Session F6: Surface Tension Effects: Interfacial Phenomena

Elastocapillary waves on ultra-soft solids exhibit dispersion

Rayleigh waves are widely used in non-destructive testing and in the study of seismology. Generally, Rayleigh waves are non-dispersive, and surface tension is not considered since the surface energy is so much smaller than the elastic energy in most solids. Herein we explore surface waves on ultra-soft solids where surface tension forces are not insignificant and where dispersion may exist. Agarose gel was explored for a range of shear moduli. Faraday waves were created on the agarose gel surface by vibrating the gel on a shaker for frequencies ranging from 40Hz to 200Hz. It was observed that the surface waves are dispersive for a range of shear moduli, an observation that cannot be explained by Rayleigh wave theory. A new analytical model that incorporates the solid surface tension was developed and explains the experimental observations.   

Effect of interference of capillary length on evaporation at meniscus

In this study, the experimental results on the evaporation characteristics of meniscus in various geometrical configurations which enable to vary a perimeter of liquid-vapor interface and a meniscus curvature were obtained, and the main factor in evaporation process was clarified. As the experimental conditions, the perimeter was adjusted from $1\mbox{mm}$ to $100\mbox{mm}$ order, and the curvature from the inverse of capillary length, $\kappa (\sim 0.4\mbox{mm}^{-1})$, to about $10\mbox{mm}^{-1}$. Measuring devices for evaporation rate, which consisted of a test section on an electric balance, was set to a reduced pressure environment for making the purified water in the test section evaporate. There is no heater in the test section and system was set to be isolated from outside environment. It was found that the evaporation rate and flux could be organized by the perimeter if the curvature is constant at $\kappa $. On the other hand, when the curvature is larger than $\kappa $, it was found that the curvature is the dominant factor in the evaporation process. It can be considered that an interference of capillary length is a key to understand these results.   

Wrinkle-to-crumple transition in thin films on curved surfaces

When a thin yet stiff film is placed on a liquid droplet, a deformation structure emerges, termed "crumples" [1]. These crumples occur as wrinkles break up into segments, and they appear to focus stress at their tips. However, their mechanism and threshold are not known. To address this problem, we study the behavior of thin polystyrene sheets (thickness $\sim$ 100 nm) placed on a cylindrical liquid-air interface that is subjected to longitudinal compression. This setup allows us to independently control both the curvature of the cylindrical meniscus and lateral confinement. We find that wrinkles give way to crumples beyond a threshold value of curvature. We study how this threshold depends on other parameters such as compression, surface tension, aspect ratio and sheet thickness. Our results are summarized in phase diagrams that demarcate wrinkles, crumples, and folds. [1] King, Schroll, Davidovitch, & Menon, PNAS 109 (2012).   

Free-standing monolayer films of ordered colloidal particles

We report a method to fabricate large area, free standing monolayer films of close-packed colloidal particles. Our method creates a wet, free-standing film of colloidal dispersion, which is then dried under controlled environment to achieve a dry, free-standing film of particles. The colloidal dispersion contains mono-dispersed hard particles (such as polystyrene or silica) mixed with relatively smaller and softer polymer particles of low glass transition temperature. During drying, hard particles present in the free standing film arrange in a hexagonal close-packed structure due to capillary interaction and form a monolayer film while the soft particles fill the interstices around hard particles and deform and coalesce to produce a continuous matrix to prevent the cracking of the monolayer film. The monolayer films exhibit strong iridescence indicating potential application in photonic devices. Simulations were performed on the Surface Evolver software to investigate the capillary interactions that lead to particle ordering.   

Kinematically irreversible particle motion in 2D suspensions due to surface-pressure-dependent surface rheology

The surface viscosity of many insoluble surfactants depends strongly on the surface pressure (or surface tension) of that surfactant. Surface pressure gradients naturally arise in interfacial flows, and surface-pressure-dependent surface rheology alters 2D suspension dynamics in significant ways. We use the Lorentz reciprocal theorem to asymptotically quantify the irreversible dynamics that break Newtonian symmetries. We first show that a particle embedded in a surfactant-laden interface and translating parallel to or rotating near an interfacial boundary experiences a force in the direction perpendicular to the boundary. Building on this, we extend the theory to compute the first effects of pressure-dependent surface viscosity on 2D particle pairs in suspension. The fore-aft symmetry of pair trajectories in a Newtonian interface is lost, leading to well-separated (when pressure-thickening) or aggregated (when pressure-thinning) particles. Notably, the relative motion is kinematically irreversible, and pairs steadily evolve toward a particular displacement. Based on these irreversible pair interactions, we hypothesize that pressure-thickening (or -thinning) leads to shear-thinning (or -thickening) in 2D suspensions.   

