Response to “Comment on ‘Velocity slip coefficients based on the hard-sphere Boltzmann equation’” [Phys Fluids 24, 079101 (2012)]

2012 ◽  
Vol 24 (7) ◽  
pp. 079102
Author(s):  
Livio Gibelli
Keyword(s):  
Boltzmann Equation ◽  
Hard Sphere ◽  
Velocity Slip ◽  
Slip Coefficients

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.

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