Session Z04: Drops: Sessile and Static Surface Interactions (12:15pm - 1:00pm CST)

Controlling evaporating droplets

Controlling the dynamics of evaporating liquid droplets is important in several industrial applications such as coating, and inkjet printing. In this talk the behaviour of a two-dimensional droplet that is slowly evaporating on a solid surface due to mass diffusion is investigated. The substrate is flat but with smooth chemical variations that lead to a space-dependent local contact angle. Detailed bifurcation analysis of the equilibrium properties of the droplet as its size is changed, reveals the emergence of a hierarchy of bifurcations that strongly depends on the particular underlying chemical pattern. Symmetric and periodic patterns lead to a sequence of pitchfork and saddle-node bifurcations that make stable solutions to become saddle nodes. Under dynamic conditions, this change in stability suggests that any perturbation in the system can make the droplet to shift laterally while relaxing to the nearest stable point. With an asymmetric periodic chemical variation, it is shown that the droplet can be made to move in certain directions as is confirmed by numerical computations of the Cahn-Hilliard and Navier-Stokes system of equations.   

Not Participating

We study the equilibrium shape of a liquid drop resting on top of a liquid surface, i.e., a floating lens. We consider the surface tension forces in non--wetting situations (negative spreading factor), as well as the effects of gravity. We obtain analytical expressions for the drop shape when gravity can be neglected. Perhaps surprisingly, when including gravity in the analysis, we find two different families of equilibrium solutions for the same set of physical parameters. These equilibrium solutions differ in the curvature sign of the external liquid surface. By means of energetic considerations, we determine the family of solutions that has the smallest energy, and therefore, the most likely to be found in nature. We compare the shape of those solutions with preliminary experiments.   

Water Drop Interface Shape Reconstruction Using Stereoscopic Digital Image Correlation

A stereoscopic technique for measuring instantaneous, three-dimensional interface shapes of irregularly shaped water drops on rough surfaces has been developed that builds on work by Schmucker et al. (Exp. Fluids, 52, 123-136, 2011). Those authors used a single camera perpendicular to the surface to image rough-surface speckle patterns and reconstruct drop shapes by measuring the shifts in the speckle pattern caused by interface refraction. While successful near the centers of drops, that technique could fail near the contact line where surface inclinations are large. This shortcoming is overcome using a stereoscopic approach where two inclined cameras are used to better capture light near the contact line. Results show equal or better reconstruction accuracy where the single-camera technique is possible and additional measurement capability for a wider array of interface shapes.   

Shape oscillations of a pinned droplet

We study using numerical simulations, the shape oscillations due to surface tension, of a spherical cap comprising of quiescent fluid pinned to a solid substrate. The eigenmodes for this configuration, for small amplitude perturbations have been presented earlier in \textit{Bostwick and Steen, J. Fluid Mech., vol. 760, 2014} and we use these in our numerical simulations. We test the limit of linearised theoretical predictions by exciting the first few eigenmodes. For sufficiently small perturbation amplitude, the agreement with linearised predictions is quite good although a systematic nonlinear correction to frequency is observed as the perturbation amplitude is increased, becoming particularly discernible after the first few oscillations. The simulations are carried out using the open source code Gerris (gfs.sourceforge.net) and we quantify the affect of non linearity and inertia of the outer fluid. A theoretical formulation taking into account the latter, will be presented. For a viscous drop, the role of the boundary layer formed at the interface, on the damping of free oscillations, will also be discussed.