The mesoscale modeling approach

The term macroscale will be used to denote multiphase models that employ a hydro-dynamic description of the disperse phase. Such models are also called multi-fluid models (because the disperse phase is treated as an effective fluid), or Euler-Euler models. The name of the latter comes from the numerical treatment of the disperse phase (i.e. discretization on a fixed grid), as opposed to Euler-Lagrange models wherein the disperse phase is tracked in a Lagrangian framework as discrete entities. We should note that, in the 

Mesoscale Model Kinetic equation Euler-Lagrange models 

Macroscale Model Hydrodynamic description Euler-Euler models 

Mesoscale model Incorporates more microscale physics in closures 

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As discussed in Chapter 2, the one-particle NDF does not usually provide a complete description of the microscale system. For example, a microscale system containing N particles would be completely described by an A-particle NDF. This is because the mesoscale variable in any one particle can, in principle, be influenced by the mesoscale variables in all N particles. Or, in other words, the N sets of mesoscale variables can be correlated with each other. For example, a system of particles interacting through binary collisions exhibits correlations between the velocities of the two particles before and after a collision. Thus, the time evolution of the one-particle NDF for velocity will involve the two-particle NDF due to the collisions. In the mesoscale modeling approach, the primary physical modeling step involves the approximation of the A-particle NDF (i.e. the exact microscale model) by a functional of the one-particle NDF. A typical example is the closure of the colli-sionterm (see Chapter 6) by approximating the two-particle NDF by the product of two one-particle NDFs. 

Chapter 1 introduces key concepts, such as flow regimes and relevant dimensionless numbers, by using two examples the PBE for fine particles and the KE for gas-particle flow. Subsequently the mesoscale modeling approach used throughout the book is explained in detail, with particular focus on the relation to microscale and macroscale models and the resulting closure problems. 

It is meaningful to examine the relation between microscale model, mesoscale model, and micromodel. For reaction kinetics, microscale and mesoscale models adopt the same kinetics that based on element reaction system. For diffusion, mesoscale model embodies two diffusion mechanisms (one for micropores and another for mesopores and macropores), and microscale model considers one diffusion mechanism since it only has micropores. No diffusion was considered within the macropores. It is obvious that the mesoscale model possesses the same theoretical foundation as the microscale model, but its application scope has been enlarged compared to the microscale model. Therefore, it could be reliably used as a tool to derive some parameters, such as effective chemical kinetics and effective diffusion parameters, for macroscale model. In the section following, we discuss the method on how to link the microscale kinetics to the lumped macroscale kinetics via the mesoscale modeling approach. 

The total number of independent variables appearing in Fq. (4.32) is thus quite large, and in fact too large for practical applications. However, as mentioned earlier, by coupling Eq. (4.32) with the Navier-Stokes equation to find the forces on the particles due to the fluid, the Ap-particle system is completely determined. Although not written out explicitly, the reader should keep in mind that the mesoscale models for the phase-space fluxes and the collision term depend on the complete set of independent variables. For example, the surface terms depend on all of the state variables A[p ( x ", ", j/p" j, V ", j/p" ). The only known way to determine these functions is to perform direct numerical simulations of the microscale fluid-particle system using all possible sets of initial conditions. Obviously, such an approach is intractable. We are thus led to reduce the number of independent variables and to introduce mesoscale models that attempt to capture the average effect of multi-particle interactions. 

Recently, several groups have taken cell-level macroscale models a step further to investigate the electrochemistry through the thickness of the electrodes using the mesoscale electrochemistry approach [19, 27, 31]. In these models, no assumptions are made about a reactive zone for the electrochemical reactions instead, the electrochemistry is modeled through the thickness of the electrodes based on a mesoscale electrochemistry approach (Section 26.2.4.2) in which the explicit charge-transfer reactions [27] or a modified Butler-Volmer approach [19, 31] are modeled. This extends the effects of the electrochemical reactions away from the electrolyte interface into the electrodes. In these cell-level models, the electrochemistry is coupled to the local species concentrations, pressures, and temperatures, and provides a more detailed view into the local conditions within the fuel cell and how these local conditions affect the overall SOFC performance. 

In previous sections, we have shown the mesoscale modeling based on the bimodal structure. In what follows, we will show the advantage of such approaches over the ones based on local equilibrium and homogeneous closures, in particular, TFMs. The comparison starts from a simple one-dimensional force balance analysis, aiming to shed light on which kind... 

Methanol to olefins (MTO), which provides a new route to produce light olefins such as ethylene and propylene from abundant natural materials (e.g., coal, natural gas or biomass), has been recently industrialized by the Dalian Institute of Chemical Physics (DICP), Chinese Academy of Sciences. In this contribution, the process development of MTO is introduced, which emphasizes the importance of mesoscale studies and focuses on three aspects a mesoscale modeling approach for MTO catalyst pellet, coke formation and control in MTO reactor, and scaling up of the microscale-MTO fluidized bed reactor to pilot-scale fluidized bed reactor. The challenges and future directions in MTO process development are also briefed. 

Despite the complexity of mesoscale structures and mechanisms, we highlight a heuristic mesoscale modeling approach starting from a zero-dimensional conceptual model (EMMS model) and ending at the SCMF CFD model. While the stability condition determines the direction of structure evolution of the system, the stability-constrained CFD model further describes the dynamics of structure evolution. The relationship between the two approaches is more or less like that of thermodynamics and chemical kinetics. 

In this chapter we focus on atomistic predictions of thermophysical and mechanical properties of HMX crystals and liquid important to the development of reliable mesoscale equations of state. The outline of the remainder of the chapter is as follows In section 2 we describe briefly the philosophy and overall approach we have taken to force field development, including the results of quantum chemistry calculations for HMX and smaller model compounds that were used in the force field parameterization. The focus of section 3 is on the properties of liquid HMX, for which experimental data are completely lacking. Structural, thermal, and mechanical properties of the three pure crystal polymorphs of HMX are presented in section 4, where the results are compared to the available experimental data. At the ends of sections 3 and 4 we discuss briefly the importance of the various properties with mesoscale models of high explosives, with an emphasis on conditions relevant to weak shock initiation. We conclude in section 5, and provide our opinions (and justifications, based on our interactions with mesoscale modelers) regarding which HMX properties and phenomena should comprise the next targets for study via atomistic simulation. 

Modeling of the PFSA membrane has been investigated for the past two decades using phenomenological approaches " based on experimental findings, atomistic modeling "" based on classical molecular mechanics, and mesoscale modeling "" "... 

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