Focusing on mesoscales: from the energy-minimization multiscale model to mesoscience

Focusing on mesoscales: from the energy-minimization multiscale model to mesoscience

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ScienceDirect Focusing on mesoscales: from the energy-minimization multiscale model to mesoscience Jinghai Li , Wei Ge, Wei Wang, Ning Yang and Wenlai Huang Mesoscale phenomena represent a common challenge in chemical engineering. This article reviews three decades of related research at IPE, CAS, spanning from the energyminimization multiscale (EMMS) model specific for gas–solid fluidization to the EMMS principle, which is probably general for all mesoscale problems. This review focuses on elucidating the following questions: Why are mesoscale problems challenging? Is there a common governing principle for mesoscale behavior? Could a common principle allow more accurate and efficient simulation of chemical processes? Finally, the concept of mesoscience is discussed, based on the potential generality of the EMMS principle. Address State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering (IPE), Chinese Academy of Sciences (CAS), Beijing 100190, PR China Corresponding author: Li, Jinghai ([email protected])

Current Opinion in Chemical Engineering 2016, 13:10–23 This review comes from a themed issue on Reaction engineering and catalysis Edited by Theo Tsotsis and Marc-Olivier Coppens 2211-3398/# 2016 Elsevier Ltd. All rights reserved.

The concept of mesoscales The prefix ‘meso’ originates from the ancient Greek word mesos, meaning ‘middle’ or ‘in between’. When studying problems or processes, it is common to consider a ‘system’ as consisting of a large number of ‘elements’. The system is also subject to influences at a boundary defined between the system and its surroundings. The word of mesoscale is not an absolute physical size, but a relative concept to describe phenomena and processes that manifest between element and system scales. These scales could be at different levels of the physical world in different physical dimensions [1]. The mesoscopic scale discussed in physics is just one example of a mesoscale. A complete chemical process usually involves three different levels, as illustrated in Figure 1. Each level is multiscale with respective complexities at the mesoscales Current Opinion in Chemical Engineering 2016, 13:10–23

between their element scales and system scales [2]; for example, atomic/molecular assembly at the material level, particle clustering at the reactor level, and process synthesis superstructure [3] at the factory level. These three mesoscales all feature dynamic heterogeneous structures, and strongly influence the behavior of systems, not only at respective levels, but also as part of the whole process. Because the systems being studied likely manifest with multilevel physics, it is important to consider the level-specific nature of mesoscale phenomena. Otherwise, two or more mesoscales at different levels could become blurred [1], leading to confusion and complexity during the study of their respective governing rules. Chemical engineers and scientists work at different levels of a chemical process, leading to disciplines such as chemistry, chemical engineering, and process system engineering, as shown in Figure 1. Researchers working at all levels, on different elements and systems, recognize the common challenge of understanding dynamic mesoscale structures. Correlating element properties with system behavior is a common focus at each level. However, there has not been any substantial breakthrough in understanding these relationships for a long time, and this lack of understanding now represents a barrier to further development in chemical engineering. Because of missing links at these mesoscales, chemical engineers must try to establish the correlation between elements and systems by coarse-graining approaches based on experimental data and assumptions. When using such averaging methods, we are working on mesoscale issues; however, we have in fact overlooked consideration of the principles that govern mesoscales. Without a better understanding of each of the three mesoscales, advances in chemical engineering will be limited. There has hitherto been no general theory to describe mesoscale structures [4]. Therefore, it is important for chemical engineers to look for new strategies to analyze mesoscale phenomena. This has motivated our studies toward solving specific problems first, then, trying to deduce general principles that may explain mesoscale problems. Our research progressed from the energy-minimization multiscale (EMMS) model [5] designed specifically for gas–solid flow to a general concept of mesoscience, which may encompass all mesoscale problems.

The EMMS model for gas–solid fluidization Fluidization is a unit operation applied widely in different industries. However, the scale-up of fluidized bed reactors

Focusing on mesoscales: from EMMS model to mesoscience Li et al. 11

Notation A: objective function of mechanism A B: objective function of mechanism B CD: effective drag coefficient for a particle, dimensionless CD,EMMS: EMMS drag coefficient for a particle, dimensionless CD0: standard drag coefficient for a particle, dimensionless dcl: cluster diameter, m dp: particle diameter, m f: volume fraction of dense phase, dimensionless Fi: ith constraint function g: gravitational acceleration, m s2 Nst: mass-specific energy consumption for suspending and transporting particles, J kg1 s1 r: radial coordinate, m R: radius, m U: superficial velocity, m s1 Uc: superficial fluid velocity for dense phase, m s1 Uf: superficial fluid velocity for dilute phase, m s1 Umf: superficial gas velocity at minimum fluidization, m s1 Us: superficial slip velocity, m s1 Wst: volume-specific energy consumption for suspending and transporting particles, J m3 s1 xi: ith structural variable X: structural variable vector Greek letters e: voidage, dimensionless emax: maximum voidage for formation of clusters, dimensionless nf: fluid kinematic viscosity, m2 s1 r: density, kg m3 rf: fluid density, kg m3 Subscripts c: dense phase f: dilute phase g: gas phase i: mesoscale interphase mf: minimum fluidization p: particle pc: dense-phase particle pf: dilute-phase particle s: solid phase Others ¯ : cross-sectional average Acronym CFB: circulating fluidized bed CFD: computational fluid dynamics CPU: central processing unit DPM: discrete particle method EMMS: energy-minimization multi-scale FD: fluid-dominated GPU: graphics processing unit PD: particle-dominated PFC: particle-fluid compromising s.t.: subject to VPE: virtual process engineering

