Drop impact on viscous liquid films

Abstract: When a liquid drop falls on a solid substrate, the air layer in between them delays the occurrence of liquid--solid contact. For impacts on smooth substrates, the air film can even prevent wetting, allowing the drop to bounce off with dynamics identical to that observed for impacts on superamphiphobic materials. In this article, we investigate similar bouncing phenomena, occurring on viscous liquid films, that mimic atomically smooth substrates, with the goal to probe their effective repellency. We elucidate the mechanisms associated to the bouncing to non-bouncing (floating) transition using experiments, simulations, and a minimal model that predicts the main characteristics of drop impact, the contact time, and the coefficient of restitution. In the case of highly viscous or very thin films, the impact dynamics is not affected by the presence of the viscous film. Within this substrate--independent limit, bouncing is suppressed once the drop viscosity exceeds a critical value as on superamphiphobic substrates. For thicker or less viscous films, both the drop and film properties influence the rebound dynamics and conspire to inhibit bouncing above a critical film thickness. This substrate--dependent regime also admits a limit, for low viscosity drops, in which the film properties alone determine the limits of repellency.

• The paper reveals that an underlying air cushion and film viscosity critically determine whether a drop bounces or adheres upon impact.
• The paper employs high-speed imaging and VoF simulations to capture the transition dynamics and measure contact times with precision.
• The paper introduces a spring-mass-damper model with viscous damping to predict critical thresholds for bounce inhibition.

Drop Impact on Viscous Liquid Films: A Detailed Analysis

The study of liquid drop impact on viscous films is a subject of interest due to its importance in both natural phenomena and various industrial applications, such as inkjet printing and coating processes. This paper rigorously investigates the dynamics of drop impact on viscous liquid films, encompassing experimental observations, numerical simulations, and theoretical modeling to elucidate the mechanisms that govern the transition from bouncing to non-bouncing (floating) behavior.

Key Observations and Methodology

The phenomena under study involve analyzing drops impacting solid-like surfaces mimicked by viscous films. The research shows that an underlying air cushion plays a critical role in preventing immediate liquid-solid contact, thus allowing for potential bouncing behavior. A comprehensive set of experiments using a variety of liquid viscosities and film thicknesses helps identify the conditions under which a drop bounces or stays adhered post-impact.

Through high-speed imaging, the researchers capture the transitional dynamics, from the initial impact to rebound or settling, providing insight into the temporal aspects of the contact time and the conditions dictating the outcome. This experimental data is complemented by direct numerical simulations utilizing a volume of fluid (VoF) method, facilitating detailed observations of interfacial dynamics and energy distribution during the impact process.

Theoretical Framework

The authors propose a minimal theoretical model grounded in the spring-mass-damper analogy, traditionally used to describe bouncing droplets on non-wetting surfaces. By incorporating viscous effects, the model extends this analogy to include the impact and interaction with viscous films. The implications of film thickness and viscosity are encapsulated within effective damping terms, allowing the exploration of substrate-independent and substrate-dependent regimes.

The model predicts a critical film thickness and viscosity beyond which the drop no longer bounces, aligning well with the observed experimental data. Furthermore, the model delineates the influence of drop and film properties on the rebound dynamics, identifying critical Ohnesorge numbers that mark the boundaries between bouncing and non-bouncing behaviors.

Results and Implications

The study yields several significant findings:

1. Substrate-Independent Regime: For thin or highly viscous films, bounce dynamics parallel those of superhydrophobic substrates, with contact times scaling with known inertio-capillary timescales.
2. Substrate-Dependent Transition: As the film becomes thicker or less viscous, its properties markedly affect the rebound, culminating in the suppression of bouncing at critical thresholds.
3. Energy Dissipation and Bounce Inhibition: The analysis highlights that energy transfer to the substrate plays a pivotal role in bounce inhibition, driven by parameters such as film viscosity and thickness.

These findings have profound implications for both theoretical and practical aspects, suggesting optimal conditions for non-coalescence in various applications. The model provides a predictive tool that could be employed in engineering contexts where control over droplet impact behavior is critical.

Future Directions

The research opens avenues for further exploration, particularly in probing regimes not fully captured by the current model, such as high Weber number impacts or interactions involving complex film rheology. Future investigations could explore the interplay of gravitational effects, film elasticity, and surface roughness to provide a more comprehensive understanding of such multiphase interactions.

In summary, this rigorous study provides a detailed account of the bouncing dynamics of drops on viscous films, enhancing our understanding and capability to predict and control impact phenomena in diverse contexts. By leveraging a combination of experiments, simulations, and theoretical insights, it paves the way for advancing fluid dynamics applications across several domains.