An improved differential form of the Boltzmann collision operator for a Rayleigh gas (or Brownian particles)
✍ Scribed by Leonardo Ferrari
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 907 KB
- Volume
- 142
- Category
- Article
- ISSN
- 0378-4371
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✦ Synopsis
A new approximate differential form of the Boltzmann collision operator for a Rayleigh gas (or Brownian particles) is derived. The calculation procedure retains all the terms of first and second order in the small quantity/x I = M/(m + M), M and m being the masses of the light particles and of the heavy particles, respectively. The special conditions under which the obtained operator can be compared (and agree) with the different one derived by Wannier for heavy ions in a cold gas, are discussed. Moreover, some properties of the new operator are studied. In particular, it is shown that, contrarily to what happens for the usual first-order approximate (Fokker-Planck) collision operator, the new operator has the Burnett functions as eigenfunctions only in the Maxwell model. Finally, the reliability and accuracy of the new operator are examined and compared with those of the usual Fokker-Planck collision operator. From this discussion, the advantages offered by the new operator in many instances result manifest.