is challenging because of dynamic mesoscale structures. Coexistence of dense particle-rich and dilute gas-rich phases is a typical occurrence caused by particle clustering phenomenon in circulating fluidized beds (CFBs). Thus, analysis of gas–solid interactions should consider the existence of clusters. In particular, computational fluid dynamics (CFD) cannot be used effectively without

accounting for the clustering phenomenon within computational grids [5], because of the large difference between the drag coefficients in the dense and dilute phases [6,7], as shown in Figure 2. If averaging approaches are used to deal with such heterogeneity in the grids, different mechanisms become blurred, and the drag coefficients in different phases will be distorted [5,8]. Thus, commercial CFD codes based on average models are poor at simulating heterogeneous multiphase flows, and need to be improved. As illustrated in Figure 3, a gas–solid fluidization system possesses heterogeneous structures, roughly consisting of dense and dilute phases with interaction at their interface. Various parameters are involved at three scales [5,9]:  Global scale: operating conditions (superficial gas velocity Ug and particle velocity Up) and material properties (density rp and diameter dp for particles, and viscosity nf and density rf for the fluid) are specified; average voidage e needs to be deduced through calculation.  Particle scale: individual particles interact with the gas with different parameters in the dense and dilute phases (here, we assumed uniformity in both dense and dilute phases); that is, voidage ef, superficial particle velocity Upf and superficial fluid velocity Uf for the dilute phase and corresponding parameters ec, Upc and Uc, respectively, for the dense phase.  Mesoscale: cluster volume fraction f and cluster diameter dcl are used to describe the interaction between the dense and dilute phases. Here, dcl only represents a simplified and equivalent measure to the characteristic particle-aggregated structure in the system, although clusters are subject to complicated dynamic changes in shape, dimension or size distribution. More delicate description of clusters requires, of course, further study or improvement.

This gives a total of eight parameters to be defined X = {ef, Upf, Uf, ec, Uc, Upc, f, dcl} (shown in red in Figure 3), which may allow other parameters to be deduced. However, only six conservation equations are available, as summarized in Figure 3. This calls for additional conditions besides conservation equations because the number of variables is larger than that of equations available. In fact, when dynamic structures are involved, their stability conditions must always be determined. While looking for these additional conditions, we recognized the need to analyze dominant mechanisms affecting the system stability, in addition to structure resolution, to identify the steady state from all possible structures satisfying conservation laws. We believe that when a system is dominated jointly by two mechanisms, it is Current Opinion in Chemical Engineering 2016, 13:10–23

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Figure 1

Three mesoscales


Material and interfacial structure

Heterogeneous flow structure

Process synthesis superstructure

Mesoscale 1

Mesoscale 2

Mesoscale 3


Boundary scales

Boundary scales:

Multiscale: Molecule/Atom

Multilevel: Disciplines:



Particle aggregate

Unit operation

Process synthesis superstructure





(Chemical technology)

(Process development)

(System integration and optimization)


Chemical engineering

Process system engineering Current Opinion in Chemical Engineering

Three levels (material, reactor and factory) and corresponding mesoscales of chemical processes [2]. Modified with permission.

Figure 2

Actual Multiscale structure

Averaging approach Uniform structure

Dilute phase Fluid-dominated CDf ≈102 Dense phase Particle-dominated 105 < CDc < 106

Mechanisms blurred Drag coefficients distorted

Homogeneous phase CD = ?

Interface Particle-fluid compromise 1.0 < CDi < 102 Current Opinion in Chemical Engineering

Drag coefficients CD in different phases in fluidization. Current Opinion in Chemical Engineering 2016, 13:10–23

Focusing on mesoscales: from EMMS model to mesoscience Li et al. 13

Figure 3

Drag coefficient:

Drag coefficient: –4.7


CDf = CD0f εf

CDc = CD0c εc

Slip velocity:

Slip velocity: Usc = UC –

Particle scale


Usf = Uf –


Voidage: εc Gas velocity: Uc Particle velocity: Upc

εfUpc 1–εf

Voidage: εf Gas velocity: Uf Particle velocity: Upf

Dense phase

Dilute phase

Drag coefficient: CDi = CD0i (1–f )

Resolution Structure


Slip velocity:

Meso scale

Usi = Uf –

εfUpc 1–εf

Resolution (1–f)

