Effective Interaction between Active Colloids and Fluid Interfaces Induced by Marangoni Flows

Chemotactic behavior for a self-phoretic Janus particle near a patch source of fuel

Many biological microswimmers are capable of chemotaxis, i.e., they can sense an ambient chemical gradient and adjust their mechanism of motility to move towards or away from the source of the gradient. Synthetic active colloids endowed with chemotactic behavior hold considerable promise for targeted drug delivery and the realization of programmable and reconfigurable materials. Here, we study the chemotactic behavior of a Janus particle, which converts "fuel" molecules, released at an axisymmetric chemical patch located on a planar wall, into "product" molecules at its catalytic cap and moves by self-phoresis induced by the product. The chemotactic behavior is characterized as a function of the interplay between the rates of release (at the patch) and the consumption (at the particle) of fuel, as well as of details of the phoretic response of the particle (i.e., its phoretic mobility). Among other results, we find that, under certain conditions, the particle is attracted to a stable "hovering state" in which it aligns its axis normal to the wall and rests (positions itself) at an activity-dependent distance above the center of the patch.

Spontaneous Multi-scale Supramolecular Assembly Driven by Noncovalent Interactions Coupled with the Continuous Marangoni Effect

Reported herein is the multi-scale supramolecular assembly (MSSA) process along with redox reactions driven by supramolecular interactions coupled with the spontaneous Marangoni effect in ionic liquid (IL)-based extraction systems. The black powder, the single sphere with a black exterior, and the single colorless sphere were formed step by step at the interface when an aqueous solution of KMnO4 was mixed with the IL phase 1-(2-hydroxyethyl)-3-methylimidazolium bis(trifluoromethylsulfonyl) imide (C2OHmimNTf2) bearing octyl(phenyl)-N,N-diisobutylcarbamoylmethylphosphine oxide (CMPO). The mechanism of the whole process was studied systematically. The phenomena were related closely to the change in the valence state of Mn. The MnO4- ion could be reduced quickly to δ-MnO2 and further to Mn2+ slowly by the hydroxyl-functionalized IL C2OHmimNTf2. Based on Mn2+, Mn(CMPO)32+, elementary building blocks (EBBs), and [EBB]n clusters were generated step by step. The [EBB]n clusters with the large enough size that were transferred to the interface, together with the remaining δ-MnO2, assembled into the single sphere with a black exterior, driven by supramolecular interactions coupled with the spontaneous Marangoni effect. When the remaining δ-MnO2 was used up, the mixed single sphere turned completely colorless. It was found that the reaction site of C2OHmim+ with Mn(VII) and Mn(IV) was distributed mainly at the side chain with a hydroxyl group. The MSSA process presents unique spontaneous phase changes. This work paves the way for the practical application of the MSSA-based separation method developed recently. The process also provides a convenient way to observe in situ and characterize directly the continuous Marangoni effect.

Transition from scattering to orbiting upon increasing the fuel concentration for an active Janus colloid moving at an obstacle-decorated interface

Efficient exploration of space is a paramount motive for active colloids in practical applications. Yet, introducing activity may lead to surface-bound states, hindering efficient space exploration. Here, we show that the interplay between self-motility and fuel-dependent affinity for surfaces affects how efficiently catalytically-active Janus microswimmers explore both liquid-solid and liquid-fluid interfaces decorated with arrays of similarly-sized obstacles. In a regime of constant velocity vs. fuel concentration, we find that microswimmer-obstacle interactions strongly depend on fuel concentration, leading to a counter-intuitive decrease in space exploration efficiency with increased available fuel for all interfaces. Using experiments and theoretical predictions, we attribute this phenomenon to a largely overlooked change in the surface properties of the microswimmers' catalytic cap upon H2O2 exposure. Our findings have implications in the interpretation of experimental studies of catalytically active colloids, as well as in providing new handles to control their dynamics in complex environments.

Sideways propelled bimetallic rods at the water/oil interface

The motion of self-propelling microswimmers is significantly affected by confinement, which can enhance or reduce their mobility and also steer the direction of their propulsion. While their interactions with solid boundaries have already received considerable attention, many aspects of the influence of liquid-liquid interfaces (LLI) on active particle propulsion still remain unexplored. In this work, we studied the adsorption and motion of bimetallic Janus sideways propelled rods dispersed at the interface between an aqueous solution of hydrogen peroxide and oil. The wetting properties of the bimetallic rods result in a wide distribution of their velocities at the LLI. While a fraction of rods remain immotile, we note a significant enhancement of motility for the rest of the particles with velocities of up to 8 times higher in comparison to those observed near a solid wall. Liquid-liquid interfaces, therefore, can provide a new way to regulate the propulsion of bimetallic particles.

