Transport phenomena simulation

Since Metropohs original work in 1949 (MetropoHs and Ulam, 1949), numerous monographs and review articles have been devoted to the Monte Carlo method. In the present study, we are concerned both with simulation of a linear transport phenomenon (namely radiative transfer) and with a solution to our integral model for a photobioreactor (see Section 1). Here, we arbitrarily chose to point out Hammersley and Handscomb s book... 

Numerical simulations of the coarsening of several particles are now possible, allowing the particles to change shape due to diffusional interparticle transport in a manner consistent with the local interphase boundary curvatures [17]. These studies display interparticle translational motions that are a significant phenomenon at high volume fractions of the coarsening phase. 

First, and most important, nonlinear dynamics provides an intellectual framework to pursue the consequences of nonlinear behavior of transport systems, which is simply not possible in an intellectual environment that is based upon a linear mentality, characterized by well-behaved, regular solutions of idealized problems. One example that illustrates the point is the phenomenon of hydrodynamic dispersion in creeping flows of nondilute suspensions. It is well known that Stokes flows are exactly reversible in the sense that the particle trajectories are precisely retraced when the direction of the mean flow is reversed. Nevertheless, the lack of reversibility that characterizes hydrodynamic dispersion in such suspensions has been recently measured experimentally [17] and simulated numerically [18], Although this was initially attributed to the influence of nonhydrodynamic interactions among the particles [17], the numerical simulation [18] specifically excludes such effects. A more general view is that the dispersion observed is a consequence of (1) deterministic chaos that causes infinitesimal uncertainties in particle position (due to arbitrarily weak disturbances of any kind—... 

The static - double-layer effect has been accounted for by assuming an equilibrium ionic distribution up to the positions located close to the interface in phases w and o, respectively, presumably at the corresponding outer Helmholtz plane (-> Frumkin correction) [iii], see also -> Verwey-Niessen model. Significance of the Frumkin correction was discussed critically to show that it applies only at equilibrium, that is, in the absence of faradaic current [vi]. Instead, the dynamic Levich correction should be used if the system is not at equilibrium [vi, vii]. Theoretical description of the ion transfer has remained a matter of continuing discussion. It has not been clear whether ion transfer across ITIES is better described as an activated (Butler-Volmer) process [viii], as a mass transport (Nernst-Planck) phenomenon [ix, x], or as a combination of both [xi]. Evidence has been also provided that the Frumkin correction overestimates the effect of electric double layer [xii]. Molecular dynamics (MD) computer simulations highlighted the dynamic role of the water protrusions (fingers) and friction effects [xiii, xiv], which has been further studied theoretically [xv,xvi]. 

An extensive discussion of experiments on exciton transport in isotopically disordered crystals and numerical simulations of this phenomenon in the framework of a percolation model may be found in the review paper by Kopel-mann (20). A more recent review of this field, including the discussion of the Anderson model, may be found in the book by Pope and Swenberg (21). 

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