Dispersed phase particles, wall

When simulating the trajectories of dispersed phase particles, appropriate boundary conditions need to be specified. Inlet or outlet boundary conditions require no special attention. At impermeable walls, however, it is necessary to represent collisions between particles and wall. Particles can reflect from the wall via elastic or inelastic collisions. Suitable coefficients of restitution representing the fraction of momentum retained by a particle after a collision need to be specified at all the wall boundaries. In some cases, particles may stick to the wall or may remain very close to the wall after they collide with the wall. Special boundary conditions need to be developed to model these situations (see, for example, the schematic shown in Fig. 4.5). 

FIGURE 4.5 Wall boundary conditions for dispersed phase particles, (a) Reflection, (b) saltation, (c) particle escapes or vanishes. 

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... 

For verification of adequacy of suggested method for disperse phase particles sizes calculation experimental investigation of emulsification process in turbulent flows limited by impenetrable wall of divergent-convergent design in hexane-water (continuous phase) system was carried out (see 2.2.7). Six-sectional tubular apparatus differ in canal geometry were used (Table 2.1). 

A characteristic feature of a diffuser-confusor reactor is the formation of circulation areas (Figure 2.13). In this case, dispersed phase particles in the near-wall flow area start to move in the opposite direction to the reaction mixture flow due to the pressure gradient. 

An apparent slip or lubrication occurs at the wall in the flow of any multi-phase systems if the disperse phase moves away from smooth walls. This arises from steric, hydrodynamic, viscoelastic and chemical forces present in suspensions flowing near smooth walls and constraints acting on the disperse phase particles immediately adjacent to the walls, see [13]. 

The solver used for this study is the same as in Chapter 9 a parallel fully compressible code for turbulent reacting two-phase flows, on both structured and unstructured grids. The fully explicit finite volume solver uses a cell-vertex discretization with a Lax-Wendroff centered numerical scheme [296] or a third order in space and time scheme named TTGC [268]. Characteristic boundary conditions NSCBC [339 329] are used for the gas phase. Boundary conditions are easier for the dispersed phase, except for solid walls where particles may bounce off. In the present study it is simply supposed that the particles stick to the wall, with either a slip or zero velocity. 

The cyclone, or inertial separation method, is a common industrial approach for segregating a dispersed phase from a continuous medium based upon the difference in density between the phases. The concept takes advantage of the velocity lag which occurs for dense particles with respect to a lower density medium when both phases are subject to an accelerating flow field, such as within a rotating vortex. The larger the acceleration, the smaller the particle which fails to follow the continuous phase streamlines and will migrate to the outer wall of the cyclone for collection. 

In Eq. (29), Vd represents the dispersed phase velocity, Fq is the drag force, Fg denotes the force of gravity, Fl is the lift force, Fs represents effects of the fluid stress gradients, Fh is the Basset history term, and F-w represents interactions with the wall. The review paper by Loth (42) presents and discusses all the forces present in Eq. (29). Flere we limit ourselves to the most important effect of drag forces. In the case of spherical solid particles of diameter d, Fd can be expressed as... 

During catalytic reactions using supported ionic liquid-type catalysts gaseous or vapor-phase reactants diffuse through the residual pore space of the catalyst, dissolve in the liquid catalyst phase, and react at catalyst sites within the thin liquid catalyst film dispersed on the walls of the pores in the support material, as illustrated in Fig. 5.6-1. The products then diffuse back out of the catalyst phase into the void pore space and further out of the catalyst particle. 

In most cases, anionic water-soluble polymers such as poly(styrene-maleic anhydride), polyacrylic acid, etc., are apphed. These kinds of emulsifiers can influence the microcapsule preparation, mean particle size, and particle size distribution. By emulsification, an electric double layer generates on the dispersed phase. Then the electrostatic interactions between the protonated amino resin prepolymer and the negatively charged orgaific phase can act as a driving force, which enable the wall material polycondensate on the surface of the oil droplets but not throughout the whole water phase. ... 

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