基于接触角分布的滑动液滴最优控制
Optimal Control of Sliding Droplets using the Contact Angle Distribution
摘要：
控制固体表面上移动和固定液滴的形状和位置是微流体应用中经常发现的重要特征。在这项工作中，我们认为一个良好的调查相场模型，包括接触线动态的状态系统（开环）最优控制问题。在这里，空间和时间上可变的液滴和固体之间的接触角被认为是控制变量。我们考虑一个合适的，能量稳定的，时间离散版本的状态方程在我们的最优控制问题。讨论了时间离散状态方程解的正则性及其连续性和可微性。进一步证明了该最优控制问题解的存在性和一阶最优性条件。我们说明了我们的结果，积极推动液滴上坡对重力在一个最佳的方式。
英文摘要：
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.
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