球形氣膠粒子在圓柱形孔隙中之熱泳運動

Thermophoresis of an Aerosol Sphere in a Circular Cylindrical Pore

吳光正(Kuang-Cheng Wu)

指導教授 ： 葛煥彰

國立臺灣大學/工學院/化學工程學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.02124

摘要

本文研究在低Reynolds數與Peclet數之下，一球形粒子在氣體中，沿一圓柱形孔隙的中心軸穩定進行之熱泳運動。其中外加之溫度梯度為均勻且平行於圓孔壁，而孔壁可為絕熱或是固定為一線性的溫度分布。由於Knudsen數很小，所以流體在粒子表面之流動可以視為一同時具備溫度躍差、熱滑移和摩擦滑移之連續體。圓孔壁的存在會對粒子的移動速度造成兩種基本的效應：第一，粒子附近的溫度梯度會受到影響，這可能使粒子加速或是減速；第二，孔壁會造成摩擦阻力而使粒子的移動減速。在本文中，為了求解能量守衡與動量守衡方程式，會同時使用球座標和圓柱座標來建立通解，至於施加邊界條件部分，則要先對在孔壁處的條件使用Fourier轉換來化簡通解，而對於在粒子表面處的條件則使用邊界取點法來求解。粒子熱泳速度的數值解結果將與在相同條件下但粒子處於無邊界之流體中的解相比較，並呈現在不同熱導度、不同粒子表面性質、與不同粒子和孔壁距離之結果。吾人使用邊界取點法所得之數值結果與使用反射法所得之近似解析解互相吻合。孔壁存在時之粒子熱泳速度會受到粒子表面性質、孔壁性質、粒子和圓孔半徑比、以及孔壁邊界熱傳條件的影響。整體來說，邊界效應對氣膠粒子熱泳的影響是非常明顯與複雜的。

關鍵字

熱泳 ； 球形氣膠粒子 ； 流體力學 ； 邊界效應 ； 圓柱形孔隙

並列摘要

The problem of the thermophoretic motion of a spherical particle in a gaseous medium along the centerline of a circular cylindrical pore is studied theoretically in the steady limit of negligible Reynolds and Peclet numbers. The imposed temperature gradient is uniform and parallel to the pore wall, which may be either insulated or prescribed with the far-field temperature distribution. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the particle surface. The presence of the pore wall causes two basic effects on the particle velocity: first, the local temperature gradients on the particle surface are altered by the wall, thereby speeding up or slowing down the particle; secondly, the wall enhances the viscous retardation of the moving particle. To solve the equations of conservation of energy and momentum, the general solutions are constructed from the fundamental solutions in both cylindrical and spherical coordinates. The boundary conditions are enforced first at the pore wall by the Fourier transforms and then on the particle surface by a collocation technique. Numerical results for the thermophoretic velocity of the particle relative to that under identical conditions in an unbounded fluid solution are presented for various relative thermal conductivity and surface properties of the particle, as well as the relative separation distance between the particle and the pore wall. The collocation results agree well with the approximate analytical solution obtained by using a method of reflections. The wall-corrected particle velocity depends on the surface properties of the particle and the wall, the ratio of particle-to-pore radii, and the thermal boundary condition at the wall. In general, the boundary effect on thermophoresis is quite significant and complicated.

並列關鍵字

Thermophoresis ； Aerosol sphere ； Fluid mechanics ； Boundary effects ； Circular cylindrical pore

參考文獻

3. Batchelor GK, Shen C. Thermophoretic deposition of particles in gas flowing over cold surfaces. J. Colloid Interface Sci. 1985;107:21-37.

4. Montassier N, Boulaud D, Renoux A. Experimental study of thermophoretic particle deposition in laminar tube flow. J. Aerosol Sci. 1991;22:677-687.

5. Messerer A, Niessner R, Poschl U. Miniature pipe bundle heat exchanger for thermophoretic deposition of ultrafine soot aerosol particles at high flow velocities. Aerosol Sci. Technol. 2004;38:456-466.

6. Balsara NP, Subramanian RS. The influence of buoyancy on thermophoretic deposition of aerosol particles in a horizontal tube. J. Colloid Interface Sci. 1987;118:3-14.

7. Ye Y, Pui DYH, Liu BYH, 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. 1991;22:63-72.