Flow induced on a waterbody by a source

We analytically study the flow induced on a saltwater surface by a freshwater point source, and on a freshwater surface by a saltwater point source. In the former case, the fluid directly below the source rises upward, and near the surface it moves away from the source. In the latter case, the fluid directly below the source moves downwards, and near the surface it moves towards the source. The analytical results are compared with the experimental results obtained using the particle image velocimetry (PIV) technique.   

Stability of a chemically active floating disk

We theoretically study the translational stability of a chemically active disk located at a flat liquid-gas interface. The initially immobile circular disk uniformly releases an interface-active agent that locally changes the surface tension and is insoluble in the bulk. If left unperturbed, the stationary disk remains motionless as the agent is discharged. Neglecting the inertial effects, we numerically test whether a perturbation in the translational velocity of the disk can lead to its spontaneous and self-sustained motion. Such a perturbation gives rise to an asymmetric distribution of the released factor that could trigger and sustain the Marangoni propulsion of the disk. An implicit Fourier-Chebyshev spectral method is employed to solve the advection-diffusion equation for the concentration of the active agent. The solution, given a linear equation of state for the surface tension, provides the shear stress distribution at the interface. This and the no-slip condition on the wetted surface of the disk are then used at each time step to semi-analytically determine the Stokes flow in the semi-infinite liquid layer. Overall, the findings of our investigation pave the way for pinpointing the conditions under which interface-bound active particles become dynamically unstable.   

Dependence of surface tension on curvature obtained from a diffuse-interface approach

From a sharp-interface viewpoint, the surface tension force is $\bf{f}=\sigma \kappa \delta(\textbf{x}-\textbf{x}_i)\bf{n}$, where $\sigma$ is the surface tension, $\kappa$ the local interface curvature, $\delta$ the delta function, and $\textbf{n}$ the unit normal vector. The numerical implementation of this force on discrete domains poses challenges that arise from the calculation of the curvature. The continuous surface tension force model, proposed by Brackbill {\it et al.} (1992), is an alternative, used commonly in two-phase computational models. In this model, $\delta$ is replaced by the gradient of a phase indicator field, whose integral across a diffuse-interface equals unity. An alternative to the Brackbill model are Phase-Field models, which do not require an explicit calculation of the curvature. However, and just as in Brackbill's approach, there are numerical errors that depend on the thickness of the diffuse interface, the grid spacing, and the curvature. We use differential geometry to calculate the leading errors in this force when obtained from a diffuse-interface approach, and outline possible routes to eliminate them. Our results also provide a simple geometrical explanation to the dependence of surface tension on curvature, and to the problem of line tension.   

Planar, free oscillations of a cylindrical fluid filament

A viscous cylindrical fluid filament of infinite axial extent is immersed in another viscous fluid at rest. We perturb the circular cross section of the filament with an azimuthal Fourier mode ($\exp\left(im\theta\right)$ with wavenumber $m$ real). Under/over damped free oscillations occur due to surface tension and we study these theoretically and through DNS. In the invisicd, irrotational approximation the dispersion relation for these oscillations was first obtained by Rayleigh (Proc. Roy. Soc. Lond., 29, 71, 1879) ignoring the inertia of the ambient fluid. Fyfe et. al. (J. Comp. Phys., 76,349-384 1988) subsequently included the inertia of the ambient fluid to the dispersion relation. We study the viscous correction to this relation, including viscosity of both the fluids. Unlike the inviscid dispersion relation which is an algebraic equation, the viscous dispersion relation turns out to be a transcendental equation. We study the roots of this equation on the complex frequency plane. In addition to the discrete spectrum, the viscous problem also has a continuous spectrum. The solution to the initial value problem which includes both, will be presented. Comparisons of analytical results with DNS results obtained from an in house developed VOF code, will be discussed.