Knudsen number

About: Knudsen number is a research topic. Over the lifetime, 5052 publications have been published within this topic receiving 104278 citations.

Pressure-driven diffusive gas flows in micro-channels: from the Knudsen to the continuum regimes

Abstract: Despite the enormous scientific and technological importance of micro-channel gas flows, the understanding of these flows, by classical fluid mechanics, remains incomplete including the prediction of flow rates. In this paper, we revisit the problem of micro-channel compressible gas flows and show that the axial diffusion of mass engendered by the density (pressure) gradient becomes increasingly significant with increased Knudsen number compared to the pressure driven convection. The present theoretical treatment is based on a recently proposed modification (Durst et al. in Proceeding of the international symposium on turbulence, heat and mass transfer, Dubrovnik, 3-18 September, pp 25-29, 2006) of the Navier-Stokes equations that include the diffusion of mass caused by the density and temperature gradients. The theoretical predictions using the modified Navier-Stokes equations are found to be in good agreement with the available experimental data spanning the continuum, transition and free-molecular (Knudsen) flow regimes, without invoking the concept of Maxwellian wall-slip boundary condition. The simple theory also results in excellent agreement with the results of linearized Boltzmann equations and Direct Simulation Monte Carlo (DSMC) method. Finally, the theory explains the Knudsen minimum and suggests the design of future micro-channel flow experiments and their employment to complete the present days understanding of micro-channel flows.

Slip Correction Measurements for Solid Spherical Particles by Modulated Dynamic Light Scattering

Abstract: The theoretical expression for the drag force on a spherical particle moving with low Reynolds number in a gas is customarily written by multiplying the Stokes' law expression by a slip correction factor of the form C x = 1 +Kn[γ1 + γ2 exp(-γ3/Kn)], where Kn is the particle Knudsen number and γ1, γ2, and γ3 are empirical constants. We have measured the drag forces on spherical polystyrene latex particles suspended in dry air using the modulated dynamic light scattering technique which is fundamentally different from the Millikan cell approach. Data are time autocorrelation functions of the intensity of light scattered by single test particles from the intersection volume of two coherent laser beams. The data provide detailed information about test particle Brownian motion including the value of the particle diffusion coefficient. Each test particle was held in air suspension by an electrostatic trap to permit measurements to be made on the same particle at air pressures ranging from 760 to 0.2 torr. Data ...

Size and frequency dependent gas damping of nanomechanical resonators

Abstract: We examine size and frequency dependent gas damping of nanobeam resonators. We find an optimal beam width that maximizes the quality factor at atmospheric pressure, balancing the dissipation that scales with surface-to-volume ratio and dominates at small widths, against the interaction with the underlying substrate via the air that dominates the behavior of the wider devices. This latter interaction is found to affect the Knudsen number corresponding to a transition out of the molecular damping regime. We examine higher order modes and tune tension mechanically to vary the frequency of individual resonators, to resolve size and frequency effects.