Laplace Pressure-Driven Drop Spreading: Quasi-Self-Similar Solution

Abstract

We present a hydrodynamic calculation of 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. The starting point is a self-similar solution reported elsewhere which is modified by the introduction of a very simple boundary condition at the current front, namely a fixed cutoff thickness hc. As the introduction of this new parameter breaks up self-similarity, we obtain the complete solution by pasting successive self-similar solutions, each one corresponding to slightly different ratios hc /h0, where h0 is the thickness at the center of the drop. The results are in excellent agreement with our own and other authors' experimental data, showing that this heuristic model gives the right correction to the original theory.