Mesoscopic Fluid Volumes

For the numerical simulation of flowing polymers, several mesoscopic models have been proposed in the last few years that describe polymer (hydro-)dynamics on a mesoscopic scale of several micrometers, typically. Among these methods, we like to mention dissipative particle dynamics (DPD) [168], stochastic rotation dynamics (sometimes also called multipartide collision dynamics) [33], and lattice Boltzmann algorithms [30]. Hybrid simulation schemes for polymer solutions have been developed recenfly, combining these methods for solvent dynamics with standard particle simulations of polymer beads (see Refs [32, 169, 170]). Extending the mesoscopic fluid models to nonideal fluids including polymer melts is currently in progress [30, 159,160,171]. 

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For most problems that involve the effects of molecular fluctuations on reactive dynamics, it is not necessary to revert to a full molecular dynamics description of the system. We are interested in particle number fluctuations of reactive chemical species that arise from reaction and diffusion processes and occur in, small fluid volume elements. The most appropriate scale for the consideration of fluctuations is the mesoscopic scale, the regime that lies... 

The bedrocks of the theoretical and computational methods that allow study of relationships between molecular and mesoscopic scale events and system properties are quantum and statistical mechanics. Thus, this volume comprises chapters that describe the development and application of quantum and statistical mechanical methods to various problems of technological relevance. The application areas include catalysis and reaction engineering, processing of materials for microelectronic applications, polymer science and engineering, fluid phase equilibrium, and combinatorial methods for materials discovery. The theoretical methods that are discussed in the various... 

In the mesoscopic description of a fluid, it is represented by a relatively small number of fields [24]. To the usual density, velocity, and temperature fields, we can add the electric field E(f, t) and the polarization field P(r, t) when we are interested in the dielectric behavior and need to take the presence of ions and dipoles into account. The dipole moment of a small volume element dV is given by P(r, t)dV. As the field P(f, t) is a fluctuating quantity, with an average, the (equilibrium) fluctuations the magnitude is determined by the free energy functional of polarization [25]... 

As discussed above, the fluid equations are derived using the assumption that macroscopic quantities like the solids volume fraction vary slowly in space. In that case, basing closure relations on local macroscopic variables seems reasonable. However, in reality, the solids volume fraction can change quite abrupdy, e.g., at emulsion—bubble interfaces or when particle clusters are formed. It might be essential to incorporate these heterogeneities that arise on mesoscopic length scales into closure relations. We wiU return to this point in Section 4.1. 

Understanding the free surface flow of viscoelastic fluids in micro-channels is important for the design and optimization of micro-injection molding processes. In this paper, flow visualization of a non-Newtonian polyacrylamide (PA) aqueous solution in a transparent polymethylmethacrylate (PMMA) channel with microfeatures was carried out to study the flow dynamics in micro-injection molding. The transient flow near the flow front and vortex formation in microfeatures were observed. Simulations based on the control volume finite element method (CVFEM) and the volume of fluid (VOF) technique were carried out to investigate the velocity field, pressure, and shear stress distributions. The mesoscopic CONNFFESSIT (Calculation of Non-Newtonian How Finite Elements and Stochastic Simulation Technique) method was also used to calculate the normal stress difference, the orientation of the polymer molecules and the vortex formation at steady state. 

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