垂直圆柱管内三层粘性薄膜的稳定性与非线性动力学
Stability and nonlinear dynamics of three-layer viscous films inside a vertical cylindrical tube
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中文总结 AI 辅助
该研究针对垂直圆柱管内三层粘性液膜结构，通过线性和非线性分析及数值模拟，揭示其稳定性特性与独特的中间层破裂机制，为分层输运过程研究提供理论基础。
中文摘要 AI 辅助
我们研究了垂直圆柱管内壁三层互不相溶粘性液膜的动力学与稳定性，该结构与分层核心-环形输运过程相关。长波渐近分析得到了控制三个界面运动的耦合非线性演化方程组。线性稳定性分析预测存在持续的长波不稳定性，即空气-核心界面的毛细（瑞利-普拉托）不稳定性，以及在某些参数区域由界面耦合产生的次级有限波数不稳定带。这些稳定性特性对层厚、粘度比和表面张力参数敏感，包含与色散关系中竞争最大值相关的模式切换。非线性模拟揭示了三种不同的动力学结果：饱和至有限振幅行波、通过塞子形成实现空气-核心闭合，以及中间液层破裂而空气核心保持开放。中间层破裂机制是三层结构特有的，在单层或两层界面的圆柱薄膜流动中无类似情况。数值延拓用于计算行波解分支及其相关极限点。与时变模拟的比较显示，行波分支成功预测了从饱和波到塞子形成的转变，但未捕捉到与中间层塌陷相关的独特破裂机制。
英文摘要
We investigate the dynamics and stability of three immiscible viscous liquid layers coating the interior of a vertical cylindrical tube, a configuration relevant to stratified core--annular transport processes. A long-wave asymptotic analysis yields a coupled system of nonlinear evolution equations governing the motion of the three interfaces. Linear stability analysis predicts a persistent long-wave instability, the capillary (Rayleigh--Plateau) instability of the air--core interface, together with secondary finite-wavenumber instability bands that emerge from interfacial coupling in certain parameter regimes. These stability characteristics depend sensitively on the layer thicknesses, viscosity ratios, and surface tension parameters, and include mode-switching associated with competing maxima in the dispersion relation. Nonlinear simulations reveal three distinct dynamical outcomes: saturation to finite-amplitude travelling waves, air-core closure through plug formation, and rupture of the intermediate liquid layer while the air core remains open. The intermediate-layer rupture mechanism is unique to the three-layer configuration which has no analogue in one- or two-interface cylindrical film flows. Numerical continuation is used to compute branches of travelling-wave solutions and their associated limit points. Comparison with time-dependent simulations shows that travelling-wave branches successfully predict the transition from saturated waves to plug formation, but do not capture the distinct rupture mechanism associated with collapse of the intermediate layer.
