Meso-scale structures

Abstract Meso-scale structure is critical to characterize complex systems in... 

MESO-SCALE STRUCTURE—A COMMON CHALLENGE FOR CHEMICAL ENGINEERING... 

Li (1991). All of these, however, suggest that reducing the meso-scale structures into two-phase description is a reasonable simplification. 

The acceleration is a direct measure to the dynamic factors. However, there are few reports, if not to say none, about that for meso-scale structures. In a recent attempt, Meng et al. (2009) made use of the multiple sensors of an X-ray computerized tomography (CT) to measure the cluster accelerations. Instead of the conventional use of CT for cross-sectionally scanning the solids distribution, they erected the X-ray fan-beam and the sensors to follow the vertical movement of clusters... 

Besides the time-averaged and the dynamic characterizations, the correlations between different scales add more complexities to the meso-scale structure. For example, the intensive exchange between meso-scale clusters and dispersed particles will reduce the cross-correlation coefficient and then make it hard to discern a cluster from broth. Such complexity requires more efforts in exploring the dominant mechanisms underlying the correlations, which will be discussed and exemplified by multi-scale CFD in later sections. 

Figure 3 Literature discrepancies in drag coefficient, in mass transfer for CFB due to meso-scale structures and in char reaction rate coefficient. For the drag coefficients, curves are adapted from Wang et al. (2010) for the mass transfer, curves are adapted from Dong et al. (2008a) for the coal reaction, different symbols refer to different coal data.

To capture the meso-scale structure and/or to predict its effects, various modeling approaches have been proposed. The spatiotemporal resolution of these approaches grows with the development of the computer capacity, including the single-scale approaches, direct numerical simulations, and multi-scale approaches. 

Computational fluid dynamics enables us to investigate the time-dependent behavior of what happens inside a reactor with spatial resolution from the micro to the reactor scale. That is to say, CFD in itself allows a multi-scale description of chemical reactors. To this end, for single-phase flow, the space resolution of the CFD model should go down to the scales of the smallest dissipative eddies (Kolmogorov scales) (Pope, 2000), which is inversely proportional to Re-3/4 and of the orders of magnitude of microns to millimeters for typical reactors. On such scales, the Navier-Stokes (NS) equations can be expected to apply directly to predict the hydrodynamics of well-defined system, resolving all the meso-scale structures. That is the merit of the so-called DNS. 

For the gas-solids two-phase flow in a CFB riser, there is no clear separation between the micro-scale (fine-grid scale of TFM continual and the meso-scale (cluster scale), as discussed in Goldhirsch (2003) and Wang and Li (2007). Thus, the meso-scale structure does not vanish... 

In fact, extremum tendencies expressing the dominant mechanisms in systems like turbulent pipe flow (Li et al, 1999), gas-liquid-solid flow (Liu et al, 2001), granular flow, emulsions, foam drainages, and multiphase micro-/nanoflows also follow similar scenarios of compromising as in gas-solid and gas-liquid systems (Ge et al., 2007), and therefore, stability conditions established on this basis also lead to reasonable descriptions of the meso-scale structures in these systems. We believe that such an EMMS-based methodology accords with the structure of the problems being solved, and hence realize the similarity of the structures between the physical model and the problems. That is the fundamental reason why the EMMS-based multi-scale CFD improves the... 

Many polymer blends or block polymer melts separate microscopically into complex meso-scale structures. It is a challenge to predict the multiscale structure of polymer systems including phase diagram, morphology evolution of micro-phase separation, density and composition profiles, and molecular conformations in the interfacial region between different phases. The formation mechanism of micro-phase structures for polymer blends or block copolymers essentially roots in a delicate balance between entropic and enthalpic contributions to the Helmholtz energy. Therefore, it is the key to establish a molecular thermodynamic model of the Helmholtz energy considered for those complex meso-scale structures. In this paper, we introduced a theoretical method based on a lattice model developed in this laboratory to study the multi-scale structure of polymer systems. First, a molecular thermodynamic model for uniform polymer system is presented. This model can... 

Bridging the gap between micro- and macro-scale is the central theme of the first contribution. The authors show how a so-called Energy-Minimization Multi-Scale (EMMS) model allows to do this for circulating fluid beds. This variational type of Computational Fluid Dynamics (CFD) modeling allows for the resolution of meso-scale structures, that is, those accounting for the particle interactions, and enables almost grid-independent solution of the gas-solids two-phase flow. 

MESO-SCALE STRUCTURES MICRO-CONTACT PRINTING (pCP)... 

Agrawal K, Loezos PN, Syamlal M, Sundaresan S The role of meso-scale structures in rapid... 

In this chapter, we have discussed only a few examples of mesoscale phenomena in fluids, for which the methods of meso-thermodynamics appeared to be applicable. However, since coarse-grained models of meso-thermodynamics, such as the Landau-Ginzburg local Helmholtz energy, demonstrate a high degree of universality, associated with the meso-scale structure, an extension of this approach to a broader variety of phenomena is very promising. 

Ito M, Tsukada M, Horio M. Three dimensional meso-scale structure of gas-solid suspensions in circulating fluidized beds, determined by the scanning laser sheet image analysis. Proc F Particle Technology Forum, Vol. 1, 1994, pp 428 33. 

The calculation of the details and dynamics of the fluctuations around the statistically stationary state, resulting from the formation of meso-scale structures... 

The permeability of technical textiles can be determined experimentally. However, this is a time and resource consuming process and no standard procedure is yet available. As in reality textiles are not perfectly periodic structures, the variation on the meso-scale structure has an important influence on the macro-scale permeability. Therefore, it is important to capture the variations in a sufficiently accurate way in order to perform reliable macro-scale simulations. Most of the analytical models give correct result for elementary and structural geometries but not for the stochastic and highly irregular porous technical textiles. Hence, more advanced models are required for the computation of permeability of technical textiles. 

Agrawal K, Loezos PN, Syamkl M, Sundaresan S The role of meso-scale structures in rapid gas-solid flows, J Fluid Mech 445 151-185, 2001. http //dx.doi.org/10.1017/ S0022112001005663. 

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