Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-17T04:19:25.979Z Has data issue: false hasContentIssue false
  • English
  • Français

Theoretical Analysis of Cylindrical Microparticle Photophoresis in a Perpendicular Optical Field with Thermal Stress Slip Model

Published online by Cambridge University Press:  22 March 2012

P.-Y. Tzeng ,
C.-H. Liu ,
W.-K. Li  and
C.-Y. Soong
P.-Y. Tzeng
Affiliation:
Department of Mechatronics, Energy and Aerospace Engineering, Chung Cheng Institute of Technology, National Defense University, Taoyuan, Taiwan 33509, R.O.C.
C.-H. Liu
Affiliation:
Department of Biomedical Engineering, Yuanpei University, Hsinchu, Taiwan 30015, R.O.C.
W.-K. Li
Affiliation:
Planning Division, Army Command Headquarters, Ministry of National Defense, Taoyuan, Taiwan 32509, R.O.C.
C.-Y. Soong*
Affiliation:
Department of Aerospace and Systems Engineering, Feng Chia University, Taichung, Taiwan 40724, R.O.C.
*
*Corresponding author ([email protected])
Get access

Abstract

The present study is concerned with a theoretical analysis of the photophoresis of a microsized long cylinder in a perpendicular optical field. Different from previous studies of photophoresis, thermal stress slip usually neglected is taken into account in the analysis. The gaseous fluid relative to the microparticle in photophoretic motion falls into slip-flow regime. Asymmetric distribution of the absorbed heat energy within the particle becomes the driving force for photophoretic motion of the cylinder-shaped particle. By evaluating heat source function distributions at various conditions, the study focuses on the effects of particle size and optical properties on the energy distribution and the resultant influences on the photophoresis. The photophoretic mobility is developed by the slip flow model with consideration of thermal stress slip. The results reveal that the photophoretic mobility decreases with the increase of particle thermal conductivity (k*) and increases with Knudsen number (Kn). The thermal stress slip effect on photophoretic velocity is more noticeable at high Kn, but disappears at the continuum limit. A long cylinder-shaped particle has higher photophoretic velocity than a spherical particle at low k*, while the situation reverses at high k*. With thermal stress slip considered, the critical condition for crossing of the photophoretic velocity curves of cylindrical and spherical particles is mildly influenced by Kn.

Keywords

PhotophoresisCylindrical particleSlip-flow regimeThermal stress slip
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 1 , March 2012 , pp. 113 - 121
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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

