| 研究生: |
詹昆潔 Chan, Kun-Chieh |
|---|---|
| 論文名稱: |
波形圓盤上熱泳及電泳效應對於粒子沈積的影響 Combined effects of thermophoresis and electrophoresis on particle deposition onto a wavy surface disk |
| 指導教授: |
陳朝光
Chen, Chao-Kuang |
| 學位類別: |
碩士 Master |
| 系所名稱: |
工學院 - 機械工程學系 Department of Mechanical Engineering |
| 論文出版年: | 2005 |
| 畢業學年度: | 93 |
| 語文別: | 中文 |
| 論文頁數: | 80 |
| 中文關鍵詞: | 波形表面 、停滯流 、電泳 、熱泳 、樣線函數 |
| 外文關鍵詞: | cubic spline, wavy surface, stagnation flow, electrophoresis, thermophoresis |
| 相關次數: | 點閱:158 下載:1 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本文以座標轉換系統探討停滯流於軸對稱波形圓盤,受到布朗擴散、對流、重力沈降、熱泳以及電泳效應的影響,氣膠粒子沈積現象的分析。統制方程式之推導由完整的Navier-Stokes方程式著手,經半相似轉換可將不規則邊界展開成一規則可計算的平面,並配合三次樣線定置法(SADI;Spline Alternating-Direction Implicit Method)求得數值解。於平板時所得的數值結果與相關的文獻比較,有良好的吻合,可知本文可確實模擬不規則平面的沈積現象。
數值結果顯示,電泳會增強粒子沈積效應,但不會隨半徑增強,而因溫度梯度造成的熱泳效應則會隨著半徑增加而增強。沈積表面的幾何形狀會影響沈積效應,使之呈現與表面類似之頻率,且當擴散與熱泳為主要機制時,表面之凸起與凹陷的位移影響的程度隨半徑增加而愈趨明顯。至於整體的平均沈積效應大約略小於平坦表面的沈積效應。
In this study, the coordinate transformation method is used to analyze the aerosol particle deposition from a stagnation flow onto an axisymmetric wavy disk by the effects coupled with Brownian diffusion, convection, sedimentation, thermophoresis and electrophoresis. The governing equations of system are derived from complete Navier-Stokes equation and particle concentration equation. The transformed governing equations can expand the irregular boundary into a calculable regular plane, and then solve it by using the spline alternating-direction implicit method (SADI). When the mathematical model is simplified to the case on flat plates, the results have good agreement with previous work. This indicates that the method presented in this study could simulate the particle deposition onto the irregular plane.
Numerical results show that the electrophoresis would increase the particle deposition but not become greater with the increase of the radius. However, the effect of thermophoresis will become greater when the radius increases. The geometric surface would influence the particle deposition and make it have a similar frequency with the surface. When Brownian diffusion and thermophoresis dominate the particle deposition, the influence of the displacement from the lumpy surface will become greater with the increase of the radius. Additionally, mean particle deposition of the wavy disk would be smaller than the flat disk.
Ahlbrg, J. H., Nilson, E. N. and Walsh, J. L., “The theory of splines and their application,” Academic Press, 1967.
Albasiny, E. L. and Hoskins, W. D., “Increase Accuracy cubic spline solutions to two-point boundary value problems,” J. Inst. Math. Applic., Vol. 9, pp. 47-55, 1972.
Batchelor, G. K., and Shen, C., “Thermophoretic deposition in gas flow over cold surface,” Journal of Colloid and Interface Science, Vol. 107, pp. 21-37, 1985.
Bai, H. and Biswas, P., “Deposition of lognormally distributed aerosols accounting for simultaneous diffusion, thermophoresis and coagulation,” J. Aerosol Sci., Vol. 21, pp. 629-640, 1990.
Chawla, T. C., Leaf, G. Chen, W. L., and Grolmes, M. A., The application of the collocation method using hermite cubic spline to nonlinear transient one-dimensional heat conduction problem,” ASME Journal of Heat Transfer, pp. 562-569, 1975.
Chen, C. K., “Application of cubic spline collocation method to solve transient heat transfer problem,” Heat Transfer in Thermal Systems Seminar-phase, N.C.K.U., Tainan, Taiwan, pp. 167-182, 1986.
Cooper, D. W., Perers, M. N. and Miller, R. J., “Predicted deposition of submicrometer particles due to diffusion and electrostatics in viscous axisymmetric stagnation-point flow,” J. Aerosol Sci., Technol. 11, pp. 133-143, 1989.
Chiu, P. and Chou, H. M., “Free Convection in the Boundary Layer Flow of a Micropolar Fluid along a Vertical Wavy Surface”, Acta Mechanical., Vol. 101, pp. 161-174, 1993.
Chiu, C. P. and Chou, H. M., “Transient analysis of natural convection along a vertical wavy surface in micropolar fluids,” International Journal of Engineering Science, Vol. 32, pp. 19-33, 1994.
Cho, C. H., Hwang, J. H. and Choi, M. S., “Deposition of polydisperse particles in a Falkner-Skan wedge flow,” J. Aerosol Sci., Vol. 27, pp. 249-261, 1996.
Fyfe, D. J., “The use of cubic splines in the solution of two-point boundary value problems,” Computer Journal, Vol. 12, pp. 188-192, 1969.
Friedlander, S. K., Fernando de la Mora, J. and Gokoglu, S., “Diffusive leakage of small particles across the dust-free layer near a hot wall,” J. Colloid Interface Sci., Vol. 125, pp. 351-355, 1988.
Goren,S.L., “Thermophoresis of aerosol particles in the laminar boundary layer on a flat surface,” J. Colliod Interface Sci., Vol. 61, pp. 77-85, 1977.
