有界面活性劑之軸對稱界面在不同黏滯性之流體模擬

Abstract

本論文把 Immersed boundary method 發展到軸對稱圓柱座標系中來模擬液滴在不可壓縮流中，液滴內外不同的黏滯度是我們所關心的。為方便分佈界面所產生的力至流體以及內插流體流速至界面的移動速度，須藉由Dirac delta function 將 Eulerian 流體和Lagrangian界面變數合併。我們使用 semi-implicit second-order projection method 來解 Navier-Stokes方程式並且利用Indicator function來更新密度和黏滯度。把液滴放入流場中，觀察有加表面活性劑與沒加表面活性劑的差異性。表面活性劑會分佈在界面中，並且影響表面張力的大小。上述的方程式，我們皆加入人工速度去調整界面上網格的位置，使其分佈均勻。

In this study, the simulation of drop deformation in incompressible flow was executed by developing an immersed boundary method in the axisym metric cylindrical coordinates. The viscosity difference between two sides of drop interface was particularly considered in this paper. We implemented a semi-implicit second-order projection scheme to solve Navier-Stokes equations. Various viscosity between two sides of drop were tested on simulation, as well as the effect of the surfactant on drop, which affect the surface tension. In addition, the distribution of marker positions were stabilized by imposing the artificial velocity and compared to the original manner without imposition of artificial velocity.