标题： 挤压液滴的屈曲不稳定性 显示英文标题

标题： Buckling instability of squeezed droplets

摘要： 受最近实验的启发，我们从理论上考虑了在有限面积表面上固定在底部的液滴的压缩问题。 我们表明，如果液滴在顶部被表面充分压缩，它将在临界压缩时始终发展出形状不稳定性。 当顶部表面为平面时，液滴在固定表面上的表观接触角为π时，形状不稳定性恰好发生，无论上表面的接触角如何，这与早期关于液桥和坐滴的研究类似，正如Plateau首次观察到的那样。 在临界压缩之后，液滴从对称形状转变为不对称形状。 使液滴变形所需的力在临界点达到峰值，然后逐渐减小，表明发生了灾难性屈曲。 我们使用二维的示例来描述液滴形状的转变，随后进行微扰分析以及三维数值模拟。 当上表面不是平面时，简单的表观接触角准则不再适用，因此进行了详细稳定性分析以预测临界压缩。 显示英文摘要

摘要： Motivated by recent experiments, we consider theoretically the compression of droplets pinned at the bottom on a surface of finite area. We show that if the droplet is sufficiently compressed at the top by a surface, it will always develop a shape instability at a critical compression. When the top surface is flat, the shape instability occurs precisely when the apparent contact angle of the droplet at the pinned surface is pi, regardless of the contact angle of the upper surface, reminiscent of past work on liquid bridges and sessile droplets as first observed by Plateau. After the critical compression, the droplet transitions from a symmetric to an asymmetric shape. The force required to deform the droplet peaks at the critical point then progressively decreases indicative of catastrophic buckling. We characterize the transition in droplet shape using illustrative examples in two dimensions followed by perturbative analysis as well as numerical simulation in three dimensions. When the upper surface is not flat, the simple apparent contact angle criterion no longer holds, and a detailed stability analysis is carried out to predict the critical compression.