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Kinetic theory of hydrodynamic flows. I. The generalized normal solution method and its application to the drag on a sphere
- Source :
- Journal of Statistical Physics, 23(3), 335. Springer
- Publication Year :
- 1980
-
Abstract
- We consider the flow of a dilute gas around a macroscopic heavy object. The state of the gas is described by an extended Boltzmann equation where the interactions between the gas molecules and the object are taken into account in computing the rate of change of the distribution function of the gas. We then show that the extended Boltzmann is equivalent to the usual Boltzmann equation, supplemented by boundary conditions imposed on the distribution function at the surface of the object. The remainder of the paper is devoted to a study of the solution of the extended Boltzmann equation in the case that the mean free path of a gas molecule is small compared to some characteristic dimension of the macroscopic object. We show that the Chapman-Enskog normal solution of the ordinary Boltzmann equation is not in general a solution of the extended equation near the surface of the object and must be supplemented by a boundary layer term. We then introduce a projection operator method which allows us to decompose the solution of the extended equation into a normal solution part and a boundary layer part when the gas flow is sufficiently slow. As a specific example of the method we consider the flow around a sphere, and derive the Stokes-Boussinesq form for the frequency-dependent force on the sphere for arbitrary slip coefficient. This derivation is the first one that starts from the Boltzmann equation for a general dilute gas and incorporates the effect of the boundary layer on the drag force.
- Subjects :
- Stokes' law
normal solutions
slip coefficients
Mathematical analysis
Lattice Boltzmann methods
Statistical and Nonlinear Physics
boundary layer
Boltzmann equation
drag force
symbols.namesake
Boundary layer
Distribution function
Drag
Natuur- en Sterrenkunde
Boltzmann constant
boundary conditions
Kinetic theory of gases
symbols
Boundary value problem
projection operator
Mathematical Physics
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 15729613
- Database :
- OpenAIRE
- Journal :
- Journal of Statistical Physics, 23(3), 335. Springer
- Accession number :
- edsair.doi.dedup.....3c7356034bbf54359eebf4e8e4c1b8e1