Session T39: Interfacial Phenomena I

Synchronization and collective motion of interfacial capillary spinners

When a millimetric body is deposited onto the interface of a vibrating liquid bath, the relative motion between the object and interface generates outward propagating waves which leads to steady propulsion. Prior work has shown that chiral objects or "spinners" in isolation can rotate at a steady rate, with both the direction of rotation and angular speed depending sensitively on the spinner geometry and driving parameters. Here, we consider the capillary wave-mediated interactions of multiple spinners. We first characterize the two-spinner problem, demonstrating that spinners are able to stably synchronize their rotation in certain parameter regimes via their mutual wavefield. The many-body problem is then considered where a rich variety of static and dynamic interaction modes are found. A model of the spinner interaction is proposed, allowing us to draw analogy to other systems exhibiting spontaneous synchronization. This highly tunable and accessible system represents a new platform for studying active and driven systems interacting through deformable substrates.   

Spontaneous rotation by symmetry breaking of a capillary wave source

When a millimetric object is deposited onto the interface of a vibrating liquid bath, the floating body generates an extended capillary wavefield with associated surface streaming flows. It has recently been shown that chiral objects placed at the interface are able to steadily rotate in a determined direction via an imbalance of wave stresses as a consequence of their imposed geometric asymmetry. Here, we consider symmetric (achiral) objects which spontaneously begin to rotate in either direction. This symmetry breaking phenomenon occurs above a critical driving acceleration, with this threshold depending on the driving frequency, fluid parameters, and wave source geometry. We characterize the dependence of the steady rotation speed on the experimental parameters, and rationalize our observations with a simple mathematical model drawing inspiration from other physical systems that exhibit spontaneous symmetry breaking.   

Self-similar regimes in the viscous Marangoni spreading of surfactant on a deep subphase

The spreading of an insoluble surfactant on a fluid interface is a fundamental fluid mechanics problem that has been investigated extensively due to its implications for flows in biology, the environment, and in technological applications. While many different regimes have been studied theoretically, analytical progress has proven challenging in the limit of a deep subphase at low Reynolds and high Péclet numbers, due to the non-local nature of the coupling between the interfacial velocity field and the concentration of surfactant [Thess, Phys. Rev. Lett. (1995)]. Recently, the problem was shown to be equivalent to the complex Burgers equation [Crowdy, SIAM J. Appl. Math. (2021)], paving the way to exact solutions obtained through the method of characteristics [Bickel, Phys. Rev. E (2022)]. Here, we study the self-similarity of the problem, providing further insights into its structure. First, a phase-plane formalism is used to identify different self-similar regimes. In the case of a pulse of outward-spreading surfactant, we find a globally valid solution exhibiting self-similarity of the first kind. On the other hand, surfactant-free holes collapsing inward exhibit self-similarity of the second kind, which only holds locally. We find that the exponents in the power-law behavior of these hole solutions can be obtained exactly using stability arguments, and distinguish two different power-law exponents that hold depending on the nature of the initial condition. We also discuss the importance of higher-order effects like surface diffusion and endogenous surfactant on these idealized solutions.   

Receding contact lines in water-ice systems

This presentation will be about theoretical and experimental investigations on the wetting behavior of water on ice. Several previous experimental observations and theoretical considerations points towards the idea that the ice-water system is not perfectly wetting. However, investigating that phenomenon systematically using classical techniques used to measure wettability is an experimental challenge, as ice and liquid water are usually not at equilibrium when coexisting. Our experiments force a well-controlled out-of-equilibrium situation, namely the receding motion of a contact line on a vertical plate of ice, and we compare the results with a model for the solidifying film. Our results show that solidification allows contact lines to stay stationary in regimes of the capillary number that are out of reach for inert systems. These results also point towards the idea that water does not perfectly wet ice.   

Exogenous-endogenous surfactant iteraction yields heterogenous spreading in complex branching networks

Experiments¹ have shown that surfactant introduced at the entrance of a maze filled with a shallow layer of milk can induce a flow in the liquid which spontaneously finds the solution path, effectively solving the maze with minimal flow into dead-end sections.  Here, we test the hypothesis that this maze-solving behaviour is due to the dynamics of a second species of surfactant endogenous to the liquid. Lubrication theory can be used to derive equations capturing the Marangoni flow induced by surfactants, which reduce to a nonlinear diffusion equation² describing the spread of the exogenous surfactant in a large-gravity and low-Reynolds-number limit.  Treating both species of surfactant as a single concentration field, we solve this equation simultaneously with a kinematic equation to track the exogenous front locations.

            To solve the governing equation on a network representing the topology of the maze, we construct a mass-conserving mimetic-finite-difference (MFD) scheme using tools from discrete calculus and graph theory. We find that the simulation qualitatively captures the maze-solving behaviour observed in the experiment, with the result dependent on only two fitting parameters: the mass ratio of exogenous to endogenous surfactant, and the initial ratio of the surfactant concentrations. A modal decomposition of the MFD Laplacian operator shows that only three dominant modes are needed to qualitatively capture the key behaviour of maze solving, and the experimentally observed behaviour of receding in dead end sections.

¹ Temprano-Coleto et al., Phys Rev Fluids. 3, 100507 (2018)

² Jensen and Halpern, J. Fluid Mech. 372, 273 (1998)   

The role of monolayer viscosity in Langmuir film hole closure dynamics

We re-examine the model proposed by Alexander et al. (Phys. Fluids, vol. 18, 2006, 062103) for the closing of a circular hole in a molecularly thin incompressible Langmuir film situated on a Stokesian subfluid. For simplicity their model assumes that the surface phase is inviscid which leads to the result that the cavity area decreases at a constant rate determined by the ratio of edge tension to subfluid viscosity. We reformulate the problem, allowing for a regularizing monolayer viscosity. The viscosity-dependent corrections to the hole dynamics are analysed and found to be non-trivial, even when the monolayer viscosity is small; these corrections may explain the departure of experimental data from the theoretical prediction when the hole radius becomes comparable to the Saffman–Delbrück length. Through fitting, under these relaxed assumptions, we find the edge tension could be as much as six times larger (∼4.0 pN) than reported previously.   

Remobilizing a stagnant cap of surfactant through fast kinetic exchange and surface diffusion

Explicit solutions are presented describing the steady remobilization of a planar interface between two viscous fluids laden with surfactant soluble to the upper fluid. In the presence of a linear extensional flow, steady stagnant caps of surfactant form resulting in an immobilized interface. We show analytically that both fast kinetic exchange with the bulk fluid and surface diffusion can mollify these sharp surfactant gradients, thereby reducing the interfacial Marangoni stresses. The case of insoluble surfactant on an interface between a viscous fluid and a constant pressure region is also treated equivalently.