下面是与EMMS原理相关文献的虚拟专刊，其中包括了介尺度科学的简单介绍，EMMS原理的发展历史，相关发表文章的列表；这个专刊描述了我们的研究工作从多尺度建模到介尺度科学的发展历史，并展望了下一步工作。

Fig. 1 Three mesoscales in the multilevel hierarchy of chemical processes (adapted from [arXiv2009])

The chemical engineering community has devoted much effort to investigating mesoscale phenomena. Our group first realized the importance of mesoscale phenomena in fluidized beds during work on particle clustering, and thereafter proposed the energy minimization multiscale (EMMS) model [CFB1988, Thesis1987, Book1994]. The EMMS model has been applied to a variety of mesoscale phenomena over the past 30 years and the universality of the EMMS principle, that is, compromise in competition between dominant mechanisms, is gradually recognized [arXiv2009, P&G2013]. Also at the reactor level, Sundaresan’s group [1, 2] used the kinetic theory-based two-fluid model as a starting point to take into account the effect of mesoscale structure on the flow, heat/mass transfer and reactions at the reactor level. From this, they developed filteredtwo-fluid models by filtering the sub-grid contributions of drag force, solids stress, reaction rate and reactant dispersion within a coarse grid. At the material level, Chatterjee *et al*. [3] developed a spatially adaptive coarse-grained Monte Carlo method that achieved high accuracy over large length and time scales, and applied it to diffusion-reaction problems in a microporous membrane. They showed that coarse-graining gives the correct thermal fluctuations, which are important to correctly model nucleation and nonlinear dynamics.

Initially, we recognized that the parameters at the particle scale must be correlated with those at the system scale to understand particle clustering, which called for an additional stability condition, as shown in Fig. 2. The compromise between the movement tendency of the gas (*W*_{st} = min) [Book1994] and that of solids (*ε* = min) [Book1994, Book2013] defined this stability condition, providing a rule to correlate parameters between the particle and system scales. The EMMS model was then established by integrating the stability condition and conservation equations. And it was used to calculate multiscale parameters for the heterogeneous structures of gas-solid fluidization, define regime transitions and the critical condition for choking [Flu1992], and calculate the radial heterogeneity in gas-solid risers [CFB1990]. In particular, the EMMS drag was formulated. These advances were summarized in a monograph entitled: *Particle-Fluid Two-Phase Flow — the energy-minimization multi-scale method* [Book1994]. The contents of this special issue are based on, and started with, this book.

The ability of the EMMS model to solve various mesoscale problems encouraged further exploration of its generality, including verifying its stability condition, thereby extending its principle to different systems and applying it to large-scale industrial problems. Based on this series of work a common principle for all mesoscale phenomena was proposed — the EMMS principle — which describes the compromise in competition between dominant mechanisms. The EMMS principle was formulated by a multiple objective variational problem [CERD2005, Book2013]. A common physical principle and mathematical formulation are necessary to define a ‘science’. Therefore, the concept of mesoscience was proposed recently as a general interdisciplinary science [arXiv2013], as summarized in detail in a recent monograph [Book2013]. This VSI collates the most relevant papers to show how the EMMS model, developed for gas-solid flows, gradually evolved into a general principle for all mesoscale problems (Figure 2).

At the same time, solution of the EMMS model, its ability to predict choking [CES2002] and application of the EMMS drag improved the accuracy and capability of computational fluid dynamics (CFD) [Partic2003, CEJ2003, CES2007cd, PT2011] and mass-transfer simulations [CES2008ab], enabling 3D, full-loop transient simulations of hydrodynamics and reactions in industrial scale units [Partic2008]. The EMMS model was able to simulate reactions occurring in large reactors by following the strategy: first global, then local, and finally detailed [PT2011]. These developments and the scalability of discrete simulation [CES2006] made it possible to propose the so-called EMMS paradigm for computation based on the EMMS principle, which features structural and logical similarity between physical problems, mathematical modeling, numerical algorithms and computer hardware [Partic2009, 2010, CES2011a]. The EMMS paradigm for computation led to the construction of a 1-petaflop multiscale supercomputer that ranked 8^{th} on the global Top Green 500 [Partic2009, CES2011a] and considerably increased simulation capability [CEJ2010, Partic2011, CES2012].

