- 學位論文
球形氣膠粒子在球形孔洞中之熱泳
Thermophoretic motion of an aerosol sphere in a spherical cavity
摘要
本研究探討一球形氣膠粒子在外加均勻的溫度梯度場作用下，於球形孔洞中任一位置上，沿著孔洞與粒子連心線之垂直方向之熱泳運動。此非軸對稱方向之粒子運動，包含了移動與轉動，皆受到孔洞邊界所帶來的效應。吾人假設相對於粒子半徑，氣體之平均自由徑很小，則可將氣體視為連續體，且在此粒子表面及孔璧上之Knudsen邊界層流體會受到所產生之熱滲透、摩擦滑移、溫度躍差以及熱應力滑移效應之影響。孔洞對熱泳產生之邊界效應，來自於熱傳導作用、流體流動之黏滯作用以及孔洞內部流體循環流動的影響。吾人求解系統之能量及動量主導方程式，配合力平衡假設，再以邊界取點之數值方法，計算出氣膠粒子之正規化熱泳速度及角速度。在改變氣膠粒子與周圍流體之熱傳導及表面特性以及氣膠粒子與孔洞之相對半徑及其中心之相對距離之情況下，將求得之邊界取點數值結果作圖分析。結果顯示，根據相關幾何及氣固特性參數的不同，孔洞引起的熱滲透循環流動可能增加或減少粒子在的熱泳速度，而此循環流動會減緩粒子之轉動速度，甚至改變其移動及轉動方向。
並列摘要
A theoretical study of the quasi-steady thermophoresis of an aerosol sphere situated at an arbitrary position within a spherical cavity normal to the line of their centers is presented. In the slip-flow regime for the gas motion, the thermal creep, thermal stress slip, frictional slip, and temperature jump are permitted at the solid surfaces. The general solutions to the conservative equations governing the temperature and fluid velocity distributions in the two spherical coordinate systems with respect to the particle and cavity centers are superimposed, and the boundary conditions are satisfied by a collocation method. The translational and rotational velocities of the particle are determined as functions of the scaled center-to-center distance between the particle and cavity (eccentricity of the particle position), their radius ratio, and their relative thermal and surface properties. When the particle is located at the cavity center, its migration velocity agrees well with the available analytical solution. In general, the thermophoretic mobility of the particle decreases with increases in the relative distance between the particle and cavity centers and in the particle-to-cavity radius ratio, but there exist some exceptions. The circulating cavity-induced thermoosmotic flow can enhance or reduce the thermophoretic translation and rotation of the particle and even reverse their directions, depending on the geometric parameters. The effect of the cavity wall on the thermophoretic translation of a particle normal to the line through their centers is slightly weaker than that parallel to this line.
參考文獻
延伸閱讀
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