Summary
The slip coefficient for a gas is computed for certain typical forms of the collision frequency. The computations are made by a numerical quadrature based on an exact formula and also by a variational procedure. There is a good agreement between the results obtained by both methods and between them and previously known results. Our calculations confirm that the slip coefficient is only slightly model dependent. It is also shown that, for any form of the collision frequency, the slip-coefficient dependence on the accommodation coefficient for tangential momentum can be found analytically, in terms of the value corresponding to complete accommodation.
Riassunto
Si calcola il coefficiente di slittamento di un gas per particolari forme della frequenza degli urti intermolecolari. I calcoli sono fatti sia mediante una quadratura numerica basata su una formula esatta che con un procedimento variazionale. C’è un buon accordo tra i risultati ottenuti con i due metodi e risultati noti in precedenza. I nostri calcoli confermano che il coefficiente di slittamento dipende poco dal modello. Si mostra anche che, per ogni forma della frequenza d’urto, la dipendenza del coefficiente di slittamento dal coefficiente di accomodamento della quantità di moto trasversale si può determinare analiticamente, in termini del valore corrispondente a un accomodamento completo.
Реэюме
Вычисляется козффициент скольжения для гаэа для некоторых типичных форм частоты соударений. Проводятся вычисления посредством численной квадратуры, основанной на точной формуле, и также посредством вариационной процедуры. Получается хорощее согласие между реэультатами, полученными обоими методами и между зтими реэультатами и предварительно иэвестными реэультатами. Нащи вычисления подтверждают, что козффициент скольжения очень слабо эависит от модели. Также покаэывается, что для любой формы частот соударений эависимость козффициента скольжения от козффициента аккомодации для тангенциального момента может быть найдена аналитически в терминах величины, соответствуюшей полной аккомодации.
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Assisted by the Air Force Office of Scientific Research under contract AF61 (051)-881, through the European Office of Aerospace Research, OAR, United States Air Force.
Sponsored in the frame of the activity of the CNR group for Fluid Dynamics at the Institute of Physical Sciences of the University of Milan. Grant N. 115.0235.0.0124.
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Cercignani, C., Foresti, P. & Sernagiotto, F. Dependence of the slip coefficient on the form of the collision frequency. Nuovo Cimento B (1965-1970) 57, 297–306 (1968). https://doi.org/10.1007/BF02710201
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DOI: https://doi.org/10.1007/BF02710201