Energy effective dispersion coefficients

Here, the densities of the gaseous and solid fuels are denoted by pg and ps respectively and their specific heats by cpg and cps. D and A are the dispersion coefficient and the effective heat conductivity of the bed, respectively. The gas velocity in the pores is indicated by ug. The reaction source term is indicated with R, the enthalpy of reaction with AH, and the mass based stoichiometric coefficient with u. In Ref. [12] an asymptotic solution is found for high activation energies. Since this approximation is not always valid we solved the equations numerically without further approximations. Tables 8.1 and 8.2 give details of the model. 

Somewhat different is the case of the induction and dispersion energies. For these the expansion in inverse powers of r is only valid in the limit of vanishing orbital overlap, and in this case the expansions of equations (38), (39) are shown to overestimate the true value of the energy when such orbital overlap is taken into account. Indeed, studies carried out for small systems68-77 show that the values of the induction and dispersion coefficients decrease with decreasing r. Formally, it is possible to account for this effect by introducing the so-called damping functions as follows ... 

It has been shown that the free energy of adhesion can be positive, negative, or zero, implying that van der Waals interactions can be attractive as well as repulsive [130,133,134]. While Eq. (14) can, strictly speaking, be expected to hold only for systems that interact by means of dispersion forces only, there are no restrictions on Eq. (15). Since this equation describes very well the fundamental patterns of the behavior of particles, including macromolecules, independent of the type of molecular interactions present, it was found to be convenient to define an "effective Hamaker coefficient that reflects the free energy of adhesion [130],... 

An estimate of the effective turbulent dispersion coefficient for any reactor is generally difficult because of the spatial variation in the dispersion coefficient within the reactor. A first-level approximation may be based on average turbulence kinetic energy and... 

Adamovic, I., Gordon, M. S. (2005). Dynamic Polarizability, Dispersion Coefficient and Dispersion Energy in the Effective Fragment Potential Method, Mol Phys., 103,379-387. 

Effective Radial and Axial Dispersion Coefficients for Mass and Energy ... 

A wide variety of molecular properties can be accurately obtained with ADF. The time-dependent DFT implementation " yields UV/Vis spectra (singlet and triplet excitation energies, as well as oscillator strengths), frequency-dependent (hyper)polarizabilities (nonlinear optics), Raman intensities, and van der Waals dispersion coefficients. Rotatory strengths and optical rotatory dispersion (optical properties of chiral molecules ), as well as frequency-dependent dielectric functions for periodic structures, have been implemented as well. NMR chemical shifts and spin-spin couplingsESR (EPR) f-tensors, magnetic and electric hyperfme tensors are available, as well as more standard properties like IR frequencies and intensities, and multipole moments. Relativistic effects (ZORA and spin-orbit coupling) can be included for most properties. 

Porous silicon layers with a porosity of 60% on n-type (lll)Si substrates were prepared by anodic etching under white illumination. Silver/porous-silicon/Si and metal Ag/Si structures were fabricated by evaporation of thin metal films onto the porous silicon or Si surface, respectively. The diffusion annealing of structures was carried out in air at 100-250C. Examination of the Ag concentration distribution in porous silicon layers and monocrystalline Si substrates was performed by successive removal of thin layers and measurement of the energy dispersive X-ray fluorescence intensity of AgK( peaks. The effective diffusion coefficients were described by ... 

Diffusion Continued) effect of, on activation energy, 104 effect of, on reaction order, 105 effect of, oh reaction rate, 95 importance of, 115 Knudsen, 484 molecular, 484 on surface, 98, 208 Diffusivity. See Effective diffusivity Dispersion (of catalyst), 19 Dispersion coefficients (axial and radial), 287, 493, 497... 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

---