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Focusing on the meso-scales of multi-scale phenomena—In search for a new paradigm in chemical engineering Jinghai Li ∗ , Wei Ge, Wei Wang, Ning Yang The EMMS Group, State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China

a r t i c l e

i n f o

Article history: Received 1 September 2010 Accepted 14 September 2010 Keywords: Meso-scale Multi-scale Complex system EMMS Multi-phase High performance computation

a b s t r a c t To celebrate the 90th birthday of Professor Mooson Kwauk, who supervised the multi-scale research at this Institute in the last three decades, we dedicate this paper outlining our thoughts on this subject accumulated from our previous studies. In the process of developing, improving and extending the energyminimization multi-scale (EMMS) method, we have gradually recognized that meso-scales are critical to the understanding of the different kinds of multi-scale structures and systems. It is a common challenge not only for chemical engineering but also for almost all disciplines of science and engineering, due to its importance in bridging micro- and macro-behaviors and in displaying complexity and diversity. It is believed that there may exist a common law behind meso-scales of different problems, possibly even in different ﬁelds. Therefore, a breakthrough in the understanding of meso-scales will help materialize a revolutionary progress, with respect to modeling, computation and application. © 2010 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

1. Meso-scales are a common challenge for understanding various multi-scale phenomena. Micro-mechanisms and macro-behavior can be correlated only when the meso-scales are physically understood. For instance, turbulence is one of the few unsolved problems in classical physics (Feynman, Leighton, & Sands, 1963), which by itself is a typical meso-scale problem. At the micro-scale, we know very well the behaviors of ﬂuid molecules and their interactions from statistical physics; at the macro-scale, ﬂuid properties such as viscosity, density and average velocity are easy to measure. However, we do not have much knowledge on what happens at the meso-scale where turbulence is triggered from laminar ﬂow. In fact, better understanding of many problems in both science and technology is more often than not blocked at the respective meso-scales (Li & Kwauk, 2003; Ge, Wang, Ren, & Li, 2008). Both physical and life systems feature a multi-level hierarchy, showing multi-scale natures at each level, as shown in Fig. 1. Although the scientiﬁc problems faced in these systems are totally different, and have been studied within different ﬁelds, there is a common recognition that all boundary scales (both micro and macro) are known quite well, except the meso-scale, which has

∗ Corresponding author. E-mail address: [email protected] (J. Li).

been a challenge to all respective ﬁelds (Li, Ge, & Kwauk, 2009). In fact, the compromise between dominant mechanisms at this scale leads to the so-called “complexity” and “diversity”, and is believed to be the source of dynamic heterogeneity, coexistence of order and disorder and non-linearity. Take hydroxyapatite for instance at the material level, as shown in Fig. 2a. It is a kind of material with the same well-known molecular composition and structure which is self-assembled in both human teeth and bones, and many more morphologies at mesoscale can be observed under different conditions. However, we do not know how to manipulate these meso-scale structures to produce different functional materials for different applications. At the reactor level, as shown in Fig. 2b, chemical engineers have obtained knowledge about the global behaviors of a reactor and micro-phenomena around a single particle (available even from a textbook). However, we have learned very little about the meso-scale clustering phenomena, which are critical for mass transfer and reactions, as well as for determining the performance of reactor to a large extent. 2. Recent progresses in different ﬁelds have indicated that a common mechanism dominating meso-scale structures may exist for different systems, as being said, the compromise among the dominant mechanisms in complex systems has led to the emergence of meso-scale structures and deﬁned the stability conditions of complex systems.

1674-2001/$ – see front matter © 2010 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

doi:10.1016/j.partic.2010.09.007

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Fig. 1. Multi-level hierarchy and multi-scale natures of physical and life systems.