The ability of the EMMS drag model to raise the predictability and scalability of CFD indicated the importance of mesoscience help to solve industrial problems and explore fundamental issues [Partic2003, CEJ2003, CES2007cd, Partic2008, CES2011a, PT2011]. The EMMS drag has been validated and applied in CFD [27-51] and it comprised one of basic modules of the software EMMS^{®} for ease of use.

This VSI starts with a book [Book1994] that integrated our earliest publications, followed by selected papers from the EMMS group, and concludes with the book “*From multiscale modeling to mesoscience – a chemical engineering perspective*” [Book2013].

In comparison to a review article, a VSI is a better way to show the development of our ideas. We leave the judgment of the rationale of mesoscience up to the readers, because the related concepts and terminology are still at a premature stage. Readers can learn how the simple concept of customized mesoscale particle clustering developed into the universal concept of mesoscience over thirty years, accompanied with verification, extension, application, elaboration and self-correction of our work.

Figure 2 shows the development of the EMMS principle from a customized mesoscale model for gas-solid fluidization (the EMMS model) to the concept of a general science (mesoscience) and its application in exploring virtual process engineering. All the relevant papers are indicated and readers can access them simply by clicking the corresponding hyperlinks in Fig. 2 or in the list of contents.

Recently, the EMMS principle has been used to develop a more general turbulence model that contains a stability condition expressing the compromise in competition between viscosity and inertia. It has also provided evidence of the compromise between minimum free energy and other mechanisms in protein folding, and in material science it has been used to understand the compromise between reaction and transport rates. These examples further indicate that the EMMS principle has a promising future in mesoscience.

All of these results contribute to establish the universal concept of mesoscience. We believe that when a common physical principle and its corresponding unified mathematical formulation are preliminarily identified, it is rational to explore a new science [arXiv2009, P&G2013, arXiv2013, Book2013]. Therefore, we expect attention to mesoscience, particularly from the perspective of the chemical engineering community [Thesis1987, CFB1988, arXiv2009, P&G2013, arXiv2013, Book2013, 1-3, 54].

Fig. 2 Mapping of the contents in this JVSI from the EMMS model to mesoscience (click the code of each paper to access it)

(Click the code of each paper to access it)

[__arXiv2009__] Li, J., Ge, W., Kwauk, M. Meso-scale phenomena from compromise—a common challenge, not only for chemical engineering. http://arxiv.org/abs/0912.5407 (2009).

[__arXiv2013__] Li, J., Huang W., Edwards P., Kwauk M., Houghton J., Slocombe D. On universality of mesoscience: science of ‘the in-between’. http://arxiv.org/abs/1302.5861 (2013).

[__Book2013__] Li, J., Ge, W., Wang, W., Yang, N., Liu, X., Wang, L., He, X., Wang, X., Wang, J., Kwauk, M. From Multiscale Modeling to Meso-Science: A Chemical Engineering Perspective. Springer-Verlag, Berlin (2013).

[__CEJ2003__] Yang, N., Wang, W., Ge, W., Li, J. CFD simulation of concurrent-up gas–solid flow in circulating fluidized beds with structure-dependent drag coefficient.Chem. Eng. J. 96, 71-80 (2003).

[__CEJ2010__] Zhang, N., Lu, B., Wang, W., Li, J. 3D CFD simulation of hydrodynamics of a 150MWe circulating fluidized bed boiler. Chem. Eng. J. 162, 821-828 (2010).

[__CERD2005__] Li J., Ge W., Zhang J., Kwauk M. Multi-scale compromise and multi-level correlation in complex systems. Chem. Eng. Res. Des. 83(6), 574-582 (2005).

[__CES1998__] Li, J., Wen, L., Ge, W., Cui, H., Ren, J. Dissipative structure in concurrent-up gas–solid flow. Chem. Eng. Sci. 53, 3367-3379 (1998).

[__CES1999a__] Li, J., Zhang, Z., Ge, W., Sun, Q., Yuan, J. A simple variational criterion for turbulent flow in pipe. Chem. Eng. Sci. 54, 1151-1154 (1999).

[__CES1999b__] Li, J., Cheng, C., Zhang, Z., Yuan, J., Nemet, A., Fett, F.N. The EMMS model — its application, development and updated concepts. Chem. Eng. Sci. 54, 5409-5425 (1999).

