Theoretical and Computational Modelling of Wetting Phenomena in Smooth Geometries

Capillarity and wetting are the study of the interfaces that separate immiscible fluids and their interaction with solid surfaces. The interest in understanding capillary and wetting phenomena in complex geometries has grown in recent years. This is partly motivated by applications, such as the micro-fabrication of surfaces that achieve a controlled wettability, but also because of the fundamental role that the geometry of a solid surface can play in the statics and dynamics of liquids that come into contact with it. In this work, the statics and dynamics of liquids in contact with smooth, but non-planar geometries are studied. The approach is theoretical, and include mathematical modelling and numerical simulations using a new lattice-Boltzmann simulation method. The latter can account for solid boundaries of arbitrary geometry and a variety of boundary conditions relevant to experimental situations. The focus is directed to two model systems. First, an analysis on the statics and dynamics of a droplet inside wedge is performed, this is accomplished by proposing the shape of the droplet, a new shape that will be referred in this document as a “liquid barrel”. Using this assumption, the static position and shape of the droplet in response to an external body force is predicted. Then, the analysis is extended to include to dynamical situations in the absence of external forces, in which the translational motion of the liquid barrel towards equilibrium it is described. The proposed analytical model was validated by comparison with full 3D lattice-Boltzmann simulations and with recent experimental results. The applicability of these ideas is materialised with the purpose of achieving energy-invariant manipulation of a liquid barrel in a reconfigurable wedge. As a second model system, the evaporation of a sessile droplet in contact with a wavy solid surface was studied. Due to the non-planar solid topography, the droplet position in equilibrium is restricted to a discrete set of positions. It is shown that when the amplitude of the surface is sufficiently high, the droplet can suddenly readjust its shape and location to a new equilibrium configuration. These events occur in a time-scale much shorter than the evaporation time-scale, a “snap”. With numerical simulations and theoretical analysis, the study reveals the causes for the snap transitions, which lie in shape bifurcations of the droplet shapes, The analysis and results are compared against recent experiments of droplets evaporating on smooth sinusoidal surfaces. With the advent of low-friction surfaces, in which static friction is practically absent, the mobility of droplets is close to ideal, and with this, predicting and controlling them in static cases becomes a challenge. The analysis and results presented in this work can be used for manipulating the position and defining the shape of droplets via the geometry of their confinements.