Neu, J.C. and Carpio Rodríguez, Ana María and Bonilla , L.L.
(2009)
*Theory of surface deposition from boundary layers containing condensable vapour and particles.*
Journal of fluid mechanics, 626
.
ISSN 0022-1120

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Official URL: http://arxiv.org/pdf/0903.1403.pdf

## Abstract

Heterogeneous condensation of vapours mixed with a carrier gas in the stagnation point boundary layer flow near a cold wall is considered in the presence of solid particles much larger than the mean free path of vapour particles. The supersaturated vapour condenses on the particles by diffusion, and particles and droplets are thermophoretically attracted to the wall. Assuming that the heat of vaporization is much larger than k(B)(T) over tilde (infinity) where (T) over tilde (infinity) is the temperature far from the wall, vapour condensation occurs in a condensation layer (CL). The CL width and characteristics depend on the parameters of the problem, and a parameter R yielding the rate of vapour scavenging by solid particles is particularly important. Assuming that the CL is so narrow that temperature, particle density and velocity do not change appreciably inside it, an asymptotic theory is found, the delta-CL theory, that approximates very well the vapour and droplet profiles, the dew point shift and the deposition rates at the wall for wide ranges of the wall temperature (T) over tilde (w) and the scavenging parameter R. This theory breaks down for (T) over tilde (w) very close to the maximum temperature yielding non-zero droplet deposition rate, (T) over tilde (w,M). If the width of the CL is assumed to be zero (0-CL theory), the vapour density reaches local equilibrium with the condensate immediately after it enters the dew surface. The 0-CL theory yields appropriate profiles and deposition rates in the limit as R -> infinity and also for any R, provided (T) over tilde (w) is very close to (T) over tilde (w,M). Nonlinear multiple scales also improve the 0-CL theory, providing good uniform approximations to the deposition rates and the profiles for large R or for moderate R and (T) over tilde (w) very close to (T) over tilde (w,M), but it breaks down for other values of (T) over tilde (w) and small R.

Item Type: | Article |
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Uncontrolled Keywords: | Homogeneus condensation; Diffusion; Flows |

Subjects: | Sciences > Physics > Solid state physics Sciences > Physics > Thermodynamics |

ID Code: | 14910 |

References: | Batchelor, G. K. & C. Shen, C. 1985 Thermophoretic deposition of particles in gas flowing over cold surfaces, J. Colloid Interface Sci., 107, 21–37. Castillo, J. L. & Rosner, D. E. 1988 A nonequilibrium theory of surface deposition from particle-laden, dilute condensible vapour-containing laminar boundary layers. Int. J. Multiphase Flow, 14, 99–120. Castillo, J. L. & Rosner, D. E. 1989 Theory of surface deposition from a unary dilute vapour-containing steam, allowing for condensation within the laminar boundary layer. Chem. Eng. Sci. 44, 925–937. Davis, E. J. 1983 Transport Phenomena with Single Aerosol Particles. Aerosol Sci. Technol. 2, 121–144. Delale, C. F. & Crighton, D. G. 1998 Prandtl-Meyer flows with homogeneous condensation. Part 1. Subcritical flows. J. Fluid Mech. 359, 23–47. Filippov, A. V. 2003 Simultaneous particle and vapour deposition in a laminar boundary layer. J. Colloid Interface Sci. 257, 2–12. |

Deposited On: | 20 Apr 2012 10:51 |

Last Modified: | 06 Feb 2014 10:12 |

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