Diffusion droplet

Less polar or nonpolar intermediates of the BZ reaction, such as Br2 or Br02, are octane-soluble and diffuse in the oil phase as single molecules with diffusion coefficients on the order of 10 cm /s [449], Consequently, the radical Br02, which serves as a second activator, and Br2, which serves as a second inhibitor, diffuse much faster than the water-soluble BZ reactants. For low values of the volume fraction cj), the inhibitor Br2 is the dominant species in the oil phase. Since it diffuses ten to hundred times faster than the activator HBr02, confined to the slow-diffusing droplets, conditions should be favorable for the observation of Turing patterns. 

Packer KJ and Rees C (1972) Pulsed NMR studies of restricted diffusion Droplet size distributions in emulsions. Journal of Colloid Interface Science 10 206-218. 

Other important characterization techniques include electrophoresis measurements of droplets [11, 12] (see Section XIV-3C), infrared absorption of the constituent species [13], and light or x-ray scattering. NMR self-diffusion measurements can be used to determine droplet sizes in W/0 emulsions [14]. 

The repulsion between oil droplets will be more effective in preventing flocculation Ae greater the thickness of the diffuse layer and the greater the value of 0. the surface potential. These two quantities depend oppositely on the electrolyte concentration, however. The total surface potential should increase with electrolyte concentration, since the absolute excess of anions over cations in the oil phase should increase. On the other hand, the half-thickness of the double layer decreases with increasing electrolyte concentration. The plot of emulsion stability versus electrolyte concentration may thus go through a maximum. 

The oil droplets in a certain benzene-water emulsion are nearly uniform in size and show a diffusion coefficient of 3.75 x 10 cm /sec at 25°C. Estimate the number of benzene molecules in each droplet. 

For a conserved order parameter, the interface dynamics and late-stage domain growth involve the evapomtion-diffusion-condensation mechanism whereby large droplets (small curvature) grow at tlie expense of small droplets (large curvature). This is also the basis for the Lifshitz-Slyozov analysis which is discussed in section A3.3.4. 

The flow of droplets is directed through a small orifice (Skimmer 1 Figure 12.1) and across a small region that is kept under vacuum by rotary pumps. In this region, approximately 90% of solvent and injected helium is removed from the incipient particle beam. Because the rate of diffusion of a substance is inversely proportional to its molecular mass, the lighter helium and solvent molecules diffuse away from the beam and are pumped away. The heavier solute molecules diffuse more slowly and pass through the first skimmer before they have time to leave the beam the solute is accompanied by residual solvent and helium. 

A second form of desolvation chamber relies on diffusion of small vapor molecules through pores in a Teflon membrane in preference to the much larger droplets (molecular agglomerations), which are held back. These devices have proved popular with thermospray and ultrasonic nebulizers, both of which produce large quantities of solvent and droplets in a short space of time. Bundles of heated hollow polyimide or Naflon fibers have been introduced as short, high-surface-area membranes for efficient desolvation. 

The surfactant is initially distributed through three different locations dissolved as individual molecules or ions in the aqueous phase, at the surface of the monomer drops, and as micelles. The latter category holds most of the surfactant. Likewise, the monomer is located in three places. Some monomer is present as individual molecules dissolved in the water. Some monomer diffuses into the oily interior of the micelle, where its concentration is much greater than in the aqueous phase. This process is called solubilization. The third site of monomer is in the dispersed droplets themselves. Most of the monomer is located in the latter, since these drops are much larger, although far less abundant, than the micelles. Figure 6.10 is a schematic illustration of this state of affairs during emulsion polymerization. 

If condensation requires gas stream cooling of more than 40—50°C, the rate of heat transfer may appreciably exceed the rate of mass transfer and a condensate fog may form. Fog seldom occurs in direct-contact condensers because of the close proximity of the bulk of the gas to the cold-Hquid droplets. When fog formation is unavoidable, it may be removed with a high efficiency mist collector designed for 0.5—5-p.m droplets. Collectors using Brownian diffusion are usually quite economical. If atmospheric condensation and a visible plume are to be avoided, the condenser must cool the gas sufftciendy to preclude further condensation in the atmosphere. 

Water-soluble initiator is added to the reaction mass, and radicals are generated which enter the micelles. Polymerization starts in the micelle, making it a growing polymer particle. As monomer within the particle converts to polymer, it is replenished by diffusion from the monomer droplets. The concentration of monomer in the particle remains as high as 5—7 molar. The growing polymer particles require more surfactant to remain stable, getting this from the uninitiated micelles. Stage I is complete once the micelles have disappeared, usually at or before 10% monomer conversion. 

