Session A39: Surface Tension Effects: General

Capillary Rise in Sharp Corners: Not Quite Universal

We study the capillary rise of viscous liquids into sharp corners formed by two surfaces whose geometry is described by power laws, h_i(x) = c_i xⁿ, i = 1,2, where c₂ > c₁ for n ≥ 1. The lubrication approximation is used to derive a partial differential equation for the evolution of the liquid column that rises into the corner. It is found that the dynamics are unaffected by potential asymmetry of the corner and that the shape of the liquid column is independent of c_i when described using the interface radius. Furthermore, despite the lack of geometric similarity of the liquid column cross-section for n>1, there exists a scaling and a similarity transformation that are independent of corner geometry. Consequently, the t^1/3 power-law for capillary rise applies regardless of the corner geometry. However, the prefactor, which corresponds to the tip altitude of the self-similar solution, is a function of n, and it is shown to be bounded and monotonically decreasing as n → ∞. Theoretical results are compared against experimental measurements of the time evolution of the tip altitude and of profiles of the interface radius as a function of altitude. The generalization to asymmetrical corners (c₁ ≠ -c₂) enables comparison of analytical and experimental results for corners with n>1.   

Interactions and Pattern Formation in a Macroscopic Magnetocapillary SALR System

When particles are deposited at a fluid interface they tend to aggregate due to capillary attraction, in an effort to minimize the overall potential energy of the system. In this work, we embed floating millimetric disks with permanent magnets to introduce a competing repulsion effect. The pairwise energy landscape of two disks is described by a Short-range Attraction and Long-range Repulsion (SALR) interaction potential, previously documented in a number of microscopic systems. The simple interaction model predicts a variety of equilibrium states, including the possibility of a local minimum energy corresponding to a finite disk spacing as observed in experiment. 2D experiments and simulations in confined geometries show that as the area packing fraction is increased, the uniform lattice state becomes unstable and localized clusters spontaneously form which eventually merge into a striped pattern.  Finally, we show that the pattern can be dynamically switched via application of an external magnetic field.   

Riding on Elastocapillary Rails

Partially wetting droplets naturally deform soft substrates by surface tension. These deformations are usually localized to a narrow region near the contact line, forming a so-called 'elastocapillary ridge'. In this study, we explore the dynamics of a droplet sliding along such a substrate, examining three variables simultaneously via interferometry: the macroscopic shape of the droplet, the microscopic formation of the elastocapillary ridge, and the associated energy dissipation. Our observations reveal a fascinating interplay between these factors. At a higher droplet velocity, the droplet becomes bullet-like, the dissipation levels off, and we observe a pair of parallel ridges that slowly fade away behind the droplet (which we call "elastocapillary rails"). This formation of the elastocapillary rails highlights that the droplet can reshape itself to minimize dissipation.   

Frozen Cheerios effect: Particle-particle interaction induced by an advancing solidification front

Particles at liquid interfaces have the tendency to cluster due to long-range capillary interactions. This is known as the Cheerios effect. Here we experimentally and theoretically study the interaction between two submerged particles near an advancing water-ice interface during the freezing process. Particles that are more thermally conductive than water are observed to attract each other and form clusters once frozen. We call this feature the frozen Cheerios effect. On the other hand, less conductive particles separate, highlighting the importance of thermal conduction during freezing. We extend the existing models for single particle trapping in ice to multiple particles and find that the overall strength of the particle-particle interaction critically depends on the solidification front velocity and on the particle-front interaction. Moreover, the thermal conductivity mismatch between the particles and water dictates the attractive/repulsive nature of the particle-particle interactions. Our findings are relevant in the context of cyropreservation procedures of food emulsions, suspensions, and for ice-templating.   