In gas–solids ﬂuidization, for example, the meso-scale structures in forms of bubbles or clusters reﬂect the compromise between the gas-ﬂow domination and solids-ﬂow domination (Li & Kwauk, 1994). As shown in Fig. 3a, when a gas–solid ﬂuidized bed is dominated by gas ﬂow, as can be observed at high gas velocity beyond the transport velocity, the solids shall be subject to ﬂow distribution and shall be pneumatically transported without distinct aggregation (i.e., Wst → min, Wst denotes volume-speciﬁc energy consumption for suspending and transporting particles (W/m3 )). When the gas ﬂow is weak such that the solid particles cannot be suspended by the gas ﬂow drag, the packed state of solid particles dominates the bed (i.e., ε → min, ε denotes voidage). Between the ﬂow patterns at these two extremes, the tendency of gas passing through particles with least resistance (i.e., Wst → min) compromises with the tendency of the particles maintaining least gravitational potential (i.e., ε → min), thus resulting in Nst → min. The meso-scale structures originate, accordingly, from this compromise by satisfying gas dominance and solids domi-

nance alternately with respect to space and time (here Nst denotes mass-speciﬁc energy consumption for suspending and transporting particles (W/kg), and Nst = Wst /p (1 − ε)). Such compromise featuring the EMMS model (Li & Kwauk, 1994, 2003) has been veriﬁed in micro-scale simulations using pseudo-particle modeling (Li, Zhang, Ge, & Liu, 2004). At the micro-scale, the dominant mechanisms are presented alternately, and the stability criterion Nst is ﬂuctuating, displaying no extremum tendency. At the meso-scale, the compromise between the dominant mechanisms gives the stability condition (Nst → min), though still with certain ﬂuctuations. Finally, at the macro- (global) scale, a clear and smooth extremum tendency is observed. It was also identiﬁed that the choking transition from the ﬂuidization state to the dilute pneumatic transport can be well explained with the transformation from gas–solids compromise to gas dominance (Li & Kwauk, 1994). Further, the interphase drag between the meso-scale structure (particle clusters) and its surrounding ﬂuid was found to be quite different from that inside the particle clusters and that in the dilute

Fig. 2. Meso-scales—challenges in multi-scale modeling and simulation in chemical engineering.

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Fig. 3. The common nature of compromise between dominant mechanisms in G/S and G/L systems—its importance in deﬁning stability conditions and in correlating different scales. (Subscripts c and f denote dense and dilute phases, subscript d denotes solids and subscript cl denotes the clusters, subscripts S and L denote small and large bubbles and subscript g denotes gas phase. Variables d, U and f denote diameter, superﬁcial velocity and volume fraction, respectively.).

broth (Li, Chen, Yan, Xu, & Zhang, 1993). Therefore, the integration of the EMMS model and the conventional two-ﬂuid model was able to capture the meso-scale structure (Yang, Wang, Ge, & Li, 2003; Wang & Li, 2007) and to predict the bi-stable state of choking (Ge & Li, 2002), as well as its dependence upon the riser height (Wang, Lu, Zhang, Shi, & Li, 2010), as corroborated in our earlier experiments (Li, Tung, & Kwauk, 1988; Li, Wen, Ge, Cui, & Ren, 1998). More applications of this EMMS-based CFD approach in processes such as petrochemical engineering and CFB combustion have shown its roles in simulating gas–solid CFBs (Benyahia, 2010; Dong, Wang, & Li, 2008; Hartge, Ratschow, Wischnewski, & Werther, 2009; Jiradilok, Gidaspow, Damronglerd, Koves, & Mostoﬁ, 2006; Nikolopoulos, Papafotiou, Nikolopoulosb, Grammelisb, & Kakaras, 2010; Qi, Li, Xi, & You, 2007; Wang et al., 2010). Similar compromise between dominant mechanisms at mesoscale also exists in gas–liquid systems such as bubble columns, and the extension of the multi-scale modeling strategy of EMMS to gas–liquid systems is therefore straightforward (Zhao, 2006; Ge et al., 2007a; Yang, Chen, Zhao, Ge, & Li, 2007; Yang, Chen, Ge, & Li, 2010). The total energy consumption NT can be decomposed into three portions. At meso-scale, bubbles may break up

