模擬帶有表面活性劑之軸對稱界面流問題

Abstract

本論文把 Immersed boundary method 發展到軸對稱圓柱座標系中。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。把液滴放入不同的流場中，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。在解完上述的方程式後，我們加 入人工速度去調整界面上網格的位置，使其分佈均勻。然後比較有加人工速度與沒加人工速度之間的差異。最後我們把液滴放到固體平面板上，測試moving contact line 的問題。

In this paper, we develop an immersed boundary method in the axisymmetric cylindrical coordinates. Coupling the Eulerian flow and Lagrangian interfacial variables by the Dirac delta function is convenient to spread the interface force and interpolate the interfacial velocities. We solve the Navier-Stokes equations by semiimplicit second-order projection scheme. Test a variety of cases that the drops deform in the different velocity field and observe the difference of the clean drop and the drop contaminated with the surfactant. The surface tension is affected by the distribution of surfactant along the interface. After those steps, we impose the artificial velocity to control the distribution of marker positions and compare this with the original manner without imposing artificial velocity. Finally, we put a drop on a solid to observe the contact line moving.