Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

This review is focused on molecular momentum transport at fluid-solid interfaces mainly related to microfluidics and nanofluidics in micro-/nano-electro-mechanical systems (MEMS/NEMS). This broad subject covers molecular dynamics behaviors, boundary conditions, molecular momentum accommodations, theoretical and phenomenological models in terms of gas-solid and liquid-solid interfaces affected by various physical factors, such as fluid and solid species, surface roughness, surface patterns, wettability, temperature, pressure, fluid viscosity and polarity. This review offers an overview of the major achievements, including experiments, theories and molecular dynamics simulations, in the field with particular emphasis on the effects on microfluidics and nanofluidics in nanoscience and nanotechnology. In Section 1 we present a brief introduction on the backgrounds, history and concepts. Sections 2 and 3 are focused on molecular momentum transport at gas-solid and liquid-solid interfaces, respectively. Summary and conclusions are finally presented in Section 4.

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Molecular momentum transport at fluid-solid interfaces in MEMS/NEMS: a review.

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

The value of tangential momentum accommodation coefficient (TMAC) is required while prescribing the boundary condition for flow of gases in the slip and transition flow regimes. The precise determination of its value is important for several other applications as well. This article reviews the experimental techniques employed by researchers over the decades to measure this coefficient and the values reported in the literature, with relevance to calculation of the slip velocity. The review shows that the value of TMAC is dependent on a number of parameters including nature of the gas, pressure of the gas, material of the surface, surface cleanliness and roughness, and surface temperature. For monatomic gases, the TMAC at about 0.93 is almost constant with respect to the Knudsen number, and this value can be employed for most commonly available surface materials. However, for nonmonatomic gases, TMAC decreases with an increase in Knudsen number; a correlation of TMAC with Knudsen number for this class of ga...

Survey on measurement of tangential momentum accommodation coefficient

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

A set of experimental measurements with a spinning rotor gauge (SRG) with 3.85, 4.00, and 4.50 mm nominal diameter steel spheres in He, Ar, and Kr is reported. The experiments covered the continuum and the slip regimes for all three gases. Theoretical results from a companion paper on the SRG, together with a calibration based on known viscosity for helium, are used to extract values of the viscosity, the velocity slip coefficient, and the tangential momentum accommodation coefficient for each of the gases. The measured viscosities are in good agreement with existing literature values.

The spinning rotor gauge: Measurements of viscosity, velocity slip coefficients, and tangential momentum accommodation coefficients

A concise and accurate result for the temperature‐jump coefficient based on the linearized BGK model and arbitrary accommodation is reported. The jump coefficient is expressed as a power series in (1‐α), and values of the expansion coefficients are given.

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Temperature‐jump problem with arbitrary accommodation

The problem of the rotatory oscillation of an axi-symmetric body in an axi-symmetric, viscous, incompressible flow at low Reynolds number has been studied. In contrast to the steady rotation of a body, which involves solving the Laplace equation, the study of an oscillating body requires solution of the Helmholtz equation which results from the simplification of the unsteady Stokes equations. In the present work, we have numerically evaluated the local stresses and torques on a selection of free, oscillating, axi-symmetric bodies in the continuum regime in an axi-symmetric viscous incompressible flow. The Helmholtz equation was solved by a Green’s function technique. The accuracy of the technique is tested against known solutions for a sphere, a prolate spheroid, a thin disk, and an infinitely long cylinder. Good agreements have been obtained. Finite cylinders have been studied and the edge correction factors for the circular disk geometry, that are basic to oscillating disk viscometers, have been calculated. It has been found that the calculated edge correction factors, based on the ratios of the real parts of the actual torques (calculated from this work) to the ideal torques, agree to within 1% to 10% with the reported values obtained by Clark et al. [Physica A 89, 539 (1977)] using the theory of Kestin and Wang [J. Appl. Mech. 24, 197 (1957)]. However, since the ratios of the real parts and the ratios of the imaginary parts of the torques do not coincide, the edge correction factors depend upon which ratio is used.

Rotatory oscillations of arbitrary axi-symmetric bodies in an axi-symmetric viscous flow: Numerical solutions

Evaporation of a liquid into a vacuum occupying a half space is investigated on the basis of the one-dimensional BGK model linearized about a drifting Maxwellian distribution. TheF
N method is used to deduce accurate numerical results for the perturbations in the density and temperature.

An approximate solution concerning strong evaporation into a half space

Rotary oscillations of several axi-symmetric bodies in axi-symmetric viscous flows with slip are investigated. A numerical method based on the Green's function technique is used wherein the relevant Helmholtz equation, as obtained from the unsteady Stokes equation, is converted into a surface integral equation. The technique is benchmarked against a known analytical solution, and accurate numerical results for local stress and torque on spheres and spheroids as function of the frequency parameter and the slip coefficients are obtained. It is found that in all cases, slip reduces stress and torque, and increasingly so with the increasing frequency parameter. The method discussed here can be potentially extended to the realistic case of an oscillating disk viscometer. Copyright © 2003 John Wiley & Sons, Ltd.

S. K. Loyalka

Papers

The spinning rotor gauge: Measurements of viscosity, velocity slip coefficients, and tangential momentum accommodation coefficients

Temperature‐jump problem with arbitrary accommodation

Rotatory oscillations of arbitrary axi-symmetric bodies in an axi-symmetric viscous flow: Numerical solutions

An approximate solution concerning strong evaporation into a half space

Rotary oscillations of axi‐symmetric bodies in an axi‐symmetric viscous flow with slip: Numerical solutions for sphere and spheroids