Projection method for droplet dynamics on groove-textured surface with merging and splitting
Projection method for droplet dynamics on groove-textured surface with merging and splitting
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DOI：
10.1137/20m1338563
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
Yuan Gao;Jian‐Guo Liu
中科院分区：
文献类型：
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作者：
Yuan Gao;Jian‐Guo Liu
我们研究了液滴放置在倾斜凹槽纹理表面上具有合并和分裂的完整动力学。液滴的运动可以由接触线动力学和平均曲率动力学决定，它们是由表面之间的竞争、三相张力和引力效应驱动的。我们将动力学重新表述为具有边界的Hilbert流形上的梯度流，在一些可微的假设下，它可以进一步化为抛物型变分不等式。为了有效地求解抛物型变分不等式，利用Trotter-Kato积公式重新研究了希尔伯特空间中障碍物问题投影法的收敛性和稳定性。在此基础上，提出了一种融合了障碍物信息和合并分裂时的相变信息的液滴动力学投影方案。演示了几个具有挑战性的例子，包括分裂和合并液滴。
We study the full dynamics of droplets placed on an inclined groove-textured surface with merging and splitting. The motion of droplets can be determined by the contact line dynamics and motion by mean curvature, which are driven by the competition between surfaces tensions of three phases and gravitational effect. We reformulate the dynamics as a gradient flow on a Hilbert manifold with boundary, which can be further reduced to a parabolic variational inequality under some differentiable assumptions. To efficiently solve the parabolic variational inequality, the convergence and stability of projection method for obstacle problem in Hilbert space is revisited using Trotter-Kato's product formula. Based on this, we proposed a projection scheme for the droplets dynamics, which incorporates both the obstacle information and the phase transition information when merging and splitting happen. Several challenging examples including splitting and merging of droplets are demonstrated.