Influence of inertia, gravity, and substrate topography on the two-dimensional transient coating flow of a thin Newtonian fluid film

The interplay between inertia, gravity, and substrate topography is examine d in this study for the transient two-dimensional flow of a thin Newtonian film. Surface tension effect is assumed to be negligible. The fluid emerges from a channel and is driven by a pressure gradient maintained inside the channel. The substrate is assumed to be stationary and of arbitrary shape. The lubrication equations are solved by expanding the flow field in terms o f orthonormal modes in the vertical direction and using the Galerkin projec tion, combined with a time-stepping implicit scheme, and integration along the flow direction. The leading-order mode is found to be clearly dominant. Gravity and substrate topography can have a significant effect on transien t behavior, but this effect varies significantly, depending on the level of fluid inertia. The wave and flow structures are examined for high- and low -inertia fluids. It is found that low-inertia fluids tend to accumulate nea r the channel exit, exhibiting a standing wave that grows with time. This b ehavior clearly illustrates the difficulty faced with coating high-viscosit y fluids. The topography of the substrate has a drastic effect on the flow. A secondary wave emerges in the presence of a bump or a depression in the substrate. The wave structure is again highly dependent on the level of ine rtia. (C) 2001 American Institute of Physics.