Application of the Cercignani-Lampis
Scattering Kernel to Channel Gas Flows
Felix Sharipov
Departamento de Fisica, Universidade Federal do Parana
Caixa Postal 19044, 81531-990 Curitiba, Brazil
http://fisica. ufpr. br/sharipov
Abstract. The Poiseuille flow, the thermal creep and the heat flux between two parallel plates are calcu-
lated applying the S model of the Boltzmann equation and the Cercignani-Lampis scattering kernel. The
calculations have been carried out in wide ranges of the rarefaction parameter and of the accommodation
coefficients of momentum and energy. Comparing the present results with experimental data the value of
the accommodation coefficients can be calculated.
I INTRODUCTION
The gas - surface interaction law in general form is expressed via a scattering kernel R(v' ->• v) as [1]
Kl/(v)= I K|fl(v'-»v)/(v')dv', (1)
Jv'
n
<0
where /(v) is the distribution function, v
;
and v are molecular velocities of the incident and reflected particles,
respectively, v
n
is the normal component of the velocity. The scattering kernel must satisfy the normalization
condition
f fl(v'->v)dv = l, (2)
Jv
n
>Q
and the reciprocity relation
where m is the molecular mass of gaseous particle, k is the Boltzmann constant and T
w
is the surface tempe-
rature.
In case of perfect accommodation the scattering kernel reads
This kernel can be successfully used in many practical calculations. However, for some noble gases, e.g. helium,
neon etc., experimental value of the mass flow rate through capillaries [2] are larger than those calculated
applying the diffuse scattering kernel. To eliminate this discrepancy the diffuse - specular Maxwell kernel
(5)
CP585, Rarefied Gas Dynamics: 22
nd
International Symposium, edited by T. J. Bartel and M. A. Gallis
© 2001 American Institute of Physics 0-7354-0025-3/01/$18.00
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