Droplet Footprint Control
Droplet Footprint Control
复制标题
液滴足迹控制
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Shawn W. Walker
中科院分区：
文献类型：
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作者：
A. Laurain;Shawn W. Walker
通过表面张力控制液滴形状具有许多技术应用，例如液滴透镜和芯片实验室。这激发了一种偏微分方程约束的形状优化方法，用于通过控制基板的表面张力来控制平坦基板上的液滴的形状。我们使用形状微分推导出一个L^2 $梯度流的方法来计算基板上的固着液滴的平衡形状。然后，我们开发了一种基于梯度的优化方法，以找到产生具有所需足迹的平衡液滴形状的基底表面张力系数（即，液-固界面具有期望的形状）。此外，我们证明了与足迹的自由边界问题的基板表面张力的灵敏度结果。数值结果也展示了该方法。
Controlling droplet shape via surface tension has numerous technological applications, such as droplet lenses and lab-on-a-chip. This motivates a partial differential equation-constrained shape optimization approach for controlling the shape of droplets on flat substrates by controlling the surface tension of the substrate. We use shape differential calculus to derive an $L^2$ gradient flow approach to compute equilibrium shapes for sessile droplets on substrates. We then develop a gradient-based optimization method to find the substrate surface tension coefficient yielding an equilibrium droplet shape with a desired footprint (i.e., the liquid-solid interface has a desired shape). Moreover, we prove a sensitivity result with respect to the substrate surface tensions for the free boundary problem associated with the footprint. Numerical results are also presented to showcase the method.