Modelling wetting-bouncing transitions of droplet impact on random rough surfaces

Abstract

Droplet impact on rough surfaces is of critical importance to various applications, yet remains incompletely understood. The present work aims to uncover droplet impact dynamics on random hydrophobic surfaces using volume of fluid simulations. Random fractal surfaces with RMS roughness ranging from 2 to 50 micrometers were generated using the Weierstrass-Mandelbrot function. Three identifiable impact outcomes including no bouncing, complete bouncing, and bouncing with breakup have been identified as Weber number varies between 5.7 and 12.9 and RMS roughness varies between 0 and 50 micrometers. We examine the spreading, retraction, re-spreading, and breakup stages of the impact events under different velocity and surface morphologies conditions. Numerical simulations show that the maximum spreading factor decreases linearly as surface roughness increases. Two scaling laws have been proposed for droplet impact on surfaces with small and large roughness values, respectively. A key finding is that the droplet contact time remains constant, independent of both Weber number and surface roughness. The joint effect of Weber number and surface roughness governs the wetting-bouncing transition, with larger roughness delaying the transition. This work elucidates the mechanisms governing droplet impact dynamics on random rough surfaces, thereby providing new insights directly relevant to droplet-based applications.

Figures (13)

• Figure 1: Random rough fractal surfaces with varying root-mean-square roughness values generated using the W-M function.
• Figure 2: Three different impact outcomes: (a) no bouncing (We=5.7, $R_q$=$50\ \mu m$), (b) complete bouncing (We=8.2, $R_q$=$20\ \mu m$), and (c) bouncing with breakup (We=12.9, $R_q$=$5\ \mu m$). The middle column shows droplet morphologies corresponding to the instant of the maximum spreading factor $\beta_m$.
• Figure 3: Droplet impact dynamics at different We. (a)-(e): spreading factor versus time. (a) We=5.7, (b) We=6.5, (c) We=8.2, (d) We=11.2, (e) We=12.9, (f) maximum spreading factor versus the RMS roughness.
• Figure 4: Maximum spreading factor $\beta_m$ as a function of We. Solid purple and green lines represent $\beta_m=1.14\textit{We}^{0.46}$ and $\beta_m=1.11\textit{We}^{0.40}$, respectively. Dashed purple and green lines represent $\beta_m=1.14(1.38+\textit{We})^{0.46}$ and $\beta_m=1.11(1.55+\textit{We})^{0.40}$, respectively.
• Figure 5: $\tau_c/\tau$ as a function of Weber number. Open symbols: simulations for a contact angle $\theta=100^{\circ}$, solid triangle: present simulations for a contact angle $\theta=165^{\circ}$, solid circle: experimental results for a contact angle $\theta=165^{\circ}~gauthier2015water$. Purple solid line and green dashed line represent $\tau_c/\tau$=3.9 and 2.5, respectively.