Multi-scale approaches

Hessel and Lowe report on hybrid, i.e. multi-scale, approaches which are currently most often favored for micro-reactor plant construction, simply for practical time and cost reasons [9, 10]. In addition, such an approach allows one to fit micro reactors in existing industrial, producing and academia, measuring environments. The micro reactor is only used where it is really needed and costs for changing the processing are kept to a minimum in such a way (Figure 1.9). 

The integration of sensing and other functions in a micro-flow system requires either monolithic, on-chip or hybrid, multi-scale approaches. Concerning the latter, Hessel and Lowe discuss the lack of compatibility of today s fluidic interfaces and report on a German project team developing a standard for micro-reactor interconnection [9, 10]. 

This approach is based on some wide-ranging preconditions. In order to bridge the gap between microscopic molecular nature of a particle surface and macroscopic properties, a multi-scale approach covering several orders of magnitude of space and time is needed. On the most basic level quantum mechanics prevail. However, it is often possible by using the Hellman-Feynman theorem [3] to transfer the intrinsic quantum mechanical nature of surfaces to the physics... 

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. 

MESO-SCALE MODELING—THE KEY TO MULTI-SCALE APPROACHES... 

Figure 1 Schematic description of multi-scale approach and modeling methods.

Different scales presented in Figure 3-1 are related to different approximation levels. For an overview of conventional molecular modelling methods, (see e.g.1-3). Bridging the above mentioned disparate time scales for the description of biologically relevant collective motions requires hierarchical, multi-scale approaches. In practice, to describe real complex (bio)molecular or material systems and processes various models have to be coupled to each other. Selected coupling mechanisms will be briefly reviewed. 

Free Energy Simulations Using Multi-scale Approaches... 

A final example might be offered in the case of melt rheology. The local constitutive behaviour is complex enough as a function of molecular architecture and its distribution, but the behaviour of such a melt in a complex processing flow has as much effect on the properties via frozen-in orientation and predisposition of the semi-crystalline morphology. A multi-scale approach to this problem is the focus of a large UK-based collaboration. ... 

A Multi-Scale Approach to Molecular Dynamics Simulations of Shock Waves... 

Wavelets possess two properties that make them especially valuable for data analysis they reveal local properties of the data and they allow multi-scale analysis. Their locality is useful e.g. for applications that require online response to changes. If the typical time scales of these changes are not known in advance a multi-scale approach is advantageous. 

As transitions might occur on different time scales a multi-scale approach is needed, i.e. it is necessary to be able to cope with slow and fast transitions while not interpreting noise as a transition. 

In a staged multi-scale approach, the energetics and reaction rates obtained from these calculations can be used to develop coarse-grained models for simulating kinetics and thermodynamics of complex multi-step reactions on electrodes (for example see [25, 26, 27, 28, 29, 30]). Varying levels of complexity can be simulated on electrodes to introduce defects on electrode surfaces, composition of alloy electrodes, distribution of alloy electrode surfaces, particulate electrodes, etc. Monte Carlo methods can also be coupled with continuum transport/reaction models to correctly describe surfaces effects and provide accurate boundary conditions (for e.g. see Ref. [31]). In what follows, we briefly describe density functional theory calculations and kinetic Monte Carlo simulations to understand CO electro oxidation on Pt-based electrodes. 

For details on the potential energy surface (PES) for CO oxidization, the reader is referred to Ref. [18]. In what follows, we describe the second stage of our Multi-scale approach. We show results of our Monte Carlo simulations, to elucidate the CO electrooxidation kinetics on Pt-based electrodes. 

This chapter discusses a staged multi-scale approach for understanding CO electrooxidation on Pt-based electrodes. In this approach, density functional theory (DFT) is used to obtain an atomistic view of reactions on Pt-based surfaces. Based on results from experiments and quantum chemistry calculations, a consistent coarse-grained lattice model is developed. Kinetic Monte Carlo (KMC) simulations are then used to study complex multi-step reaction kinetics on the electrode surfaces at much larger lengthscales and timescales compared to atomistic dimensions. These simulations are compared to experiments. We review KMC results on Pt and PtRu alloy surfaces. 

To achieve this goal, a so-called multi-scale approach (Figure 10.12) can be adopted in which the gas-solid flows are considered at different distinct levels of... 

Figure 10.12 Multi-scale approach to dense gas-solid flow. In the DNS and DPM models, the solid phase is represented by the actual particles. At the TFM level, the solid phase is considered as a continuum. In DBM the fluid is considered as discrete phase. Phenomenological models are based on the assumptions described above.

Feyel, F. and Chaboche, J.L. (2000) Fe multi-scale approach for modeling the elasto-viscoplastic behaviour of long fiber SiC/Ti composite materials. Computer Methods in Applied Mechanics and Engineering, 183,309-330. 

In order to achieve these goals, we have adopted a multi-scale approach that comprises molecular and mesoscopic models for the liquid crystal. The molecular description is carried out in terms of Monte Carlo simulations of repulsive ellipsoids (truncated and shifted Gay-Berne particles), while the mesoscopic description is based on a dynamic field theory[5] for the orientational tensor order parameter, Q. ... 

It is possible to add more levels of description to the multi-scale approach considered here. As an instance, the Gay-Berne potential used to represent the interactions may be regarded as a coarse graining of an atomistic-detailed interaction potential, which may be computed through ab initio calculations. Or, on the field theory side, we may want to add the density modulations by adding a second field p r,t) to the mesoscopic description. 

Reed EJ, Fried LE, Manaa MR, Joannopoulos JD (2005) A multi-scale approach to molecular dynamic simulations of shock waves. In Manaa RM (ed) Chemistry at extreme conditions. Elsevier, Amsterdam, p 297... 

J. Becker, C. Wieser, S. Fell, and K. Steiner, A multi-scale approach to material modeling of fuel cell diffiision media , Int. J. Heat Mass Transfer, 54,1360 (2011). 

Photo-oxidation of some aaylic-urethane thermoset networks was induced by chromophoric impurities that absorb UV light and produce radicals, initiating a radical oxidation of the polymer [145]. The authors introduced a quantitative kinetic model based on the identified mechanisms and a multi-scale approach from the molecular to the macroscopic level. 

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