具化學反應圓柱粒子之熱泳運動

Abstract

本論文探討一有化學反應之圓柱粒子，於一存在外加垂直於其軸向之均勻溫度梯度的氣體中所進行之熱泳運動，在Knudsen數較小的滑移流動情況下之氣固界面，可以用溫度跳躍、熱滑移、摩擦滑移和熱應力滑移的效應來描述。吾人求解適當的熱傳導/熱生成和流體運動主導方程式，得到解析型式的圓柱粒子熱泳速度。熱泳速度為熱應力滑移係數的線性函數，熱應力滑移的影響會隨著Knudsen數的增大而增強。當粒子內化學反應之組成因數不是位置的函數時，熱泳速度會因為吸熱反應而減少，因為放熱反應而增加。當化學反應組成因數是一個位置函數時，熱泳速度的方向有可能偏離於外加溫度梯度的方向。在固定的系統性質下，由於圓柱粒子的比表面積比球形粒子來的小，化學反應對於圓柱粒子之熱泳速度的影響比對於球形粒子來得明顯。

The thermophoresis of a circular cylindrical particle bearing a chemical reaction in agas prescribed with a uniform temperature gradient in the direction perpendicular to its axisisanalyzed. The Knudsen number is assumed to be moderately small so that the fluid motion is in the slip-flow regime with effects of temperature jump, thermal creep, frictional slip, and thermal stress slip at the particle-gas interface. The appropriategoverning equations of heat conduction/generation and fluid motionare solved analytically and the thermophoretic velocity of the particle is obtained in closed forms. The thermophoretic velocity is a linear function of the thermal stress slip coefficient whose effect increases with an increase in the Knudsen number.When the composition-dependent factor of the chemical reaction within the particle does not depend on position, the thermophoretic velocity is diminished as the reaction is endothermic and augmented as the reaction is exothermic.When this factor is a function ofposition, the particle velocity can deflect from the direction of the imposed temperature gradient. For specified system characteristics,the effect of the chemical reaction on the thermophoreticvelocity of a circular cylindrical particle is significantly greater than thatof a spherical particle due to its smaller specific surface area.