多孔球形粒子之暫態緩慢移動

Abstract

本論文以多孔球形粒子模型模擬可滲透聚合物鏈團或絮聚體等微奈米粒子於不可壓縮牛頓流體中受一恆定力作用所造成之起始緩慢移動。由修正的暫態Stokes及Brinkman方程式描述多孔球形粒子內外流體之運動狀態並以拉普拉斯轉換分別求解多孔粒子內外的流速分佈，再分析粒子所受拖曳力即可求得轉換 (s) 域中相關變數及粒子暫態速度解析解函數，最後以拉普拉斯逆轉換數值解比較時間 (t) 域中多孔粒子暫態速度和加速度與粒子孔隙度、粒子內流體滲透參數、粒子與流體相對密度和無因次時間等參數間的關係及變化趨勢。 結果顯示，粒子速度如同預期會隨外加力作用時間逐漸增加，並且質量密度較大粒子的速度增長會落後於密度較低的粒子。於大部分條件下，粒子暫態速度會隨粒子孔隙度增加遞增，而高流體滲透性的多孔粒子相較於低滲透性的相同粒子會具有更大的暫態速度，但相對終端速度之速度百分比增長則可能落後於滲透性較小的粒子。多孔粒子的加速度為時間的單調遞減函數及流體滲透性的單調遞增函數。實際應用上，多孔粒子的暫態蠕動行為可能比不可滲透粒子更加重要。

The start-up creeping motion of a porous spherical particle, which models a permeable polymer coil or floc of nanoparticles, in an incompressible Newtonian fluid generated by the sudden application of a body force is investigated for the first time. The transient Stokes and Brinkman equations governing the fluid velocities outside and inside the porous sphere, respectively, are solved by using the Laplace transform. An analytical formula for the transient velocity of the particle as a function of relevant parameters is obtained. As expected, the particle velocity increases over time, and a particle with greater mass density lags behind a corresponding less dense particle in the growth of the particle velocity. In general, the transient velocity is an increasing function of the porosity of the particle. On the other hand, a porous particle with a higher fluid permeability will have a greater transient velocity than the same particle with a lower permeability, but may trail behind the less permeable particle in the percentage growth of the velocity. The acceleration of the porous particle is a monotonic decreasing function of the elapsed time and a monotonic increasing function of its fluid permeability. In particular, the transient behavior of creeping motions of porous particles may be much more important than that of impermeable particles.