scholarly journals Modeling of Knudsen Layer Effects in Micro/Nanoscale Gas Flows

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Nishanth Dongari ◽  
Yonghao Zhang ◽  
Jason M Reese
Keyword(s):  
Free Path ◽  
Flow Behavior ◽  
Constitutive Relations ◽  
Slip Flow ◽  
Theoretical Models ◽  
Mean Free Path ◽  
Dynamics Simulation ◽  
Navier Stokes ◽  
Gas Flows ◽  
Planar Wall

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.

scholarly journals The Importance of Mean Free Path in Determining Gas Micro Flow Behaviour

2010 ◽  
Author(s):  
Nishanth Dongari ◽  
Yonghao Zhang ◽  
Jason M. Reese
Keyword(s):  
Free Path ◽  
Power Law ◽  
Constitutive Relations ◽  
Mean Free Path ◽  
Path Model ◽  
Dynamics Simulation ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Micro Channels ◽  
The Mean

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.

scholarly journals An Extension to the Navier-Stokes-Fourier Equations by Considering Molecular Collisions With Boundaries

2008 ◽  
Author(s):  
Erik J. Arlemark ◽  
S. Kokou Dadzie ◽  
Jason M. Reese
Keyword(s):  
Free Path ◽  
Velocity Slip ◽  
Mean Free Path ◽  
Navier Stokes ◽  
Gas Flows ◽  
Molecular Collisions ◽  
Path Expression ◽  
The Mean ◽  
Definition Of ◽  
Further Development

In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equations (NSF) extended by a description of molecular collisions with solid boundaries and discontinuous velocity slip and temperature jump boundary conditions. By considering the molecular collisions with the solid boundaries in gas flows we capture some of the near wall effects that the conventional NSF with linear stress/strain-rate and heat-flux/temperature-gradient relationships seem to be unable to describe. The model that we propose incorporates the molecular collisions with solid boundaries as an extension to the conventional definition of the average travelling distance of molecules before experiencing intermolecular collisions (the mean free path). By considering both of these types of collisions we obtain an effective mean free path expression, which varies with distance to surfaces. The effective mean free path is proposed to be used to obtain new definitions of effective viscosity and effective thermal conductivity, which will extend the applicability of NSF equations to higher Knudsen numbers. We show results of simple flow cases that are solved using this extended NSF model and discuss limitations to the model due to various assumptions. We also mention interesting ideas for further development of the model based on a more detailed gas description.

scholarly journals Event-Driven Molecular Dynamics Simulation of Hard-Sphere Gas Flows in Microchannels

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Volkan Ramazan Akkaya ◽  
Ilyas Kandemir
Keyword(s):  
Molecular Dynamics ◽  
Hard Sphere ◽  
Stokes Equations ◽  
Hard Spheres ◽  
Flow Characteristics ◽  
Dynamics Simulation ◽  
Navier Stokes ◽  
Gas Flows ◽  
Linearized Boltzmann Equation ◽  
Event Driven

Classical solution of Navier-Stokes equations with nonslip boundary condition leads to inaccurate predictions of flow characteristics of rarefied gases confined in micro/nanochannels. Therefore, molecular interaction based simulations are often used to properly express velocity and temperature slips at high Knudsen numbers (Kn) seen at dilute gases or narrow channels. In this study, an event-driven molecular dynamics (EDMD) simulation is proposed to estimate properties of hard-sphere gas flows. Considering molecules as hard-spheres, trajectories of the molecules, collision partners, corresponding interaction times, and postcollision velocities are computed deterministically using discrete interaction potentials. On the other hand, boundary interactions are handled stochastically. Added to that, in order to create a pressure gradient along the channel, an implicit treatment for flow boundaries is adapted for EDMD simulations. Shear-Driven (Couette) and Pressure-Driven flows for various channel configurations are simulated to demonstrate the validity of suggested treatment. Results agree well with DSMC method and solution of linearized Boltzmann equation. At low Kn, EDMD produces similar velocity profiles with Navier-Stokes (N-S) equations and slip boundary conditions, but as Kn increases, N-S slip models overestimate slip velocities.

scholarly journals Investigating the Effect of Solid Boundaries on the Gas Molecular Mean-Free-Path

2009 ◽  
Author(s):  
Erik J. Arlemark ◽  
Jason M. Reese
Keyword(s):  
Molecular Dynamics ◽  
Boundary Conditions ◽  
Free Path ◽  
Mean Free Path ◽  
Gas Flows ◽  
Standard Temperature ◽  
Binary Collisions ◽  
The Mean ◽  
Temperature And Pressure ◽  
Definition Of

A key parameter for micro-gas-flows, the mean free path, is investigated in this paper. The mean free path is used in various models for predicting micro gas flows, both in the governing equations and their boundary conditions. The conventional definition of the mean free path is based on the assumption that only binary collisions occur and is commonly described using the macroscopic quantities density, viscosity and temperature. In this paper we compare the prediction by this definition of the mean free paths for helium, neon and argon gases under standard temperature and pressure conditions, with the mean free paths achieved by measurements of individual molecules using the numerical simulation technique of molecular dynamics. Our simulation using molecular dynamics consists of a cube with six periodic boundary conditions, allowing us to simulate an unconfined gas “package”. Although, the size of this package is important, since its impact on computational cost is considerable, it is also important to have enough simulated molecules to average data from. We find that the molecular dynamics method using 20520 simulated molecules yields results that are within 1% accuracy from the conventional definition of the mean free paths for neon and argon and within 2.5% for helium. We can also conclude that the normal approximation of only considering binary collisions is seemingly adequate for these gases under standard temperature and pressure conditions. We introduce a single planar wall and two parallel planar walls to the simulated gas of neon and record the mean free paths at various distances to the walls. It is found that the mean free paths affected by molecular collisions with the walls corresponds well with theoretical models up to Knudsen numbers of 0.2.

