Mesoscale, definition

Fig. 6.16 Definition of damage at the macroscale, mesoscale, and microscale of a composite damage is considered at three different length scales. The microscale is concerned only with the fiber-matrix interaction, The mesoscale concerns the interaction of fibers and matrix with cracks or other defects. The macroscopic properties are independent of any microstructural length dimension. When going from a finer scale to a coarser scale, the description of the finer scale is made through average quantities.

The transport equations appearing in macroscale models can be derived from the kinetic equation using the definition of the moment of interest. For example, if the moment of interest is the disperse-phase volume fraction, then it suffices to integrate over the mesoscale variables. (See Section 4.3 for a detailed discussion of this process.) Using the velocity-distribution function from Section 1.2.2 as an example, this process yields... 

The remaining chapters in this book are organized as follows. Chapter 2 provides a brief introduction to the mesoscale description of polydisperse systems. There, the mathematical definition of a number-density function (NDF) formulated in terms of different choices for the internal coordinates is described, followed by an introduction to population-balance equations (PBE) in their various forms. Chapter 2 concludes with a short discussion on the differences between the moment-transport equations associated with the PBE and those arising due to ensemble averaging in turbulence theory. This difference is very important, and the reader should keep in mind that at the mesoscale level the microscale turbulence appears in the form of correlations for fluid drag, mass transfer, etc., and thus the mesoscale models can have non-turbulent solutions even when the microscale flow is turbulent (i.e. turbulent wakes behind individual particles). Thus, when dealing with turbulence models for mesoscale flows, a separate ensemble-averaging procedure must be applied to the moment-transport equations of the PBE (or to the PBE itself). In this book, we are primarily... 

In the particle-based definition of the NDF, we begin at the microscale and write a dynamic equation for the rate of change of the disperse-phase particle properties at the mesoscale. The simplest system, which we consider first, is a collection of interacting particles in a vacuum wherein the particles interact through collisions and short-range forces. Such a system is referred to as a granular system. We then consider a disperse two-phase system, wherein the particles are dispersed in a fluid. 

In order to account for variable particle numbers, we generalize the collision term iSi to include changes in IVp due to nucleation, aggregation, and breakage. These processes will also require models in order to close Eq. (4.39). This equation can be compared with Eq. (2.16) on page 37, and it can be observed that they have the same general form. However, it is now clear that the GPBE cannot be solved until mesoscale closures are provided for the conditional phase-space velocities Afp)i, (Ap)i, (Gp)i, source term 5i. Note that we have dropped the superscript on the conditional phase-space velocities in Eq. (4.39). Formally, this implies that the definition of (for example) [Pg.113]

Traditional chemical reaction engineering deals with smaller sizes, typically with tubing and pipe sizes ranging from about 1 mm to 10 m. This will be termed the macroscale. Table 16.1 provides definitions of three smaller scales meso, micro, and nano. These terms have been used in a variety of ways in the literature. The term mi-croreactor is sometimes used for systems defined here as mesoscale. The definitions in Table 16.1 are rational if somewhat arbitrary. They are based on the characteristic size of flow channels. 

Here, Pc is the mixture density of the dense phase. U up i is defined by J Uf-U/), where Uf and U are mean velocities of the dilute and dense phases, respectively. This definition of mesoscale slip velocity differs a little bit from that in the cluster-based EMMS model, because the continuous phase transforms from the dilute phase to the dense phase. And their quantitative difference is l-f)PgUgc/Pc, which is normally negligible for gas-solid systems. Similarly, the closure of Fdi switches to the determination of bubble diameter. And it is well documented in literature ever since the classic work of Davidson and Harrison (1963). Compared to cluster diameter, bubble diameter arouses less disputes and hence is easier to characterize. The visual bubbles are normally irregular and in constantly dynamic transformation, which may deviate much from spherical assumption. Thus, the diameter of bubble here can also be viewed as drag-equivalent definition. 

This is one of the simple and most commonly used method to perform multiscale simulation. By definition calculation of parameters for classical MD simulation from quantum chemical calculation is also a multiscale simulation. Therefore, most of the force filed e.g., OPLS," AMBER, GROMOS available for simulations of liquid, polymers, biomolecules are derived from quantum chemical calculations can be termed as multiscale simulation. To bridge scales from classical MD to mesoscale, different parameter can be calculated and transferred to the mesoscale simulation. One of the key examples will be calculation of solubiUty parameter from all atomistic MD simulations and transferring it to mesoscale methods such dissipative particle dynamics (DPD) or Brownian dynamics (BD) simulation. Here, in this context of multiscale simulation only DPD simulation along with the procedure of calculation of solubility parameter from all atomistic MD simulation will be discussed. 

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