Session H19: Focus Session: Interfacial Active Matter I

Interfacial flow around a pusher bacterium

Bacteria are prototypical active colloids that self-organize into coherent structures. However, their accumulation at fluid interfaces dramatically alters their behavior. We visualize the flow around swimming bacteria trapped on fluid interfaces by analyzing correlated displacements between bacteria and passive tracers. The observed flow fields are described by hydrodynamic multipoles for Stokes flow in an incompressible interface whose magnitudes and positions depend on the microbe's trapped configuration. Bacteria swim along noisy curved trajectories determined by the angle of their bodies with respect to the interface. By studying the motion of tracers entrained by their flow, we determine their enhanced diffusivity. Furthermore, we predict pair interactions that differ significantly from their bulk counterparts. This study identifies key factors that impact active colloidal dynamics at interfaces. These include the interplay of swimmer trapped configuration and far field flow, the importance of interfacial stresses and non-equilibrium fluctuations, and how these determine the dynamics of individual swimmers and their collective behaviors. These concepts can guide the design of microrobots for enhanced transport in multiphase systems.   

Interfacial Hydrodynamic Mulitpoles, their Comparison to Experiment, and Open Issues

While hydrodynamic multipoles have proven indispensable for describing the fluid mechanics of active (self-propelled), driven (externally forced) colloids in bulk fluids, a suitable description for colloids adsorbed to fluid interfaces was lacking. Here, we derive hydrodynamic multipoles for the typical stress conditions encountered in colloidal systems. Owing to the small scale of the colloidal agents, the Marangoni number is large even for scant surfactant, and fluid interfaces act as incompressible layers. For active colloids in particular, we find that an infinitesimally separated pairs of point forces at the interface do not fully describe the leading-order hydrodynamics as is true in the bulk, and "new" modes of flow arise from these pronounced Marangoni effects. The predicted modes capture the detailed structure of flows measured experimentally by correlated displacement velocimetry, including those around Brownian (thermally-driven) colloids and bacteria at fluid interfaces. Finally, we address open issues regarding our assumption of interfacial incompressibility and regimes where it may break down.   

Collective surfing of two self-propelled swimmers laden liquid-air interface with the aid of self-induced Marangoni flow

Some bacterial species such as Bacillus subtilis, Flavobacteria, etc. are known to produce a certain type of chemical (surfactin), which lowers the surface tension of the carrier fluid and creates a surface tension-driven Marangoni flow. We have studied the motion of two hydrodynamically coupled force-free, swimmers (pushers) confined to move along a planar liquid-air interface without and with the presence of self-induced Marangoni flow. In the absence of the Marangoni flow, we reported a closed analytical form of two types of linearly unstable planar rotational equilibria. In type 1 orbit, the pushers follow a unique circular trajectory, where the swimmers are always oriented head-to-head. In type 2 orbit, the pushers are moving along circles with different radii. In both cases, the relative orientation between the pushers and their distance remains constant. Our numerical results reveal the possibility of a persistent stable orbiting motion of two pushers in the presence of self-induced Marangoni flow. All simulations were performed at low Reynolds number and non-zero Peclet number.   

Microswimmers interacting with deformable interfaces

Active microscopic swimmers at low Re in confined domains exhibit responses that differ from their passive counterparts.  For instance, while swimming in the vicinity of a plane boundary in a quiescent fluid, “pusher” type microswimmers, such as the bacteria E. coli, tend to preferentially migrate towards the boundary even in the dilute suspension limit, whereas, denser suspensions tend to exhibit more complex confinement-dependent spatiotemporal patterns. The dynamics of such systems depends crucially on the nature of the intervening boundary; namely free-slip versus no-slip, in case of plane boundaries, or non-deforming versus deforming interfaces. We analyze the latter case involving the coupled hydrodynamics of a dilute suspension of microswimmers in the vicinity of a deformable interface. We characterize the nature of the interface deformation due to the swimming motion and address how the swimming is itself modified by the interface. The analysis treats the role of the swimmer type (pusher or puller), the finite swimmer size and interface deformation due to both surface tension and resistance to bending. We highlight the non-trivial ways in which the local and non-local effects influence the coupled hydrodynamics.   

