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Abstract. We present the results of investigations into the distribution of molecular free paths in rarefied gases using molecular dynamics simulations. Our tests on a range of different gas densities and confinements (unbounded, single bounding wall, and parallel bounding walls) indicate that the molecules perform Lévy-type flights, irrespective of the presence of a bounding wall. The free paths most closely follow a power-law distribution. Simulations of gases confined by planar surfaces indicate that the local molecular mean free path varies sharply close to a solid surface. These results may yield new insight into diffusive transport in rarefied gases, in particular, the constitutive behaviour of gas flows in micro and nanoscale devices.

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][26][27][28][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 NavierStokes 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.

We propose a power-law based effective mean free path (MFP) model so that the Navier-Stokes-Fourier equations can be employed for the transition-regime flows typical of gas micro/nanodevices. The effective MFP model is derived for a system with planar wall confinement by taking into account the boundary limiting effects on the molecular free paths. Our model is validated against molecular dynamics simulation data and compared with other theoretical models. As gas transport properties can be related to the mean free path through kinetic theory, the Navier-Stokes-Fourier constitutive relations are then modified in order to better capture the flow behavior in the Knudsen layers close to surfaces. Our model is applied to fully developed isothermal pressure-driven (Poiseuille) and thermal creep gas flows in microchannels. The results show that our approach greatly improves the near-wall accuracy of the Navier-Stokes-Fourier equations, well beyond the slip-flow regime.

We test an extended continuum-based approach for analyzing micro-scale gas flows over a wide range of Knudsen number and Mach number. In this approach, additional terms are invoked in the constitutive relations of Navier-Stokes-Fourier equations, which originate from the considerations of phoretic motion as triggered by strong local gradients of density and/or temperature. Such augmented considerations are shown to implicitly take care of the complexities in the flow physics in a thermo-physically consistent sense, so that no special boundary treatment becomes necessary to address phenomenon such as Knudsen paradox. The transition regime gas flows, which are otherwise to be addressed through computationally intensive molecular simulations, become well tractable within the extended quasi-continuum framework without necessitating the use of any fitting parameters. Rigorous comparisons with direct simulation Monte Carlo (DSMC) computations and experimental results support this conjecture for cases of isothermal pressure driven gas flows and high Mach number shock wave flows through rectangular microchannels.

We use molecular dynamics (MD) simulations to investigate the dynamic wetting of nanoscale water droplets on moving surfaces. The density and hydrogen bonding profiles along the direction normal to the surface are reported, and the width of the water depletion layer is evaluated first for droplets on three different static surfaces: silicon, graphite, and a fictitious superhydrophobic surface. The advancing and receding contact angles, and contact angle hysteresis, are then measured as a function of capillary number on smooth moving silicon and graphite surfaces. Our results for the silicon surface show that molecular displacements at the contact line are influenced greatly by interactions with the solid surface and partly by viscous dissipation effects induced through the movement of the surface. For the graphite surface, however, both the advancing and receding contact angles values are close to the static contact angle value and are independent of the capillary number; i.e., viscous dissipation effects are negligible. This finding is in contrast with the wetting dynamics of macroscale water droplets, which show significant dependence on the capillary number.

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Gas flows in micro-channels are, in general, theoretically treated with the Maxwell slip velocity as a boundary condition for the convection velocity at the wall. It is pointed out that wall slip is conventionally introduced in theoretical/numerical treatments of gas flows through micro-channels to obtain agreement with experimental results. In the present paper, we provide an alternative by solving the extended Navier-Stokes equations for compressible gas flows in micro-channels using the conventional no-slip velocity boundary condition for the convection velocity. Results obtained with this approach are presented and compared with experiments. It is also shown that the theoretical treatment of micro-channel gas flows using the "extended Navier-Stokes equations" also permits the phenomena such as the Knudsen paradox, to be treated in an analytical manner. Comparison with experimental data suggests that the derived analytical solution has excellent agreement up to Knudsen number of approximately 1, which shows the validity of extended Navier-Stokes equations with the conventional no-slip velocity boundary condition up to the early transition regime of micro-channel gas flows.