Sergey Macheret

Sergey O. Macheret (born December 25, 1957) is an American physicist and aerospace engineer known for his contributions to plasma science and engineering. Macheret formulas for endothermic exchange reactions and Macheret-Fridman model[1] of vibration-dissociation coupling are widely used for analysis of hypersonic and other chemically reacting flows.

Sergey Macheret
Born	Sergey Olegovich Macheret December 25, 1957
Scientific career
Fields	plasma physics, plasma chemistry, aeronautics
Institutions	Kurchatov Institute, Princeton University, Lockheed Martin Skunk Works, Purdue University
Doctoral advisor	Alexander A. Fridman

Biography

Macheret received his PhD degree from Kurchatov Institute in 1985. He has been a professor at Purdue University School of Aeronautics and Astronautics since 2014.[2]

Macheret formulas

The formulas[3] are used for estimation of non-equilibrium rate coefficients of the simple-exchange endothermic reaction: ${\displaystyle XY(v)+Z\rightarrow X+YZ}$. Such reactions appear in low-temperature nonequilibrium plasmas where substantial fraction of energy input goes into vibrational excitation of molecules. The formulas are obtained by applying classical mechanics methods for high temperatures and semi-classical approximation for moderate temperatures.

Assumptions:

1. Translational-vibrational non equilibrium: ${\displaystyle T>T_{v}}$ or ${\displaystyle T<T_{v}}$.

2. Collisions are collinear and rotational energy effects are negligible.

3. The duration of collision is much faster than the period of molecule vibration.

4. The vibrational energy obeys Boltzmann distribution.

Formulas and relations:

${\displaystyle k(T,T_{v})=Z(T,T_{v})k^{0}(T)}$

Nonequilibrium factor in the high temperature case (${\displaystyle T\geq \theta }$):

${\displaystyle Z(T,T_{v})=\exp \left[-{\frac {E_{a}-W}{\alpha _{M}T_{v}+(1-\alpha _{M})T}}-{\frac {W}{T}}+{\frac {E_{a}}{T}}\right]}$

${\displaystyle \alpha _{M}={\frac {m_{Y}(m_{X}+m_{Y}+m_{Z})}{(m_{X}+m_{Y})(m_{Y}+m_{Z})}},\quad W=E_{a}(1-{\frac {f_{v}}{\alpha _{M}}})}$

Nonequilibrium factor in the low temperature case (${\displaystyle T<\theta }$):

${\displaystyle Z(T,T_{v})=\left[f_{v}\exp(-{\frac {T_{v}}{\theta }})+(1-f_{v})\exp(-{\frac {T}{\theta }})\right]^{E_{a}/\theta }\exp \left({\frac {E_{a}}{T}}\right)}$

References

1. Macheret, S. O.; Fridman, A. (1994). Mechanisms of nonequilibrium dissociation of diatomic molecules. AIAA and ASME Joint Thermophysics and Heat Transfer Conference, 6 th, Colorado Springs, CO.
2. "Prof. Macheret page at Purdue University School of Aeronautics and Astronautics".
3. Chernyi, G.G.; Losev, S.A.; Macheret, S.O.; Potapkin, B.V. (2002). Physical and Chemical Processes in Gas Dynamics: Cross Sections and Rate Constants for Physical and Chemical Processes, Volume 1. Reston, VA: AIAA. pp. 206–209. ISBN 1-56347-518-9.

External links

• Sergey Macheret at Google Scholar