Particles with Edges

Arguably the simplest particles with edges are lens shaped. As with spheres, cylinders, and discs, such particles possess infinite axial symmetry but also one edge. They could, in principle, be prepared by spreading a photo-polymerizable hydrophobic 

The orientation of such a solid lens on one surface of a foam film requires that the air-water surface forms the same contact angle at the relevant three-phase contact line at all points on that line. The particle can therefore be orientated either with the three-phase contact line on the edge or at some position on the curved surfaces of the lens. If the particle satisfies the condition 18B° - B2, then orienta- 

Two three-phase contact lines converge on edge to form a hole and cause foam film rupture 

FIGURE 4.54 Role of edge in rupture of foam fihn by solid lens-shaped particle. 

Rupturing (depending on critical thickness of film on solid see text) 

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Recall that this equation could be minimized with respect to particle radius to determine the critical particle size, r, as given by Eq. (3.35). This critical radius could then be used to determine the height of the free energy activation energy barrier, AG, as given by Eq. (3.36). A similar derivation can be performed for a cubic particle with edge length, a. 

Several factors can affect the accuracy of Fraunhofer diffraction (i) particles smaller than the lower limit of Fraunhofer theory (ii) nonexistent ghost particles in particle size distribution obtained by Fraunhofer diffraction applied to systems containing particles with edges, or a large fraction of small particles (below 10 pm) (iii) computer algorithms that are unknown to the user and vary with the manufacturer s software version (iv) the composition-dependent optical properties of the particles and dispersion medium and (v) if the density of all particles is not the same, the result may be inaccurate. 

S.3 Smooth Particles with Edges in Absence of Spread Oil Layers... 

In the case of smooth particles with edges then, as with air-water-air films, a more complex set of conditions for rupture of oil-water-air films arises. Here we consider the case where the oil exhibits partial wetting so that no spread oil layer is present at... 

FIGURE 4.83 Effect of axially symmetrical particle with edges on stability of oil-water-air pseudoemulsion film with 0p < 0 < 180° - 0p and 0aw > Gp with 0p < 90°. 

Type I Mg powder shall consist of shavings, turnings, flakes, plates or any combination of these which meets the granulation requirement. Type II Mg powder shall consist of oblong chip-like particles with rounded edges. Type III Mg powder shall consist of granular or spheroidal particles... 

In quiescent liquids and in bubble columns, buoyancy-driven coalescence is more important. Large fluid particles with a freely moving surface will also have a low-pressure region at the edge of the particle where the velocity is maximum. This low-pressure region will not only allow the bubble to stretch out and form a spherical cap but also allow other bubbles to move into that area and coalesce. Figure 15.14 shows an example of this phenomenon. 

SEM representative images of the surface treated natural graphite SLC-1015 and its untreated precursor SL-20 are shown by Figure 1. The graphite particles with the rounded edges having less active sites tend to limit the reaction on its surfaces and thus improve its cycling performance and safety. 

This model consists of a one-dimensional chain of elastically colliding particles with alternate masses m and M. In order to prevent total momentum conservation we confine the motion of particles of mass M (bars) inside separate cells. Schematically the model is shown in Fig.4 particles with mass m move horizontally and collide with bars of mass M which, besides suffering collisions with the particles, are elastically reflected back at the edges of their cells. In between collisions, particles and bars move freely. 

In the state of band edge level pinning, the electron level of redox particles with the state density of DredoxCe), relative to the electron level rf semiconductor with the state density of Dsc(e), remains unchanged at the electrode interface irrespective of electrode potential. On the other hand, in the state of Fermi level pinning, the electron level of redox particles relative to the electron level of semiconductor electrode depends on the electrode potential in the same way as occurs with metal electrodes (quasi-metallization of semiconductor electrodes). 

Microdiffraction patterns are taken from individual particles after the reduction treatment and are shown in Figs. 3a-d. Most particles with platelet shape and straight edges produce similar microdiffraction patterns, one of which is shown in Fig. 3a. It is indexed as PtsSi with CusAu structure on [100] zone axis. Figs. 3b and 3c show the diffraction patterns from the not reacted Pt on [100] and [310] zone axes, respectively. Particles with irregular forms show various diffractions and a considerable amount of them can be attributed to Pt Sis. One such pattern is shown in Fig. 3d, exhibiting Pt Sis on [152] zone axis. 

Table 2.2 Particles with N dge varying from 2 to 8 number of total (N,), surface (Ns), faces edge (N d) and corner...

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