论文标题
与肥皂膜的通用特性的自相似性，在滚动阶段泡泡
Self-similarity with universal property for soap film and bubble in roll-off stage
论文作者
论文摘要
所有孩子都喜欢吹肥皂气泡，这些气泡也会出现在我们的浴缸中，当我们洗碗时。我们分析肥皂泡颈拉伸时的稀疏和破裂。为了形成鲜明对比的是，其边界开放的更广泛研究的薄膜，我们将其集中在气泡上，以保守的空气体积V。例如膜（F），非平衡状态可以分为四个气泡（B）的四个机制（B）：（1）滚动，（2）CUSP接近，（3）Pinch-off和（4）分手。我们在F-1，B-1和B-3中建立了自相似性的存在，以及F-1和B-1中的普遍特性，用于肥皂膜的特征。前者意味着，在被倒计时时间τ重新缩放后，可以将连续时间的轮廓映射到主曲线。在后者的情况下，后者需要此主曲线对于膜的不同环尺寸r和不同的v和r对于气泡进行相同，同时保持V/r^3固定。通用属性的展览表明，内存擦除的过程比制度3早。我们还发现，最小半径尺度为H_ {min} 〜τ^{1/2}，独立于V和拉力速度。请注意，我们的讨论的有效性受到10^{ - 2} 〜10^{ - 3} s的滚动制度持续时间的限制。
All children enjoy blowing soap bubbles that also show up in our bath and when we wash dishes. We analyze the thinning and breaking of soap bubble neck when it is stretched. To contrast with the more widely studied film whose boundaries are open, we concentrate on the bubble with a conserved air volume V. Like film (F), non-equilibrium state can be divided into four regimes for bubble (B): (1) roll-off, (2) cusp approach, (3) pinch-off and (4) breakup. We establish the existence of self-similarity in F-1, B-1 and B-3, and universal property in F-1 and B-1 for the profile of soap membrane. The former means that the profile at successive times can be mapped to a master curve after being rescaled by the countdown time τ. Whiles, the latter further requires this master curve to be identical for different ring sizes R for film and different V and R for bubble while keeping V/R^3 fixed. The exhibition of universal property indicates that the process of memory erasing starts earlier than regime 3. We also found that the minimum radius scales as h_{min}~τ^{1/2}, independent of V and pulling speed. Note that the validity of our discussion is limited by the duration of roll-off regime from 10^{-2}~10^{-3} s.
