We investigate experimentally the behavior of self-propelled water-in-oil droplets, confined in capillaries of different square and circular cross-sections. The droplet's activity comes from the formation of swollen micelles at its interface. In straight capillaries the velocity of the droplet decreases with increasing confinement. However at very high confinement, the velocity converges toward a non-zero value, so that even very long droplets swim. Stretched circular capillaries are then used to explore even higher confinement. The lubrication layer around the droplet then takes a non-uniform thickness which constitutes a significant difference with usual flow-driven passive droplets. A neck forms at the rear of the droplet, deepens with increasing confinement, and eventually undergoes successive spontaneous splitting events for large enough confinement. Such observations stress the critical role of the activity of the droplet interface on the droplet's behavior under confinement. We then propose an analytical formulation by integrating the interface activity and the swollen micelles transport problem into the classical Bretherton approach. The model accounts for the convergence of the droplet's velocity to a finite value for large confinement, and for the non-classical shape of the lubrication layer. We further discuss on the saturation of the micelles concentration along the interface, which would explain the divergence of the lubrication layer thickness for long enough droplets, eventually leading to the spontaneous droplet division.
Using a 3D Lagrangian tracking technique, we determine experimentally the trajectories of non-tumbling E. coli mutants swimming in a Poiseuille flow. We identify a typology of trajectories in agreement with a kinematic "active Bretherton-Jeffery" model, featuring an axi-symmetric self-propelled ellipsoid. In particular, we recover the "swinging" and "shear tumbling" kinematics predicted theoretically by Zöttl et al. Moreover using this model, we derive analytically new features such as quasi-planar piece-wise trajectories, associated with the high aspect ratio of the bacteria, as well as the e…
Recently, an active microswimmer was constructed where a micron-sized droplet of bromine water was placed into a surfactant-laden oil phase. Due to a bromination reaction of the surfactant at the interface, the surface tension locally increases and becomes non-uniform. This drives a Marangoni flow which propels the squirming droplet forward. We develop a diffusion-advection-reaction equation for the order parameter of the surfactant mixture at the droplet interface using a mixing free energy. Numerical solutions reveal a stable swimming regime above a critical Marangoni number M but also stopp…
Active colloidal rafts perform swimming strokes that propel their host droplets
Université de Bordeaux（波尔多大学）；Collège de France（法兰西公学院）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Meiji University（明治大学）
Inspired by recent experiments using synthetic microswimmers to manipulate droplets, we investigate the low-Reynolds-number locomotion of a model swimmer (a spherical squirmer) encapsulated inside a droplet of comparable size in another viscous fluid. Meditated solely by hydrodynamic interactions, the encaged swimmer is seen to be able to propel the droplet, and in some situations both remain in a stable co-swimming state. The problem is tackled using both an exact analytical theory and a numerical implementation based on boundary element method, with a particular focus on the kinematics of th…
We present here first-of-a-kind experimental measurements of the flow field around a swimming water droplet, using confocal PIV in three dimensions. The droplet is denser than the continuous oil phase, and swims close and parallel to the bottom wall. The measured flow field is first quantitatively characterized and compared to the flow field obtained for an axisymmetric swimmer in unbounded flow. Important qualitative differences are observed, in particular the emergence of a strong isotropic radial flow field in the planes parallel to the wall. These fundamental differences stress the critica…
Active fluids are a class of non-equilibrium systems where energy is injected into the system continuously by the constituent particles themselves. Many examples, such as bacterial suspensions and actomyosin networks, are intrinsically chiral at a local scale, so that their activity involves torque dipoles alongside the force dipoles usually considered. Although many aspects of active fluids have been studied, the effects of chirality on them are much less known. Here we study by computer simulation the dynamics of an unstructured droplet of chiral active fluid in three dimensions. Our model o…
We investigate the collective dynamics of self-propelled droplets, confined in a one dimensional micro-fluidic channel. On one hand, neighboring droplets align and form large trains of droplets moving in the same direction. On the other hand, the droplets condensates, leaving large regions with very low density. A careful examination of the interactions between two "colliding" droplets demonstrates that local alignment takes place as a result of the interplay between the dispersion of their speeds and the absence of Galilean invariance. Inspired by these observations, we propose a minimalistic…
