论文标题
胶卷在锥体上的薄膜沉积
Film deposition of a self-propelled droplet on a cone with slip
论文作者
论文摘要
我们使用锥形底物上的时间依赖性润滑方程来研究自螺旋粘性液滴的动态润湿，用于不同的锥形半径，锥角和滑动长度。发现液滴速度随锥角和滑动长度而增加，但随锥半径降低。我们表明，在液滴的后退部分中形成了一部电影，就像古典Landau-Landau-levich-derjaguin（LLD）电影一样。胶片厚度$ h_f $被发现随着滑移长度$λ$而减小。通过使用膜区域和准静态液滴中匹配的渐近谱的方法，我们获得了与所有滑动长度的润滑方法的结果相同的膜厚度。我们确定了渐近方制度的两个缩放法律：$ h_fh'_ o \ sim ca^{2/3} $对于$λ\ ll h_f $和$ h_f h_f h''^{3} _o \ sim（ca/λ）^2 $ for $λ\ gg h_f $ at $ 1/ $ CA $是毛细管数。我们将连续理论预测的液滴的位置和形状与分子动力学模拟进行了比较，这是密切一致的。我们的结果表明，操纵液滴尺寸，锥角度和滑动长度提供了不同的方案，用于引导液滴运动并用膜涂上基板。
We study the dynamic wetting of a self-propelled viscous droplet using the time-dependent lubrication equation on a conical-shaped substrate for different cone radii, cone angles and slip lengths. The droplet velocity is found to increase with the cone angle and the slip length, but decrease with the cone radius. We show that a film is formed at the receding part of the droplet, much like the classical Landau-Levich-Derjaguin (LLD) film. The film thickness $h_f$ is found to decrease with the slip length $λ$. By using the approach of matching asymptotic profiles in the film region and the quasi-static droplet, we obtain the same film thickness as the results from the lubrication approach for all slip lengths. We identify two scaling laws for the asymptotic regimes: $h_fh''_o \sim Ca^{2/3}$ for $λ\ll h_f$ and $h_f h''^{3}_o\sim (Ca/λ)^2$ for $λ\gg h_f$, here $1/h''_o$ is a characteristic length at the receding contact line and $Ca$ is the capillary number. We compare the position and the shape of the droplet predicted from our continuum theory with molecular dynamics simulations, which are in close agreement. Our results show that manipulating the droplet size, the cone angle and the slip length provides different schemes for guiding droplet motion and coating the substrate with a film.