at one location and then coalesce at another after traveling certain distance in time and in space. Therefore, energy dissipation during bubble breaking up and coalescence, Nbreak , represents a kind of meso-scale dissipation. On the other hand, Nturb and Nsurf dissipate directly at micro-scale. The former represents the viscous dissipation of liquid while the latter stands for the energy dissipation due to the response of bubble interface to liquid turbulence, such as shape oscillation and slip of liquid along bubble surfaces. The stability condition was recognized to be subject to the compromise between liquid dominance and gas dominance, and expressed as the minimization of micro-scale energy dissipation, that is, Nsurf + Nturb → min or the maximization of meso-scale energy dissipation, i.e., Nbreak → max, as shown in Fig. 3b. With such a modeling strategy, a conceptual dual-bubble-size (DBS) model was established, and the regime transition in bubble columns can be successfully captured as a jump change in the model calculation of gas holdup and theoretically interpreted as a shift of the location of the global minimum point of the micro-scale energy dissipation from one ellipsoid of iso-surface to another in a 3D space of structure parameters (Chen, Yang, Ge, & Li, 2009b; Yang et al., 2010).

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Table 1 Comparison between G/S and G/L systems, showing the similar principle of compromise in stability conditions and regime transitions (adapted from Ge and Li, 2002 and Chen, Yang, Ge, & Li, 2009c). Systems

Gas–solid

Dominant mechanisms

A: Wst → min B: ε → min Compromise between A and B: Nst =

Stability condition

Gas–liquid

Wst (1−ε)p

→ min

A: Nturb → min B: Nsurf → min Compromise between A and B: Nst = Nsurf + Nturb → min

System bifurcation arising from the compromise between A and B

Nst (Normalized by NT )

1.0

0.9

N st → min X = X( d

S 1 , d L1 ,U gS 1 )

0.8

Transition point

0.7

N st → min X = X ( d

0.6

0.5 0.00

0.05

0.10

S 2 , d L 2 ,U gS 2 )

0.15

0.20

Superficial gas velocity, Ug(m/s)

Regime transition driven by stability condition

Subscript mf denotes the state of minimum ﬂuidization. For the deﬁnition of other symbols in this table, please refer to the caption of Fig. 3.

The similarity between gas–solid and gas–liquid systems on the compromise of dominant mechanisms can be summarized in Table 1. The stability conditions arising from the compromise between different dominant mechanisms drive the structure evolution of gas–solid and gas–liquid systems, and therefore lead to the regime transitions. Similar examples can be found in biological emulsions as well, where the compromise between the hydrophilic and lipophilic effects of the surfactants leads to different morphologies of the meso-scale clusters of surfactant molecules (the micelles). When lipophilic effect becomes dominant, the hydrophobic tails of the surfactant molecules will be imbedded in the oil phase in steady state, and otherwise in the water phase. However, when these two effects are comparable, the compromise between these two dominant mechanisms results in formation of micro-emulsion droplets. Extremum tendencies can be quantiﬁed for each effect and only one tendency is realized in the process when its effect is dominant. However, in all cases, a ﬂuctuating decay of the stability criterion, proposed to describe the compromise of these two effects, can be observed, which has demonstrated the role of stability condition in forming emulsion structure. More examples in this regard can be found in Ge et al. (2007a). From the above studies, we have recognized that the mesoscales are dependent scales for most problems, meaning that the behavior at such scales is subject to its neighboring scales whose behavior is more or less deﬁned by independent parameters including material properties and operating conditions. In other words, the meso-scale behavior is typically shaped through self-organization with constraints of the properties of their elements and the system characteristics well-known to us, but the process and the mechanism for this self-organization are barely understood.

