those of the liquid surface waves. The clusters interact with small-scale turbulent structures of the air in the core of the spray, and with large-scale structures of the air in the shear and entrainment layers of outer regions of the spray. The phenomenon of cluster formation accounts for the observation of many flame surfaces rather than a single flame in spray combustion. Each flame surrounds a cluster of droplets, and ignition and combustion appear to occur in configurations of flames surrounding droplet clusters rather than individual droplets. 

It turns out that the average lifetime, the key quantity to characterize the isomerization dynamics of a liquid-droplet cluster, satisfies an Arrhenius-like exponential law with what we call microcanonical temperature (Section V). This quantity has been introduced to characterize a variational structure of a... 

The ultrasonification process is connected with the rapidly increased oil-water interfacial area as well as the significant re-organization of the droplet clusters or droplet surface layer. This may lead to the formation of additional water-oil interface (inverse micelles) and, thereby, decrease the amount of free emulsifier in the reaction medium. This is supposed to be more pronounced in the systems with non-ionic emulsifier. Furthermore, the high-oil solubility of non-ionic emulsifier and the continuous release of non-micellar emulsifier during polymerization influence the particle nucleation and polymerization kinetics by a complex way. For example, the hairy particles stabilized by non-ionic emulsifier (electrosteric or steric stabilization) enhance the barrier for entering radicals and differ from the polymer particles stabilized by ionic emulsifier. The hydro-phobic non-ionic emulsifier (at high temperature) can act as hydrophobe. 

The transition from non-adsorbing to adsorbing polymers can be achieved simply by changing the surfactant and thus increasing the attraction between polymer and surfactant. Hydrophilic polymers in w/o-droplet microemulsions lead to polymers incorporated in the droplets (Scheme 4.5). Attractive interactions lead to adsorption at the inside of the surfactant film. With increasing chain length confinement effects eventually occur (Scheme 4.6). In this case, the polymer is incorporated in more droplets and the droplets form clusters. Polymers adsorbing on the outside can also lead to droplet clusters. 

Scheme 4.6 Increasing the polymer size of an adsorbed confined polymer inside a droplet microemulsion. Large polymers lead to droplet clusters. Polymers adsorbed on the outside can also lead to droplet clusters.

When small liquid droplets are formed and left in a vacuum for a long time at a temperature slightly higher than a room temperature, they are subjected to a phase transition by rapid volume expansion into a mixture of gas and small droplets. Clusters are formed by further volume expansion of the small droplets. The method of preparing clusters in the gas phase by taking advantage of these phenomena is developed by Nish and his coworkers, and is named liquid jet method. 

In typical microemulsion systems, a prominent composition region shows bicontinuous structures. With probes and quenchers confined to either oil or water, the domains in the bicontinuous region may be so large in all dimensions that normal exponential decays are observed. Only in the region with discrete droplets, and in a transition region where droplets cluster and merge, can the micellar type of quenching be expected. However, if the amphiphilic probes and quenchers are bound to the interfacial surfactant film in the bicontinuous microemulsions, one would expect 2-D behavior. 

Figure 8 The three different quenching pathways within droplet clusters in microemulsions. L denotes an excited lumophore and Q a quencher molecule. Although in reality the different reaction pathways compete, for illustration purposes they are pictured here as subsequent processes. After a quenching reaction has finished, the considered droplet is shaded.

For a collection of droplets, the evaporation process of one particular drop can be influenced by the neighboring droplets depending on their distance and relative location. The study of Bellan and Harstad [6] concluded that in a dense droplet cluster, evaporation occurs primarily due to diffusion effects (that is when Sh 2), while convection plays a dominant role in the more dilute regions of a spray. A detailed discussion of the mass and heat transfer of a collection of drops, together with appropriate references, can be found in the text of Sirignano [25]. 

F. Akamatsu, Y. Mizutani, M. Katsuki, S. Tsushima, Y.D. Cho Measurement of local group combustion numbta- of droplet clusters in a premixed spray stream, Proc. Combust. Inst., 26, 1723-1729 (1996). 

It may be mentioned here that the conductance of w/o microemulsions also becomes a function of the pressure. Boned et al. [70,71] have studied the effect of pressure up to 1000 bar on the conductance and viscosity of two microemulsion systems (a) water-AOT-undecane, and (b) glycerol-AOT-isooctane. The first system was an aqueous microemulsion, and the second was a nonaqueous one. The systems were also studied as a function of volume fraction, in the dispersion ( = water plus AOT or glycerol plus AOT). In both systems, the percolation thresholds, were obtained. In aqueous microemulsion, as the pressure increased, the f continuously decreased indicating higher droplet-droplet attractive interaction whereas in nonaqueous microemulsion there was almost no change in the , values. It seems from the above that there was droplet cluster formation in aqueous... 

B.K. Paul, R.K. Mitra, and S.P. Moulik 2006 Microemulsions Percolation of condnc-tion and thermodynamics of droplet clustering, in Encyclopedia of Surface and Colloid Science ed. P. Somasundaran, 2nd Edition, Taylor Francis, Boca Raton, EL, pp. 3927-3956. 

S.P. Moulik, G.C. De, B.B. Bhowmik, and A.K. Panda 1999 Physicochemical studies on microemulsions. 6. Phase behavior, dynamics of percolation, and energetics of droplet clustering in water/AOT/ -heptane system influenced by additives (sodium cholate and sodium salicylate), J. Phys. Chem. B 103, 7122-7129. 

P. Alexandradis, J.P. Holzwarth, and T.A. Hatton 1995 Thermodynamics of droplet clustering in percolating AOT water-in-oU microemulsions, J. Phys. Chem. 99, 8222-8232. 

S.K. Hait, A. Sanyal, and S.P. Moulik 2002 Physicochemical studies on microemulsions. 8. The effects of aromatic methoxy hydrotropes on droplet clustering and understanding of the dynamics of conductance percolation in water/oil microemulsion systems, J. Phys. Chem. B 106, 12642-12650. 

The AG°i values calculated using the association model [42,43] are negative for all formulations, indicating the spontaneous nature of droplet clustering. The values of and A5°i are positive. The clustering phenomenon is accompanied by (1) the removal of oil barriers surrounding the dispersed droplets and (2) the... 

Physiochemical studies on microemulsions. 7. Dynamics of percolation and energetics of clustering in water/AOT/isooctane and water/AOT/decane w/o microemulsions in the presence of hydrotopes (sodium salicylate, a-napthol, 3-napthol, resorcinol, catechol, hydroquinone, pyrogallol and urea) and bile salt (sodium cholate). J Phys Chem 105, 7145-7154 (b) Hait, S. K., Sanyal, A., and Moulik, S. P. (2002). Physiochemical studies on microemulsions. 8. The effects of aromatic methoxy hydrotropes on droplet clustering and understanding of dynamics of conductance percolation in water/oU microemulsions. J Phys Chem B 106,12642-12650. 

A steep increase in conductivity at intermediate water concentrations can be explained by percolation transition, and every ME mixture will exhibit a specific critical water volume ratio/concentration at which percolation occurs. The increased conductivity leading up to the is caused by an increased number of (still) individual water droplets. The conductivity measured around and above the (j) is due to dynamic droplet clusters or transient water channels, and microscopically droplets do not exist anymore at this stage. The critical water concentration needed to induce percolation usually ranges from 0.1 to 0.26 depending on the ME components, specifically the type of cosurfactant, and the temperature. 

---