Mughal A, Cox S J, Schröder-Turk G E
Department of Mathematics, Aberystwyth University, Aberystwyth, Ceredigion SY23 3BZ, UK.
Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg - Staudtstr. 7, 91058 Erlangen, Germany.
Interface Focus. 2017 Aug 6;7(4):20160106. doi: 10.1098/rsfs.2016.0106. Epub 2017 Jun 16.
We investigate the equilibrium properties of a single area-minimizing bubble trapped between two narrowly separated parallel curved plates. We begin with the case of a bubble trapped between concentric spherical plates. We develop a model which shows that the surface energy of the bubble is lower when confined between spherical plates than between flat plates. We confirm our findings by comparing against Surface Evolver simulations. We then derive a simple model for a bubble between arbitrarily curved parallel plates. The energy is found to be higher when the local Gaussian curvature of the plates is negative and lower when the curvature is positive. To check the validity of the model, we consider a bubble trapped between concentric tori. In the toroidal case, we find that the sensitivity of the bubble's energy to the local curvature acts as a geometric potential capable of driving bubbles from regions with negative to positive curvature.
我们研究了被困在两个紧密间隔的平行弯曲板之间的单个面积最小化气泡的平衡特性。我们从被困在同心球板之间的气泡情况开始。我们建立了一个模型，该模型表明，气泡在球形板之间受限的情况下，其表面能比在平板之间时更低。我们通过与表面演化器模拟结果进行比较来证实我们的发现。然后，我们推导了一个关于任意弯曲平行板之间气泡的简单模型。结果发现，当板的局部高斯曲率为负时，能量较高；而当曲率为正时，能量较低。为了检验该模型的有效性，我们考虑了被困在同心环面之间的气泡。在环面情况下，我们发现气泡能量对局部曲率的敏感度起到了一种几何势的作用，能够驱使气泡从负曲率区域移动到正曲率区域。