Self-propulsion of symmetric interfacial swimmers

Marangoni effects are involved in a variety of capillary and interfacial phenomena. One instance which made its way into popular science is interfacial boats, which self-propel by releasing surfactant asymmetrically. Remarkably, as demonstrated experimentally with millimetric camphor-loaded disks, self-propulsion is also possible for symmetric objects through a spontaneous symmetry breaking, which, however, remains only partially elucidated. We propose a generic toy model, amenable to analytic treatment, that captures the swimming mechanism and predicts semi-quantitatively the swimming velocity. To go beyond this simple picture, we use numerical methods which can handle the complex couplings at work. We identify the nature of the bifurcation where motion sets in and characterize the swimming far above this threshold, and show that the role of Marangoni flow is very different in those two regimes.   

A remotely controlled Marangoni surfer

Drawing motivation from organisms that effectively traverse the air-water interface, we conceptualized and created a self-powered and remotely-controlled robotic platform destined for practical applications. Prioritizing drag reduction and biomimicry in design, our robotic surfer relies solely on the Marangoni effect for both propulsion and change of direction. To make this engineering challenge a reality, we developed custom-made flow control and steering mechanisms. These features were complemented with integrated power and fuel sources, and a remote transmitter, a receiver, and two servos, overall resulting in a non-tethered robotic surfer capable of self-propulsion and steering. Our experimental trials investigating the robot's transnational motion indicate that there is a clear positive trend in the speed with increasing the release rate of the propellant in the form of a power law. We rationalize this behavior using a simple scaling analysis based on an energy argument.   

Optimal Marangoni surfing

We study the surfing motion of active spheroidal particles located at a flat liquid-gas interface. The particles create and maintain a surface tension gradient by asymmetrically discharging a surface tension-reducing agent. We employ theory and numerical simulation to investigate the Marangoni propulsion of these active surfers. First, we use the reciprocal theorem in conjunction with singular perturbation expansions to calculate the leading-order corrections to the propulsion speed of the surfers due to the advective transport of momentum and mass when the Reynolds and Peclet numbers (denoted by Re and Pe, respectively) are small but finite. We learn, perhaps surprisingly, that the propulsion speed increases rather significantly with the negative of ln(Re) and ln(Pe), when both parameters are very small. Next, we apply numerical simulations to examine the effects of intermediate and large values of Re and Pe on the propulsion speed. Consistent with the theoretical predictions, our simulations reveal that the normalized propulsion speed initially increases with increasing Re and Pe from zero. Interestingly, however, we find that the speed then reaches a maximum and afterward sharply declines when Re and Pe become large. That there exist certain intermediate Reynolds and Peclet numbers at which the Marangoni propulsion reaches a peak is a new finding that can guide engineers to design Marangoni surfers with superior performance.   

Non-equilibrium capillary self-assembly

Existing, well-established principles of interfacial capillary self-assembly focus on the behavior of such systems at equilibrium, wherein the resultant self-assembled structures reside in a local minimum of a free-energy landscape. Inspired by recent experiments involving overdamped, microscopic colloids, we herein study experimentally and theoretically the structural rearrangements between ground states of clusters of millimetric spheres bound by capillary attractions. The structural rearrangements are driven by chaotic Faraday waves, which in turn play the role of an active bath. In contrast to colloids, inertial effects are non-negligible in our macroscopic system, prompting the development of a Langevin model of the particle dynamics, informed by the fundamental aspects of the fluid system. Our highly tunable experimental system addresses the relative paucity of model systems for studying inertial active and driven matter and informs new directions for non-invasive, directed self-assembly at the macroscale.   

Cheerios effect drives the formation of fire ant rafts

Fire ants survive waterproof floods by linking their bodies together to form waterproof rafts.  How do the ants find each other on the water surface?  We performed experiments with varying numbers of ants on the water surface and found that in fact, ants in numbers less than ten cannot form stable rafts.  We observe ants swim in random directions even when around neighbors and kick each other away when coming into contact. These repulsive effects result in the breakup of small rafts. Surface tension, on the other hand, attracts ants together through the Cheerio effect, which draws small floating objects together. Combining the two mechanisms, a stability criterion emerges where the rafts need to be above a critical size to generate sufficient capillary forces to remain stable.  We observed this stability transition in both experiments and numerical simulations.  Our work shows that ants rely on capillarity to reconcile their needs to swarm and explore their surroundings.