On the basis of our research in the last three decades, it was proposed that this common mechanism of compromise can be formulated as a Multiple Objective Variational (MOV) problem (Li & Kwauk, 2003). This means that meso-scale structures show up in complex systems in the form of dynamic combinations of different states dominated by respective dominant mechanisms, such that the meso-scale structure of gas–solid systems is a spatio-temporal combination of a dilute state deﬁned by Wst = min and a dense state by ε = min. In summary, meso-scale phenomena are a common challenge in understanding the multiscale world, which can be seen as a connection between micro-mechanisms and macro-behavior, where the dominant mechanisms compromise with each other, leading to complexity and diversity. Progress in this respect will result in breakthrough in the relevant ﬁelds, and promote the development of complexity science. 3. To understand the behavior of meso-scale structures and explore their mechanism, high performance computation is necessary and promising. This MOV formulation, derived from EMMS, may deﬁne a multiscale computation paradigm to narrow down the currently existing gap between the peak performance and real computational capability of the supercomputers by keeping the consistency between the physical model, the software, the hardware and the problem to be solved, that is, multi-scale processing units should be in place in accordance with the natures of respective scales, giving the possibility of optimizing the communication, storage and computation at each scale and between scales.

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Fig. 4. A multi-scale discrete simulation approach to complex systems (adapted from Ge et al., 2007b).

At the micro-scale, computation is simple but costly since the information and interaction between a huge number of elements must be computed, but limited only to their immediate neighbors, giving the possibility to conduct only local communication. At meso-scale, it is not necessary to deal with the detailed interaction between these elements while spatio-temporal compromise between bulks of elements, that is, stability condition, rules the computation. The computing cost at this scale is reduced as compared to fully discrete simulations, though the computing complexity is increased. At the global scale, complexity is further increased because of the inclusion of operating conditions and boundary condition, but the cost is reduced due to the global nature of computation. To practice this multi-scale paradigm, the physical model, the simulation algorithm and the computer architecture are better resolved into a multi-scale direct-link structure as shown in Fig. 4 (Ge, Guo, Jiang, & Li, 2007b). On each scale, the elements (physical, computational or hardware) interact only with its immediate neighbors, all long-range correlations, mainly dominated by compromise, are imposed indirectly via the corresponding elements in the upper layer. If we are able to design computers according to the structure shown in Fig. 4, either with separate processing units (PUs) for three scales or by integrating PUs with three scales, we will be able to optimize the performance of the computers. Unfortunately, no hardware or software platform is in place currently for us to use. Therefore, this structure was ﬁrst materialized from the software aspect by integrating computational ﬂuid dynamics (CFD) of multiphase ﬂow to the EMMS model (Wang & Li, 2007; Yang et al., 2003). That is, the EMMS model was applied at the meso-scale to describe the sub-grid heterogeneity that was not resolved in the CFD model. The idea was later implemented in the hardware aspect using commercial components of central processing units (CPUs) and graphic processing units (GPUs), achieving high-efﬁciency, low-cost supercomputing for the simulation of multi-scale systems (Chen et al., 2009a). Using this mode for gas–solids system simulation, the EMMS model can be ﬁrst applied at the macro-scale (global or reactor scale) to determine the ﬂow regime and to provide an overall distribution of ﬂow parameters in the system. Then the EMMS model is applied to calculate the approximate state at the meso-scale, and the coupled EMMS-CFD approach is then applied to describe the evolution of dynamic meso-scale structure. This paradigm is now being practiced on our CPU + GPU supercomputer of 1 petaﬂops (Chen et al., 2009a). Preliminary tests are promising, but not ﬁnished yet. Further, the discrete simulation can be used at micro-scale to simulate the details of ﬂuid–solid interactions.