Dominant mechanisms Average voidage:

Cluster diameter: Cluster fraction:

1. Force balance in dense phase:




2. Force balance in dilute phase:


Wst = min

Operating condition: Gas viscosity: vf Gas density: ρf Particle diameter: dp Particle density: ρp

Material property

3. Pressure balance between two phases:

Global scale

Drag coefficient:

Compromise in Competition

4. Continuity of gas: 2

5. Continuity of solids:

(1–ε)U 5

Slip velocity: εU p 1–ε

6. Cluster diameter:

Conservation equations

The EMMS Model

Stability condition

Current Opinion in Chemical Engineering

Physical concept and formulation of the EMMS model. Detailed definitions and formulations of all parameters can be found in Ref. [5].

critical to first analyze the respective variational criteria for all involved dominant mechanisms and then evaluate their compromise in competition. For example, for gas–solid fluidization, two dominant mechanisms are the extremal tendencies for gas and solids. The former can be expressed as energy consumption for suspending and transporting particles per unit volume Wst = min, while the latter can be described as average voidage e = min [7]. The compromise in competition between the dominant mechanism of particles described by e = min, and that of the gas described by Wst = min, defines the stability condition of the system, and correlates the parameters at different scales. That is, the variational criteria for the EMMS model can be expressed as [7]:   W st min (1) e which was integrated into a single variational criterion by analyzing the physical relationship between them; that is, the energy consumption for suspending and transporting particles per unit mass of particles Nst = (Wst/ ((1  e)rp)) = min [5,9], leading to the EMMS model.

Using the EMMS model, eight parameters at three scales can be solved and regime transitions (such as bubbling, turbulent, fast and dilute transport) with different transport behavior can be defined. Here, the compromise between e = min and Wst = min plays an important role in determining system behavior. Depending on the extent of the relative dominance of the two mechanisms, three regimes are generally possible, subject to operating conditions. As summarized in Figure 4 and detailed in [10,11], the fluid-dominated (FD) state features Wst = min, while the particle-dominated (PD) state is characterized by e = min. Changing the relative dominance between Wst = min and e = min causes the particle-fluid compromising (PFC) states to form. The three regimes are characterized by distinct structures:  PD regime: When gas velocity is low, the influence of gas on system structure is negligible, so the system is exclusively PD; that is, e = min while Wst = min is suppressed.  PFC regime: With increasing dominance of gas over solids (Wst = min over e = min), there is a critical Current Opinion in Chemical Engineering 2016, 13:10–23

14 Reaction engineering and catalysis

Figure 4

FD state is suppressed and PD state is realized completely

PD state and FD State appear alternately with respect to space and time

PD state is suppressed and FD state is realized completely

1.00 0.89


0.78 0.67 0.56 0.45




PD regime


PFC regime

Wst min ε

ε = min (Fixed bed)

(Fluidization) Regime transition from PD to PFC

t FD regime

Wst = min (Dilute transport) Regime transition from PFC to FD

Dominance of fluid over particles (Incerasing gad velocity) Current Opinion in Chemical Engineering

Regime transitions and mesoscale complexity described by the EMMS model for gas–solid fluidization. FD is fluid-dominated, PD is particledominated, and PFC is particle-fluid compromise. Experimental data from [12].

condition at which e = min loses its absolute dominance over Wst = min and has to compromise with Wst = min, leading to the formation of an FD state, which coexists with the PD state. Complex dynamic changes in this regime, with respect to time and space, reflect the appearance of mesoscale phenomena. As the gas dominance increases further, the PD state is gradually suppressed while the FD state is intensified, indicated by the volume fraction changes of the states featuring e = min and Wst = min, respectively. The extent to which these two mechanisms are realized (represented by the magnitudes of the corresponding states) is illustrated in the diagrams at the top of Figure 4. The fraction of the PD state and its realization extent decrease while those of the FD state increase with increasing dominance of Wst = min over e = min. Because of the dynamic changes induced by the compromise in competition between e = min and Wst = min, this regime is characterized by mesoscale phenomena, high complexity and dissipation.  FD regime: When the dominance of Wst = min reaches another critical value, e = min is completely suppressed Current Opinion in Chemical Engineering 2016, 13:10–23

and Wst = min is fully realized, so that the FD state dominates the system, producing a uniform structure in the idealized case; as a result, mesoscale phenomena nearly disappear. The transition between the PD and PFC regimes is defined by the minimum fluidization velocity Umf, while the transition between the PFC and FD regimes is determined by analyzing either the evolution of relative dominance between particles (e = min) and fluid (Wst = min) [7,13] or the extremal behavior of Nst [14]. While greater complexity and diversity of regime transitions may occur when the relative dominance between different mechanisms changes for various systems in different fields, the three regimes (PD, PFC and FD) discussed above are general and governed by the principle of compromise in competition, which we introduce later in more detail. This principle is an important concept obtained from the EMMS model. Initially, the model had to be solved using non-linear optimization programs, making it difficult to achieve

Focusing on mesoscales: from EMMS model to mesoscience Li et al. 15

convergence to the steady state [9]. Later, the EMMS model could be easily solved numerically to identify all regime transitions [14]. An online solver of the EMMS model can now be accessed at: emmsmodel.php. It should be noted that the correlation of cluster diameter (Eq. 6 in Figure 3) needs to be improved to remove the uncertainty from emax based on experimental data [15]. Though efforts have been made [16,17], this problem is still unsolved, calling for fundamental research on the dynamic formation and dissolution of clusters. This is currently a weakness of the EMMS model.