Versatile Microfluidics Separation of Colloids by Combining External Flow with Light-Induced Chemical Activity

Separation of particles by size, morphology, or material identity is of paramount importance in fields such as filtration or bioanalytics. Up to now separation of particles distinguished solely by surface properties or bulk/surface morphology remains a very challenging process. Here a combination of pressure-driven microfluidic flow and local self-phoresis/osmosis are proposed via the light-induced chemical activity of a photoactive azobenzene-surfactant solution. This process induces a vertical displacement of the sedimented particles, which depends on their size and surface properties . Consequently, different colloidal components experience different regions of the ambient microfluidic shear flow. Accordingly, a simple, versatile method for the separation of such can be achieved by elution times in a sense of particle chromatography. The concepts are illustrated via experimental studies, complemented by theoretical analysis, which include the separation of bulk-porous from bulk-compact colloidal particles and the separation of particles distinguished solely by slight differences in their surface physico-chemical properties.

Recent Process in Microrobots: From Propulsion to Swarming for Biomedical Applications

Recently, robots have assisted and contributed to the biomedical field. Scaling down the size of robots to micro/nanoscale can increase the accuracy of targeted medications and decrease the danger of invasive operations in human surgery. Inspired by the motion pattern and collective behaviors of the tiny biological motors in nature, various kinds of sophisticated and programmable microrobots are fabricated with the ability for cargo delivery, bio-imaging, precise operation, etc. In this review, four types of propulsion-magnetically, acoustically, chemically/optically and hybrid driven-and their corresponding features have been outlined and categorized. In particular, the locomotion of these micro/nanorobots, as well as the requirement of biocompatibility, transportation efficiency, and controllable motion for applications in the complex human body environment should be considered. We discuss applications of different propulsion mechanisms in the biomedical field, list their individual benefits, and suggest their potential growth paths.

A lattice Boltzmann model for self-diffusiophoretic particles near and at liquid-liquid interfaces

We introduce a novel mesoscopic computational model based on a multiphase-multicomponent lattice Boltzmann method for the simulation of self-phoretic particles in the presence of liquid-liquid interfaces. Our model features fully resolved solvent hydrodynamics, and, thanks to its versatility, it can handle important aspects of the multiphysics of the problem, including particle wettability and differential solubility of the product in the two liquid phases. The method is extensively validated in simple numerical experiments, whose outcome is theoretically predictable, and then applied to the study of the behavior of active particles next to and trapped at interfaces. We show that their motion can be variously steered by tuning relevant control parameters, such as the phoretic mobilities, the contact angle, and the product solubility.

Modeling of chemically active particles at an air-liquid interface

The collective motion of chemically active particles at an air-liquid interface is studied theoretically as a dynamic self-organization problem. Based on a physical consideration, we propose a minimal model for self-propelled particles by combining hydrodynamic interaction, capillary interaction, driving force by Marangoni effect, and Marangoni flow. Our model has successfully captured the features of chemically active particles, that represent dynamic self-organized states such as crystalline, chain, liquid-like and spreading states.

Self-/Magnetic-Propelled Catalytic Nanomotors Based on a Janus SPION@PEG-Pt/PCL Hybrid Nanoarchitecture: Single-Particle versus Collective Motions

In this paper, we synthesized superparamagnetic iron oxide nanoparticles (NPs) functionalized with (3-aminopropyl)triethoxysilane (Fe₃O₄@APTES). The synthesized NPs were coated with succinic anhydride (Fe₃O₄@COOH) in the next step. Half the surface of the NPs was shielded with wax microparticles via the Pickering emulsion technique, and the unshielded side was covered with poly(ethylene glycol) methyl ether. Platinum nanoparticles (Pt NPs) were deposited between PEG chains by the oxidation-reduction method through an in situ procedure to obtain a metal-polymer composite. These deposited Pt NPs have the potential to catalyze the decomposition of hydrogen peroxide at the surface of Janus nanomotors (JNMs). After de-waxing of the NPs, Irgacure 2959 (as the initiator) was reacted with the bare side of the NPs to provide the opportunity to grow poly(ε-caprolactone) (PCL) chains on the surface of the nanomotors through the "grafting from" method. The diffusion coefficient and velocity of the JNMs (before and after the PCL reaction) in the aqueous solution of 1, 2, 3, 5, and 10% (w/w) hydrogen peroxide and in the presence of different concentrations of NaCl solutions (0, 5, and 10% (w/v)) were investigated by mean square displacement analysis for single-particle or collective motions of JNMs. In addition, the simultaneous effect of an external magnetic field and the NaCl concentration on the movement direction of JNMs was also evaluated in the presence of hydrogen peroxide (10%). Increasing the ionic strength through NaCl addition permits the JNMs to move with relatively lower amounts of fuel [i.e., 2% (w/w)]. The collective motion investigation of the JNMs showed the highest speed in the media with 10% (w/w) hydrogen peroxide and 5% (w/v) NaCl solution (about 1215.78 μm²/s) due to the surfactant effect of the Janus architecture.

