多個同軸滑移球形粒子繞其軸線之緩慢轉動

Abstract

本論文在低雷諾數下，對一不可壓縮流體中多個同軸之滑移球形粒子圍繞其軸線穩定旋轉的周圍流場進行分析。這些粒子的半徑、滑移係數和角速度可以不同，並且它們相鄰二粒子的間距也可以不同。通過邊界取點法，吾人半解析地求解了控制流體流動的Stokes方程式。在適當條件下，發現粒子之間的相互作用效應值得注意。對於兩個球形粒子的旋轉，邊界取點法所得到的流體作用於粒子之力矩結果與文獻中使用雙生多極展開法所獲得的解析近似解具有良好的一致性。對於三個球形粒子的旋轉，粒子之間的相互作用效應顯示第三個粒子的存在可以明顯地影響原本作用在其他兩個粒子上的力矩。此相互作用效應對較小或較不滑移的粒子比對較大或較滑移的粒子影響更大。流體作用於多個粒子鏈的旋轉力矩結果則明顯顯示了粒子之間的屏蔽效應。

The flow field around a straight chain of multiple slip spherical particles rotating steadily in an incompressible Newtonian fluid about their line of centers is analyzed at low Reynolds numbers. The particles may vary in radius, slip coefficient, and angular velocity, and they are permitted to be unevenly spaced. Through the use of a boundary collocation method, the Stokes equation governing the fluid flow is solved semi-analytically. The interaction effects among the particles are found to be noteworthy under appropriate conditions. For the rotation of two spheres, our collocation results for their hydrodynamic torques are in good agreement with the analytical asymptotic solution in the literature obtained by using a method of twin multipole expansions. For the rotation of three spheres, the particle interaction effect indicates that the existence of the third particle can influence the torques exerted on the other two particles noticeably. The interaction effect is stronger on the smaller or less slippery particles than on the larger or more slippery ones. Torque results for the rotation of chains of many particles visibly show the shielding effect among the particles.