Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-26T05:57:18.142Z Has data issue: false hasContentIssue false
  • English
  • Français

Role of the Knudsen layer in determining surface reaction rates based on sticking coefficients

Published online by Cambridge University Press:  26 August 2009

PENG ZHANG  and
CHUNG K. LAW
PENG ZHANG
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
CHUNG K. LAW*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: cklaw@princeton.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A theory on weakly rarefied low-Mach-number flows with surface reactions based on small sticking coefficients was formulated for a binary gas mixture with an irreversible surface reaction, and then extended to a multicomponent mixture with multi-step surface reactions for the situation when all chemically active species are small in concentration compared to a major inert species. Particular interest was placed on the interaction between the Knudsen layer and the surface reactions. Results show that the Knudsen layer modifies not only the incident flux of the molecules striking the surface but also the temperature-sensitive sticking coefficients, and consequently the surface reaction rates. The surface reactions in turn modify the flow structure in the Knudsen layer through the non-zero net flux at the surface. The rate expressions for the surface reactions based on sticking coefficients were derived, and the slip boundary conditions for the temperature and the species concentration suitable for application were established. The widely used Motz–Wise correction formula for the surface reaction rate was revised and the underlying assumptions leading to its derivation were shown to be inappropriate.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 634 , 10 September 2009 , pp. 113 - 135
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abramowitz, M. 1953 Evaluation of the integral ∫0∞ e−u 2−x/udu. J. Math. Phys. 32, 188–192.CrossRefGoogle Scholar
Albertoni, S., Cercignani, C. & Gotusso, L. 1963 Numerical evaluation of the slip coefficient. Phys. Fluids 6, 993–996.CrossRefGoogle Scholar
Andries, P., Aoki, K. & Perthame, B. 2002 A consistent BGK-type model for gas mixtures. J. Stat. Phys. 106, 993–1018.CrossRefGoogle Scholar
Bhatnagar, P. L., Gross, E. P. & Krook, M. 1954 A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511–525.CrossRefGoogle Scholar
Boley, C. D. & Yip, S. 1972 Modelling theory of the linearized collision operator for a gas mixture. Phys. Fluids 15, 1424–1433.CrossRefGoogle Scholar
Cercignani, C. 1975 Theory and Application of the Boltzmann Equation. Elsevier Science.Google Scholar
Cercignani, C. 2005 Slow Rarefied Flows: Theory and Application to Micro-Electro-Mechanical Systems. Birkhäuser.Google Scholar
Cercignani, C. & Daneri, A. 1963 Flow of a rarefied gas between two parallel plates. J. Appl. Phys. 34, 3509–3513.CrossRefGoogle Scholar
Cercignani, C. & Lampis, M. 1971 Kinetic model for gas-surface interaction. Transp. Theory Stat. Phys. 1, 101–114.CrossRefGoogle Scholar
Ceyer, S. T. 1990 New mechanisms for chemistry at surfaces. Science 249, 133–139.CrossRefGoogle ScholarPubMed
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-Uniform Gases. Cambridge University Press.Google Scholar
Coltrin, M. E., Kee, R. J., Rupley, F. M. & Meeks, E. 1996 Surface Chemikin-III: A Fortran Package For Analyzing Heterogeneous Chemical Kinetics at A Solid-surface–Gas-phase Interface. SAND96-8217.CrossRefGoogle Scholar
Dorsman, R. & Kleijn, C. R. 2007 A general correction to surface reaction models based on reactive sticking coefficients. Chem. Vapor Depos. 13, 91–97.CrossRefGoogle Scholar
Garzó, V., Santos, A. & Brey, J. J. 1989 A Kinetic model for a multicomponent gas. Phys. Fluids A 1, 380–383.CrossRefGoogle Scholar
Gupta, R. N., Scott, C. D. & Moss, J. N. 1985 Slip-boundary equations for multicomponent nonequilibrium airflow. Tech. Rep. Paper 2452. NASA.Google Scholar
