By Marita Casasola
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Extra info for Acupuntura en los animales
38) represents the ratio of the characteristic times: ε = τrap /τsl , τrap ∼ τel-rot , τsl ∼ θ . 2), we apply the Chapman–Enskog method modified for non-equilibrium gas flows with rapid and slow processes. 4. 43) was proposed in [60, 145], where the distribution functions and governing equations were derived in the zero- and first-order approximations, the expressions for the transport and relaxation terms were obtained, and the algorithm for the calculation of the transport coefficients was developed.
Slow processes make an important contribution to the variation of the main macroscopic parameters of a moving gas. Processes with the characteristic time much greater than θ , can be assumed frozen while studying a gas flow on the time scale θ . A mathematical consequence of the existence of rapid and slow processes in real gas flows, is that the small parameter ε in the kinetic equations appears in both the differential operator and the integral operator for slow processes . 38) rap ε = τrap /τsl ∼ τrap /θ 1 is the small parameter, and Jci j , Jcisl j are the collision operators for rapid and slow processes, respectively.
26) for the differential part of Eq. 25), we can represent its solutions in the following structural form: (1) (0) fci j = fci j 1 1 1 · ddk − Bci j : ∇v− − Aci j · ∇ ln T − ∑ Ddk n n dk ci j n 1 1 − Fci j ∇ · v − Gci j . 27) for the diffusive driving force dci . The free term Gci j in Eq. 30) is connected to the slow relaxation processes: non-equilibrium chemical reactions and vibrational energy exchange. The functions Aci j and Ddk ci j are vector functions of the peculiar velocity cc , the functions Bci j are tensor functions of cc , and Fci j and Gci j are scalar functions.
Acupuntura en los animales by Marita Casasola