Burgeoning interest in the area of bacteria-powered micro robotic systems prompted us to study the dynamics of cargo transport by single bacteria. In this paper, we have studied the swimming behaviour of oil-droplets attached as a cargo to the cell bodies of single bacteria. The oil-droplet loaded bacteria exhibit super-diffusive motion which is characterized by high degree of directional persistence. Interestingly, bacteria could navigate even when loaded with oil-droplets as large as 8 microns with an effective increase in rotational drag by more than 2 orders when compared to free bacteria.…
To explore and react to their environment, living micro-swimmers have developed sophisticated strategies for locomotion - in particular, motility with multiple gaits. To understand the physical principles associated with such a behavioural variability,synthetic model systems capable of mimicking it are needed. Here, we demonstrate bimodal gait switching in autophoretic droplet swimmers. This minimal experimental system is isotropic at rest, a symmetry that can be spontaneously broken due to the nonlinear coupling between hydrodynamic and chemical fields, inducing a variety of flow patterns tha…
Here we characterize the motility of athermal swimming droplets within the framework of active rotational diffusion. Just like active colloids, their trajectories can be modeled with a constant velocity $V$ and a slow angular diffusion, but the random changes in direction are not thermally driven. Instead, $V$ is determined by the interfacial tension gradient along the droplet surface, while local micellar fluctuations lead to droplet reorientation with a persistence time $τ$. We show that the origin of locomotion is the difference in the critical micellar concentration $Δ$CMC in the front and…
Active matter comprised of self-propelled interacting units holds a major promise for extraction of useful work from its seemingly chaotic out-of-equilibrium dynamics. Streamlining active matter to produce work is especially important at microscale, where the viscous forces prevail over inertia and the useful modes of transport require very specific non-reciprocal type of motion. Here we report that microscopic active droplets representing aqueous dispersions of swimming bacteria Bacillus subtilis show unidirectional propulsion when placed in an inactive nematic medium. Random motion of bacter…
The swimming of cells, far from any boundary, can arise in the absence of long-range liquid-crystalline order within the cytoplasm, but simple models of this effect are lacking. Here we present a two-dimensional model of droplet self-propulsion involving two scalar fields, representing the cytoplasm and a contractile cortex. An active stress results from coupling between these fields; self-propulsion results when rotational symmetry is spontaneously broken. The swimming speed is predicted, and shown numerically, to vary linearly with the activity parameter and with the droplet area fraction. T…
Enhanced diffusion is an emergent property of many experimental microswimmer systems that usually arises from a combination of ballistic motion with random reorientations. A subset of these systems, autophoretic droplet swimmers that move as a result of Marangoni stresses, have additionally been shown to respond to local, self-produced chemical gradients that can mediate self-avoidance or self-attraction. Via this mechanism, we present a mathematical model constructed to encode experimentally observed self-avoidant memory and numerically study the effect of this particular memory on the enhanc…
Gold-capped Janus particles immersed in a near-critical binary mixture can be propelled using illumination. We employ a non-isothermal diffuse interface approach to investigate the self-propulsion mechanism of a single colloid. We attribute the motion to body forces at the edges of a micronsized droplet that nucleates around the particle. Thus, the often-used concept of a surface velocity cannot account for the self-propulsion. The particle's swimming velocity is related to the droplet shape and size, which is determined by a so-called critical isotherm. Two distinct swimming regimes exist, de…
We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming microorganisms or artificial microswimmers. In contrast to approaches, which start from active velocity fields produced by the system, we consider active surface force or body force densities or active stresses as the origin of autonomous swimming. For negligible Reynolds number and given activity we first calculate the external and the internal ow fields as well as the center of mass velocity and an angular velocity of the droplet at fixed time. To construct trajectories from single time snapshots…
