球形氣膠粒子在微圓管中之熱泳

Abstract

本論文探討一球形膠體粒子在氣體中，於均勻外加溫度梯度下，沿著一微圓管中心軸進行之熱泳運動，其中管壁條件可為絕熱以及外加線性溫度分佈兩者任一。由於Knudsen數較小，可將氣體視為連續流動相，並在粒子表面考慮溫度躍差、熱滑移、及摩擦滑移的現象。微圓管對熱泳之邊界效應，其一來自於氣膠粒子與管壁間產生的熱傳導交互作用，另一為流體之黏滯作用。在低Peclet數以及低Reynolds數的假設下，吾人求解系統之能量及動量主導方程式，得到溫度及流速分佈，再配合邊界取點之數值方法，計算出氣膠粒子之熱泳速度。在變化氣膠粒子與周圍流體之熱傳導及表面特性、氣膠粒子與圓管之相對半徑、以及管壁熱滲透效應之情況下所得到之邊界取點數值結果，與使用反射法所得到之解析解相當符合。這些結果顯示不同的管壁條件以及管壁熱滲透效應對於粒子熱泳速度的影響甚為顯著。在管壁沒有熱滑移現象時，熱泳速度隨著氣膠粒子與圓管半徑比增大而減少，而當管壁具有熱滑移現象而產生熱滲透時，此熱滲透產生的反向流場甚至可以轉變氣膠粒子熱泳速度方向。一般而言，管壁的邊界效應對於氣膠粒子的熱泳有不可忽略的影響。

A theoretical study is presented for the thermophoretic motion of a spherical particle along the axis of a circular microtube filled with a gaseous medium. The imposed temperature gradient is uniform and parallel to the tube wall, which may be either insulated or prescribed with the linear temperature distribution. The Knudsen number is small so that the fluid flow is described by a continuum model with temperature jump, thermal creep, and frictional slip at the solid surfaces. The general solutions to the thermal and hydrodynamic governing equations are constructed in combined cylindrical and spherical coordinates, and the boundary conditions at the particle surface are enforced by a collocation method. The collocation solutions for the thermophoretic mobility of the confined particle, which agree well with the asymptotic formula obtained by using a method of reflections, are obtained for various values of the particle, tube wall, and fluid characteristics. An insulated tube wall and a tube wall prescribed with the far-field temperature distribution affect the thermophoresis of the particle quite differently. The mobility of a particle confined by a tube wall without thermal creep decreases with an increase in the particle-to-tube radius ratio. When the thermal creep coefficient of the tube wall is comparable to that of the particle, the thermoosmotic flow of the fluid induced by the tube wall strongly dominates the migration of the particle and can simply reverse its direction. In general, the boundary effect of the confining tube on thermophoresis is significant.