Modeling rigorous

The yield stress can in principle be predicted from the polarization model. Rigorous calculation of the movement of one sphere in a flowing ER fluid under an electric field requires computation of the dielectric and hydrodynamic forces on that sphere. But these forces depend on the location and movement of all surrounding spheres, which are themselves responding to similar forces. Thus, one must solve a many-body problem, and this requires computer simulation. 

The VOF approach allows one to model various interfacial phenomena for example, wall adhesion and surface (or interfacial) tension can be modeled rigorously using this approach. Brackbill et al. (1992) developed a continuous surface force (CSF) model to describe interfacial surface tension. CSF model replaces surface force by a smoothly varying volumetric force acting on all the fluid elements in the interface transition region. For two-phase flows (dispersed or secondary phase is denoted by subscript 2), surface force, Fsf can be written (Brackbill et al., 1992) ... 

The main advantage of using a Lagrangian framework for dispersed phase particles is that particle-level phenomena can be modeled rigorously. Species and enthalpy conservation equations for individual particles can be written ... 

Within the limits of the assumptions on which the model is predicated, the results are reasonable, and the model could be used as a preliminary tool in evaluation of discharge episodes. However, there is a need to improve capabilities and to test the model rigorously. Among the areas where future development and research are needed the following appear to be the most pressing ... 

The kinetic model rigorously accounts for heat and material balances. Kinetic models are excellent tools for predicting individual component yields, heat balances, and temperature profiles across reactors. It is only writh the... 

Homogeneous and heterogeneous models Lumped and distributed models Rigorous (relatively rigorous) and empirical models Linear and nonlinear models... 

During the past 20 years, academic and industrial researchers developed composition-based kinetic models with hundreds or even thousands of lumps and pure compounds. The QSRC (quantitative stracture-reactivity correlation) and LFER (linear free energy relationship) lumping techniques are discussed in Chapter 20 by Professor Klein and Chapter 9 by Professor Mochida. The structure-oriented liunping (SOL) approach of Quann and Jaffe yields models rigorous enough for use in closed-loop real-time optimizers (CLRTO), which automatically adjust setpoints for commercial process units several times each day. ... 

The structure of gels has been discussed with respect to static and dynamic structural models. Rigorously constructed theoretical models assume homogeneous structure. Real gels are heterogeneous due to various... 

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