范德华力对管内气泡运动的影响
The influence of van der Waals interactions on a bubble moving in a tube
摘要：
本文研究了在圆柱形毛细管中匀速前进的粘性可忽略的长气泡的非定常薄膜动力学。气泡取代粘性的非润湿流体，在其界面和管壁之间形成薄膜。该膜被认为足够薄，使得范德华吸引力形式的分子间力是显著的，并且薄膜破裂是可能的。在可忽略的分子间力的情况下，存在稳态溶液，其中在气泡界面和管壁之间的环形区域中沉积均匀厚度的膜。然而，一旦分子间相互作用是重要的，界面被扰动脱离其稳定状态，并且（i）扰动在到达气泡的后弯月面之前充分增长，使得破裂发生;或者（ii）扰动由于弱的分子间力而保持小，直到其通过后弯月面离开气泡界面。我们得到，无论是数值和渐近，时间尺度上发生破裂，因此，我们找到一个临界毛细管数，取决于气泡的长度和强度的分子间力，低于该膜预计破裂。
英文摘要：
We consider the unsteady thin-film dynamics of a long bubble of negligible viscosity that advances at a uniform speed in a cylindrical capillary tube. The bubble displaces a viscous, nonwetting fluid, creating a thin film between its interface and the tube walls. The film is considered thin enough that intermolecular forces in the form of van der Waals attractions are significant and thin-film rupture is possible. In the case of negligible intermolecular forces, a steady-state solution exits where a film of uniform thickness is deposited in the annular region between the bubble interface and the tube walls. However, once intermolecular interactions are important, the interface is perturbed out of its steady state and either (i) the perturbation grows sufficiently before reaching the rear meniscus of the bubble such that rupture occurs; or (ii) the perturbation remains small due to weak intermolecular forces until it leaves the bubble interface through the rear meniscus. We obtain, both numerically and asymptotically, the time-scale over which rupture occurs, and thus, we find a critical capillary number, depending on the bubble length and the strength of the intermolecular forces, below which the film is predicted to rupture.
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