62 research outputs found

    Transition regime analytical solution to gas mass flow rate in a rectangular micro channel

    Get PDF
    We present an analytical model predicting the experimentally observed gas mass flow rate in rectangular micro channels over slip and transition regimes without the use of any fitting parameter. Previously, Sone [1] reported a class of pure continuum regime flows that requires terms of Burnett order in constitutive equations of shear stress to be predicted appropriately. The corrective terms to the conventional Navier-Stokes equation were named the ghost effect. We demonstrate in this paper similarity between Sone ghost effect model and newly so-called ‘volume diffusion hydrodynamic model’. A generic analytical solution to gas mass flow rate in a rectangular micro channel is then obtained. It is shown that the volume diffusion hydrodynamics allows to accurately predict the gas mass flow rate up to Knudsen number of 5. This can be achieved without necessitating the use of any adjustable parameters in boundary conditions or parametric scaling laws for constitutive relations. The present model predicts the non-linear variation of pressure profile along the axial direction and also captures the change in curvature with increase in rarefaction

    Molecular free path distribution in rarefied gases

    Get PDF
    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

    Modeling of Knudsen layer effects in micro/nanoscale gas flows

    Get PDF
    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

    Behaviour of microscale gas flows based on a power-law free path distribution function

    Get PDF
    We investigate a power-law form for the probability distribution function of free paths of dilute gas molecules in a confined region. A geometry-dependent effective molecular mean free path (MFP) model is then derived for a planar wall confinement, by taking into account the boundary limiting effects on the molecular paths. The power-law based effective MFP is validated against molecular dynamics simulation data and compared with exponential effective MFP models. The Navier-Stokes constitutive relations are then modified according to the kinetic theory of gases i.e. transport properties can be described in terms of the free paths which the molecules describe between collisions. Results for isothermal pressure-driven Poiseuille gas flows in micro-channels are reported, and we compare results with conventional hydrodynamic models, solutions of the Boltzmann equation and experimental data

    Molecular dynamics studies of anomalous transport in rarefied gas flows

    Get PDF
    We investigate the thermodynamically non-equilibrium gas dynamics by measuring molecular free path distribution functions, inter-molecular collision rates and wall dependent mean free path (MFP) profiles using the molecular dynamics (MD) method. The simulations cover a wide range of fluid densities for single-wall case, parallel walls cases and a cube with all periodic walls. The simulations are validated by deducing the theoretical unconfined MFP values at standardpressure and temperature conditions. The free path MD measurements of individual molecules convey that conventional exponential distribution function is not valid under rarefied conditions and molecules follow L´evy type flights, irrespective of the presence of a wall. MFP profile measurements for confined planar surfaces in the transition flow regime show sharp gradients close to the wall, while theoretical models predict shallower gradients. As gas transport properties can be related to the MFP through kinetic theory, our MD data may help to modify the constitutive relationships, which may then be fed into the Navier-Stokes equations for better effective modeling of micro gas flows in the transition flow regime

    The importance of mean free path in determining gas micro flow behaviour

    Get PDF
    We investigate whether a power-law form of probability distribution function better describes the free paths of dilute gas molecules in a confined system. An effective molecular mean free path model is derived, which allows the mean free path to vary close to bounding surfaces. Our model is compared with molecular dynamics simulation data, and also other classical mean free path models. As gas transport properties can be related to the mean free path through kinetic theory, the Navier-Stokes constitutive relations are then modified and applied to various benchmark test cases. Results for isothermal pressure-driven Poiseuille flows in micro-channels are reported, and we compare our results with conventional hydrodynamic models, solutions of the Boltzmann equation, and experimental data. Our new approach provides good results for mean free path and cross-sectional flow velocity profiles up to Knudsen numbers around 1, and for integral flow parameters such as flow rate and friction factor up to Knudsen number of 10. We discuss some limitations of our power-law model, and point to the way forward for further development
    corecore