Hamel, B. B. 1965 Kinetic model for binary gas mixtures. Phys. Fluids 8, 418–425.CrossRefGoogle Scholar
Hu, T. & Glumac, N. G. 2002 The effects of temperature jump on CVD modelling. Chem. Vapor Depos. 8, 205–212.3.0.CO;2-4>CrossRefGoogle Scholar
Ivchenko, I. N., Loyalka, S. K. & Tompson, R. V. Jr., 2007 Analytical Methods for Problems of Molecular Transport. Springer.CrossRefGoogle Scholar
Ivchenko, I. N. & Yalamov, Y. I. 1971 On diffusion slip of a binary gas mixture. Fluid Dyn. 6, 570–574.CrossRefGoogle Scholar
Jeans, J. H. 1925 The Dynamical Theory of Gases. Cambridge University Press.Google Scholar
Kee, R. J., Coltrin, M. E. & Glarborg, P. 2003 Chemically Reacting Flow: Theory and Practice. Wiley.CrossRefGoogle Scholar
Kogan, M. N. 1969 Rarefied Gas Dynamics. Plenum Press.CrossRefGoogle Scholar
Kogan, M. N. 1973 Molecular gasdynamics. Annu. Rev. Fluid Mech. 5, 383–404.CrossRefGoogle Scholar
Kogan, M. N. & Makashev, N. K. 1971 Role of the Knudsen layer in the theory of heterogeneous reactions and in flows with surface reactions. Fluid Dyn. 6, 913–920.CrossRefGoogle Scholar
Kogan, M. N. & Makashev, N. K. 1972 Boundary conditions for flows with chemical reaction occurring on a surface. Fluid Dyn. 7, 116–125.CrossRefGoogle Scholar
Laporte, O. 1937 Absorption coefficients for thermal neutrons. Phys. Rev. 52, 72–74.CrossRefGoogle Scholar
Law, C. K. 2006 Combustion Physics. Cambridge University Press.CrossRefGoogle Scholar
Loyalka, S. K. 1971 Velocity slip coefficient and the diffusion slip velocity for a multicomponent gas mixture. Phys. Fluids 14, 2599–2604.CrossRefGoogle Scholar
Loyalka, S. K. & Ferziger, J. H. 1967 Model dependence of the slip coefficient. Phys. Fluids 10, 1833–1839.CrossRefGoogle Scholar
Loyalka, S. K. & Ferziger, J. H. 1968 Model dependence of the temperature slip coefficient. Phys. Fluids 11, 1668–1671.CrossRefGoogle Scholar
Motz, H. & Wise, H. 1960 Diffusion and heterogeneous reaction. III. Atom recombination at a catalytic boundary. J. Chem. Phys. 32, 1893–1894.CrossRefGoogle Scholar
Nocilla, S. 1961 On the interaction between stream and body in free-molecule flow. In Rarefied Gasdynamics: Second International Symposium (ed. Talbot, L.), pp. 169–207. Academic Press.Google Scholar
Nocilla, S. 1963 The surface re-emission law in free molecule flow. In Rarefied Gasdynamics: Third International Symposium (ed. Laurmann, J. A.). pp. 327–346. Academic Press.Google Scholar
Pao, Y. 1971 a Application of kinetic theory to the problem of evaporation and condensation. Phys. Fluids 14, 306–312.CrossRefGoogle Scholar
Pao, Y. 1971 b Temperature and density jumps in the kinetic theory of gases and vapours. Phys. Fluids 14, 1340–1346.CrossRefGoogle Scholar
Polyanin, A. D. & Manzhirov, A. V. 1998 Handbook of Integral Equations. CRC Press.CrossRefGoogle Scholar
Scott, C. D. 1973 Wall boundary equations with slip and catalysis for multicomponent, nonequilibrium gas flows. Tech. Rep. TM X-58111. NASA.Google Scholar
Shen, C. 1983 The concentration-jump coefficient in a rarefied binary gas mixture. J. Fluid Mech. 137, 221–231.CrossRefGoogle Scholar
Siewert, C. E. & Sharipov, F. 2002 Model equations in rarefied gasdynamics: viscous-slip and thermal-slip coefficients. Phys. Fluids 14, 4123–4129.CrossRefGoogle Scholar
Sirovich, L. 1962 Kinetic modelling of gas mixtures. Phys. Fluids 5, 908–918.CrossRefGoogle Scholar
Sone, Y. 2006 Molecular Gasdynamics: Theory, Techniques and Applications. Birkhäuser.Google Scholar
Szekely, J., Evans, J. W. & Sohn, H. Y. 1976 Gas–Solid Reactions. Academic Press.Google Scholar
Welander, P. 1954 The temperature jump in a rarefied gas. Arkiv foer Fysik 7, 503–537.Google Scholar
Xu, B. & Ju, Y. 2006 Theoretical and numerical studies of non-equilibrium slip effects on a catalytic surface. Combust. Theory Modelling 10, 961–979.CrossRefGoogle Scholar
Zharov, V. A. 1972 Determination of the slippage rate for a binary mixture of gases. Fluid Dyn. 7, 274–279.CrossRefGoogle Scholar