Spherical droplet

Apart from chemical composition, an important variable in the description of emulsions is the volume fraction, outer phase. For spherical droplets, of radius a, the volume fraction is given by the number density, n, times the spherical volume, 0 = Ava nl2>. It is easy to show that the maximum packing fraction of spheres is 0 = 0.74 (see Problem XIV-2). Many physical properties of emulsions can be characterized by their volume fraction. The viscosity of a dilute suspension of rigid spheres is an example where the Einstein limiting law is [2]... 

The conductivity of a dilute emulsion can be treated by classic theory (see Maxwell [6]) assuming spherical droplets... 

Again consider a single spherical droplet of minority phase ( [/ = -1) of radius R innnersed m a sea of majority phase. But now let the majority phase have an order parameter at infinity that is (slightly) smaller than +1, i.e. [i( ) = < 1. The majority phase is now supersaturated with the dissolved minority species,... 

Fig. 7. Types of dispersion of a polymer (dark regions) in the matrix of an immiscible polymer. The spherical droplets (a) are progressively extended into...

The theory has beea exteaded to evaluate sheet breakup (19). This model (19) assumes that the fastest growing wave detaches at the leading edge ia the form of a ribboa with a width of a half-waveleagth. The ribboa ioimediately coatracts iato multiple ligaments, which subsequeatly reshape themselves iato spherical droplets. The characteristic dimension of the ligament, Dy is as foUows, where / is the sheet thickness at the breakup locatioa. 

Droplet Dispersion. The primary feature of the dispersed flow regime is that the spray contains generally spherical droplets. In most practical sprays, the volume fraction of the Hquid droplets in the dispersed region is relatively small compared with the continuous gas phase. Depending on the gas-phase conditions, Hquid droplets can encounter acceleration, deceleration, coUision, coalescence, evaporation, and secondary breakup during thein evolution. Through droplet and gas-phase interaction, turbulence plays a significant role in the redistribution of droplets and spray characteristics. 

The traditional view of emulsion stability (1,2) was concerned with systems of two isotropic, Newtonian Hquids of which one is dispersed in the other in the form of spherical droplets. The stabilization of such a system was achieved by adsorbed amphiphiles, which modify interfacial properties and to some extent the colloidal forces across a thin Hquid film, after the hydrodynamic conditions of the latter had been taken into consideration. However, a large number of emulsions, in fact, contain more than two phases. The importance of the third phase was recognized early (3) and the lUPAC definition of an emulsion included a third phase (4). With this relation in mind, this article deals with two-phase emulsions as an introduction. These systems are useful in discussing the details of formation and destabilization, because of their relative simplicity. The subsequent treatment focuses on three-phase emulsions, outlining three special cases. The presence of the third phase is shown in order to monitor the properties of the emulsion in a significant manner. 

The validity of mean field theory for N —y oo has striking consequences for the initial stages of phase separation. " In a metastable state slightly inside the coexistence curve, the nucleation free energy barrier is due to spherical droplets with a radius R The free energy excess of a droplet is written in terms of bulk and surface terms " "... 

So far in this chapter, consideration has been given to transfer taking place in a single direction of a rectangular coordinate system. In many applications of mass transfer, one of the fluids is injected as approximately spherical droplets into a second immiscible fluid, and transfer of the solute occurs as the droplet passes through the continuous medium. 

Spherical droplet in a liquid, mass transfer 617 Spiral heat exchangers 550 Spray dryers 393... 

This is also observed to be the case for free droplets [116]. Indeed, simulations started from isotropic droplets below the smectic B-isotropic transition form cylindrical rather than spherical droplets these are apparent in Fig. 22. In this way, the molecules can align in parallel layers with the... 

On the contaminated and slightly hydrophobic surface, the spherical droplets grow continuously with time, as shown in the sequence of images in Figure 11. This behavior is... 

On samples prepared with a substrate temperature above 41°C, only spherical droplets were observed. Although no change could be observed in the droplets for several days, we noticed that by applying a strong attractive electrostatic force, the tip could induce... 

Finite amounts of glycerol (its viscosity is 945 cP at 25°C) can be dispersed in AOT/heptane or in CTAB/heptane + chloroform systems. The resulting solutions consist of thermodynamically stable, spherical droplets of glycerol stabilized by the surfactant [33,235]. The presence of glycerol within the micellar core results in a reduction of the surfactant mobility [137]. 

Emulsification processes produce spherical droplets of the internal phase to minimize the interfacial area... 

From the starting structures (PDB file), the full complement of hydrogens is added using a utility within CHARMM. The entire protein is then solvated within a sphere of TIP3P model waters, with radius such that all parts of the protein were solvated to a depth of at least 5 A. A quartic confining potential localized on the surface of the spherical droplet prevented evaporation of any of the waters during the course of the trajectory. The fully solvated protein structure is energy minimized and equilibrated before the production simulation. 

Many other interesting examples of spontaneous reflection symmetry breaking in macroscopic domains, driven by boundary conditions, have been described in LC systems. For example, it is well known that in polymer disperse LCs, where the LC sample is confined in small spherical droplets, chiral director structures are often observed, driven by minimization of surface and bulk elastic free energies.24 We have reported chiral domain structures, and indeed chiral electro-optic behavior, in cylindrical nematic domains surrounded by isotropic liquid (the molecules were achiral).25... 

Abstract The self-organized and molecularly smooth surface on liquid microdroplets makes them attractive as optical cavities with very high quality factors. This chapter describes the basic theory of optical modes in spherical droplets. The mechanical properties including vibrational excitation are also described, and their implications for microdroplet resonator technology are discussed. Optofluidic implementations of microdroplet resonators are reviewed with emphasis on the basic optomechanical properties. 

Equation (6.50) is often referred to as the Thomson s (or Kelvin s) equation. As an example of the effect of this equation, the vapour pressure of a spherical droplet of molten Zn at the melting temperature is shown as a function of the droplet radius in Figure 6.14. 

It should be noted that some problems may arise in the techniques or devices for producing monodisperse or near-monodis-perse sprays. One of the problems is droplet coalescence. Initially uniform droplets may coalesce rapidly to create doublets or triplets, particularly in a dense and turbulent spray, deteriorating the monodispersity of the droplets. This problem may be lessened by using appropriate dispersion air around the spray.[88] Another problem is non-spherical droplet shapes that make estimations of monodispersity difficult. 

REP, a rod of metal or alloy, referred to as a consumable electrode, is rotated at high speed about its longitudinal axis. Simultaneously, it is melted gradually at one of its ends by a heat source, such as an arc, a plasma, or an electron beam, etc. A thin film of the molten metal is detached from the rod end and ejected from the periphery of the rod by centrifugal force, forming spherical droplets. The atomization is conducted in an inert atmosphere, usually argon. Helium may be used to increase arc stability and convective cooling efficiency of droplets. 

In the idealized mode, liquid jet breakup and droplet formation are fairly regular. The liquid jet running downwards collapses, forming droplets of uniform size at uniform spacing. After breakup, the liquid jet of length 4.51 d0 converts into a spherical droplet so that ... 

Table 3.2. Classification and Criteria of Breakup Regimes of Round Liquid Jets in Co-flowing Air as Compared to Those of Thin Liquid Sheets and Spherical Droplets in Air Stream 210 ...

The first stage, called dynamic stage, is the period during which a spherical droplet is flattened and deformed into a planetary ellipsoid with its major axis perpendicular to the flow direction as a result of the external pressure distribution. The eccentricity of the elliptical profile changes with time. 

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