Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T00:57:35.662Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinetic Theory and Boundary Conditions for Fluids

Published online by Cambridge University Press:  20 November 2018

Jon Schnute  and
Marvin Shinbrot
Jon Schnute
Affiliation:
University of British Columbia, Vancouver, British Columbia
Marvin Shinbrot
Affiliation:
University of Victoria, Victoria, British Columbia
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A rigorous derivation of the molecular theory of a confined, deterministic gas is given. Then, a molecular reflection law is presented with the property that the corresponding fluid does not slip at the boundary. It is also shown that, within a certain reasonable class of reflection laws, the one we give is the only one that leads to no-slip.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 6 , December 1973 , pp. 1183 - 1215
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Brush, S. G., Interatomic forces and gas theory from Newton to Lennard-Jones, Arch. Rational Mech. Anal. 39 (1970), 1–29.Google Scholar
2. Elrick, Richard M. II and Emrich, Raymond J., Tracer study of pipe flow behavior to within two microns of the wall, Phys. Fluids 9 (1966), 28–32.Google Scholar
3. Grad, Harold, Principles of the kinetic theory of gases, Handbuch der Physik, Flügge, S., ed., V. XII (Springer-Verlag, Berlin, 1958).Google Scholar
4. Grad, Harold, On the kinetic theory of rarified gases, Comm. Pure Appl. Math. 2 (1949), 331–407.Google Scholar
5. Lamb, Horace, Hydrodynamics, 5th ed. (Cambridge University Press, Cambridge, 1924).Google Scholar
6. James Clerk, Maxwell, On stresses in rarified gases arising from inequalities of temperatures, Philos. Trans. Roy. Soc. London Ser. A, Part I, 1879. Reprinted in The Scientific Papers of James Clerk Maxwell, Niven, W. D., ed. Dover Publ., Inc. No date.Google Scholar
7. James, Serrin, Mathematical principles of classical fluid mechanics, Handbuch der Physik, Flügge, S., ed. v. VIII/1 (Springer-Verlag, Berlin, 1959).Google Scholar
8. Marvin, Shinbrot, Lectures on fluid mechanics (Gordon and Breach, New York, 1973).Google Scholar
9. Stokes, G. G., Mathematical and physical papers (Cambridge University Press, Cambridge, 1880).Google Scholar
10. Truesdell, C., The mathematical foundations of elasticity and fluid dynamics, J. Rational Mech. Anal. 1 (1952), 125–300.Google Scholar
11. Tsien, H. S., Superaerodynamics, mechanics of rarified gases, J. Aero. Sci. 13 (1946), 653–664.Google Scholar
12. Carlo, Cercignani, Mathematical methods in kinetic theory (Plenum Press, New York, 1969).Google Scholar