圆柱表面非牛顿流体薄膜流动

圆柱形表面上的薄膜流动跟自然界和工业系统中的很多现象和应用广泛的联系在一起，例如蜘蛛丝上的液滴，水收集，去盐以及纳米纤维的制造等。这种重力-表面张力驱动的流动表现出极为丰富的动力学现象，例如绝对/对流不稳定，整体运动的液滴串。在过去几十年里，绝大多数研究都集中在牛顿流体薄膜流动问题。而在工业应用系统、日常生活中所遇到的流体绝大多数都是非牛顿流体，例如高分子溶液。绝大多数高分子溶液都表现出剪切稀化和粘弹性效应。流体学术界对于剪切稀化、粘弹性效应对圆柱上的薄膜流动的稳定性、以及非线性不变解的影响仍然缺乏足够的认识。本项目拟从实验、数值计算、理论建模这三个角度对竖直圆柱表面上的非牛顿流体薄膜流动进行深入研究，重点考察剪切稀化、粘弹性效应对流动的线性稳定性(时间稳定性、绝对/对流稳定性）的影响，和非线性不变解与流动形态的关联。

Liquid film flows on cylindrical surfaces are widely connected with natural phenomena and industrial applications, e.g. liquid beads on spider silk, water collection, desalination and manufacture of nanofibers. The gravity-surface tension driven flow shows rich dynamical phenomena, such as absolute/convective instability and droplet trains. In the past decades, most researches were focused on Newtonian liquid film flows. However, in industrial applications and our daily lives, most liquids we encountered with are non-Newtonian, e.g. polymer solutions. Most of these polymer solutions exhibit shear-thinning and viscoelastic characteristics. How the shear-thinning and viscoelastic effects modify the flow instability as well as the nonlinear invariant solutions in a liquid film flowing on a cylinder remain open. The project aims to investigate a non-Newtonian liquid film flowing down a vertical cylinder experimentally, numerically and theoretically. The influences of shear-thinning and viscoelastic effects on the linear stability (temporal stability, absolute/convective stability) and the intrinsic connection between the nonlinear invariant solutions and flow patterns will be examined.