We report on the emergence of spontaneously rotating clusters in active emulsions. Ensembles of self-propelling droplets sediment and then self-organise into planar, hexagonally ordered clusters which hover over the container bottom while spinning around the plane normal. This effect exists for symmetric and asymmetric arrangements of isotropic droplets and is therefore not caused by torques due to geometric asymmetries. We found, however, that individual droplets exhibit a helical swimming mode in a small window of intermediate activity in a force-free bulk medium. We show that by forming an …
A micron-sized droplet of bromine water immersed in a surfactant-laden oil phase can swim (S. Thutupalli, R. Seemann, S. Herminghaus, New J. Phys. 13 073021 (2011)). The bromine reacts with the surfactant at the droplet interface and generates a surfactant mixture. It can spontaneously phase-separate due to solutocapillary Marangoni flow, which propels the droplet. We model the system by a diffusion-advection-reaction equation for the mixture order parameter at the interface including thermal noise and couple it to fluid flow. Going beyond previous work, we illustrate the coarsening dynamics o…
The Marangoni effect refers to fluid flow induced by a gradient in surface tension at a fluid-fluid interface. We determine the full three-dimensional Marangoni flow generated by a non-uniform surface tension profile at the interface of a self-propelled spherical emulsion droplet. For all flow fields inside, outside, and at the interface of the droplet, we give analytical formulas. We also calculate the droplet velocity vector $\mathbf{v}^D$, which describes the swimming kinematics of the droplet, and generalize the squirmer parameter $β$, which distinguishes between different swimmer types ca…
Chemically-active droplets exhibit complex avoiding trajectories. While heterogeneity is inevitable in active matter experiments, it is mostly overlooked in their modelling. Exploiting its geometric simplicity, we fully-resolve the head-on collision of two swimming droplets of different radii and demonstrate that even a small contrast in size critically conditions their collision and subsequent dynamics. We identify three fundamentally-different regimes. The resulting high sensitivity of pairwise collisions is expected to profoundly affect their collective dynamics.
Biological microswimmers are known to navigate upstream of an external flow (positive rheotaxis) in trajectories ranging from linear, spiral to oscillatory. Such rheotaxis stems from the interplay between the motion and complex shapes of the microswimmers, e.g. the chirality of the rotating flagella, the shear flow characteristics, and the hydrodynamic interaction with a confining surface. Here, we show that an isotropic, active droplet microswimmer exhibits a unique oscillatory rheotaxis in a microchannel despite its simple spherical geometry. The swimming velocity, orientation, and the chemi…
Active droplets emit a chemical solute at their surface that modifies their local interfacial tension. They exploit the nonlinear coupling of the convective transport of solute to the resulting Marangoni flows to self-propel. Such swimming droplets are by nature anti-chemotactic and are repelled by their own chemical wake or their neighbours. The rebound dynamics resulting from pairwise droplet interactions was recently analysed in detail for purely head-on collisions using a specific bispherical approach. Here, we extend this analysis and propose a reduced model of a generic collision to char…
We report the first experimental realization of a chiral artificial microswimmer exhibiting the helical motion. We found that a cholesteric liquid crystal droplet with a helical director field swims in a helical path driven by the Marangoni flow in an aqueous surfactant solution. We confirmed that the handedness of the droplet determines that of the helical path. This result strongly suggests that the helical motion is originated from the chirality of the cholesteric liquid crystal. To study the mechanism of the emergence of the helical motion, we propose a coupled time-evolution equations in …
One objective of active matter science is to unveil principles by which chaotic microscale dynamics could be transformed into useful work. A nematic liquid crystal environment offers a number of possibilities, one of which is a directional motion of an active droplet filled with an aqueous dispersion of swimming bacteria. In this work, using the responsiveness of the nematic to the electric field and light, we demonstrate how to control the direction and speed of active droplets. The dielectric response of nematic to the electric field causes two effects: (i) reorientation of the overall direc…
Active particles, including swimming microorganisms, autophoretic colloids and droplets, are known to self-organize into ordered structures at fluid-solid boundaries. The entrainment of particles in the attractive parts of their spontaneous flows has been postulated as a possible mechanism underlying this phenomenon. Here, combining experiments, theory and numerical simulations, we demonstrate the validity of this flow-induced ordering mechanism in a suspension of active emulsion droplets. We show that the mechanism can be controlled, with a variety of resultant ordered structures, by simply a…