EMMS drag A direct output of the EMMS model is the EMMS drag considering the heterogeneity in grids CD,EMMS, which can be deduced from the drag coefficients of the dense phase CDc, dilute phase CDf and interphase CDi [6] as shown in Figure 3. It has been applied to correct the average drag in the conventional two-fluid model (TFM) based on the assumption of homogeneity within computational grids. To aid the inclusion of CD,EMMS into the TFM, Yang et al. [18] introduced acceleration terms for particles into the EMMS model, and then determined a correction factor to transform the homogeneous drag into CD,EMMS. Then, CD,EMMS was extended to the sub-grid level [19], producing a matrix of correction factors related to both local slip velocity and voidage in any CFD grid. Later, CD,EMMS was also integrated with multiphase discrete approaches [20–23]. Details of CD,EMMS are presented in [6,11], and its applications in CFD are reviewed in [11].

Extension of the EMMS model In addition to CD,EMMS, another important concept of the EMMS model is the strategy it follows to define the variational criteria for the steady states of mesoscale structures and processes; namely, the compromise in competition between different dominant mechanisms. This principle was originally proposed as a hypothesis, and has since been verified by experiments, numerical simulations and extension to different systems.  Extension to gas–liquid systems: Following the strategy of the EMMS model for gas–solid systems, a stability condition was proposed for gas–liquid systems [24]. Then, a dual-bubble-size model was established by resolving a system into small-bubble and large-bubble phases governed by different dominant mechanisms. This model readily predicts the structures in gas–liquid systems [25] and is unique in predicting the shoulder phenomenon, which is similar to choking in gas–solid systems.  Extension to turbulent flows: The flow structure is resolved into a laminar component dominated by

viscosity and a turbulent component dominated by inertia. The whole flow structure is governed by the compromise in competition between the minimum of viscous dissipation and the maximum of total or turbulent dissipation. This model has been validated by its reasonable prediction of radial velocity profiles in pipe flows [26] and detailed vortex structures in liddriven cavity flow [27].  Extension to other systems: The successes of the EMMS model and its extension to gas–liquid and turbulent flows encouraged further efforts to investigate different systems such as gas–liquid–solid [28], proteins [29], granular flow [24], emulsions [24], material preparation [30], catalysis [31] and a reaction-diffusion system (WL Huang, JH Li, unpublished data). All of these systems supported the strategy followed by the EMMS model. Thus, all of these complex structures could be resolved into two components dominated by different mechanisms. These dominant mechanisms compromise as they compete, leading to dynamic structures with two different components that appear alternately with respect to both space and time.

The EMMS principle When we recognized that all the systems we have studied followed the principle of compromise in competition between dominant mechanisms, we realized that the strategy followed in the EMMS model is general to a certain extent. Therefore, it was proposed that the EMMS principle could generally describe the governing principle of compromise in competition for mesoscale phenomena. All nonequilibrium complex systems, such as those at each level of chemical engineering (see Figure 1), consist of element scales, system scales and mesoscales in between. Because of the inherent heterogeneity in these systems, conservation laws alone are not sufficient to define the system behavior; stability conditions defined by variational criteria are necessary to correlate the parameters of different scales to define their steady states. In addition, such complex systems must be jointly governed by at least two dominant mechanisms. Consider mechanism A = extremum1 and mechanism B = extremum2 as a general case to simplify later discussion. If more than two mechanisms are involved, it is likely that these mechanisms can be grouped into two dominant mechanisms [1], or considered separately as individual components that compromise. One mechanism drives the system to one state and the other forces the system to the other state. Three possible regimes are found by changing the dominance of B over A, that is, B-dominated, B–A compromise and A-dominated, as summarized in Figure 9 and exemplified in Figure 4 with Wst = min and e = min being mechanisms A and B, respectively. The inherent complexity of mesoscale phenomena originates from the compromise in competition between these two mechanisms, which gives rise to spatiotemporal structural Current Opinion in Chemical Engineering 2016, 13:10–23

16 Reaction engineering and catalysis

evolution; that is, the coexistence of the A-dominated and B-dominated states in an alternating manner with respect to both time and space [10,32]. Therefore, the EMMS principle is physically expressed as a compromise in competition between dominant mechanisms, and mathematically formulated into a multi-objective variational problem [1,10,11] as follows: Structural variables : X ¼ fx1 ; x2 ; . ..xn g  Compromise between AðXÞ Extremalizing competing mechanisms : BðXÞ s:t: Conservation laws : Fi ðXÞ ¼ 0; i ¼ 1; 2; . . .; m ðm < nÞ

(2) Here, ‘competition’ means respective extremal tendencies of A and B, while ‘compromise’ refers to the mutual constraint between them.

