Transient two-dimensional coating flow of a viscoelastic fluid film on a substrate of arbitrary shape
This paper examines transient two-dimensional flows of a thin film of Oldroyd-B fluid on a stationary solid substrate of arbitrary shape. The fluid is driven by a pressure gradient in a channel from which it emerges. The investigation is motivated by the fact that in coating process, for example, the orgin of some problems may appear at the early stages before steady state is achieved, if it is achieved at all. In particular, the investigation focuses on the effects of viscosity, elasticity, inertia, gravity and substrate topography, under the lubrication assumption. As for the mathematical technique, the film equations are solved by expanding the flow field in Fourier series in the height direction. The Galerkin projection method is then applied to derive the equations governing the expansion coefficients. Finally, a time-stepping implicit finite difference discretization, together with a sixth-order Runge-Kutta scheme, is utilized to calculate the evolution of the shape of free surface and the flow field with time. In analyzing the results, the author finds that the viscosity ratio, fluid elasticity, gravity and substrate topography can have a significant effect on transient behavior. However, these effects depend on the level of fluid inertia. For low inertia the fluid tends to accumulate near the channel exit, exhibiting a standing wave that grows with time. The topography of the substrate affects the flow significantly. In the presence of a bump, for example, the flow of a high-inertia fluid can generate a secondary wave that moves downstream of the primary wave.
stationary solid substrate of arbitrary shape
time-stepping implicit finite difference discretization
scientific article; zbMATH DE number 1556243