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Theory of homogeneous vapour condensation and surface deposition from boundary layers

Published online by Cambridge University Press:  06 July 2012

M. D. Camejo  and
L. L. Bonilla
M. D. Camejo
Affiliation:
G. Millán Institute of Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
L. L. Bonilla*
Affiliation:
G. Millán Institute of Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain School of Engineering and Applied Sciences. Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA
*
†Email address for correspondence: [email protected]
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Abstract

Homogeneous condensation of vapours mixed with a carrier gas in the stagnation point boundary layer flow near a cold wall is considered. There is a condensation region near the wall with supersaturated vapour. Assuming that the surface tension times the molecular area is much larger than the thermal energy far from the wall, droplets are nucleated exclusively in a narrow nucleation layer where the Zeldovich flux of clusters surpassing the critical nucleus size is at a maximum. The vapour condenses in the free molecular regime on the droplets, which are thermophoretically attracted to the wall. Unlike the narrow condensation region for heterogeneous condensation on solid particles, in the case of homogeneous condensation the condensation region is wide even when the rate of vapour scavenging by droplets is large. A singular perturbation theory of homogeneous vapour condensation in boundary layer flow approximates very well the vapour and droplet density profiles, the nucleation layer and the deposition rates at the wall for wide ranges of the wall temperature and the scavenging parameter . A key point in the theory is to select a trial vapour number density profile among a one parameter family of profiles between an upper and a lower bound. The maximum of the Zeldovich flux for supercritical nuclei provides the approximate location of the nucleation layer and an approximate droplet density profile. Then the condensate number of molecules and the vapour density profile are calculated by matched asymptotic expansions that also yield the deposition rates. For sufficiently large wall temperatures, a more precise corrected asymptotic theory is given.

JFM classification

Boundary Layers: Boundary layer structure Phase change: Condensation/evaporation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 706 , 10 September 2012 , pp. 534 - 559
Copyright
Copyright © Cambridge University Press 2012

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