Falling liquid films with blowing and suction

TL;DR

This paper models the effects of blowing and suction on thin viscous film flows down inclined planes, analyzing stability, bifurcations, and transitions to control interfacial instabilities relevant to industrial applications.

Contribution

It derives new long-wave models incorporating blowing and suction, and explores their steady states, stability, and nonlinear dynamics through numerical and analytical methods.

Findings

Steady states cease to exist at high suction speeds due to film drying.

Suction can stabilize or destabilize the film depending on parameters.

Transitions between traveling waves and steady states are characterized.

Abstract

Flow of a thin viscous film down a flat inclined plane becomes unstable to long wave interfacial fluctuations when the Reynolds number based on the mean film thickness becomes larger than a critical value (this value decreases as the angle of inclination with the horizontal increases, and in particular becomes zero when the plate is vertical). Control of these interfacial instabilities is relevant to a wide range of industrial applications including coating processes and heat or mass transfer systems. This study considers the effect of blowing and suction through the substrate in order to construct from first principles physically realistic models that can be used for detailed passive and active control studies of direct relevance to possible experiments. Two different long-wave, thin-film equations are derived to describe this system; these include the imposed blowing/suction as well as inertia, surface tension, gravity and viscosity. The case of spatially periodic blowing and suction is considered in detail and the bifurcation structure of forced steady states is explored numerically to predict that steady states cease to exist for sufficiently large suction speeds since the film locally thins to zero thickness giving way to dry patches on the substrate. The linear stability of the resulting nonuniform steady states is investigated for perturbations of arbitrary wavelengths, and any instabilities are followed into the fully nonlinear regime using time-dependent computations. The case of small amplitude blowing/suction is studied analytically both for steady states and their stability. Finally, the transition between travelling waves and non-uniform steady states is explored as the suction amplitude increases.