Nonlinear transient high-speed non-Newtonian flow of thin films

该项目研究了在封闭和开放系统中高速流动的牛顿和粘弹性薄膜的非线性稳定性，通常在薄膜加工和润滑行业中遇到。也将考虑纳米通道中的流动，如在纳米流体器件中遇到的。虽然由单原子分子组成，但纳米流体流通常具有（可压缩的）非牛顿特性，因为碰撞分子之间的分子平均自由程相对较长，从而允许动量和能量在长距离上传递，类似于聚合物流体。虽然蠕动薄膜流，这主要是由表面张力的影响，在过去已被广泛研究，惯性和弹性的影响相对被忽略，因为在处理对流和弹性性质的非线性的困难。这些非线性效应对于高速流动和发展的初始阶段是主要的，这些阶段通常是真实的过程中出现长期困难的阶段。因此，该项目的重点是开放的薄膜流动与自由表面，如在涂料行业中遇到的，和薄层流动之间的两个调制刚性边界，如在润滑和纳米系统中遇到的。提出了一种统一的谱方法来求解边界层型薄膜方程。从一个基本的角度来看，薄膜流在高速涉及激波的形成，是高度敏感的初始条件给定的双曲线性质的流动。从实践的角度来看，这项工作应该提供洞察的起源和原因的膜不稳定性和破裂在一个给定的过程。更重要的是，建模和仿真旨在为薄膜工业提供不稳定性开始的工艺条件，并因此为制造商提供控制或避免不稳定性和工艺故障所需的工具。

The project examines the nonlinear stability of Newtonian and viscelasic thin films flowing at high speed in confined and open systems, typically as encountered in the film processing and lubrication industry. Flow in nano channels will also be considered, as encountered in nanoflidic devices. Although consisting of monatomic molecules, nano fluidic flows are typically of (compressible) non-Newtonian character because of the relatively long molecular mean-free path between colliding molecules, thus allowing momentum and energy to transferred over long distances, similarly to polymeric fluids. While creeping thin-film flows, which are mainly dominated by surface tension effects for open films, have been extensively investigated in the past, the influence of inertia and elasticity has been relatively ignored because of the difficulty in dealing with nonlinearities of convective and elastic nature. These nonlinear effects are dominant for flow at high speed and in the initial stages of development, which are often the stages when long-term difficulties emerge in real processes. The project thus focuses on open film flow with a free surface, as encountered in the coating industry, and flow of thin layer between two modulated rigid boundaries, as encountered in lubrication and nano systems. A unified spectral methodology is proposed to solve the thin-film equations, which are of the boundary-layer type. From a fundamental perspective, thin-film flow at high speed involves shock formation and is highly sensitive to initial conditions given the hyperbolic nature of the flow. From a practical perspective, the work should provide insight into the origins and causes of film instability and rupture in a given process. More importantly, the modeling and simulation are aimed at providing the film industry with the process conditions for the onset of instability, and, consequently, at providing the manufacturer with the required tools to control or avoid instability and process breakdown.