Emulsions Brownian motion

Perrin found that, if an emulsion of gamboge were allowed to settle, the granules did not all fall flat to the bottom of the vessel, but remained permanently forming a kind of atmospheric haze extending to a short distance into the liquid. The suspended particles were seen under the microscope to be in Brownian motion. 

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. 

Finally Jean Perrin presented an extensive (97 pages) Rapport sur les Preuves de la R6alit6 Moleculaire in which he summarized his famous experiments on the Brownian motion of emulsion droplets suspended in a liquid and discussed the fluctuations, the determination of the elementary charge, the a decay of some radioactive nuclei, and the corresponding production of helium. The last section of the paper contains a comparison of the values of Avogadro s number deduced by completely different methods. The very satisfactory agreement between all these values provides the proof of molecular reality announced in the title of the paper.11... 

This section contains a general description of the principles by which the Coulter Model N4 Sub-Micron Particle Analyzer, used in this study to characterize artificial gas-in-water emulsions (see Section 10.4), determines sample particle size. The measuring principles are based on the theory of Brownian motion and photon correlation spectroscopy (ref. 464,465 see also Sections 10.2 and 10.4). 

First a coarse O/W emulsion is prepared and, on heating, phase inversion occurs. After cooling down through the microemulsion zone, the finely dispersed nature of the microemulsion is partially retained and emulsions with drop sizes of about 100 nm result [28-30]. They show considerable long-term stability as a consequence of the Brownian motion of the oil droplets [31] and pump sprayable deodorants are one of the cosmetic products based on this technology. 

Anthony Pearson The deviatoric stress is an important feature. I used the term stress there, but when one does these calculations on multiphase mixtures, suspension, emulsions—one is really looking not at the stresses initially, but one tends to be looking at rates of deformation. Although you get no Brownian motion, you do get very considerable structure development. My question is, is there any way in which thermodynamics can deal with structure development in a nonequilibrium state If you stop shearing the material, the structure disappears. 

Attempts to describe the unlimited increase of the viscosity of dispersions and emulsions observed when their concentrations approach the maximum values (tPmax) meet great theoretical difficulties. Various approaches were developed to overcome these difficulties. Thus, for example, Russel et al. [58] suggested that account should be taken of the Brownian motion of particles in colloidal dispersions in the form of a hydrodynamic contribution. They showed that this contribution which is to be taken into account in considering a slow flow (with slow shear rates y), increases considerably with increasing dispersion concentration. For a description of the dependence of viscosity on concentration the above authors obtained an exact equation only in the integral form. At low shear rates it gives the following power series ... 

The rheological properties of a dense emulsion with close-packed droplets depends on whether or not the droplets are small enough to be agitated significantly by Brownian motion. If not, because of the high packing density of the droplets, the emulsions should be elastic and have a finite elastic modulus at low frequencies. For liquids with viscosities near that of water, Brownian behavior should dominate for particle radii less than or equal to 1 fim, while non-Brownian behavior occurs when a > 10 m. 

Prud homme are about a factor of three larger than the predictions of Eq. (9-55), if Y() and C (Newtonian viscosity plateau at low shear rates, while Eq. (9-55) predicts yield behavior at low shear rates, with a power-law viscosity-shear rate slope of—1. The emulsions of Otsubo and Prud homme are evidently affected to some extent by Brownian motion, which is not accounted for in Eq. (9-55). Further experimental and theoretical work on emulsion rheology will be required to establish general scaling rules for these complex emulsions. 

For monodisperse or unimodal dispersion systems (emulsions or suspensions), some literature (28-30) indicates that the relative viscosity is independent of the particle size. These results are applicable as long as the hydrodynamic forces are dominant. In other words, forces due to the presence of an electrical double layer or a steric barrier (due to the adsorption of macromolecules onto the surface of the particles) are negligible. In general the hydrodynamic forces are dominant (hard-sphere interaction) when the solid particles are relatively large (diameter >10 (xm). For particles with diameters less than 1 (xm, the colloidal surface forces and Brownian motion can be dominant, and the viscosity of a unimodal dispersion is no longer a unique function of the solids volume fraction (30). 

It may be logical to think that the higher the surfactant concentration, the more stable the emulsion. This is not always true. Indeed, a surfactant in excess forms micelles, which are significantly smaller than the emulsion droplets. Droplets are of the order of a micrometer and micelles are 5 to 100 nm. Droplets are surrounded by numerous micelles which bombard them constantly due to Brownian motion. When two droplets happen to be close to each other the collisions of the micelles are no longer isotropic. There are fewer micelles between the two droplets. The result from the unbalanced collisions is that the droplets are actually brought into contact. 

Flocculation is the mutual aggregation of colliding droplets. In stationary emulsions, droplet collisions arise from Brownian motion (small droplets) and/or from the creaming/sedimentation process (larger droplets). In the latter, the mechanism is often referred to as sedimentation/creaming flocculation. Finally, droplet aggregation can also occur in sheared emulsions. It is important to point out that the droplet size distribution is not altered by the flocculation and creaming/sedimentation destabilization mechanisms. 

There are many systems that can fluctuate randomly in space and time and cannot be described by deterministic equations. For example. Brownian motion of small particles occurs randomly because of random collisions with molecules of the medium in which the particles are suspended. It is useful to model such systems with what are known as stochastic differential equations. Stochastic differential equations feature noise terms representing the behavior of random elements in the system. Other examples of stochastic behavior arise in chemical reaction systems involving a small number of molecules, such as in a living cell or in the formation of particles in emulsion drops, and so on. A useful reference on stochastic methods is Gardiner (2003). 

Seed Crystals. Crystals inside droplets may occasionally stick out of the surface over several nanometers. If such a drop encounters another one by Brownian motion (see Section 13.2.1), the protruding crystal may occasionally pierce the surface of that droplet. If the latter is still fully liquid, the crystal may act as a seed and induce crystallization. This has been observed to occur in emulsions of hexadecane in water, where part of the drops were solid and part liquid (undercooled). It is a slow process, for instance taking two weeks for completion. It has been calculated that about one in 107 or 108 encounters was effective in such a case. 

In order not to extend this topic too fat we will restrict ourselves to general mechanisms responsible for the lifetime and stability of foams. The mechanisms in emulsions are similar, although complicated by the distribution of diameter and shape of the oil droplets and its Brownian motion. Foams are regular systems as demonstrated by Kruglyakov et al. (1991) and shown in Fig. 3.16. 

Mayonnaise, on the other hand, is a relatively stable emulsion due mostly to high viscosity (more precisely, viscoelasticity), though surfactants are also present. The oil and water in mayonnaise cannot separate into phases because the emulsion droplets do not have enough energy for much movement. In less viscous emulsions, surfactants are responsible for stability. They reduce interfacial tension for the formation of small particles that either repel or very weakly attract each other. Brownian motion must be able to counter the effects of interparticle attraction, sedimentation, or creaming, which is floatation. Micellar suspensions could also be considered microemulsions, although this is debatable. 

If particles are known to be spherical in shape and nondeformable in the relatively weak flow fields associated with Brownian motion (this may be expected in the case of synthetic latex particles, many proteins, and viruses and probably also holds for certain emulsion particles with rigid ordered interfaces, the Stokes radius will closely correspond to the hard sphere radius R, related to Rg through Rg = 3/5 R and may also be similar to that observed in the electron microscope Rem. The value of Rg should, however, on detailed inspection be greater than the radii measured by the latter methods because it includes bound solvent molecules. The discrepancy can be used to estimate the degree of solvation 81 grams solvent/gram of the particle through the relation ... 

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]. 

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