Abstract
In this paper we continue the study of solutions of the extended Boltzmann equation started previously. In particular, we study an iterated solution of the equation that can be used to describe the flow of a rarefied gas around a macroscopic object. We discuss the rarefied flow and then show how the iterated solution can be extended into the hydrodynamic regime. The results for the drag force and for the distribution function of the gas molecules are shown to be identical to the results obtained in a previous paper by a generalization of the normal solution method. We also discuss the special properties of both rarefied and continuum flows around a cylinder and show that in both regions one must take into account Oseen-like terms which naturally appear in the extended Boltzmann equation. In the hydrodynamic regime we obtain Lamb's formula for the force on the cylinder. By relating the terms in the iterated expression to dynamical events taking place in the fluid, we are able to discuss the dynamical origin of the results obtained here.
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References
H. van Beijeren and J. R. Dorfman,J. Stat. Phys. 23:335 (1980).
J. R. Dorfman, H. van Beijeren, and C. F. McClure,Arch. Mech. Stosow. 28:33 (1976).
L. Landau and E. M. Lifshitz,Fluid Mechanics (Pergamon Press, New York, 1959).
C. F. McClure, Ph.D. Thesis, Department of Physics and Astronomy, University of Maryland, College Park, Maryland (1972); J. R. Dorfman, W. A. Kuperman, J. V. Sengers, and C. F. McClure,Phys. Fluids 16:2347 (1973). C. F. McClure, J. R. Dorfman, and J. V. Sengers (to appear).
Y. P. Pao and D. R. Willis,Phys. Fluids 12:534 (1969).
M. Lunc and J. Lubonski,Arch. Mech. Stosow. 8:597 (1956);Bull. Acad. Polon.5:47 (1957).
G. E. Kelly and J. V. Sengers,J. Chem. Phys. 57:1441 (1972);61:2800 (1974).
A. L. Cooper and B. B. Hamel,Phys. Fluids 16:35 (1973).
Y. Kan, Ph.D. Dissertation, Department of Physics and Astronomy, University of Maryland, College Park, Maryland (1975); Y. Kan and J. R. Dorfman,Phys. Rev. A 16:2447 (1977).
V. C. Liu, S. C. Pang, and H. Jew,Phys. Fluids 8:788 (1965); D. R. Willis,Phys. Fluids 9:2522 (1966); Y. L. Wang, Ph.D. Thesis, Department of Physics and Astronomy, University of Maryland, College Park, Maryland (1974).
Y. Kan, J. R. Dorfman, and J. V. Sengers, inProc. Seventh Symposium on Thermophysical Prop., A. Cezairliyan, ed. (Am. Soc. of Mech. Engin., New York, 1977), p. 652.
J. R. Dorfman, inFundamental Problems in Statistical Mechanics III, E. G. D. Cohen, ed. (North-Holland, Amsterdam, 1975); P. Resibois and Y. Pomeau,Phys. Rep. 19C:63 (1975).
P. Resibois and M. DeLeener,Classical Kinetic Theory of Fluids (Wiley-Interscience, New York, 1977), Chapter V.
M. H. Ernst, B. Cichocki, J. R. Dorfman, J. Sharma, and H. van Beijeren,J. Stat. Phys. 18:237 (1978).
A. Onuki,J. Stat. Phys. 18:475 (1978); Ph.D. Thesis, University of Tokyo (1975).
H. Lamb,Hydrodynamics (Cambridge Univ. Press, Cambridge, 1932).
G. Scharf,Phys. Fluids 13:848 (1970).
C. Cercignani,Mathematical Methods in Kinetic Theory, (Plenum Press, New York, 1969);Theory and Application of the Boltzmann Equation (Elsevier, New York, 1975).
C. Cercignani, C. D. Pagani, and P. Bassanini,Phys. Fluids 11:1399 (1968).
J. R. Mehaffey and R. J. Cukier,Phys. Rev. Lett. 38:1039 (1977);Phys. Rev. A 17:1181 (1978); see also H. van Beijeren and J. R. Dorfman,Phys. Rev. A 19:416 (1979).
D. Bedeaux and P. Mazur,Physica 76:235, 247 (1974);78:505 (1974).
S. R. de Groot and P. Mazur,Non-Equilibrium Thermodynamics (North-Holland, Amsterdam, 1962).
J. P. Hansen and I. R. McDonald,Theory of Simple Liquids (Academic Press, New York, 1976), p. 274.
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A preliminary report on the work described here and in Part I was given in Ref. 2.
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van Beijeren, H., Dorfman, J.R. Kinetic theory of hydrodynamic flows. II. The drag on a sphere and on a cylinder. J Stat Phys 23, 443–461 (1980). https://doi.org/10.1007/BF01011575
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DOI: https://doi.org/10.1007/BF01011575