However, in the case of mini- and microemulsions, processing methods reduce the size of the monomer droplets close to the size of the micelle, leading to significant particle nucleation in the monomer droplets (17). Intense agitation, cosurfactant, and dilution are used to reduce monomer droplet size. Additives like cetyl alcohol are used to retard the diffusion of monomer from the droplets to the micelles, in order to further promote monomer droplet nucleation (18). The benefits of miniemulsions include faster reaction rates (19), improved shear stabiHty, and the control of particle size distributions to produce high soHds latices (20). 

The completion stage is identified by the fact that all the monomer has diffused into the growing polymer particles (disappearance of the monomer droplet) and reaction rate drops off precipitously. Because the free radicals that now initiate polymerization in the monomer-swollen latex particle can more readily attack unsaturation of polymer chains, the onset of gel is also characteristic of this third stage. To maintain desirable physical properties of the polymer formed, emulsion SBR is usually terminated just before or at the onset of this stage. 

The spreading rate of a polymer droplet on a surface has been measured (363,364). The diffusion constant was at least an order of magnitude smaller than that of the bulk. The monomer—surface friction coefficient for polystyrene has been measured on a number of surfaces and excellent... 

Mini-emulsion processes have been developed where the monomer is emulsified under high energy with either a long-chain alcohol or a polymer producing very small droplets. The long-chain alcohol retards the diffusion of the monomer out of the droplets (65). Polymerization takes place primarily... 

The vapor cloud of evaporated droplets bums like a diffusion flame in the turbulent state rather than as individual droplets. In the core of the spray, where droplets are evaporating, a rich mixture exists and soot formation occurs. Surrounding this core is a rich mixture zone where CO production is high and a flame front exists. Air entrainment completes the combustion, oxidizing CO to CO2 and burning the soot. Soot bumup releases radiant energy and controls flame emissivity. The relatively slow rate of soot burning compared with the rate of oxidation of CO and unbumed hydrocarbons leads to smoke formation. This model of a diffusion-controlled primary flame zone makes it possible to relate fuel chemistry to the behavior of fuels in combustors (7). 

Evaporation and burning of Hquid droplets are of particular interest in furnace and propulsion appHcations and by applying a part of the Burke and Schumann approach it is possible to obtain a simple model for diffusion flames. 

Most theories of droplet combustion assume a spherical, symmetrical droplet surrounded by a spherical flame, for which the radii of the droplet and the flame are denoted by and respectively. The flame is supported by the fuel diffusing from the droplet surface and the oxidant from the outside. The heat produced in the combustion zone ensures evaporation of the droplet and consequently the fuel supply. Other assumptions that further restrict the model include (/) the rate of chemical reaction is much higher than the rate of diffusion and hence the reaction is completed in a flame front of infinitesimal thickness (2) the droplet is made up of pure Hquid fuel (J) the composition of the ambient atmosphere far away from the droplet is constant and does not depend on the combustion process (4) combustion occurs under steady-state conditions (5) the surface temperature of the droplet is close or equal to the boiling point of the Hquid and (6) the effects of radiation, thermodiffusion, and radial pressure changes are negligible. 

There are two essential consequences of this relation. Because larger droplets sediment or rise much faster (a 5-p.m drop rises 625 times faster than a 0.2-p.m droplet), the process is equal to shearing, leading to enhanced flocculation. The ratio between flocculation due to shear and to diffusion of droplets is proportional to the cube of the radius. Secondly, flocculation to droplet aggregates means an enhanced sedimentation rate. Sis drops ia an octahedral arrangement gives approximately four times the sedimentation rate. 

Two kinds of barriers are important for two-phase emulsions the electric double layer and steric repulsion from adsorbed polymers. An ionic surfactant adsorbed at the interface of an oil droplet in water orients the polar group toward the water. The counterions of the surfactant form a diffuse cloud reaching out into the continuous phase, the electric double layer. When the counterions start overlapping at the approach of two droplets, a repulsion force is experienced. The repulsion from the electric double layer is famous because it played a decisive role in the theory for colloidal stabiUty that is called DLVO, after its originators Derjaguin, Landau, Vervey, and Overbeek (14,15). The theory provided substantial progress in the understanding of colloidal stabihty, and its treatment dominated the colloid science Hterature for several decades. 

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