scholarly journals Poiseuille and thermal transpiration flows of a highly rarefied gas: over-concentration in the velocity distribution function

2011 ◽  
Vol 669 ◽  
pp. 242-259 ◽  
Author(s):  
SHIGERU TAKATA ◽  
HITOSHI FUNAGANE
Keyword(s):  
Mass Flow ◽  
Hard Sphere ◽  
Rarefied Gas ◽  
Velocity Distribution Function ◽  
Molecular Gas ◽  
Approximation Procedure ◽  
Molecular Models ◽  
Iterative Approximation ◽  
Thermal Transpiration ◽  
Linearized Boltzmann Equation

Poiseuille and thermal transpiration flows of a highly rarefied gas are investigated on the basis of the linearized Boltzmann equation, with a special interest in the over-concentration of molecules on velocities parallel to the walls. An iterative approximation procedure with an explicit error estimate is presented, by which the structure of the over-concentration is clarified. A numerical computation on the basis of the procedure is performed for a hard-sphere molecular gas to construct a database that promptly gives the induced net mass flow for an arbitrary value of large Knudsen numbers. An asymptotic formula of the net mass flow is also presented for molecular models belonging to Grad's hard potential. Finally, the resemblance of the profiles between the heat flow of the Poiseuille flow and the flow velocity of the thermal transpiration is pointed out. The reason is also given.

Plane Thermal Transpiration of a Rarefied Gas Between Two Walls of Maxwell-Type Boundaries With Different Accommodation Coefficients

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Toshiyuki Doi
Keyword(s):  
Boltzmann Equation ◽  
Mass Flow Rate ◽  
Knudsen Number ◽  
Mass Flow ◽  
Flow Rate ◽  
Poiseuille Flow ◽  
Rarefied Gas ◽  
Thermal Transpiration ◽  
Wide Range ◽  
Accommodation Coefficients

Plane thermal transpiration of a rarefied gas between two walls of Maxwell-type boundaries with different accommodation coefficients is studied based on the linearized Boltzmann equation for a hard-sphere molecular gas. The Boltzmann equation is solved numerically using a finite difference method, in which the collision integral is evaluated by the numerical kernel method. The detailed numerical data, including the mass and heat flow rates of the gas, are provided over a wide range of the Knudsen number and the entire range of the accommodation coefficients. Unlike in the plane Poiseuille flow, the dependence of the mass flow rate on the accommodation coefficients shows different characteristics depending on the Knudsen number. When the Knudsen number is relatively large, the mass flow rate of the gas increases monotonically with the decrease in either of the accommodation coefficients like in Poiseuille flow. When the Knudsen number is small, in contrast, the mass flow rate does not vary monotonically but exhibits a minimum with the decrease in either of the accommodation coefficients. The mechanism of this phenomenon is discussed based on the flow field of the gas.

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.

A Database for Couette Flow Rate Considering the Effects of Non-Symmetric Molecular Interactions

2002 ◽  
Vol 124 (4) ◽  
pp. 869-873 ◽  
Author(s):  
Wang-Long Li
Keyword(s):  
Couette Flow ◽  
Molecular Interactions ◽  
Flow Rate ◽  
Molecular Gas ◽  
Mems Devices ◽  
Magnetic Head ◽  
Linearized Boltzmann Equation ◽  
Accommodation Coefficients ◽  
Molecular Gas Film Lubrication ◽  
Film Lubrication

A complete database for Couette flow rate (QCD,α1,α2,0.1⩽α1,α2⩽1.0,0.01⩽D⩽100, where D=inverse Knudsen number) for ultra-thin gas film lubrication problems is advanced. When the accommodation coefficients (AC) of the two lubricating surfaces are different α1≠α2, the Couette flow rate in the modified molecular gas film lubrication (MMGL) equation should be corrected. The linearized Boltzmann equation (under small Mach number conditions) is solved numerically for the case of non-symmetric molecular interactions α1≠α2. The Couette flow rate is then calculated, and the database is constructed. The present database can be easily implemented in the MMGL equation. In addition, the present database extends the previously published results for 0.1⩽α1,α2⩽0.7. The database for low ACs is valuable in the analysis and applications of MEMS devices (bushings of electrostatic micro motors, micro bearings, magnetic head/disk interfaces, etc.), and their future development.

Sign in / Sign up

Export Citation Format

Share Document