Dispersed phase particles

In simulating physical operations carried out in stirred vessels, generally one has the choice between a Lagrangian approach and a Eulerian description. While the former approach is based on tracking the paths of many individual fluid elements or dispersed-phase particles, the latter exploits the continuum concept. The two approaches offer different vistas on the operations and require different computational capabilities. Which of the two approaches is most... 

As the dispersed phase moves, the bubbles (gas in liquid) or drops (liquid in liquid or gas) may either coalesce or rupture, depending on the conditions existing. Sometimes packings or stirrers are introduced to facilitate these phenomena. When the dispersed-phase particles arrive at the top of the column, they coalesce and form a bulk interface with the continuous phase, across which transfer processes can continue. 

Hoffman (37) has offered a variety of circumstantial evidence supporting the random coil model. In A-B block copolymers of styrene and butadiene, for instance, the characteristic dimension of the dispersed phase particles depends on the molecular weight of blocks in the dispersed phase according to ... 

C.4.2 Equilibrium Solubilities of Small Dispersed-Phase Particles... 

At moderate volume fractions of dispersed phase (< )), particles or polymers can collide or entangle, again increasing energy dissipation. 

The effect of cure temperature is more difficult to analyze. An increase of cure temperature produces three different effects an increase of the reaction rate, a decrease of the viscosity, and an increase (UCST) or a decrease (LCST) of the initial miscibility. It has been observed that as the viscosity at the cloud point, r CP, decreases there is an increase in the average size of dispersed phase particles and a corresponding decrease in their concentration. 

Particle-laden multiphase flows, usually turbulent, cover a wide range of applications, such as pollution control, sediment transport, combustion processes, erosion effects in gas turbines, and so on. One of the most important aspects of particle-laden turbulent flows is the mutual interactions between particles and turbulence. PIV techniques, as a powerful tool other than numerical simulation method and theoretical analysis, have been applied to this research field of particle-laden multiphase flows. Note that, dispersed-phase particles in particle-laden... 

The majority of theories describing the concentration dependence of viscosity of diluted and moderately concentrated disperse systems is based on the hydrodynamic approach developed by Einstein [1]. Those theories were fairly thoroughly analyzed in the reviews written by Frish and Simha [28] and by Happel and Brenner [29], In a fairly large number of works describing the dependence of viscosity on concentration the final formulas are given in the form of a power series of the volume concentration of disperse phase particles — [Pg.111]

The coefficient before the volume fraction of disperse phase particles in Eq. (44) was found on the basis of Vand s theory [34] of the immobilization of the dispersion... 

The majority of theoretical relations given above depend on a single parameter — the volume fraction of disperse phase particles-

numerical constants. Careful analysis, however, shows that the equations of... 

Another important method for photonic crystal fabrication employs colloidal particle self-assembly. A colloidal system consists of two separate phases a dispersed phase and a continuous phase (dispersion medium). The dispersed phase particles are small solid nanoparticles with a typical size of 1-1000 nanometers. Colloidal crystals are three-dimensional periodic lattices assembled from monodispersed spherical colloids. The opals are a natural example of colloidal photonic crystals that diffract light in the visible and near-infrared (IR) spectral regions due to periodic modulation of the refractive index between the ordered monodispersed silica spheres and the surrounding matrix. 

A two-dimensional treatment has been presented. The model is currently being extended to three dimensions to account for surface flaws in a three-dimensional material subjected to a drawing process and bulk flaws or dispersed phase particles in a three-dimensional matrix. 

This eqiiation accoxmts for the effect of the solvent, presence of charged particles (second term) and pectin (third term) on viscosity (r = 0.996). Sxmimarizing, the viscosity of some complex liquids is adequately represented by empirical equations that have as a structural parameter the volume fraction of the dispersed phase. Particle deformation, specific interactions between particles and the presence of a non-Newtonian continuous phase, all which contribute to the structure of a complex liquid, are more difficult to model. 

McHugh, T.H., and Krochta, J.M. (1994b). Dispersed phase particle size effects on water-vapor permeability of whey protein beeswax edible emulsion films. J. Food Processing Preservation. 18, 173-188. 

Multiphase flows involving dispersed phases (particles, droplets or bubbles) using mixed Eulerian-Lagrangian approaches both with one-way and two-way coupling... 

Let s calculate the dispersed phase particle size from Eq. 10.44 ... 

Counters such as the Coulter Counter determine the number of particles in a known volume of an electrolyte solution. The suspension is drawn through a small orifice that has an electrode on either side. The dispersed phase particles interfere with current flow, causing the resistance to change. Resistance changes are related to the particle volume. 

For multiphase flow processes, turbulent effects will be much larger. Even operability will be controlled by the generated turbulence in some cases. For dispersed fluid-fluid flows (as in gas-liquid or liquid-liquid reactors), the local sizes of dispersed phase particles and local transport rates will be controlled by the turbulence energy dissipation rates and turbulence kinetic energy. The modeling of turbulent multiphase flows is discussed in the next chapter. 

Simulations of trajectories of dispersed phase particles from equations for individual particles... 

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