Verification of the EMMS principle Experiments both in the literature and our laboratory support the EMMS principle. For gas–solid fluidization, the EMMS model reveals the coexistence of dense and dilute phases, and this structure disappears suddenly at a critical point called choking, which has been confirmed experimentally [5] and verified numerically [10,32] by using pseudo-particle modeling [33]. For gas–liquid bubbling flow, the EMMS model predicts dual bubble size in the A–B compromising regime [25], as observed experimentally [34]. For general verification, numerical approaches were also used to generate dynamic structures of, emulsion, granular flow, foam drainage, turbulence, micro-gas–liquid flow and gas–liquid–solid flow [24]. Using these structures, the proportions of each variational criterion acting on the system were calculated to see if they tended to extrema. All simulations confirmed the applicability of the EMMS principle to these systems [11].

Application of the EMMS principle The EMMS principle has been used to study complex systems, solving various industrial problems and upgrade CFD simulations:  As a principle in fundamental research: In addition to its application to flow systems, the EMMS principle has been used to study other complex systems such as the dynamic structures of proteins [35], material preparation [30], where the diffusion rate compromises with the reaction rate to shape materials. Recently, the EMMS principle has been used to investigate reactiondiffusion systems and catalysis [31] (WL Huang, JH Li, unpublished data). The EMMS principle has also been applied to determine distribution functions in statistical approaches [36,37].  Upgrading CFD: As outlined in Figure 5, the EMMS model has been applied to CFD in two steps. In the first step, the steady-state EMMS model is used at the global reactor scale such that the drag counterbalances the gravity in both dense and dilute phases. That produces the initial distribution of the whole system, including radial and axial distributions, with which the simulation is sped up by starting with an initial state as close as possible to the final steady state. On the basis of the initial distribution, the TFM simulation starts to produce the average parameters in each computational cell. Then, the transient EMMS model is used in the second step to modify the average drag by considering the heterogeneity in any computational cell. The EMMS drag CD,EMMS is then fed back into the TFM to produce the more accurate flow field. Figure 6 shows that the first step substantially shortens computational time, and the second step markedly improves the accuracy of simulation. In addition, the

Figure 5

EMMS Model

Step 1:

Step 2:

Steady-state modeling of whole system

transient simulation in local cell

Flow Field Boundary Condition Initial Distribution


Average Parameters in a Cell

Decomposition into Heterogeneous Structure in a Cell


Operating Condition Current Opinion in Chemical Engineering

Application of the EMMS model in CFD simulation [18,19,38]. Current Opinion in Chemical Engineering 2016, 13:10–23

Focusing on mesoscales: from EMMS model to mesoscience Li et al. 17

Figure 6


Solid flux (kg/(m2s))


Traditional initial distribution without EMMS drag


Improvement of accuracy

Traditional initial distribution + EMMS drag




Initial distribution set by EMMS + EMMS drag

0 -5


5 Time saved




Time(s) Current Opinion in Chemical Engineering

Acceleration and improvement of CFD simulations using the EMMS model. Data from [18,38].

feasibility of using coarser computational grids when employing CD,EMMS allows the simulation capability to be extended so that industrial reactors can be simulated at an acceptable computational cost. CD,EMMS has been widely used to modify drag calculations in both commercial and in-house codes, as reviewed in [11]. The integration of CD,EMMS with Barracuda VR1 is commercially available, and its user-defined functions for CFX1, MFIX, OpenFOAM and Fluent1 are also available through EMMS1 or can be generated by users themselves.  Industrial application: Because of the improved predictability and extended capability supplied by the EMMS drag in CFD simulations of multiphase systems, solving industrial problems has become feasible. Cooperative projects have been established with many companies; for example, TOTAL for extending the EMMS principle to liquid–solid polymer systems; BASF for liquid–liquid emulsification systems; BP for simulation of gas–liquid mixing tanks and bubble column systems; Unilever for aerated processes in food processing; Synfuel China for Fischer-Tropsch synthesis; PetroChina for slurry bed reactors; SINOPEC for

fluid catalytic cracking processes; ALSTOM for CFB boilers; and JINMEI for coal gasifiers.

