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

该项目研究了牛顿薄膜和粘滞薄膜在封闭和开放系统中高速流动的非线性稳定性，通常是在薄膜加工和润滑行业中遇到的。纳米通道中的流动也将被考虑，就像在纳米流体器件中遇到的那样。虽然纳米流体由单原子分子组成，但由于碰撞分子之间相对较长的分子平均自由路径，使得动量和能量可以长距离传递，因此纳米流体具有典型的（可压缩的）非牛顿特性，类似于聚合物流体。过去人们对薄膜蠕动流动进行了广泛的研究，其中薄膜蠕动流动主要是由开放薄膜的表面张力效应主导的，但由于难以处理对流和弹性性质的非线性，惯性和弹性的影响相对被忽视。这些非线性效应在高速流动和发展初期占主导地位，而这些阶段往往是实际过程中出现长期困难的阶段。因此，该项目侧重于自由表面的开放膜流动，如在涂层工业中遇到的，以及在两个调制刚性边界之间的薄层流动，如在润滑和纳米系统中遇到的。提出了一种统一的光谱方法来求解边界层型薄膜方程。从基本的角度来看，薄膜高速流动涉及激波形成，并且由于流动的双曲性质，对初始条件高度敏感。从实践的角度来看，这项工作应该提供对给定过程中膜不稳定和破裂的起源和原因的见解。更重要的是，建模和仿真的目的是为薄膜工业提供不稳定发生的工艺条件，从而为制造商提供控制或避免不稳定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.