在過往的經驗中，發現當群聚顆粒夠小時，很容易產生顆粒結塊之現象，但之前的顆粒碰撞模擬問題，大多是大顆粒的模擬問題，因此多不考量吸附力的影響。然而若將顆粒粒徑大小降至微米之數量級，此時，便需要考量顆粒間吸附力帶來的影響。而以往的文獻中較少討論到如何在模擬微小顆粒碰撞時加入吸附力作用與結塊的條件，因此本論文研究主要為提供一個合理吸附力作用下顆粒碰撞的衍生硬球碰撞模式，同時將該模式運用在微小顆粒的運動模擬當中並觀察微小顆粒的運動情形及結塊過程。
顆粒間的碰撞模擬中，微小顆粒的尺寸設定為半徑1μm~10μm，顆粒碰撞問題則採取雙體碰撞硬球模式的方法進行計算，同時仿照Bradley Model來定量微小顆粒碰撞時所產生的吸附力大小，而吸附力的影響時間則參考Lennard-Jones's Potential Model之理論來決定。另外，由於顆粒數目較大的關係，在進行碰撞搜索時相當耗時，因此為了節省計算資源，在研究中採用了具有高效率的鄰接小區域搜索法，可節省約90 % 的時間。模擬結果顯示，若只討論兩兩顆粒碰撞的情況下，可以發現當顆粒間約化半徑愈小時，其「兩顆粒間最小擺脫結塊正向相對速度」值就愈大，換言之，兩顆粒尺寸愈小愈容易產生結塊。另外加入所發展的衍生硬球模式不只可以定量出兩兩顆粒會不會產生結塊之條件，同時即使不結塊，其最後兩兩顆粒之碰撞後正向相對速度也會跟著影響，而不只是原來單純地受到恢復係數之影響。
而將大量顆粒置於一虛擬週期變化重力場中，可以發現重力場常數的大小會因顆粒尺寸之大小而影響顆粒結塊的生成速度，同時也會影響單一時間下其總累積碰撞次數。然而若給予足夠時間的話，最後微小顆粒都會結塊成一個大顆粒。
從研究中有提及的各個模擬環境，都顯現出當兩兩顆粒尺度愈大時，雖然彼此間吸附力跟著上升，但約化質量也跟著上升，因此除非兩兩顆粒間的正向相對速度很小，否則其顆粒尺度對於動量變化的影響還是遠大於吸附力之影響；所以在微小顆粒碰撞模擬中，才需要考量吸附力所帶來造成顆粒結塊之影響。

It is popular to perform the Eulerian-Lagrangian approach to simulate the two-phase flow using a hard-sphere model. The cohesive force between small particles is significant; however, the standard hard-sphere model does not consider the cohesive force between the colliding particles. Because of this, it is necessary to develop an extended hard-sphere model considering the influence of cohesive force to simulate some problems such as industrial processes that involve agglomeration phenomena. A reasonable extended hard-sphere model should quantify the cohesive force between two particles and define the duration of the cohesive force influences. The quantification of cohesive force is based on the Bradley model as well as a modification of the ideal van der Waals force model. The duration of the cohesive force acting on two colliding particles refers to the Lennard-Jones model. In addition, in this paper, in order to save computer resources, a link-list method rather than a full-search domain method is used as the particle collision inspection method.
The developed extended hard-sphere model is used to simulate the motion of micro-size particles and to observe the agglomeration phenomenon in different test cases.
According to the results of the simulations, we conclude four points as follows. First, as the reduced radius of colliding particles becomes smaller, agglomeration appears more easily. Next, the extended hard-sphere model not only could quantify the agglomeration conditions but also the effect of the post-collisional relative velocity. Third, in a simulation with periodic gravity, the agglomeration rate is based on particle size and the magnitude of the gravity constant. Over a long period of time, the micro-size particles agglomerate into a bigger particles. Lastly, the results of all of the different tests discussed in this thesis show that when the size of two colliding particles increases, the cohesive force and the reduced mass between the two colliding particles would increases as well. However, in the case of the impulse, the influence of particle size is greater than the effect of cohesive forces unless the pre-collisional relative velocity is very small.

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