Perspective 1: multiscale computational paradigm based on the EMMS principle The EMMS principle defines the relationship between parameters at different scales, and formulates the stability conditions for mesoscales and system scales [39], as summarized in Figure 7, taking gas–solid fluidization as an example:  System scale: Computation is governed by the global stability condition, operating conditions and boundary conditions, the radial profiles of different parameters are defined by the cross-sectional stability condition N st¯ ¼ min under specified boundary and operating conditions; that is, the radial profiles are subject to N st¯ [39]. The stability conditions define a global effect governed by the compromise in competition between different dominant mechanisms so that different regimes of operation and their transitions (typically reflective, even sudden changes) can be defined.  Mesoscale: Computation is dominated by the mesoscale stability condition and the interaction between grids. Current Opinion in Chemical Engineering 2016, 13:10–23

18 Reaction engineering and catalysis

Figure 7 System stability

Nst =

Subject to external constraints affecting the compromise between two dominant mechanisms

Mesoscale stability

R 2 ∫ Nst (r)(1 – ε(r))rdr = min R2 (1 – ε– ) 0

Nst(r0) = min

Subject to the dominant compromise in competition between two mechanisms with the effect of interaction between grids

f(r0), εc(r0)

Nst(r1) = min

1 – f(r0), εf(r0)

f(r1), εc(r1)

Nst(rn) = min


1 – f(r1), εf(r1)


f(rn), εc(rn) 1 – f(rn), εf(rn)

Element interaction Approximately formulating the interactions between individual particles and the fluid assuming uniformity in both the dense and dilute phases for simplification

dcl(r0) Ugc(r0)


dcl(r1) Upc(r0) Ugf(r0) Ug(r0)

Upf(r0) Ugc(r1)


Upc(r1) Ugf(r1) Ug(r1)



dcl(rn) Ugc(rn)

Upc(rn) Upf(rn) Ugf(rn) Ug(rn)

Up(rn) r


R Current Opinion in Chemical Engineering

Three-scale simulation of the radial hydrodynamics of CFB risers using the EMMS model. Modified from [11,41].

The stability condition Nst(r) = min [39] is used to formulate the bulk structural characteristics and the interaction between the two phases in grids, as well as the interactions between grids. The statistical characteristics of structures (typically heterogeneous and dynamic) are defined.  Element scale: Computation mainly addresses the interaction at the element scale. Particle-fluid interaction is approximated and formulated using a two-phase model; that is, the dense and dilute phases are governed by fluid and particle interactions in each phase, respectively. The stability conditions cease to function as a whole, and the dominant mechanisms start to appear individually and alternately in space and time. At this scale, the systems display a largely discrete nature, where short-range, local interactions between elements dominate. This model yields a reasonable prediction of the radial distribution of particle velocity using experimental data for particle concentration and gas velocity [39]. Later on, profiles of all parameters were predicted directly from operating conditions, geometries and material properties [40]. Considering the generality of multiscale structures and the inherent logic in different systems, the EMMS principle can be developed into a multiscale computational paradigm featuring scale-dependent computation, communication and storage, as shown in Figure 7. Current Opinion in Chemical Engineering 2016, 13:10–23

This means that simulation of complex systems should be implemented on different scales using different numerical methods with communication between different scales. Therefore, a multiscale architecture, constructed from multiscale hardware that is consistent with the EMMS paradigm in both structure and logic, is needed to achieve structural and logical similarity between the simulated system, physical model, numerical method and computing hardware. This will optimize computational capability, storage capacity and communication expense. In addition, instead of directly tracking each individual element, computation could start with global distribution, then resolve mesoscale structure, and finally track dynamics at the element scale. To confirm the advantages of the EMMS paradigm, a supercomputer with a peak performance of 1.0 Pflops (see the left of Figure 8) has been constructed using commercially available hardware. This supercomputer contains several central processing units (CPUs) dedicated to the system scale, a large number of graphics processing units (GPUs) for the element scale and a moderate number of CPUs and GPUs for the mesoscale [41,42]. The possibility to realize real-time simulation has been also explored by establishing a virtual process engineering (VPE) platform [43], as shown in Figure 8. Although real-time simulation is still not possible, recent progress is promising. In 2011, it took 1 week to simulate the real process of 40 s for the full-loop of a

Focusing on mesoscales: from EMMS model to mesoscience Li et al. 19

Figure 8

Current Opinion in Chemical Engineering

Version 1.0 of VPE: On the right is an experimental unit. A screen of the same height as that of the unit is shown in the middle. A computer controls both the experiment and simulation to allow online comparison. Modified from [11].

dimensional CFB with diameter of 10 cm and height of 6 m [43]. Recently, the simulation was upgraded from the TFM to discrete approaches, and a real process of more than 100 s was simulated within 1 week, for the same CFB [44]. A visible level of online and real-time demonstration was realized for a two-dimensional simulation [21,45] of the ETH-CFB system in [46]. Available CPUs are suitable to consider the complexity at the system scale, while GPUs are efficient for parallel computation at the element scale. However, the development of specific processing units is required to perform computation at the mesoscale, where particular features are needed for high-efficiency computation [41]. We predict that virtual reality in chemical engineering could be enabled if the EMMS paradigm can be implemented in terms of physical modeling, numerical methods, and computer construction. This is far beyond our capability, and calls for interdisciplinary collaboration between different fields.

