Influencing contact-line behavior in dynamic wetting through thermocapillarity and surface topography

Abstract

Dynamic wetting involves an advancing fluid displacing a receding fluid on a solid surface. This phenomenon can be seen in day-to-day occurrences such as water droplets sliding on a glass window on a rainy day, where the droplet displaces the air surrounding the glass surface as it slides, and in industrial processes such as slot-die coating, where the coating liquid displaces the surrounding air to coat a moving substrate. A three-phase contact line is present wherever the solid surface, and the advancing and receding fluids intersect. Controlling the behavior of contact lines is key to improving the efficiency of industrial processes. The work in this thesis focuses on developing mathematical models to investigate contact-line behavior in geometries which are motivated by important industrial applications. The first part of the thesis focuses on developing a Galerkin-finite-element model for a parallel-plate geometry motivated by the slot-die coating process, where it is found that generating a thermal Marangoni flow toward the contact line delays wetting failure to faster substrate speeds, which is crucial for increasing production rates in industrial processes. In the second part, a lubrication-theory-based model is developed to study the motion of droplets of a Newtonian liquid on substrates with topographical defects due to pressure-driven flow of a surrounding fluid. Above a critical pressure gradient, the shear force acting on the droplet exceeds the retention force due to surface tension, causing the contact line to depin from the defects which leads to the droplet sliding on the substrate freely. The influence of substrate topography, wettability, viscosity, and droplet volume on the critical pressure gradient is studied and the findings provide insights into optimizing applications such as crossflow microemulsification, oil recovery, and surface cleaning. Lastly, a lubrication-theory-based model is developed to study the motion of droplets of a Newtonian liquid on inclined substrates with a three-dimensional topographical defect. Above a critical inclination angle, the gravitational force acting on the droplet exceeds the surface-tension force, causing the droplet to depin and slide freely. The influence of key geometric features of the defect on the critical inclination angle is investigated. These findings can provide guidelines for designing substrates for applications such as fog harvesting and droplet-based microfluidics.