本文採用單弛豫晶格波茲曼方法結合Cahn-Hilliard 模型計算了剪切流下濃度對液滴互 動和剪切速率的影響。在研究液滴濃度的影響時，將液滴濃度分為三個方向：x方向、y方 向、z方向。此研究僅關注x方向和y方向上濃度的影響。對於給定的x方向濃度，y方向 濃度的增加會使液滴更容易合併。相反，對於給定的y方向濃度，x方向濃度的增加會導致 聚結更具挑戰性。而對於剪切速率的影響，我們發現結果會隨著特徵速度的改變而改變，速 度越高，液滴聚結的可能性就越大，我們也對遠離臨界毛細管數的區域進行驗證，並發現特 徵速度的影響僅作用於臨界毛細管數的附近。

In this thesis, the single-relaxation lattice Boltzmann method combined with the CahnHilliard model is employed to calculate the influence of concentration on droplet coalescence and shear rate under shear flow. When investigating the impact of droplet concentration, the droplet concentration is divided into three directions: x-direction, y-direction, and z-direction.
The analysis only focuses on the effects of concentration in the x-direction and y-direction. For a given x-direction concentration, an increase in y-direction concentration results making it easier for droplets to merge. Conversely, for a given y-direction concentration, an increase in xdirection concentration leads to more challenging to coalescence. And regarding the influence of shear rate, the results will vary with changes in characteristic velocity. The higher the velocity, the greater the likelihood of droplet coalescence.

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