Side wall effects on the instability of thin gravity-driven films—From long-wave to short-wave instability

Abstract

We study the effects of side walls on the primary instability of a gravity-driven thin liquid film flowing down a flat channel. The influences of different capillary boundary layer effects at the side walls on the instability of the free surface are resolved experimentally, by varying the crosswise side wall distance of the measurement positions between 5 mm and the channel center-line. The height of the capillary elevation and, thus, the resulting pretensioning of the free surface and the magnitude of a possible velocity overshoot have been adjusted by changing the contact angle between the liquid and the side wall. The influence of the contact angle on the stability of the flow, and especially its range, is remarkable. The difference of the neutral stability curves for the two investigated contact angles is up to 25% and remains significant even up to a side wall distance of 17 times the capillary length. Irrespective of the contact angle, the type of the free surface instability undergoes a transition from long-wave in the center of the channel to short-wave, as is well known for boundary layer flows, when the side wall distance is reduced. Furthermore, we have found that the presence of a velocity overshoot tends to destabilize the free surface.