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

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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.