| Summary: | 碩士 === 國立臺灣大學 === 化學工程學研究所 === 106 === 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.
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