But, how to feedback the results at this scale to the global and meso-scale is still a challenging issue. 4. Computation in engineering is undergoing a revolutionary change due to the increasing understanding of meso-scale phenomena in physics and the quick development of computer technology, showing the dawning of virtual process engineering. However, it is clear that the complete structural consistency between software, hardware, and the problem is still not seen since we used GPU for both meso- and micro-scales. Several years ago, as shown in Fig. 5, we used to run CPU clusters for parallel computation. Now, the mode of CPU + GPU computation has become a widely adopted practice and is still growing up into a popular paradigm for parallel computation. We are still waiting to see the progress of computer technology, moving to develop more optimized computing hardware for meso-scale structure, for which we have not yet known and we have coined a name “xPU” for it. With xPUs, meso-scale theories and multi-scale computation integrated, we will be able to build advanced simulators for chemical processes in the industry, which will give the possibility of online optimization, i.e., the virtual process engineering (VPE). We do not know what will be the next paradigm of chemical engineering, but we are certain that the VPE will undoubtedly make a new paradigm. However, it will also be related to the development of computer technology and to our growing understanding of meso-scale problems. It calls for transdisciplinary cooperation between chemical engineers and computer scientists, and can be realized only when we know the mechanism of meso-scale compromise and its correlation with neighboring scales. In this perspective, chemical engineering is now at a critical time of development, transforming from its traditional experimentdominated mode to a computation-promoted mode. Whether VPE can be realized is so much dependent on the understanding of meso-scale rules and behavior and whether the knowledge generated can be utilized by computer scientists to build multi-scale computers. By now, we have seen changes are fast approaching, and have recognized the increasing necessity to open our door to welcome interdisciplinary scientists to join in, otherwise, MOV formulation cannot be fully practiced with the current available hardware. When we could resolve the mechanisms at different scales and establish the correlation law between scales, we would be able to optimize PUs at different scale with respect to computation,

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Fig. 5. Development of parallel computation paradigm.

storage and communication. That will be the objective of the so-called green computation. Acknowledgments First we would thank Professor Mooson Kwauk for his threedecade supervision of this series of work and his continuing encouragement on future work. Thanks should be extended to all our colleagues in the EMMS group who were or are involved in this research, especially to Xianfeng He, Xiaowei Wang, Xinhua Liu, Junwu Wang, Feiguo Chen, Ying Ren, Ming Xu, Jian Wang, Limin Wang, Bona Lu, Yaning Liu, Jianhua Chen, Yuhua Wang, Jingdong He, Jiayuan Zhang and Nan Zhang for their recent contributions in writing to this paper. Financial support from NSFC, MOST, CAS, and all industrial partners is also greatly appreciated, which has enabled us to focus on such a fundamental problem as meso-scale! References Benyahia, S. (2010). On the effect of subgrid drag closures. Industrial & Engineering Chemistry Research, 49(11), 5122–5131. Chen, F., Ge, W., Guo, L., He, X., Li, B., Li, J., et al. (2009a). 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. Chen, J., Yang, N., Ge, W., & Li, J. (2009b). Modeling of regime transition in bubble columns with stability condition. Industrial & Engineering Chemistry Research, 48, 290–301. Chen, J., Yang, N., Ge, W., & Li, J. (2009c). Computational ﬂuid dynamics simulation of regime transition in bubble columns incorporating the Dual-Bubble-Size model. Industrial & Engineering Chemistry Research, 48, 8172–8179. Dong, W., Wang, W., & Li, J. (2008). A multiscale mass transfer model for gas–solid riser ﬂows: Part 1—Sub-grid model and simple tests. Chemical Engineering Science, 63, 2798–2810. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman lectures on physics Boston: Addison-Wesley. Ge, W., Chen, F., Gao, J., Gao, S., Huang, J., Liu, X., et al. (2007a). Analytical multi-scale method for multi-phase complex systems in process engineering—Bridging reductionism and holism. Chemical Engineering Science, 62(13), 3346–3377. Ge, W., Guo, L., Jiang, Y., & Li, J. (2007b). A multi-layer direct-link cluster system for particle simulation. China Patent Application 200710099551.8. 2007-05-24. Ge, W., & Li, J. (2002). Physical mapping of ﬂuidization regimes—The EMMS approach. Chemical Engineering Science, 57(18), 3993–4004.

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