论文标题
使用接触角度分布对滑动液滴的最佳控制
Optimal Control of Sliding Droplets using the Contact Angle Distribution
论文作者
论文摘要
控制在固体表面上移动和固定的液滴的形状和位置是在微流体应用中经常发现的重要特征。在这项工作中，我们将包括接触线动力学在内的经过良好研究的相位场模型视为（开环）最佳控制问题的状态系统。在这里，液滴和实体之间的空间和时间变化的接触角被视为控制变量。我们在最佳控制问题中考虑了状态方程的合适，能量稳定的时间离散版本。我们讨论了解决时间离散状态方程及其连续性和不同性能的规律性。此外，我们显示了解决方案的存在和状态一阶最佳条件，以解决最佳控制问题。我们通过以最佳方式积极将液滴推向重力来说明我们的结果。
Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. In this work, we consider a well investigated phase field model including contact line dynamics as the state system for an (open-loop) optimal control problem. Here the spatially and temporally changeable contact angles between droplet and solid are considered as the control variables. We consider a suitable, energy stable, time discrete version of the state equation in our optimal control problem. We discuss regularity of the solution to the time discrete state equation and its continuity and differentiability properties. Furthermore, we show existence of solutions and state first order optimality conditions to the optimal control problem. We illustrate our results by actively pushing a droplet uphill against gravity in an optimal way.
