Multiple preparative chromatography

Volkov, S. A.; Reznikov, V. I.; Zel'venskii, V. Yu.; Sakodinskii, K. I.

doi:10.1007/bf02261373

Cited by 1 publication

(2 citation statements)

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“…. When there is a sharp change in the gas properties, as for the heated layers discussed above, then ~ 0.1 (Volkov and Johnson 2013). However, if the heat is primarily absorbed over a board range of below , then ~ 1 is sufficient.…”

Section: Criteria For Transonic Solutionsmentioning

confidence: 98%

“…Ignoring the thermal conductivity in Equation (2), this corresponds to the enthalpy of fluid particles becoming sufficient to produce a transonic, isentropic expansion starting at r 0 . For smaller λ a non-equilibrium region, called a Knudsen layer, forms above and there is a steep transition with decreasing λ to supersonic escape at λ ~2.1 and ~2.8-3.5 for monatomic and diatomic gases respectively (Volkov & Johnson 2013).…”

Section: Heatingmentioning

confidence: 99%

See 1 more Smart Citation

Molecular-Kinetic Simulations of Escape From the Ex-Planet and Exoplanets: Criterion for Transonic Flow

Johnson¹,

Volkov²,

Erwin³

2013

ApJ

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The equations of gas dynamics are extensively used to describe atmospheric loss from solar system bodies and exoplanets even though the boundary conditions at infinity are not uniquely defined. Using molecular-kinetic simulations that correctly treat the transition from the continuum to the rarefied region, we confirm that the energy-limited escape approximation is valid when adiabatic expansion is the dominant cooling process. However, this does not imply that the outflow goes sonic. In fact in the sonic regime, the energy limited approximation can significantly under estimate the escape rate. Rather large escape rates and concomitant adiabatic cooling can produce atmospheres with subsonic flow that are highly extended. Since this affects the heating rate of the upper atmosphere and the interaction with external fields and plasmas, we give a criterion for estimating when the outflow goes transonic in the continuum region. This is applied to early terrestrial atmospheres, exoplanet atmospheres, and the atmosphere of the explanet, Pluto, all of which have large escape rates. The paper and its erratum, combined here, are published: ApJL 768, L4 (2013); ApJ, 779, L30 (2013).

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Section: Criteria For Transonic Solutionsmentioning

confidence: 98%

Section: Heatingmentioning

confidence: 99%