Direct visualization of viscous dissipation and wetting ridge geometry on lubricant-infused surfaces

Lubricants have long been used to reduce friction between solid surfaces. More recently, the use of lubricants to minimize friction between liquid drops and solid surfaces has gained traction, driven by advancements in surface fabrication techniques. Understanding energy dissipation mechanisms and the influence of lubricant properties and surface geometry is crucial for controlling drop friction on lubricated surfaces. Lubricant-infused surfaces (LIS), also known as slippery liquid-infused porous surfaces (SLIPS), typically consist of a micro/nanoscopic solid scaffold imbibed with lubricant. Drops exhibit minimal adhesion on LIS because the lubricant fully spreads, masking surface defects. This work investigates both flat and microstructured lubricated surfaces to understand the role of microstructures in drop dynamics. LIS are exceptionally effective at repelling a wide range of liquids, including low surface tension oils, making them suitable for diverse applications such as heat exchangers, medical devices, and self-cleaning surfaces. However, drops on LIS experience significantly more friction (1–2 orders of magnitude) than on superhydrophobic surfaces, primarily due to the interplay between capillary and viscous forces within the drop and the lubricant meniscus (wetting ridge). Previous research suggests that energy dissipation primarily occurs in the wetting ridge and the lubricant film beneath the drop, but direct visualization has been lacking. This paper aims to construct dissipation heatmaps to visualize energy dissipation and directly image the shape and size of the wetting ridge at various drop speeds and lubricant viscosities to understand lubricant transport during drop motion.

Prior research has investigated drop friction on LIS, focusing on the role of the wetting ridge in energy dissipation. Studies have suggested that energy dissipation is largely localized within the wetting ridge and the underlying lubricant film, particularly when the lubricant viscosity exceeds that of the drop. However, these findings have largely been based on indirect measurements and theoretical models, lacking direct visualization of the energy dissipation patterns. Previous work has also highlighted the importance of lubricant retention in LIS for maintaining low-friction properties and preventing contamination. Depletion of the lubricant, caused by factors such as drop motion, shear flows, and evaporation, can significantly compromise the long-term functionality of LIS. The existing literature demonstrates a need for a comprehensive understanding of both the energy dissipation mechanisms and the dynamics of lubricant transport in LIS.

This research employed a combination of advanced numerical simulations and experimental techniques. Lattice Boltzmann simulations, a state-of-the-art method capable of simulating multiphase flows with tunable viscosities, surface tensions, and complex solid geometries, were used to model the motion of drops on LIS. The simulations allowed for the investigation of different scenarios, including 2D, quasi-3D, and full 3D simulations with both flat and pillar-structured surfaces. Periodic boundary conditions were employed to minimize edge effects, while simulations were stopped before drops crossed the periodic boundary to avoid the influence of a Landau-Levich lubricant film deposited by the drop in previous passes. Dimensionless parameters such as Bond number (Bo) and capillary number (Ca) were utilized to characterize the applied force and drop velocity. A wide range of Bo and Ca values were investigated, and in most simulations, the lubricant viscosity was ten times higher than the drop viscosity. The experimental methodology involved a bespoke setup using laser scanning confocal microscopy to directly image the dynamic wetting ridge. Water drops and silicone oil lubricants with varying viscosities were used, and the solid surfaces were composed of a regular array of micropillars with controlled properties. The innovative experimental approach involved fixing the drop position while moving the lubricated surface at controlled velocities, allowing for extended imaging and exploration of a wide range of capillary numbers. This method effectively replicated the scenario of a drop moving over a stationary surface but enabled imaging over much larger distances than typically feasible with a fixed field of view.

The study yielded several significant findings. Firstly, dissipation heatmaps revealed that the majority of energy dissipation in the lubricant (over 75%) occurs directly in front of and behind the moving drop, with relatively little dissipation at the lateral sides. This pattern was consistent for both flat and pillar surfaces, highlighting the dominance of lubricant properties over surface geometry in the dissipation mechanism. Secondly, the relationship between the applied force and the capillary number followed the scaling law F ~ γwCa^(2/3), irrespective of surface geometry or simulation dimensionality. While previous experimental studies reported a transition to a 1/3 exponent at high capillary numbers, the simulations did not reproduce this transition, which was attributed to differences in the ratio between wetting ridge height and equilibrium film thickness. Thirdly, analysis of velocity profiles and viscous dissipation showed that the dominant contribution to dissipation arises from velocity gradients in the xz-plane (x being the direction of motion and z being perpendicular to the surface). Fourthly, both simulations and experimental observations confirmed an asymmetry in the wetting ridge, with the height of the rear ridge consistently exceeding that of the front ridge. The height of both ridges decreased with increasing capillary number according to a power law. The experimental data confirmed this asymmetry, showcasing a critical speed below which the ridge shape barely differed from its static state, similar to the Landau-Levich problem. Finally, the data revealed that the ratio of the dynamic to static wetting ridge height follows a universal scaling law, h/h0 ~ 1.1(Ca/Cac)^(-0.28), encompassing a wide range of parameters including lubricant viscosity, drop velocity, contact angles, surface geometries, and lubricant thicknesses.

The findings significantly advance the understanding of drop dynamics on LIS. The localization of dissipation in front of and behind the drop provides a simplified model for friction calculations, potentially reducing the computational complexity. The universality of the scaling law and the minor influence of surface geometry challenge prior assumptions and suggest that lubricant properties are more important than surface texture in governing friction. The observed asymmetry in the wetting ridge and its dependence on capillary number shed light on lubricant depletion during drop motion. Faster drops, corresponding to higher capillary numbers, transport less lubricant due to a decrease in the wetting ridge volume. This finding has implications for the design and optimization of LIS, particularly for applications requiring long-term lubricant stability and minimizing contamination.

This study provides valuable insights into the energy dissipation mechanisms and lubricant transport dynamics on LIS. The dominance of lubricant properties over surface geometry in determining friction, the asymmetric nature of the wetting ridge and its dependence on speed, and the resultant implications for lubricant depletion are significant contributions. Future research should investigate the transition in scaling exponents between friction force and capillary number observed in experiments, potentially focusing on the effect of thin lubricant films and dissipation in the rear wetting ridge. Further investigation into strategies to enhance lubricant retention and maintain LIS performance under diverse conditions is also warranted.

The simulations, while advanced, are subject to limitations inherent in the diffuse interface method, potentially leading to a slight overestimation of dissipation. The experimental setup focused on imaging the wetting ridge without the cloak, so the interaction between the cloak and the wetting ridge is not fully characterized. The transition in scaling exponents observed experimentally but not in simulations needs further investigation, possibly involving parameter regimes not explored in this study.