Advanced models of fuel droplet heating and evaporation

IT is not often that a reissue of the collected papers of an outstanding scientific man has been called for. Some of the papers cannot fail to have historical value because of the part which their original publication played in the development of science; but that value alone would not be sufficient to secure the demand. The work involved must be of present-day importance. Therefore its consequences must still be in process of development; and it follows that if, as in the present case, the republication follows the first publication after an interval of half a century, the main papers involved must have been of very epoch-making type. The condition of present value is a sufficient test; but the most essential condition is that of permanent value. Present value persisting after the lapse of fifty years suggests permanence, and at least points to some enduring quality—the direct impress of the distinctive personality of the man. The Scientific Papers of James Clerk Maxwell. Edited By W. D. Niven. (Photographic Reprint by arrangement with the Cambridge University Press.) Vol. 1. Pp. xxxii + 607. Vol. 2. Pp. viii + 806. (Paris: J. Hermann, 1927.) 3 livres 6.

The Scientific Papers of James Clerk Maxwell

Accurate modeling of gas microflow is crucial for the microfluidic devices in MEMS. Gas microflows through these devices are often in the slip and transition flow regimes, characterized by the Knudsen number of the order of 10−2~100. An increasing number of researchers now dedicate great attention to the developments in the modeling of non-equilibrium boundary conditions in the gas microflows, concentrating on the slip model. In this review, we present various slip models obtained from different theoretical, computational and experimental studies for gas microflows. Correct descriptions of the Knudsen layer effect are of critical importance in modeling and designing of gas microflow systems and in predicting their performances. Theoretical descriptions of the gas-surface interaction and gas-surface molecular interaction models are introduced to describe the boundary conditions. Various methods and techniques for determination of the slip coefficients are reviewed. The review presents the considerable success in the implementation of various slip boundary conditions to extend the Navier–Stokes (N–S) equations into the slip and transition flow regimes. Comparisons of different values and formulations of the first- and second-order slip coefficients and models reveal the discrepancies arising from different definitions in the first-order slip coefficient and various approaches to determine the second-order slip coefficient. In addition, no consensus has been reached on the correct and generalized form of higher-order slip expression. The influences of specific effects, such as effective mean free path of the gas molecules and viscosity, surface roughness, gas composition and tangential momentum accommodation coefficient, on the hybrid slip models for gas microflows are analyzed and discussed. It shows that although the various hybrid slip models are proposed from different viewpoints, they can contribute to N–S equations for capturing the high Knudsen number effects in the slip and transition flow regimes. Future studies are also discussed for improving the understanding of gas microflows and enabling us to exactly predict and actively control gas slip.

A review on slip models for gas microflows

1. Introduction and preliminaries 2. Molecular orbitals-potentials-dynamics, and quantum energy states 3. Carrier energy transport and transition theories 4. Phonon energy storage, transport and transition kinetics 5. Electron energy storage, transport and transition kinetics 6. Fluid particle energy storage, transport and transformation kinetics 7. Photon energy storage, transport and transition kinetics.

Heat Transfer Physics

The present review is dedicated to the velocity slip and temperature jump coefficients applied to modeling of gas flows. Such coefficients are used when a moderate gas rarefaction must be taken into account. In this case, calculations of gas flows can be performed on the basis of continuum mechanics equations applying the velocity slip and temperature jump boundary conditions. Thus, the velocity slip and temperature jump coefficients have the same importance in gas dynamics as the transport coefficients such as viscosity, thermal conductivity, and diffusion coefficients. A critical analysis of theoretical and experimental data on the slip and jump coefficients available in the open literature is presented in an accessible form so that it can be easily understandable for nonspecialists in rarefied gas dynamics. The most reliable results are selected and tabulated. The results cover a single gas with the complete and noncomplete accommodation on a solid surface, gaseous mixtures, and polyatomic gases. Many examples of applications of the slip and jump boundary conditions are given. The review will be useful as a reference for mathematicians, physicists, and engineers dealing with flows of moderately rarefied gases.

Data on the Velocity Slip and Temperature Jump on a Gas-Solid Interface

The viscous slip coefficient was calculated for binary gaseous mixtures on the basis of the McCormack kinetic model of the Boltzmann equation, which was solved by the discrete velocity method. The calculations were carried out for the three mixtures of noble gases: neon–argon, helium–argon, and helium–xenon. It was showed that for the mixture of helium and xenon, which has a large ration of the molecular masses, the slip coefficient significantly differs from that for a single gas. A comparison of the present results with those obtained by the moment method applied to the Boltzmann equation showed that the McCormack model equation provides reliable results with modest computational efforts. An example of application of the viscous slip coefficient was given.

Velocity slip and temperature jump coefficients for gaseous mixtures. I. Viscous slip coefficient

The flow of binary gaseous mixtures through rectangular microchannels due to small pressure, temperature, and molar concentration gradients over the whole range of the Knudsen number is studied. The solution is based on a mesoscale approach, formally described by two coupled kinetic equations, subject to diffuse scattering boundary conditions. The model proposed by McCormack substitutes the complicated collision term and the resulting kinetic equations are solved by an accelerated version of the discrete velocity method. Typical results are presented for the flow rates and the heat fluxes of two different binary mixtures (Ne–Ar and He–Xe) with various molar concentrations, in two-dimensional microchannels of different aspect (height to width) ratios. The formulation is very efficient and can be used instead of the classical method of solving the Navier–Stokes equations with slip boundary conditions, which is restricted by the hydrodynamic regime. Moreover, the present formulation is a good alternative to the direct simulation Monte Carlo method, which often becomes computationally inefficient.

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Flow of gaseous mixtures through rectangular microchannels driven by pressure, temperature, and concentration gradients

The mass flow, heat flux, and diffusion flux of rarefied gas mixture through a tube caused by gradients of pressure, temperature, and concentration were calculated over a wide range of the Knudsen number on the basis of the kinetic equation. The thermodynamic fluxes are presented in the form that allows us to prove the Onsager relations and then to reduce the number of kinetic coefficients determining the solution down to six. The numerical values of the kinetic coefficients are tabulated and the velocity profiles are given in figures.

Gaseous mixture flow through a long tube at arbitrary Knudsen numbers

Velocity slip and temperature jump coefficients for gaseous mixtures. IV. Temperature jump coefficient

The flow of binary gaseous mixtures between two parallel plates driven by gradients of pressure, temperature and concentration is studied, based on the McCormack model of the Boltzmann equation. The coupled kinetic equations are solved numerically by the discrete velocity method. The mass flow, the heat flux and the diffusion flux, which are the mixture quantities of practical importance, are expressed in terms of the so-called thermodynamic fluxes. The latter are written in a form that allows us to verify the Onsager–Casimir reciprocity relations. In addition, analytical expressions for these quantities are derived in the limit case of the hydrodynamic regime. Thus, the numerical solution together with these expressions provides the solution in the whole range of the gas rarefaction. The influence of the intermolecular interaction potential is also investigated by comparing the results for the rigid sphere model with those for a realistic potential. Numerical results are presented for two binary mixtures of noble gases (Ne–Ar and He–Xe) for various values of the molar concentrations.

Denize Kalempa

Papers

Velocity slip and temperature jump coefficients for gaseous mixtures. I. Viscous slip coefficient

Flow of gaseous mixtures through rectangular microchannels driven by pressure, temperature, and concentration gradients

Gaseous mixture flow through a long tube at arbitrary Knudsen numbers

Velocity slip and temperature jump coefficients for gaseous mixtures. IV. Temperature jump coefficient

Gaseous mixture flow between two parallel plates in the whole range of the gas rarefaction