[__CES2001__] Liu, M., Li, J., Kwauk, M. Application of the energy-minimization multi-scale method to gas–liquid–solid fluidized beds. Chem. Eng. Sci. 56, 6805-6812 (2001).

[__CES2002__] Ge, W., Li, J. Physical mapping of fluidization regimes—the EMMS approach. Chem. Eng. Sci. 57, 3993-4004 (2002).

[__CES2003a__] Li, J., Kwauk, M. Exploring complex systems in chemical engineering—the multi-scale methodology. Chem. Eng. Sci. 58, 521-535 (2003). (where there is a typo on Page 532, in the 5th line from the bottom of Step 7, the set of dominant mechanisms should be equal to minimum, that is, (*E*_{1}(** X**), ...,

[__CES2003b__] Ge, W., Li, J. Macro-scale phenomena reproduced in microscopic systems—pseudo-particle modeling of fluidization. Chem. Eng. Sci. 58, 1565-1585 (2003).

[__CES2004__] Li, J., Zhang, J., Ge, W., Liu, X. Multi-scale methodology for complex systems. Chem. Eng. Sci. 59, 1687-1700 (2004).

[__CES2005__] Zhang, J., Ge, W., Li, J. Simulation of heterogeneous structures and analysis of energy consumption in particle–fluid systems with pseudo-particle modeling. Chem. Eng. Sci. 60, 3091-3099 (2005).

[__CES2006__] Ma, J., Ge, W., Wang, X., Wang, J., Li, J. High-resolution simulation of gas–solid suspension using macro-scale particle methods. Chem. Eng. Sci. 61, 7096-7106 (2006).

[__CES2007a__] Ge, W., Chen, F., Gao, J., Gao, S., Huang, J., Liu, X., Ren, Y., Sun, Q., Wang, L., Wang, W., Yang, N., Zhang, J., Zhao, H., Zhou, G., Li, J. Analytical multi-scale method for multi-phase complex systems in process engineering—Bridging reductionism and holism. Chem. Eng. Sci. 62, 3346-3377 (2007).

[__CES2007b__] Yang, N., Chen, J., Zhao, H., Ge, W., Li, J. Explorations on the multi-scale flow structure and stability condition in bubble columns. Chem. Eng. Sci. 62, 6978-6991 (2007).

[__CES2007c__] Wang, W., Li, J. Simulation of gas–solid two-phase flow by a multi-scale CFD approach—of the EMMS model to the sub-grid level. Chem. Eng. Sci. 62, 208-231 (2007).

[__CES2007d__] Lu, B., Wang, W., Li, J., Wang, X., Gao, S., Lu, W., Xu, Y., Long, J. Multi-scale CFD simulation of gas–solid flow in MIP reactors with a structure-dependent drag model. Chem. Eng. Sci. 62, 5487-5494 (2007).

[__CES2008a__] Dong, W., Wang, W., Li, J. A multiscale mass transfer model for gas–solid riser flows: Part 1 — Sub-grid model and simple tests. Chem. Eng. Sci. 63, 2798-2810 (2008).

[__CES2008b__] Dong, W., Wang, W., Li, J. A multiscale mass transfer model for gas–solid riser flows: Part II—Sub-grid simulation of ozone decomposition. Chem. Eng. Sci. 63, 2811-2823 (2008).

[__CES2011a__] Ge, W., Wang, W., Yang, N., Li, J., Kwauk, M., Chen, F., Chen, J., Fang, X., Guo, L., He, X., Liu, X., Liu, Y., Lu, B., Wang, J., Wang, J., Wang, L., Wang, X., Xiong, Q., Xu, M., Deng, L., Han, Y., Hou, C., Hua, L., Huang, W., Li, B., Li, C., Li, F., Ren, Y., Xu, J., Zhang, N., Zhang, Y., Zhou, G., Zhou, G. Meso-scale oriented simulation towards virtual process engineering (VPE)—The EMMS Paradigm. Chem. Eng. Sci. 66, 4426-4458 (2011).

[__CES2011b__] Yang, N., Wu, Z., Chen, J., Wang, Y., Li, J. Multi-scale analysis of gas–liquid interaction and CFD simulation of gas–liquid flow in bubble columns. Chem. Eng. Sci. 66, 3212-3222 (2011).

