Dispersed phase particles, hard

There are two main approaches for the numerical simulation of the gas-solid flow 1) Eulerian framework for the gas phase and Lagrangian framework for the dispersed phase (E-L) and 2) Eulerian framework for all phases (E-E). In the E-L approach, trajectories of dispersed phase particles are calculated by solving Newton s second law of motion for each dispersed particle, and the motion of the continuous phase (gas phase) is modeled using an Eulerian framework with the coupling of the particle-gas interaction force. This approach is also referred to as the distinct element method or discrete particle method when applied to a granular system. The fluid forces acting upon particles would include the drag force, lift force, virtual mass force, and Basset history force.Moreover, particle-wall and particle-particle collision models (such as hard sphere model, soft sphere model, or Monte Carlo techniques) are commonly employed for this approach. In the E-E approach, the particle cloud is treated as a continuum. Local mean... 

The crucial question is at what value of <)> is the attraction high enough to induce phase separation De Hek and Vrij (6) assume that the critical flocculation concentration is equivalent to the phase separation condition defined by the spinodal point. From the pair potential between two hard spheres in a polymer solution they calculate the second virial coefficient B2 for the particles, and derive from the spinodal condition that if B2 = 1/2 (where is the volume fraction of particles in the dispersion) phase separation occurs. For a system in thermodynamic equilibrium, two phases coexist if the chemical potential of the hard spheres is the same in the dispersion and in the floe phase (i.e., the binodal condition). 

Where the two phases are completely compatible, a homogeneous polyblend results which behaves like a plasticized resin (one phase). If two polymers are compatible, the mixture is transparent rather than opaque. If the two phases are incompatible, the product is usually opaque and rather friable. When the two phases are partially compatibilized at their interfaces, the polyblend system may then assume a hard, impact-resistant character. However, incompatible or partially compatible mixtures may be transparent if the individual components are transparent and if both components have nearly the same refractive indices. Furthermore, if the particle size of the dispersed phase is much less than the wavelength of visible light (requiring a particle size of 0.1/a or less), the blends may be transparent. 

The hybrid materials having silica content below 50 wt% were composed of polyimide matrix with finely dispersed silica particles, and their hardness values were very close to that of the matrix polyimide. On the other hand, the hybrid materials having a silica content over 50 wt% were very hard and tough, and their hardness values increased with increasing silica content. In the latter hybrid materials, the silica formed a continuous phase with polyimide as the minor phase that probably acts as binder. This is a new type of polyimide-based composite, and may be referred to as polyimide-reinforced silica glass , al-... 

Several systems may be used such as polymeric thickeners, fine particulate solids such as bentonite clays and oxides or combinations of the latter with polymers (1). The nature and level of the gelling agent required to prevent appreciable settling of particles and formation of hard "cakes" or clays depends on the density difference between disperse phase and medium, volume fraction of the disperse phase and interaction of the antisettling system with particles of the pesticide. 

Many disperse-phase systems involve collisions between particles, and the archetypical example is hard-sphere collisions. Thus, Chapter 6 is devoted to the topic of hard-sphere collision models in the context of QBMM. In particular, because the moment-transport equations for a GBPE with hard-sphere collisions contain a source term for the rate of change of the NDF during a collision, it is necessary to derive analytical expressions for these source terms (Fox Vedula, 2010). In Chapter 6, the exact source terms are derived... 

The nature (e.g., the softening range) of a hard occlusion in the interior of a rubber particle can never be determined by dynamic mechanical methods. Any dispersed phase can only be characterized in the region of higher modulus. Its low modulus or higher temperature properties are completely lost. Thus, the relaxation spectrum of a composite is generally not a superposition of the component spectra. 

In contrast to the pearlite structure, which is lamellar (Figure 2.15), tempered martensite contains the carbide particles as a spheroidal dispersed phase. While the tempered martensite is soft and tough, the parent martensite is hard and abrasion resistant. 

Coagulation rate are proportional to the square of number of concentration (weak dependence forces on the particle size). Nanoparticles in the gas phase always agglomerate or may be redispersed with polydispersity. Hard particles (partially sintered) can agglomerate by dispersing the particles due to size affections or by controlling the reaction s nucleation at room temperature. 

Several methods may be used to determine the adsorbed layer thickness, 8. Most of the methods depend on measuring the hydrodynamic radius of the particles with and without the adsorbed polymer layer. For example, one may measure the relative viscosity, of a dispersion with an adsorbed polymer layer. Assuming that the particles behave as hard spheres (when 8 is small compared with the particle radius R) of noninteracting units (low volume fraction of the disperse phase), can be related to the effective volume fraction, [Pg.355]

Aerogel particles can also be used as the dispersed phase in composite materials, such as elastomers for tires or paints. The incorporation of aerogels will provide them with additional hardness, resistance to wear, and also exert a thickening effect on the mixture [135]. As colloidal abrasives, they even show some insecticide properties because they remove the protecting lipid layer on insects [193]. 

---