Simulated dispersion

Rather than solve the variance equation for a number of variables directly, this method allows us to simulate the output of the variance, for example the simulated dispersion of a stress variable given that the random variables in the problem can be characterized. 

Simulated dispersion snapshots following pressurized hydrogen release at times (a) 2.4 s, (b) 6.2 s, (c) 9.6 s, and (d) 12.4 s after start of release. (From Rigas, F. and Sklavounos, S., lnt.. Hydrogen Energ., 30, 1501, 2005. With permission from International Association of Hydrogen Energy.)... 

Fig. 2.9. Use of a flush model to simulate dispersive mixing. Two fluids enter a unit volume of an aquifer where they react with each other and minerals in the aquifer, displacing the mixed and reacted fluid.

Brownian Dynamics is then used to simulate the macroscopic mobility of the water molecules. The water mobility near to the clay surface is identified to the water mobility calculated by MD simulations. The ordering of the simulated dispersions was selected to be compatible with the information obtained... 

Wilcock A, Tebbens J, Fuss F, Wagner J, Brewster M. Spectrophotometric analysis of electrochemically treated, simulated, dispersed dyebath effluent. Text Chem Color 1992 24 29-37. 

In order to further substantiate this conclusion, it is of interest to compare it with the prediction obtained from a simple theoretical model. Glueckauf s well-known transport model (19, p. 449-453), supplemented by the more modern concept of hydro-dynamic dispersion, is well suited for this purpose. The model simulates dispersion-affected solute transport with ion exchange for which diffusion processes are rate limiting. In his development, Glueckauf assumes 1) exchange takes place in porous... 

The recent progress in experimental techniques and applications of DNS and LES for turbulent multiphase flows may lead to new insights necessary to develop better computational models to simulate dispersed multiphase flows with wide particle size distribution in turbulent regimes. Until then, the simulations of such complex turbulent multiphase flow processes have to be accompanied by careful validation (to assess errors due to modeling) and error estimation (due to numerical issues) exercise. Applications of these models to simulate multiphase stirred reactors, bubble column reactors and fluidized bed reactors, are discussed in Part IV of this book. 

Arslan, I. Treatability of a simulated disperse dyebath by ferrous iron, ozonation, and ferrous iron-catalyzed ozonation. J. of Hazardous Materials 2001, SS5,229-241. 

It should be noted, however, that DFT simulations tend to simulate dispersive interactions poorly, so that in many cases interactions of non-polar adsorbates within the pores of microporous solids are better treated using well-parametrised forcelield methods that use established atom-atom pan-potentials. 

A hierarchy of computational models is available to simulate dispersed gas-liquid-solid flows in three-phase slurry and fluidized bed reactors [84] continuum (Euler-Euler) method, discrete particle/bubble (Euler-Lagrange) method, or front tracking/capturing methods. While every method has its own... 

Figure 4 Structure in Monte Carlo-simulated dispersion (particle diameter 1.190 p.m, ionic strength 0.1 mol m ). The radial distribution function g(r) is plotted against the reduced separation r/

Figure 9 Relaxation of pair correlations in Brownian dynamics simulated dispersion (particle diameter 46 nm, volume frriction 3x10 ", ionic strength 10 mol m ). The van Hove distinct correlation function Gj(r, t) at time t is plotted against rja, where r is the centre-to-centre separation and a is the particle...

Figure 9.9. Clusters formed in a porous or pigmented body can be described by a hyperbolic function which constitutes a fractal dimension in data space, a) Simulated dispersion of monosized pores which occupy 20 % of the available space, b) Typical clusters which may be found in such a dispersion, displaying orthogonal and diagonal connections, c) Size distribution of the clusters present in (a) presented as a log-log plot.

It is considered that this approach, which attempts to measure the effective particle size achieved in a close match to the vehicle used, by a simulated dispersion technique, is the correct approach to determining particle size in industrial and manufacturing applications. 

A number of methods exist to simulate dispersed multiphase flows. When choosing a particular simulation method, it is important to consider first the relevant length scales. The most obvious length scales are, from large to small, the dimensions of the confinement (equipment dimensions), the dimensions of the discrete elements (particles, bubbles, or droplets), and the mean free path of the molecules in the continuous fluid phase. The molecular mean free path ranges firom less than a nanometer in a liquid to the order of 100 nm in a gas at ambient pressure. Discrete molecular effects such as Brownian forces and molecular slip conditions are therefore very important in nanofluidic and small microfluidic devices (Hadjiconstantinou, 2006). They are also very important for the dynamic behavior of nano (structured) particles in gas flows and colloidal particles suspended in a liquid. In these... 

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