Mesoscale model diffusion

Sewell and co workers [145-148] have performed molecular dynamics simulations using the HMX model developed by Smith and Bharadwaj [142] to predict thermophysical and mechanical properties of HMX for use in mesoscale simulations of HMX-containing plastic-bonded explosives. Since much of the information needed for the mesoscale models cannot readily be obtained through experimental measurement, Menikoff and Sewell [145] demonstrate how information on HMX generated through molecular dynamics simulation supplement the available experimental information to provide the necessary data for the mesoscale models. The information generated from molecular dynamics simulations of HMX using the Smith and Bharadwaj model [142] includes shear viscosity, self-diffusion [146] and thermal conductivity [147] of liquid HMX. Sewell et al. have also assessed the validity of the HMX flexible model proposed by Smith and Bharadwaj in molecular dynamics studies of HMX crystalline polymorphs. 

In the mesoscale model, setting Tf = 0 forces the fluid velocity seen by the particles to be equal to the mass-average fluid velocity. This would be appropriate, for example, for one-way coupling wherein the particles do not disturb the fluid. In general, fluctuations in the fluid generated by the presence of other particles or microscale turbulence could be modeled by adding a phase-space diffusion term for Vf, similar to those used for macroscale turbulence (Minier Peirano, 2001). The time scale Tf would then correspond to the dissipation time scale of the microscale turbulence. 

As mentioned above, the mesoscale model can contain stochastic processes, which lead to the diffusion terms appearing in Eq. (5.2). Using A p as an example, we can write... 

The inverse process of dissolution, namely solute molecules leaving the lattice of the crystalline particles or the amorphous particles because the particle is in contact with an under-saturated solution (i.e. S < 1), is typically controlled by diffusion. Therefore, the mesoscale model reported in Eq. (5.29) can be used to calculate the rate of the size change due to dissolution. 

Chapter 5 focuses on selected mesoscale models from the literature for key physical and chemical processes. The chapter begins with a general discussion of the mesoscale modeling philosophy and its mathematical framework. Since the number of mesoscale models proposed in the literature is enormous, the goal of the chapter is to introduce examples of models for advection and diffusion in real and phase space... 

The radiative flux terms (in S f, ) are typically separated into short-wave and long-wave fluxes. The short-wave fluxes, also called solar fluxes, are separated into direct and diffuse irradiance. The direct irradiance is the non-scattered flux, while the difflise irradiance is the scattered radiative flux from the sun. The direct irradiance is sometimes further separated into visible and near-infrared components. In cloudy model atmospheres, parametrizations based on cloud liquid water content, or more crudely on arbitrary attenuation based on relative humidity, are used. Typically only diffuse irradiance is permitted for overcast model conditions. Some models weight the fluxes for partly cloudy skies, using separate parametrizations for clear and overcast sky conditions. Polluted atmospheres also require parametrization of their effect on solar irradiance, although only a few mesoscale models have explored this issue. 

Mesoscale Modeling for Reaction-Diffusion in Catalyst Pellet 296... 

Apparendy, there lacks an expHcit hnk between the microscale and macroscale models discussed above. In this section, a mesoscale model is introduced to describe the reaction—diffusion in a single catalyst pellet. The significance of this model can be embodied at least in two aspects a necessary link between the microscale model and macroscale model and the theoretical basis for MTO catalyst design optimization. 

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. 

Above, we gave one example of the relationship between our dimensionless simulation parameters and physical dimensional values. The characteristic time scales given in the first paragraph in this section can be rescaled for different values of the diffusion coefficient and for different length scales in the system. (Namely, the distance between two lattice sites, could be chosen to be a different value one should, however, keep in mind that the model is a mesoscale model.)... 

This function accounts for the mesoscale region and comprises most of the listed distribution functions [154]. It includes three empirical parameters, a, pK, and aw. Having ascertained the relationships between these parameters and the properties of anomalous self-diffusion, fractal morphology, and polydispersity of the finite pore-size, physical significance can be assigned to these parameters in the framework of the percolation models [152],... 

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