Heat Conduction in Nanostructured Materials Predicted by Phonon Bulk Mean Free Path Distribution

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Giuseppe Romano ◽  
Jeffrey C. Grossman
Keyword(s):  
Free Path ◽  
Nanostructured Materials ◽  
Thermal Transport ◽  
High Efficiency ◽  
Theoretical Models ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Computational Effort ◽  
Boltzmann Transport ◽  
Computational Framework

We develop a computational framework, based on the Boltzmann transport equation (BTE), with the ability to compute thermal transport in nanostructured materials of any geometry using, as the only input, the bulk cumulative thermal conductivity. The main advantage of our method is twofold. First, while the scattering times and dispersion curves are unknown for most materials, the phonon mean free path (MFP) distribution can be directly obtained by experiments. As a consequence, a wider range of materials can be simulated than with the frequency-dependent (FD) approach. Second, when the MFP distribution is available from theoretical models, our approach allows one to include easily the material dispersion in the calculations without discretizing the phonon frequencies for all polarizations thereby reducing considerably computational effort. Furthermore, after deriving the ballistic and diffusive limits of our model, we develop a multiscale method that couples phonon transport across different scales, enabling efficient simulations of materials with wide phonon MFP distributions length. After validating our model against the FD approach, we apply the method to porous silicon membranes and find good agreement with experiments on mesoscale pores. By enabling the investigation of thermal transport in unexplored nanostructured materials, our method has the potential to advance high-efficiency thermoelectric devices.

scholarly journals On the modelling of isothermal gas flows at the microscale

2008 ◽  
Vol 604 ◽  
pp. 235-261 ◽  
Author(s):  
DUNCAN A. LOCKERBY ◽  
JASON M. REESE
Keyword(s):  
Boundary Conditions ◽  
Constitutive Relations ◽  
Navier Stokes ◽  
Test Case ◽  
Gas Flows ◽  
Hydrodynamic Models ◽  
Slip Boundary ◽  
Knudsen Numbers ◽  
Isothermal Gas ◽  
Non Equilibrium

This paper makes two new propositions regarding the modelling of rarefied (non-equilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking high-order, or extended, hydrodynamic models for these flows. This standing time-varying shear-wave problem does not require boundary conditions to be specified at a solid surface, so is useful for assessing whether fluid models can capture rarefaction effects in the bulk flow. We assess a number of different proposed extended hydrodynamic models, and we find the R13 equations perform the best in this case.Our second proposition is a simple technique for introducing non-equilibrium effects caused by the presence of solid surfaces into the computational fluid dynamics framework. By combining a new model for slip boundary conditions with a near-wall scaling of the Navier--Stokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional second-order slip model. We show that this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strain-rate inversion that is evident from molecular simulations. The model's generality to non-planar geometries is demonstrated by examining low-speed flow around a micro-sphere. It shows a marked improvement over conventional predictions of the drag on the sphere, although there are some questions regarding its stability at the highest Knudsen numbers.

Elastohydrodynamic Lubrication of Air-Lubricated Rollers

1996 ◽  
Vol 118 (3) ◽  
pp. 623-628 ◽  
Author(s):  
Y. B. Chang ◽  
F. W. Chambers ◽  
J. J. Shelton
Keyword(s):  
Numerical Model ◽  
Film Thickness ◽  
Free Path ◽  
Close Contact ◽  
Slip Flow ◽  
Elastohydrodynamic Lubrication ◽  
Mean Free Path ◽  
Pressure Profiles ◽  
The Mean ◽  
Air Film

The lubricating air film between two rotating rollers in close contact was studied numerically. The numerical model used in this study accounts for the effects of air compressibility, material deformation, and the slip flow which occurs when the air film thickness is not much larger than the mean-free-path of the air molecules. The air film profiles and the pressure profiles for the nip region between the rollers were calculated. It was found that the calculated air film thicknesses are lower than predicted by the liquid elastohydrodynamic calculation. From this study, equations for the minimum air film thickness, the air film thickness at the center of contact, and the amount of air that passes through the nip were obtained. This study has application to the prediction of the amount of air entrained in a winding roll.

Low-Speed Slip Flow Over a Wedge

1970 ◽  
Vol 37 (2) ◽  
pp. 454-460 ◽  
Author(s):  
K. E. Kasza ◽  
W. L. Chow
Keyword(s):  
Boundary Layer ◽  
Free Path ◽  
Asymptotic Method ◽  
Slip Velocity ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Velocity Slip ◽  
Mean Free Path ◽  
Low Speed ◽  
Boundary Layer Equations

The problem of low-speed slip flow of a rarefied gas over a wedge has been solved using Meksyn’s asymptotic method of integrating the boundary-layer equations. Detailed results are given for slip velocity and developing velocity profiles for various wedge angles. The solution tends far downstream asymptotically to the Falkner and Skan profiles of conventional nonslip flow. In addition, the first correction to the skin friction due to velocity slip is found to be of the order of the first power of the molecular mean free path of the gas.

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