Implication of scaling hierarchy associated with nonequilibrium: field and particulate

The advent of nanotechnology has necessitated a better understanding of how material microstructure changes at the atomic level would affect the macroscopic properties that control the performance. Such a challenge has uncovered many phenomena that were not previously understood and taken for granted. Among them are the basic foundation of dislocation theories which are now known to be inadequate. Simplifying assumptions invoked at the macroscale may not be applicable at the micro- and/or nanoscale. There are implications of scaling hierrachy associated with in-homegeneity and nonequilibrium. of physical systems. What is taken to be homogeneous and equilibrium at the macroscale may not be so when the physical size of the material is reduced to microns. These fundamental issues cannot be dispensed at will for the sake of convenience because they could alter the outcome of predictions. Even more unsatisfying is the lack of consistency in modeling physical systems. This could translate to the inability for identifying the relevant manufacturing parameters and rendering the end product unpractical because of high cost. Advanced composite and ceramic materials are cases in point. Discussed are potential pitfalls for applying models at both the atomic and continuum levels. No encouragement is made to unravel the truth of nature. Let it be partiuclates, a smooth continuum or a combination of both. The present trend of development in scaling tends to seek for different characteristic lengths of material microstructures with or without the influence of time effects. Much will be learned from atomistic simulation models to show how results could differ as boundary conditions and scales are changed. Quantum mechanics, continuum and cosmological models provide evidence that no general approach is in sight. Of immediate interest is perhaps the establishment of greater precision in terminology so as to better communicate results involving multiscale physical events.

Pressure drops of single and two-phase flows through T-type microchannel mixers

In this paper, preliminary experimental results are presented on pressure drop characteristics of single and two-phase flows through two T-type rectangular microchannel mixers with hydraulic diameters of 528 and 333 mum, respectively. It is shown that both N-2 and water single-phase laminar flows in microchannels, with consideration of experimental uncertainties, are consistent with classic theory, if additional effects, such as entrance effects that will interfere with the interpretation of experimental results, are eliminated by carefully designing the experiments. The obtained pressure drop data of N-2-water two-phase flow in micromixers are analyzed and compared with existing flow pattern-independent models. It is found that the Lockhart-Martinelli method generally underpredicts the frictional pressure drop. Thereafter, a modified correlation of C value in the Chisholm's equation based on linear regression of experimental data is proposed to provide a better prediction of the two-phase frictional pressure drop. Also among the homogeneous flow models investigated, the viscosity correlation of McAdams indicates the best performance in correlating the frictional pressure drop data (mean deviations within +/-20% for two micromixers both). Finally it is suggested that systematic studies are still required to accurately predict two-phase frictional performance in microchannels. (C) 2004 Elsevier B.V. All rights reserved.

Energy-Momentum of a Cosmological Brane Model and the Gauge Hierarchy

We analyze in this paper the general covariant energy-momentum tensor of the gravitational system in general five-dimensional cosmological brane-world models. Then through calculating this energy-momentum for the cosmological generalization of the Randall-Sundrum model, which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the "visible" brane is a general feature of this model. This is the origin of the gauge hierarchy from a gravitational point of view. Our results are also consistent with the fact that a gravitational system has vanishing total energy.