Collapse of a granular raft: a single particle perspective

Particle-laden interfaces are interesting composite systems due to their potential application in emulsion stabilization, drug delivery, handling of hazardous materials. When the particles are heavier than the liquid phase and non-Brownian in nature, they self-assemble on the interface via capillarity to form granular rafts. In recent work, we experimentally observed that the bi-axial compression of the granular raft leads to two distinct modes of failure: collective creasing versus single particle expulsion, as a function of the particle size and the density difference between the upper and lower fluids. Despite the success of a barebones continuum model to describe our experiments, the connection between the single particle behavior and the raft failure is missing from our understanding. By combining new visualization experiments and modeling, we aim to uncover the connection between the position of the individual particle on the interface and the raft's macroscopic response to compression.   

PTV Analysis of Passive Microgravity Bubble Separations Analogous to Steady Capillary Nucleate Boiling in Space

On earth, heat transfer away from a heated surface can easily be achieved by nucleate boiling, as buoyancy due to gravity ensures that the gas bubbles that form rise to the liquid surface. In the microgravity environments found aboard spacecraft, this seemingly simple task becomes non-trivial as bubbles do not rise with buoyancy. In cases of high heat flux, wall-bound vapor bubbles coalesce, blanketing the heated surface and preventing heat removal. In 2022, a series of demonstrations were performed by astronaut Kjell Lindgren aboard the International Space Station exploiting conduit geometry to mimic steady nucleate boiling. The 'boiling flask' container is capable of passive bubble separations in a manner that replaces the role of gravity during nucleate boiling on earth. The analogous isothermal demonstrations introduce air bubbles into the flask vertex at a near constant rate. The partially asymmetrically confined bubbles are driven downstream where they merge with the free surface. In this work, the migration and distribution of the bubbles and liquid films are analyzed using particle tracking velocimetry (PTV). It is observed how bubble trajectories, velocities, and coalescence are dependent on gas flow rate, bubble volume, conduit liquid fill level, and conduit geometry. The phenomena is found to be dependent on the inscribed bubble diameters within the channel geometry.   

Liquid Collection on Superomniphilic Wavy Surfaces

There is great need for functional surfaces to promote efficient liquid collection from droplet-laden air flows, with applications including water harvesting, building climate control, thermal power generation, and desalination. Current state-of-the-art flat surfaces utilize hydrophobicity to promote high droplet mobility for improved drainage, but the surfaces lose their hydrophobicity at high supersaturation conditions. In this work, we design a self-regulating omniphilic surface for much improved liquid collection rates, with inspiration from the remarkable fog and dew collection ability of the Welwitschia mirabilis, a plant which can survive for thousands of years in the Namib Desert. The surface is designed with a periodic wavy structure, with millimeter-scale features tuned such that liquid deposition is focused on the peaks and the pressure-driven flow from peak to valley is dominated by capillary forces rather than gravity. The filmwise transport is then critical for the instantaneous wicking of liquid into the valley region where it is sheltered from the bulk flow, thus minimizing re-entrainment and evaporation. As such, this is a self-regulating and highly durable surface for efficient long-term liquid collection, with many energy and sustainability applications.   

Unsteady evolution of slip and drag in surfactant-contaminated superhydrophobic channels

We examine the unsteady transport of soluble surfactant in a laminar channel flow bounded between two superhydrophobic surfaces (SHSs) that are periodic in the streamwise and spanwise directions. We assume that the channel length is much larger than the streamwise period, the streamwise period is much larger than the channel height and spanwise period, and that bulk diffusion is sufficiently strong for cross-channel concentration gradients to be small. By combining long-wave and homogenisation theories, we derive an unsteady advection-diffusion equation for surfactant transport over long lengthscales and slow timescales, which is coupled to a quasi-steady advection-diffusion equation for surfactant transport over each plastron. We predict the propagation speed of disturbances to the surfactant concentration field and describe the nonlinear evolution of disturbances via interaction with the SHS. The propagation speed of disturbances falls below the average streamwise velocity as the surfactant becomes less soluble, via coupling between bulk and interfacial transport. We show that wave-steepening effects can lead to shock formation in the surfactant flux distribution. These findings reveal the spatio-temporal evolution of the slip velocity and predict the drag reduction for microchannel applications.