[__CES2012__] Xiong, Q., Li, B., Zhou, G., Fang, X., Xu, J., Wang, J., He, X., Wang, X., Wang, L., Ge, W., Li, J. Large-scale DNS of gas–solid flows on Mole-8.5. Chem. Eng. Sci. 71, 422-430 (2012).

[__PT1998__] Qian, G., Sun, G., Wen, L., Li, J. Micro-scale measurement of dynamic flow structure in circulating fluidized beds. Powder Technology 100, 76-77 (1998).

[CFB1990] Li, J., Reh, L., Kwauk, M. Application of energy minimization principle to hydrodynamics of circulating fluidized beds. In: Circulating fluidized bed technology III, Basu, P., Horio, M., Hasatani, M., Eds., Pergamon, London, pp.105-111 (1990).

[Flu1992] Li, J., Kwauk, M., Reh, L. Role of energy minimization in gas/solid fluidization. In: Fluidization VII, Engineering Foundation, New York, pp.83-91 (1992).

[CFB1997] Ge, W., Li, J. Pseudo-particle approach to hydrodynamics of particle-fluid systems. In: Circulating fluidized bed technology V, Science Press, Beijing, pp.260–265 (1997).

[__IECR2001__] Li, J., Kwauk, M. Multiscale nature of complex fluid-particle systems. Ind. Eng. Chem. Res. 40, 4227-4237 (2001).

[__Partic2003__] Yang, N., Wang, W., Ge, W., Li, J. Choosing structure-dependent drag coefficient in modeling gas-solid two-phase flow. China Particuology 1, 38-41 (2003).

[__Partic2008__] Zhang, N., Lu, B., Wang, W., Li, J. Virtual experimentation through 3D full-loop simulation of a circulating fluidized bed. Particuology 6, 529-539 (2008).

[__Partic2009__] Chen, F., Ge, W., Guo, L., He, X., Li, B., Li, J., Li, X., Wang, X., Yuan, X. Multi-scale HPC system for multi-scale discrete simulation—Development and application of a supercomputer with 1 Petaflops peak performance in single precision. Particuology 7, 332-335 (2009).

[__Partic2010__] Li, J., Ge, W., Wang, W., Yang, N. Focusing on the meso-scales of multi-scale phenomena—In search for a new paradigm in chemical engineering. Particuology 8, 634-639 (2010).

[__Partic2011__] Xu, J., Qi, H., Fang, X., Lu, L., Ge, W., Wang, X., Xu, M., Chen, F., He, X., Li, J. Quasi-real-time simulation of rotating drum using discrete element method with parallel GPU computing. Particuology 9, 446-450 (2011).

[__P&G2013__] Li J. From customized multiscale modeling to general mesoscience – The principle of compromise. In: Powders and Grains 2013: Proceedings of the 7th International Conference on Micromechanics of Granular Media, July 8–12, 2013, Sydney, Australia, AIP Conf. Proc. 1542, pp. 7-11; doi: http://dx.doi.org/ 10.1063/ 1.4811859 (2013).

[CFB1988] Li, J., Tung, Y., Kwauk, M. Multiscale modeling and method of energy minimization in particle-fluid two-phase flow. In: Circulating Fluidized Bed Technology II, Basu, P. Large, J.F., Eds., Pergamon, London, pp. 89-103 (1988).

[__Book1994__] Li, J., Kwauk, M. Particle-fluid two-phase flow: the energy-minimization multiscale method. Metallurgical Industry Press, Beijing (1994).

[Thesis1987] Li, J. Multiscale-modeling and method of energy minimization for particle-fluid two-phase flow. Ph.D. Thesis, Institute of Chemical Metallurgy, Chinese Academy of Sciences, Beijing (1987).

[__PT2000a__] Li, J. Compromise and resolution — Exploring the multi-scale nature of gas–solid fluidization. Powder Technol. 111, 50-59 (2000).

[__PT2000b__] Cui, H., Li, J., Kwauk, M., An, H., Chen, M., Ma, Z., Wu, G. Dynamic behaviors of heterogeneous flow structure in gas–solid fluidization. Powder Technol. 112, 7-23 (2000).

[__PT2011__] Liu, Y., Chen, J., Ge, W., Wang, J., Wang, W. Acceleration of CFD simulation of gas-solid flow by coupling macro-/meso-scale EMMS model. Powder Technol. 212, 289–295 (2011).

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