Surface area sphericity ratio

In use, the ELM Is dispersed In a continuous phase and separates two miscible phases. Under agitation, the ELM phase separates Into spherical globules of emulsion which have typical diameters of 10 ym to 1 mm. Each globule contains many droplets of encapsulated Inner or receiving phase with a typical size of 1 to 10 ym In diameter. The formation of many globules of emulsion produces large surface area/volume ratios of 1000 to 3000 mVm for very rapid mass transfer (20). Due to this dispersed emulsion configuration, ELMs or liquid surfactant membranes are commonly referred to as double emulsions. 

Sphericity. Sphericity, /, is a shape factor defined as the ratio of the surface area of a sphere the volume of which is equal to that of the particle, divided by the actual surface area of the particle. 

Because of ESE, and because of the real forces acting on the particles in the surface layer, there is a tendency for spontaneous contraction of the interfacial area. In practice, such a contraction can be realized only in the case of liquid phases, where the particles can move freely relative to each other. Hence, liquids tend to assume spherical shape with a minimum ratio of surface area to volume (liquid drops), at least when the volume is small and gravitation does not interfere, and when they are not in contact with solid surfaces. 

In the past few years, a range of solvation dynamics experiments have been demonstrated for reverse micellar systems. Reverse micelles form when a polar solvent is sequestered by surfactant molecules in a continuous nonpolar solvent. The interaction of the surfactant polar headgroups with the polar solvent can result in the formation of a well-defined solvent pool. Many different kinds of surfactants have been used to form reverse micelles. However, the structure and dynamics of reverse micelles created with Aerosol-OT (AOT) have been most frequently studied. AOT reverse micelles are monodisperse, spherical water droplets [32]. The micellar size is directly related to the water volume-to-surfactant surface area ratio defined as the molar ratio of water to AOT,... 

Although pyrophoric metals can come in various shapes (spherical, porous spheres or flakes), the calculation to be shown will be based on spherical particles. Since it is the surface area to volume ratio that determines the critical condition, then it would be obvious for a metal flake (which would be pyrophoric) to have a smaller mass than a sphere of the same metal. Due to surface temperature, however, pyrophoric flakes will become spheres as the metal melts. 

Zeolite crystal size can be a critical performance parameter in case of reactions with intracrystalline diffusion limitations. Minimizing diffusion limitations is possible through use of nano-zeolites. However, it should be noted that, due to the high ratio of external to internal surface area nano-zeolites may enhance reactions that are catalyzed in the pore mouths relative to reactions for which the transition states are within the zeolite channels. A 1.0 (xm spherical zeolite crystal has an external surface area of approximately 3 m /g, no more than about 1% of the BET surface area typically measured for zeolites. However, if the crystal diameter were to be reduced to 0.1 (xm, then the external surface area becomes closer to about 10% of the BET surface area [41]. For example, the increased 1,2-DMCP 1,3-DMCP ratio observed with decreased crystallite size over bifunctional SAPO-11 catalyst during methylcyclohexane ring contraction was attributed to the increased role of the external surface in promoting non-shape selective reactions [65]. 

Example 7-1 Consider a silica gel catalyst that has been peUetized into spherical peUets 4 mm diameter. The surface area is measured to be 100 m /g, and the density of sUica is 3 g/cm Find the ratio of the area of the catalyst to the external surface area of the pellet. 

Bacteria can grow incredibly fast. Under some conditions, it takes a bacterial cell only 10-20 min to double its size and to divide to form two cells.4 An animal cell may take 24 h for the same process. Equally impressive are the rates at which bacteria transform their foods into other materials. One factor contributing to the high rate of bacterial metabolism may be the large surface to volume ratio. For a small spherical bacterium (coccus) of diameter 0.5 xm, the ratio of the surface area to the volume is 12 x 106 m , while for an ameba of diameter 150 xm the ratio is only 4 x 104 m 1 (the ameba can increase this by sticking out some pseudopods). Thimann33 estimated that for a 90-kg human, the ratio is only 30 m 1. 

A molecule at the surface is attracted more strongly from below because the molecules of the gas are separated much more widely, and the attraction is inversely proportional to the distance between molecules. This imbalance of forces creates a membrane-like surface. It causes a liquid to tend toward a minimum surface area. For instance, a drop of water falling through air tends to be spherical since a sphere has the minimum surface-to-volume ratio. 

Deformation of a Sphere in Various Types of Flows A spherical liquid particle of radius 0.5 in is placed in a liquid medium of identical physical properties. Plot the shape of the particle (a) after 1 s and 2 s in simple shear flow with y 2s1 (b) after 1 s and 2 s in steady elongational flow with e = 1 s 1. (c) In each case, the ratio of the surface area of the deformed particle to the initial one can be calculated. What does this ratio represent ... 

In devolatilizing systems, however, Ca 1 and the bubbles deform into slender S-shaped bodies, as shown in Fig. 8.12. Hinch and Acrivos (35) solved the problem of large droplet deformation in Newtonian fluids. They assumed that the cross section of the drop is circular, of radius a, and showed that the dimensionless bubble surface area, A, defined as the ratio of the surface area of the deformed bubble A to the surface area of a spherical bubble of the same volume, is approximated by (36) ... 

Mixing by molecular diffusion. This is the ultimate and finally the only process really able to mix the components of a fluid to the molecular scale. The time constant for this process is the diffusion time t = yLy is a shape factor and L is the ratio of the volume to the external surface area of the particle. For instance let us consider various shapes slabs (thickness 2R, case of lamellar structure with striation thickness 6 = 2R), long cylinders (diameter 2R, case of filamentous structure), and spheres (diameter 2R, case of spherical aggregates). 

---