Fractal geometry model for effective thermal conductivity of three-phase porous media

An approximate model, a fractal geometry model, for the effective thermal conductivity of three-phase/unsaturated porous media is proposed based on the thermal-electrical analogy technique and on statistical self-similarity of porous media. The proposed thermal conductivity model is expressed as a function of porosity (related to stage n of Sierpinski carpet), ratio of areas, ratio of component thermal conductivities, and saturation. The recursive algorithm for the thermal conductivity by the proposed model is presented and found to be quite simple. The model predictions are compared with the existing measurements. Good agreement is found between the present model predictions and the existing experimental data. This verifies the validity of the proposed model. (C) 2004 American Institute of Physics.

Electric characteristics of pseudo-spark during breakdown phase

An analysis of the time-dependent resistive voltage and power deposition during the breakdown phase of pseudo-spark is presented. The voltage and current were measured by specially designed low-inductance capacitive voltage divider and current measuring resistor. The measured waveforms of voltage and current are digitized and processed by a computer program to remove the inductive component, so as to obtain resistive voltage and power deposition. The influence of pressure, cathode geometry and charging voltage of storage capacitors on the electrical properties in the breakdown phase are investigated. The results suggest that the breakdown phase of pseudo-spark consists of three stages. The first stage is mainly hollow cathode discharge. In the second stage, field-enhanced thermionic emission takes place, resulting in a fast voltage drop and sharp rise of discharge current. The third stage of discharge depends simply on the parameters of the discharge circuit.

Effects of contact resistance on thermal-conductivity of composite media with a periodic structure

The thermal conductivity of periodic composite media with spherical or cylindrical inclusions embedded in a homogeneous matrix is discussed. Using Green functions, we show that the Rayleigh identity can be generalized to deal with thermal properties ot these systems. A new calculating method for effective conductivity of composite media is proposed. Useful formulae for effective thermal conductivity are derived, and meanings of contact resistance in engineering problems are explained.

Thermal-conductivity of periodic composite media with spherical inclusions

The thermal conductivity of periodic composite media with spherical inclusions embedded in a homogeneous matrix is discussed. Using Green's function, we show that the Rayleigh identity can be generalized to deal with the thermal properties of these systems. A technique for calculating effective thermal conductivities is proposed. Systems with cubic symmetries (including simple cubic, body centered cubic and face centered cubic symmetry) are investigated in detail, and useful formulae for evaluating effective thermal conductivities are derived.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.