Analytical Model for Crown Spreading During Drop Impact onto Wetted Walls: Effect of Liquids Viscosity on Momentum Transfer

Abstract

Drop impact onto wetted surfaces is of relevance to any spray coating application since the maximum spreading diameter and the residual film thickness of the applied liquid droplets affect the efficient distribution of the coating materials. In this paper, we propose a modification to existing models for crown propagation during single drop impact onto a wall-film based on the stagnation-point flow solution of Hiemenz. This offers two main advantages: a simple estimation of the film thickness decay rate, induced by the impulse transfer from impacting droplet to resting wall-film. Besides, the self-similarity of Hiemenz’s solution allows a straightforward estimation of the momentum losses during radial liquid spreading along the wall. The incorporation of these estimations into existing inviscid models provides an excellent agreement with experiments over the entire crown elevation phase. Additionally, the effect of fluid viscosity and initial film thickness on the momentum transfer from droplet to wall-film is highlighted.