Laplace pressure driven drop spreading

Abstract

This work concerns the spreading of viscous droplets on a smooth rigid horizontal surface, under the condition of complete wetting (spreading parameter S≳0) with the Laplace pressure as the dominant force. Owing to the self-similar character foreseeable for this flow, a self-similar solution is built up by numerical integration from the center of symmetry to the front position to be determined, defined as the point where the free-surface slope becomes zero. Mass and energy conservation are invoked as the only further conditions to determine the flow. The resulting fluid thickness at the front is a small but finite (≊10−7) fraction of the height at the center. By comparison with experimental results the regime is determined in which the spreading can be described by this solution with good accuracy. Moreover, even within this regime, small but systematic deviations from the predictions of the theory were observed, showing the need to add terms modifying the Laplace pressure force.