Calculation of soret‐shifted dew points by continuous mixture thermodynamics

Soret‐modified hydrocarbon mass transport across compressed nonisothermal gases

“…Indeed, the temperature dependence of α T ,12 for y 1 ≪ 1 becomes quite strong, requiring that α T ,12 ( T ) be retained in (not factored out of) all integrals of the form ∫(α T ,12 ( T ; p )/ T ) dT . As will be seen (Section “Soret‐Enhancement Factor F (Soret) …”), such integrals play an important role in the present class of nonisothermal, dilute‐solute mass transfer problems, including steady‐states with no net mass transfer (see, e.g., Rosner et al29–31). It is interesting to note that, irrespective of pressure (in the range considered), above ca.…”

“…In view of our present objectives, our treatment/choice of illustrations has been deliberately focused/simplified (limited to binary systems at “infinite dilution”, one‐dimensional‐steady compressed gas “films”, an approximate TIP‐based Soret factor extrapolation procedure, and VES), but these methods can be improved/tested further and extended to more realistic situations, including multicomponent convective‐diffusion boundary layers (see, e.g., Rosner et al,30, 33 and Garcia‐Ybarra and Castillo54). Indeed, extensions of this work are the subject of follow‐on studies already underway in our HTCRE‐research group.…”

Bivariate population balance model of ethanol‐fueled spray combustors

“…Although there appears to be no conceptual or procedural obstacles to using our present characteristics‐based numerical scheme to treat combustors fired with sprays containing 3, 4, 5,… species, when this number becomes impractically large, resort can be made to a rational choice of fewer “pseudo‐species” using the methods of continuous mixture thermodynamics/transport (see, e.g., Rosner et al19 and Arias‐Zugasti and Rosner14).…”

Multivariate Population Balances via Moment and Monte Carlo Simulation Methods: An Important Sol Reaction Engineering Bivariate Example and “Mixed” Moments for the Estimation of Deposition, Scavenging, and Optical Properties for Populations of Nonspherical Suspended Particles

“…Suppose, further, that one was interested in the diffusion-controlled mass rate of partial condensation of these molecules on a “cold” surface exposed to, or containing, this mixture. In the absence of an appreciable Ludwig−Soret contribution, this rate will often 33 be proportional to the triple integral where D eff [ m ,σ,ε, T ( x , t )] is the pseudo-binary Fick diffusion coefficient through the prevailing background gas, given, say, by Chapman−Enskog theory, and the integral is carried out over all positive values of m , σ, and ε. Then, because the Chapman−Enskog collision integrals can usually be approximated as a power law (say, −0.17 exponent) in the relevant dimensionless temperature T /(ε eff / k B ), where ε eff ≈ (εε N 2 ) 1/2 , one finds that total local mass deposition rate, ṁ ‘ ‘( x , t ), will be approximately proportional to a particular mixed moment: M i , j , k of n ( m ,σ,ε; x , t ) with respect to m , σ, and ε, where i = 1, j = − 4 / 3 , and k = −0.057.…”

“…Homologous Compounds: Reduction to the Univariate Case. In contrast, suppose we were dealing with an extensive family of heavy, straight-chain alkanes, for which, say, σ( m ) ∼ m 0.51 and 83 ε( m ) ∼ m 0.48 . In that “degenerate” case ṁ ‘ ‘( x , t ) would be approximately proportional to the i th moment of n with respect to m , written M i , where i ≈ 0.29.…”