Perspective 2: from the EMMS principle to mesoscience Recognizing the possible generality of the EMMS principle and its potential to enable real-time computation, we proposed the concept of mesoscience to further explore the common principle underlying all mesoscale problems [1,11,47]. However, it might not be feasible for chemical engineers to directly formulate a general theory for all mesoscales. Instead, we should collect more evidence by studying specific mesoscale problems in engineering to

gradually confirm or extend this generality. We should extend gradually from specificity to generality, because the diverse and complex nature of mesoscale problems is currently limiting the capabilities of theoretical studies, particularly for chemical engineers. The EMMS principle reveals that the complex dynamic structures at mesoscales are governed jointly by different dominant mechanisms, and can be formulated as a multiobjective variational problem. We need to further confirm the following two points: (1) Whether variational criteria derived from dominant mechanisms for different systems, currently treated individually from system to system, can be unified; (2) Whether it is possible to integrate two or more dominant mechanisms for a specific system into a single variational criterion. On the one hand, the EMMS principle needs more evidence to further confirm the generality of compromise in competition. On the other hand, the two points above need to be clarified to extend its generality and allow easier utilization. This motivates our proposal on the concept of mesoscience. Regarding the second point, the EMMS principle has given the answer by clarifying the three-regime feature of nonequilibrium systems, as summarized in Figure 9. That is, when a single dominant mechanism governs a system exclusively, such as an A-dominated or B-dominated regime (see Figure 9), a single variational criterion is sufficient. When two or more dominant mechanisms are involved, such as for the A–B compromising regime, Current Opinion in Chemical Engineering 2016, 13:10–23

20 Reaction engineering and catalysis

Figure 9




A-B compromise Element 1


A1 B1 Mesoscale 1





B2 System 1 Element 2

Mesoscale 2



Level 1

Level 2

System 2 Element 3 ...

Level ...

Level-Specific Current Opinion in Chemical Engineering

Level-specific and regime-specific nature of compromises in competition at mesoscales.

it is difficult to deduce a single variational criterion directly because of the opposing tendencies of different dominant mechanisms. Compromise in competition between two variational criteria derived from two different mechanisms has to be taken into account. This may explain why the nonequilibrium thermodynamics of dissipative structures are difficult to explore directly using a single general variational criterion [4], and why aspects of this research area are still under debate. Neglecting the regime-specific feature and the principle of compromise in competition is the cause. One area of debate [48] is whether the variational criterion for nonequilibrium systems is the minimum [49] or maximum [50] of dissipation (usually equivalent to entropy production rate). This is related to the first point to a certain extent. Considering the EMMS principle, we predict that these two variational criteria, governing separate dominant mechanisms, are both involved in shaping the structures of complex systems. Either of the two alone may be only designated as either an A-dominated or Bdominated regime governed exclusively by a single mechanism. However, in the A–B compromising regime, these two functions have to compromise with each other because they are represented by driving forces in different directions of structural evolution. That is, the minimum dissipation tends to drive the system to one state, while the maximum dissipation drives the system toward the other. It is the compromise in competition between these two opposing variational criteria that allows realization of their respective extremal tendencies, either at the same time at different locations or at the same location at different time, leading to the complexity of mesoscale dynamic structures. Current Opinion in Chemical Engineering 2016, 13:10–23

There is some evidence that supports this prediction. A single extremal dissipation can be observed in both the Adominated and B-dominated regimes, but not in the A–B compromising regime. For instance, in turbulent flows, the viscous dissipation tends toward a minimum, which compromises with the maximum of turbulent dissipation [26,27]. Our recent work on a reaction-diffusion system also confirmed this deduction in which maximization and minimization of entropy production compromise with each other in the A–B compromising regime (WL Huang, JH Li, unpublished data). Gas–solid systems also show the same such that e = min (representing the maximum dissipation) compromises with Wst = min [6] (corresponding to the minimum dissipation). Therefore, these two opposing variational criteria should be formulated separately. They drive complex systems toward different directions of evolution via different dissipative mechanisms. Eventually, two extrema have to compromise in their competition to reach their respective relative extremal values with a mutual constraint, although these values are different from those without compromise. A global analysis of dissipation without distinguishing one mechanism from another is not sufficient to correctly formulate the respective dissipations and analyze their compromise because of the mechanismdependent or regime-specific feature of dissipation. Although the generality of the compromise in competition between the mechanisms related to minimum of dissipation and that for maximum of dissipation needs to be evidenced further, its applicability is confirmed, at least, for the above three cases. It can be deduced that searching a single variational criterion in term of entropy production (or dissipation) is right for either A– or B–dominated regime, as practiced