1. Benincasa, D. S., Barber, P. W., Zhang, J. Z., Hsieh, W. F. and Chang, R. K., “Spatial Distribution of the Internal and Near-field Intensities of Large Cylindrical and Spherical Scatterers,” Applied Optics, 26, pp. 1348–1356 (1987).CrossRefGoogle ScholarPubMed
2. Bohren, C. F. and Huffman, D. R., Absorption and Scattering of Light by Small Particles, Wiley-Interscience, New York (2004).Google Scholar
3. Chernyak, V. and Beresnev, S., “Photophoresis of Aerosol Particles,” Journal of Aerosol Science, 24, pp. 857–866 (1993).CrossRefGoogle Scholar
4. Dusel, P. W., Kerker, M. and Cooke, D. D., “Distribution of Absorption Centers within Irradiated Spheres,” Journal of the Optical Society of America, 69, pp. 55–59 (1979).CrossRefGoogle Scholar
5. Greene, W. M., Spjut, R. E., Bar-Ziv, E., Longwell, J. P. and Sarofim, A. F., “Photophoresis of Irradiated Spheres: Evaluation of the Complex Index of Refraction,” Langmuir, 1, pp. 361–365 (1985).CrossRefGoogle Scholar
6. Gukasyan, A. A. and Yalamov, Y. I., “Photophoretic Motion of Moderately Large Aerosol Particle,” Journal of Russian Laser Research, 5, pp. 297–298 (1984).Google Scholar
7. Happel, J. and Brenner, H., Low Reynolds Number Hydrodynamics, Marfinus Nijhoff, The Netherlands (1983).CrossRefGoogle Scholar
8. Keh, H. J. and Tu, H. J., “Thermophoresis and Photophoresis of Cylindrical Particles,” Colloids Surface A, 176, pp. 213–223 (2001).CrossRefGoogle Scholar
9. Kennard, E. H., Kinetic Theory of Gases, McGraw-Hill, New York (1938).Google Scholar
10. Li, W. K., Soong, C. Y., Tzeng, P. Y. and Liu, C. H., “Analysis of Transition and Mobility of Microparticle Photophoresis with Slip Flow Model,” Microfluidics and Nanofluidics, 10, pp. 199–209 (2011).CrossRefGoogle Scholar
11. Lienhard, J. H., A Heat Transfer Textbook, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ (1987).Google Scholar
12. Liu, C. H., Soong, C. Y., Li, W. K. and Tzeng, P. Y., “Internal Electric Field Distribution within a Micro-Cylinder-Shaped Particle Suspended in an Absorbing Gaseous Medium,” Journal of Quantitative Spectroscopy and Radiative Transfer, 111, pp. 483–491 (2010).CrossRefGoogle Scholar
13. Lockerby, D. A., Reese, J. M., Emerson, D. R. and Barber, R. W., “Velocity Boundary Condition at Solid Walls in Rarefied Gas Calculations,” Physical Review E, 70, 017303 (2004).CrossRefGoogle ScholarPubMed
14. Mackowski, D.W., “Photophoresis of Aerosol Particles in the Free Molecular and Slip-Flow Regimes,” International Journal Heat and Mass Transfer, 32, pp. 843–854 (1989).CrossRefGoogle Scholar
15. Orr, C. and Keng, E. Y. H., “Photophoretic Effects in the Stratosphere,” Journal of Atmospheric Science, 21, pp. 475–478 (1964).2.0.CO;2>CrossRefGoogle Scholar
16. Owen, J. F., Barber, P. W., Dorain, P. B. and Chang, R. K., “Enhancement of Fluorescence Induced by Microstructure Resonances of a Dielectric Fiber,” Physical Review Letters, 47, pp. 1075–1078 (1981).CrossRefGoogle Scholar
17. Owen, J. F., Chang, R. K. and Barber, P. W., “Internal Electric Field Distributions of a Dielectric Cylinder at Resonance Wavelengths,” Optics Letters, 6, pp. 540–542 (1981).CrossRefGoogle ScholarPubMed
18. Reed, L. D., “Low Knudsen Number Photophoresis,” Journal of Aerosol Science, 8, pp. 123–131 (1977).CrossRefGoogle Scholar
19. Ruppin, R., “Electromagnetic Energy Inside an Irradiated Cylinder,” Journal of the Optical Society of America A, 15, pp. 1891–1985 (1998).CrossRefGoogle Scholar
20. Ruppin, R., “Extinction by a Circular Cylinder in an Absorbing Medium,” Optics Communications, 211, pp. 335–340 (2001).CrossRefGoogle Scholar
21. Soong, C. Y., Li, W. K., Liu, C. H. and Tzeng, P. Y., “Effect of Thermal Stress Slip on Micro-Particle Photophoresis in Gaseous Media,” Optics Letters, 35, pp. 625–627 (2010).CrossRefGoogle Scholar
22. Sun, W., Loeb, N. G. and Fu, Q., “Finite-Difference Time Domain Solution of Light Scattering and Absorption by Particles in an Absorbing Medium,” Optics Letters, 41, pp. 5728–5743 (2002).Google Scholar
23. Sun, W., Loeb, N. G., Tanev, S. and Videen, G., “Finite-Difference Time Domain Solution of Light Scattering by an Infinite Dielectric Column Immersed in an Absorbing Medium,” Applied Optics, 44, pp. 1977–1983 (2005).CrossRefGoogle Scholar
24. Sun, W., Loeb, N. G. and Lin, B., “Light Scattering by an Infinite Circular Cylinder Immersed in an Absorbing Medium,” Applied Optics, 44, pp. 2338–2342 (2005).CrossRefGoogle Scholar
25. Talbot, L., Cheng, R. K., Schefer, R. W. and Willis, D. R., “Thermophoresis of Particles in Heated Boundary Layer,” Journal of Fluid Mechanics, 101, pp. 737–758 (1980).CrossRefGoogle Scholar
26. Tehranian, S., Giovane, F., Blum, J., Xu, Y. L. and Gustafson, B. A. S., “Photophoresis of Micrometer-Sized Particles in the Free-Molecular Regime,” International Journal Heat and Mass Transfer, 44, pp. 1649–1657 (2001).CrossRefGoogle Scholar
27. Yalamov, Y. I., Kutukov, V. B. and Shchukin, E. R., “Theory of the Photophoretic Motion of Large-Size Volatile Aerosol Particle,” Journal of Colloid and Interface Science, 57, pp. 564–571 (1976).CrossRefGoogle Scholar