Abstract
We consider an ensemble of dusty particulates absorbing ambient gas. The general non-stationary solution to the kinetic equation describing the dust distribution is obtained. In particular, it is shown that gas absorption may reduce the effective translational temperature of the dust component below the ambient gas temperature.
Original language | English |
---|---|
Pages (from-to) | 141-145 |
Number of pages | 5 |
Journal | Physics Letters A |
Volume | 293 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - 28 Jan 2002 |
Funding
This work was performed under the financial support granted by the Sfb 555 of the Deutsche Forschung Gemeinschaft and the Netherlands Organization for Scientific Research (NWO), grant #047-008-013. One of us (A.M.I.) also acknowledges the support from the Integration Foundation, project #A0029. Appendix A It is a matter of straightforward substitution to verify that the general solution to Eq. (11) with an initial condition f d ( P , M ,0)= f 0 ( P , M ) is given by (A.1) f d (P,M,t)= ∫ 0 ∞ dP′ P′M 2/3 σ(μ(M,t)) Pμ(M,t) 1/3 σ(M) 1 πΔ(M,t) exp − P 2 M 2/3 +P 2 ′ μ(M,t) 2/3 4Δ(M,t) sinh PP′M 1/3 μ(M,t) 1/3 2Δ(M,t) f 0 P′,μ(M,t) , where μ ( M , t ) is a root of the equation (A.2) ∫ μ(M,t) M dM′ σ(M′) =j 0 t and Δ(M,t)= 2 5 T n M 5/3 −μ(M,t) 5/3 . Evaluating the average kinetic energy, 〈 P → 2 /2M〉 , with the help of Eq. (A.1) one can check that it tends to 6/5 T n even for an arbitrary mass distribution.
Keywords
- Brownian motion
- Dusty systems