軟質粒子在非同心孔洞中之低雷諾數轉動

Low-Reynolds-Number Rotation of a Soft Particle inside an Eccentric Cavity

周晉宇(Jing-Yu Chou)

指導教授 ： 葛煥彰

國立臺灣大學/工學院/化學工程學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202201976

摘要

本論文以半解析的方式探討一個軟質球形粒子於一個充滿黏性流體的球形孔洞中，在非同心位置上以其共同直徑為轉軸，所進行的穩態低雷諾數轉動。軟質粒子的構造為一個流體不可滲透的硬質核心固體，外圍包覆著一層流體可滲透的多孔物質。多孔層內外之流體速度分布分別由 Brinkman 及 Stokes 方程式主導，速度表示式可由兩個分別以粒子中心及孔洞中心為原點的球座標系統之通解組合而成。對於將速度式代入邊界條件所得到的方程組，可由邊界取點法數值求解計算出流體速度及作用於轉動粒子的力矩。由計算結果可得軟質粒子轉動所受正規化力矩與粒子結構(如多孔層的厚度及流體可滲透度)和粒子在孔洞中的相對位置及大小之關係。孔洞對於軟質粒子轉動的阻礙影響會比對於相應之完全硬質粒子為小。正規化力矩大致上會隨硬質核心對孔洞半徑比值增加而遞增，但在多孔層厚度占比較大且流體可滲透度較大時，正規化力矩隨硬質核心對孔洞半徑比值增加可能會先減後增，且最小值會小於該軟質粒子在相應無邊界流體中轉動所受之正規化力矩。此外，粒子在孔洞中所受正規化力矩大致上會隨其偏心程度增加而遞增，但在多孔層可滲透度及相對厚度較大時，也會出現正規化力矩隨偏心程度增加而略為遞減的情形。

關鍵字

粒子轉動 ； 軟質粒子 ； 蠕動流 ； 力矩 ； 邊界效應

並列摘要

The steady low-Reynolds-number rotation of a spherical soft particle (a hard core coated with a permeable porous layer) in a viscous fluid within a nonconcentric spherical cavity about their common diameter is semi-analytically studied in this thesis. To solve the Stokes and Brinkman equations for the fluid velocity, a solution is constituted by the general solutions in two spherical coordinate systems originated from the particle and cavity centers and the boundary conditions are satisfied by a collocation technique. Numerical results of the hydrodynamic torque on the soft sphere are obtained as a function of the core-to-particle radius ratio, particle-to-cavity radius ratio, relative center-to-center distance of the particle and cavity, and ratio of the particle radius to the permeation length in the porous layer over the entire ranges. The effect of the cavity on the torque of a rotating soft particle is weaker than that of a corresponding hard particle (or soft one with lower permeability or thinner thickness of its porous layer). While the normalized torque of a soft sphere in general is an increasing function of the particle-to-cavity radius ratio, a weak minimum of it (surprisingly, less than the value of an unconfined particle) may occur for a particle with a small to mediate core-to-particle radius ratio and a high permeability inside a nonconcentric cavity at a moderate value of the particle-to-cavity radius ratio. Also, this torque in general is an increasing function of the eccentricity of the particle location, but it may decrease slightly with an increase in the eccentricity for a particle with a small to mediate core-to-particle radius ratio and a high permeability.

並列關鍵字

Particle rotation ； Soft sphere ； Creeping flow ； Hydrodynamic torque ； Boundary effect

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