Topic

# Knudsen number

About: Knudsen number is a(n) research topic. Over the lifetime, 5052 publication(s) have been published within this topic receiving 104278 citation(s).

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TL;DR: A review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena as mentioned in this paper.

Abstract: Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Peclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world.

3,792 citations

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TL;DR: In this paper, a laser-Doppler velocimeter (LDV) study of velocity profiles in the laminar boundary layer adjacent to a heated flat plate revealed that the seed particles used for the LDV measurements were driven away from the plate surface by thermophoretic forces, causing a particle free region within the boundary layer of approximately one half the boundary-layer thickness.

Abstract: A laser-Doppler velocimeter (LDV) study of velocity profiles in the laminar boundary layer adjacent to a heated flat plate revealed that the seed particles used for the LDV measurements were driven away from the plate surface by thermophoretic forces, causing a particle-free region within the boundary layer of approximately one half the boundary-layer thickness. Measurements of the thickness of this region were compared with particle trajectories calculated according to several theories for the thermophoretic force. It was found that the theory of Brock, with an improved value for the thermal slip coefficient, gave the best agreement with experiment for low Knudsen numbers, λ/R = O(10−1), where λ is the mean free path and R the particle radius.Data obtained by other experimenters over a wider range of Knudsen numbers are compared, and a fitting formula for the thermophoretic force useful over the entire range 0 [les ] λ/R [les ] ∞ is proposed which agrees within 20% or less with the majority of the available data.

1,277 citations

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Brown University

^{1}TL;DR: In this paper, a general boundary condition that accounts for the reduced momentum and heat exchange with wall surfaces is proposed and its validity is investigated and it is shown that it is applicable in the entire Knudsen range and is second-order accurate in Kn in the slip flow regime.

Abstract: Rarefied gas flows in channels, pipes, and ducts with smooth surfaces are studied in a wide range of Knudsen number (Kn) at low Mach number (M) with the objective of developing simple, physics-based models. Such flows are encountered in microelectromechanical systems (MEMS), in nanotechnology applications, and in low-pressure environments. A new general boundary condition that accounts for the reduced momentum and heat exchange with wall surfaces is proposed and its validity is investigated. It is shown that it is applicable in the entire Knudsen range and is second-order accurate in Kn in the slip flow regime. Based on this boundary condition, a universal scaling for the velocity profile is obtained, which is used to develop a unified model predicting mass flow rate and pressure distribution with reasonable accuracy for channel, pipe, and duct flows in the regime (0 Kn). A rarefaction coefficient is introduced into this two-parameter model to account for the increasingly reduced intermolecular collisions...

979 citations

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01 Jan 1958

TL;DR: In this article, the subject of the kinetic theory of gases is considered to be coextensive with the theory of the Boltzmann equation, and only the original equation of Maxwell and of Boltzman for classical point molecules and short range forces are considered.

Abstract: For the purposes of this article, the subject of the kinetic theory of gases is considered to be coextensive with the theory of the Boltzmann equation We consider only the original equation of Maxwell and of Boltzmann for classical point molecules and short range forces, putting aside the equally interesting but distinct questions which arise from the inclusion of internal degrees of freedom, quantum interactions, inverse square forces, and imperfect gases The special case of a Knudsen gas of freely streaming particles is only touched on, mainly for purposes of comparison

850 citations

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TL;DR: In this article, the authors present a review of the main parameters, determining rarefied gas flows through a capillary, and a critical analysis of corresponding numerical data and analytical results available in the literature.

Abstract: The present review, containing 178 references, is dedicated to one of the largest and most important branches of the rarefied gas dynamics, namely internal flows. A critical analysis of the corresponding numerical data and analytical results available in the literature was made. The most reliable data were selected and tabulated. The review will be useful as a reference for mathematicians, physicists and aerodynamicists interested in rarefied gas flows. In this paper the complete ranges of the main parameters, determining rarefied gas flows through a capillary, are covered. The capillary length varies from zero, when the capillary degenerates into a thin orifice, to infinity when the end effects can be neglected. The Knudsen number, characterizing the gas rarefaction, varies from zero when the gas is considered as a continuous medium to infinity when the intermolecular collisions can be discounted. The pressure and temperature drops on the capillary ends vary from the small values when the linear theory i...

652 citations