Focusing on mesoscales: from EMMS model to mesoscience Li et al. 21

in thermodynamics, but not likely in the A–B compromise regime due to multiple dissipative mechanisms with different extremum behaviors. Even if a single extremal function does exist, it should not be in term of total dissipation (or entropy production). The current debate mentioned above may be ended by considering the principle of compromise in competition so that different variational criteria can be unified by distinguishing three regimes (ref. Figure 9). The limited amount of evidence currently available is not sufficient to verify the generality of the coexistence and compromise between the minimum and maximum of dissipation in complex systems. We need to study more systems at different levels of various fields to confirm the real situation due to the level-specific nature of complex systems. The regime-specific nature and the level-specific nature, as summarized in Figure 9, are critical to understand mesoscale phenomena in different fields. A mesoscience program has been launched by the National Natural Science Foundation of China to finance researchers from different fields focusing on the first two levels of mesoscale problems in Figure 1; that is, the material and the reactor levels [51]. On the basis of our three decades of work on the principle of compromise in competition to explain different mesoscale problems, a possible framework [10], the EMMS principle, was proposed, and then extended toward mesoscience [1,11]:  Identifying the level and regime: Because the dominant mechanisms and corresponding variational criteria are both level-specific and regime-specific, as shown in Figure 9, it is crucial to identify the element, system, and system boundary correctly. On the other hand, the operating regime of the system should be determined to evaluate if a single variational criterion is sufficient.  Identifying state variables: State variables defining the behavior of the studied system should be properly identified, particularly, those describing the mesoscale structure should be included if the system is in the A–B compromising regime.  Formulating conservation laws: Parameters are correlated at different scales and interactions are formulated between different scales under the specified operating conditions, material properties and boundary conditions. All conventional theories could be applied at this step.  Establishing variational criteria: The regime-dependent nature of the system should be identified to reveal concrete dominant mechanisms on the basis of conservation formulations, from which corresponding variational criteria can be formulated for different regimes. It is critical to note that extremal behaviors of dissipations are very much subject to whether they are with respect to unit volume or unit mass in the system.

 Solving multi-objective variational problem: Integrating the conservation formulations and variational criteria results in a multi-objective variational problem. In the case of an A-dominated or B-dominated regime, solution of the formulation is simple because there is a single variational criterion. However, for the A–B compromising regime, it is challenging to deal with two or more variational criteria, and requires mathematical expertise. In addition, analyzing the physical and chemical processes and the related mechanisms involved will help to optimize the final variational criteria by searching for a reasonable combination of them or sometimes integrating them into a single function. It is evident that mesoscience gives a new perspective on currently challenging issues at mesoscales [52], to which all conventional knowledge is applicable; however, the principle of compromise in competition must be involved. Further experimental evidence and integration of knowledge from different fields are critical to verify this principle and its generality, such as the design of structured products with multiple components, formulation engineering and the nature-inspired chemical engineering [53]. In return, the research in these fields will benefit from mesoscience.

Conclusions This review summarizes the consecutive developments on the EMMS method, from a specific model to a possible general principle with conceptual updates based on the newest understandings. Three decades of research on different mesoscale problems has recently revealed the importance of mesoscience in advancing chemical engineering. Although we are confident in the utility of mesoscience for successfully solving complex problems at both fundamental and industrial levels, we have yet to confirm the existence of a general principle, and even to modify the EMMS model itself. No single discipline is capable of addressing this challenge alone, and interdisciplinary collaboration is necessary [52,54]. Engineering disciplines can collect evidence by studying actual problems while theoretical disciplines can aid by formulating generality. Exploring mesoscience is a great opportunity to expand understanding in different disciplines. A new paradigm of scientific research in the coming decades is expected to open a new era of science and technology. For chemical engineering, virtual reality will be a new research tool, in which the mesoscale approach will play an important role not only in physical modeling, but also in computation.

Acknowledgements The authors thank their colleagues at the EMMS Group for their long-term cooperation and contributions to the EMMS model previously and mesoscience recently. In particular, we thank Drs. Junwu Wang, Limin Wang and Xinhua Liu for their contributions to this article, and Drs. Xiaowei Wang and Jian Wang for their help in the whole writing process. The aid of Drs. Yongsheng Han, Ying Ren, and Fanyong Meng in reading Current Opinion in Chemical Engineering 2016, 13:10–23

22 Reaction engineering and catalysis

the text and confirming related information is highly appreciated. The support of NSFC on the mesoscience program (91334000) titled: Mechanism and Manipulation at Mesoscales of Multi-phase Reaction Systems and the cooperation with industries, as listed in the text, are strongly appreciated.

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Li JH, Kwauk M: Particle-fluid Two-phase Flow: The Energyminimization Multi-scale Method. edn 1. Beijing: Metallurgical Industry Press; 1994. Original monograph on the EMMS model, open access: http://www. 8_5/qq2yhjzhto0x.pdf. 6.

Li JH, Chen AH, Yan ZL, Xu GW, Zhang XJ: Particle-fluid interacting in circulating fluidized beds. In Preprint of the 4th International Conference on Circulating Fluidized Beds. Edited by Avidan AA. AIChE; 1993:48-53.

7. Li JH, Kwauk M: Multiscale nature of complex fluid–particle  systems. Ind Eng Chem Res 2001, 40:4227-4237. Discussing the concept of compromise in competition. 8.

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