Hales, J. M., Schwendiman, L. C. and Horst, T. W., “Aerosol transport in a naturally convected boundary layer,” Int. J. Heat Mass Transfer, Vol. 15, pp. 1837-1850, 1972.
Homsy, G. M., Geyling, F. T. and Walker, K. L., “Blausius series for thermophoresis deposition of small particles,” J. Colliod Interface Sci., Vol. 83, pp.495-501, 1981.
Hwang, J. and Daily, J. W., “Electric field enhanced deposition inflame-synthesized materials manufacturing,” J. Aerosol Sci., Vol. 26, pp. 5-18, 1995.
Isa, M. and Usmani, R. A., “Quintic spline solution of a boundary value problem,” International Journal of Computer Mathematics, Vol. 11, pp. 169-184, 1982.
Jain, M. K. and Azia, T., “Cubic spline solution of two-point boundary value problems with significant first derivatives,” Computer Methods in Applied Mechanics and Engineering, Vol. 39, pp. 83-91,1983.
Liggett, J. A. and Salmon, J. R., “Cubic spline boundary element,” Int. J. Numerical Methods in Engineering, Vol. 17, pp. 543-556, 1981.
MILNE-THOMSON, L.M., “Theoretical Hydrodynamics, 5th edn,” MacMil-lan, New York, 1968.
Mills, A. F., Hang, X. and Ayazi, F. “The effect of wall suction and thermophoresis on aerosol particle deposition from a laminar boundary layer on a flat plate,” Int. J. Heat Mass Transfer, Vol. 27, pp.1110-1113, 1984.
Napolitano, M., “Efficient ADI and spline ADI Methods for the steady-state Navior-Stokes equations,” International Journal for Numerical Methods in Fluids, Vol. 4, pp. 1101-1115, 1984.
Opiolka, S., Schmidt, F. and Fissan, H., “Combined effects of electrophoresis and thermophoresis on particle deposition onto flat surfaces,” J. Aerosol Sci., Vol. 25, pp. 665-671, 1994.
Peterson, T. W., Stratmann, F. and Fissan, H., “Particle deposition on wafers: a comparison between two modeling approaches,” J. Aerosol Sci., Vol. 20, pp. 683-693, 1989.
Peters, M. H., Cooper, D. W. and Miller, R. J., “The effects of electrostatic andinertial forces on the diffusive deposition of small particles onto large disks: viscous axisymmetric stagnation point flow approximations,” J. Aerosol Sci., Vol. 20, pp. 123-136, 1989.
Peters, M. H. and Cooper, D. W., “The effects of electrostatic forces on thermophoretic suppression of particle diffusional deposition onto hot surfaces,” J. Colloid Interface Sci., Vol. 140, pp. 48-56, 1990.
Rubin, S. G. and Graves, R. A., “Viscous flow solution with a cubic spline approximation,” Computers and Fluids, Vol. 1, No. 5, pp. 1-36, 1975.
Raggett, G. F., Stone, J. A. R., and Wisher, S. J., “The cubic spline solution of practical problems modeled by hyperbolic partial differential equations,” Computer Methods in Applied Mechanics and Engineering, Vol. 8, pp. 139-151, 1976.
Rubin, S. G. and Khosla, P. K., “Higher-order numerical solution using cubic splines,” AIAA Journal, Vol. 14, pp. 851-858, 1976.
Rubin, S. G. and Khosla, P. K., “Polynomial interpolation methods for viscous flow calculation,” Journal of Computational Physics, Vol. 24, pp. 217-244, 1977.
Stratmann, F., Fissan, H. and Peterson, T. W., “Particle deposition onto a flat surface from a point particle source,” J Envir. Sci., pp. 39-41, 1988.
Shen, C., “Thermophoretic deposition of particles onto cold surface of bodies in two dimensional and axi-symmetric flows,” Journal of Colloid and Interface Science, Vol. 127, pp. 104-115, 1989.
Talbot, L., Cheng, R. K., Scheffer, R. W. and Wills, D. P., “Thermophoresis of particle in a heated boundary layer,” Journal of Fluid Mechanics, Vol. 101, pp. 737-758, 1980.
Turner, J. R., Liguras, D. K. and Fissan, H. J., “Clean room applications of particle deposition from stagnation flow: electrostatic effects,” J. Aerosol Sci., Vol. 20, pp. 403-417, 1989.
Tsai, R., Chang, Y. P. and Lin, T. Y., “Combined effects of thermophoresis and electrophoresis on particle deposition onto a wafer,” J. Aerosol Sci. Vol. 29, No. 7, pp. 811-825, 1998.
Wanga, P. and Kahawita, R., “A two-dimensional numerical model of estuarine circulation using cubic spline,” Canadian Journal of Civil Engineering, Vol. 10, pp. 116-124, 1983.
Wangb, P. and Kahawita, R., “Numerical integration of partial differential equations using cubic splines,” International Journal of Computer Mathematics, Vol. 13, No. 3-4, pp. 271-286, 1983.
Wang, P., Lin, S., and Kahawita, R., “The cubic spline integration technique for solving fusion welding problems,” Journal of Heat Transfer, Vol. 107, pp. 485-489, 1985.
Ye, Y., Pui, D. Y. H., Liu, B. Y. H., Opiolka, S., Blumhorst, S. and Fissan, H., “Thermophoretic effect of particle deposition on a free standing semiconductor wafer in a clean room,” J. Aerosol Sci., Vol. 22, pp. 63-72, 1991.
Yang, Y. T., Chen, C. K., Lin, M. T., “Natural convection of non-Newtonian fluids along a wavy vertical plate including the magnetic field effect,” International Journal of Heat and Mass Transfer, Vol. 39, No. 13, pp. 2831-2842, 1996.