Viscous-slip, thermal-slip, and temperature-jump coefficients based on the linearized Boltzmann equation (and five kinetic models) with the Cercignani–Lampis boundary condition

2010 ◽  
Vol 29 (3) ◽  
pp. 181-191 ◽  
Author(s):  
R.D.M. Garcia ◽  
C.E. Siewert
Keyword(s):  
Boundary Condition ◽  
Boltzmann Equation ◽  
Kinetic Models ◽  
Temperature Jump ◽  
Thermal Slip ◽  
Linearized Boltzmann Equation

The Slip Problems for a Simple Gas

1971 ◽  
Vol 26 (6) ◽  
pp. 964-972 ◽  
Author(s):  
S.K. Loyalka
Keyword(s):  
Boltzmann Equation ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Polyatomic Gas ◽  
Extra Effort ◽  
Linearized Boltzmann Equation ◽  
Multicomponent Gas ◽  
Interaction Law ◽  
Temperature Jump Coefficient ◽  
Polyatomic Gas Mixtures

Abstract Simple and accurate expressions for the velocity slip coefficient, the slip in the thermal creep, and the temperature jump coefficient are obtained by applying a variational technique to the linearized Boltzmann equation for a simple gas. Completely general forms of the boundary conditions are used, and the final results are presented in a form such that the results for any particular intermolecular force law or the gas-surface interaction law can easily be calculated. Further, it is shown that, with little extra effort, the present results can be easily extended to include the case of a polyatomic gas. It is felt that the present work, together with a recent paper in which the author has considered the solutions of the linearized Boltzmann equation for a monatomic multicomponent gas mixture, provide the desired basis for the consideration of the various slip problems associated with the polyatomic gas mixtures.

Kinetic Models and the Linearized Boltzmann Equation

1959 ◽  
Vol 2 (4) ◽  
pp. 432 ◽  
Author(s):  
Eugene P. Gross ◽  
E. Atlee Jackson
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Models ◽  
Linearized Boltzmann Equation

scholarly journals Assessment and development of the gas kinetic boundary condition for the Boltzmann equation

2017 ◽  
Vol 823 ◽  
pp. 511-537 ◽  
Author(s):  
Lei Wu ◽  
Henning Struchtrup
Keyword(s):  
Experimental Data ◽  
Boundary Condition ◽  
Boltzmann Equation ◽  
Rarefied Gas ◽  
Thermal Slip ◽  
Thermal Transpiration ◽  
Rarefied Gas Flows ◽  
The Boltzmann Equation ◽  
Kinetic Boundary ◽  
Slip Coefficients

Gas–surface interactions play important roles in internal rarefied gas flows, especially in micro-electro-mechanical systems with large surface area to volume ratios. Although great progress has been made to solve the Boltzmann equation, the gas kinetic boundary condition (BC) has not been well studied. Here we assess the accuracy of the Maxwell, Epstein and Cercignani–Lampis BCs, by comparing numerical results of the Boltzmann equation for the Lennard–Jones potential to experimental data on Poiseuille and thermal transpiration flows. The four experiments considered are: Ewart et al. (J. Fluid Mech., vol. 584, 2007, pp. 337–356), Rojas-Cárdenas et al. (Phys. Fluids, vol. 25, 2013, 072002) and Yamaguchi et al. (J. Fluid Mech., vol. 744, 2014, pp. 169–182; vol. 795, 2016, pp. 690–707), where the mass flow rates in Poiseuille and thermal transpiration flows are measured. This requires that the BC has the ability to tune the effective viscous and thermal slip coefficients to match the experimental data. Among the three BCs, the Epstein BC has more flexibility to adjust the two slip coefficients, and hence for most of the time it gives good agreement with the experimental measurements. However, like the Maxwell BC, the viscous slip coefficient in the Epstein BC cannot be smaller than unity but the Cercignani–Lampis BC can. Therefore, we propose to combine the Epstein and Cercignani–Lampis BCs to describe gas–surface interaction. Although the new BC contains six free parameters, our approximate analytical expressions for the viscous and thermal slip coefficients provide useful guidance to choose these parameters.

Theory of Boundary Conditions for the Boltzmann Equation

1977 ◽  
Vol 32 (6) ◽  
pp. 521-531 ◽  
Author(s):  
L. Waldmann
Keyword(s):  
Boltzmann Equation ◽  
Boundary Conditions ◽  
Temperature Jump ◽  
Functional Relation ◽  
Linearized Boltzmann Equation ◽  
Kinetic Boundary ◽  
The Difference ◽  
Molecular Distribution Function ◽  
Transport Relaxation ◽  
Slip Coefficients

Abstract In preceding papers, Refs. 1,2, boundary conditions were developed for transport-relaxation equations by aid of a general reciprocity postulate for the interface. The same method is now used for the linearized Boltzmann equation. A new scheme emerges: the kinetic boundary conditions consist in a linear functional relation between interfacial "forces and fluxes" - in the sense of non-equilibrium thermodynamics - which are, broadly speaking, given by the sum and the difference of the molecular distribution function and its time-reversed, at the wall. The general properties of the kernels occurring in this atomistic boundary law are studied. The phenomenological surface coefficients of (generalized) linear thermo-hydrodynamics, as e. g. temperature jump, slip coefficients etc., can in a simple way be expressed by the kernel of the atomistic boundary law. This kernel is explicitly worked out for completely thermalizing wall collisions.

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