scholarly journals Higher order slip according to the linearized Boltzmann equation with general boundary conditions

2011 ◽  
Vol 369 (1944) ◽  
pp. 2228-2236 ◽  
Author(s):  
Silvia Lorenzani
Keyword(s):  
Boltzmann Equation ◽  
Collision Operator ◽  
Velocity Slip ◽  
Lattice Boltzmann Methods ◽  
Linearized Boltzmann Equation ◽  
Potential Applications ◽  
Microscale Flows ◽  
Scattering Kernel ◽  
Linearized Collision Operator ◽  
Slip Coefficients

In the present paper, we provide an analytical expression for the first- and second-order velocity slip coefficients by means of a variational technique that applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator and the Cercignani–Lampis scattering kernel of the gas–surface interaction. The polynomial form of the Knudsen number obtained for the Poiseuille mass flow rate and the values of the velocity slip coefficients are analysed in the frame of potential applications of the lattice Boltzmann methods in simulations of microscale flows.

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 Theory for a Dilute Gas of Particles with Spin. II. Relaxation Coefficients

1968 ◽  
Vol 23 (12) ◽  
pp. 1893-1902
Author(s):  
S. Hess ◽  
L. Waldmann
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Interaction Potential ◽  
Collision Operator ◽  
Dilute Gas ◽  
Order Of Magnitude ◽  
Generalized Boltzmann Equation ◽  
Linearized Collision Operator ◽  
Relaxation Coefficients

The relaxation coefficients to be discussed are given by collision brackets pertaining to the linearized collision operator of the generalized Boltzmann equation for particles with spin. The order of magnitude of various nondiagonal relaxation coefficients which are of interest for the SENFTLEBEN-BEENAKKER effect is investigated. Those nondiagonal relaxation coefficients which are linear in the nonsphericity parameter ε (ε essentially measures the ratio of the nonspherical and the spherical parts of the interaction potential), as well as some diagonal relaxation coefficients are expressed in terms of generalized Omega-integrals.

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.

UNIFORM L2-STABILITY ESTIMATES FOR THE RELATIVISTIC BOLTZMANN EQUATION

2009 ◽  
Vol 06 (02) ◽  
pp. 295-312 ◽  
Author(s):  
SEUNG-YEAL HA ◽  
HO LEE ◽  
XIONGFENG YANG ◽  
SEOK-BAE YUN
Keyword(s):  
Boltzmann Equation ◽  
Collision Operator ◽  
Stability Estimate ◽  
Classical Solutions ◽  
Stability Estimates ◽  
Type Estimate ◽  
Relativistic Boltzmann Equation ◽  
The Stability ◽  
L2 Stability ◽  
Linearized Collision Operator

In this paper, we derive an a prioriL2-stability estimate for classical solutions to the relativistic Boltzmann equation, when the initial datum is a small perturbation of a global relativistic Maxwellian. For the stability estimate, we use the dissipative property of the linearized collision operator and a Strichartz type estimate for classical solutions. As a direct application of our stability estimates, we establish that classical solutions in Glassey–Strauss and Hsiao–Yu's frameworks satisfy a uniform L2-stability estimate.

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