Light-induced manipulation of passive and active microparticles

We consider sedimented at a solid wall particles that are immersed in water containing small additives of photosensitive ionic surfactants. It is shown that illumination with an appropriate wavelength, a beam intensity profile, shape and size could lead to a variety of dynamic, both unsteady and steady state, configurations of particles. These dynamic, well-controlled and switchable particle patterns at the wall are due to an emerging diffusio-osmotic flow that takes its origin in the adjacent to the wall electrostatic diffuse layer, where the concentration gradients of surfactant are induced by light. The conventional nonporous particles are passive and can move only with already generated flow. However, porous colloids actively participate themselves in the flow generation mechanism at the wall, which also sets their interactions that can be very long ranged. This light-induced diffusio-osmosis opens novel avenues to manipulate colloidal particles and assemble them to various patterns. We show in particular how to create and split optically the confined regions of particles of tunable size and shape, where well-controlled flow-induced forces on the colloids could result in their crystalline packing, formation of dilute lattices of well-separated particles, and other states.

Active spheres induce Marangoni flows that drive collective dynamics

For monolayers of chemically active particles at a fluid interface, collective dynamics is predicted to arise owing to activity-induced Marangoni flow even if the particles are not self-propelled. Here, we test this prediction by employing a monolayer of spherically symmetric active [Formula: see text] particles located at an oil-water interface with or without addition of a nonionic surfactant. Due to the spherical symmetry, an individual particle does not self-propel. However, the gradients produced by the photochemical fuel degradation give rise to long-ranged Marangoni flows. For the case in which surfactant is added to the system, we indeed observe the emergence of collective motion, with dynamics dependent on the particle coverage of the monolayer. The experimental observations are discussed within the framework of a simple theoretical mean-field model.

Study of Active Janus Particles in the Presence of an Engineered Oil-Water Interface

We present a systematic study of motion of Pt@SiO₂ Janus particles at a liquid-liquid interface. A special microfluidic trap is used for creating such an interface. The increased surface energy of the large surface results in partial wetting of the substrate, leaving patches of oil on the glass surface. This allows us to directly compare the motion at the two interfaces, i.e., oil-water and solid-water interface within the same setting, guaranteeing identical conditions in terms of additional parameters. The propulsion behavior of Janus particles is found to be quantitatively similar at both surfaces. The interplay of reaction product absorption by oil, slip locking by surfactant, microscale friction, lubrication efficiency, and potential Marangoni effect controls the resemblance of motion characteristics at the two interfaces. Additionally, we also observed guidance effect on the Janus particles by the pinning line of oil patches, similar to solid side walls.

Inhomogeneous surface tension of chemically active fluid interfaces

We study the dependence of the surface tension of a fluid interface on the density profile of a third suspended phase. By means of an approximated model for the binary mixture and of a perturbative approach, we derive closed-form expressions for the free energy of the system and for the surface tension of the interface. Our results show a remarkable non-monotonous dependence of the surface tension on the spatial separation between the peaks of the density of the suspended phase. Our results also predict the local value of the surface tension in the case in which the density of the suspended phase is not homogeneous along the interface.

Floor- or Ceiling-Sliding for Chemically Active, Gyrotactic, Sedimenting Janus Particles

Chemically active particles achieve motility without external forces and torques ("self-propulsion") due to catalytic chemical reactions at their surfaces, which change the chemical composition of the surrounding solution (called "chemical field") and induce hydrodynamic flow of the solution. By coupling the distortions of these fields back to its motion, a chemically active particle experiences an effective interaction with confining surfaces. This coupling can lead to a rich behavior, such as the occurrence of wall-bound steady states of "sliding". Most active particles are density mismatched with the solution and, thus, tend to sediment. Moreover, the often employed Janus spheres, which consist of an inert core material decorated with a cap-like, thin layer of a catalyst, are gyrotactic (i.e., "bottom-heavy"). Whether or not they may exhibit sliding states at horizontal walls depends on the interplay between the active motion and the gravity-driven sedimentation and alignment, such as the gyrotactic tendency to align the axis along the gravity direction being overcome by a competing, activity-driven alignment with a different orientation. It is therefore important to understand and quantify the influence of these gravity-induced effects on the behavior of model chemically active particles moving in the vicinity of walls. For model gyrotactic, self-phoretic Janus particles, here we study theoretically the occurrence of sliding states at horizontal planar walls that are either below ("floor") or above ("ceiling") the particle. We construct "state diagrams" characterizing the occurrence of such states as a function of the sedimentation velocity and of the gyrotactic response of the particle, as well as of the phoretic mobility of the particle. We show that in certain cases sliding states may emerge simultaneously at both the ceiling and the floor, while the larger part of the experimentally relevant parameter space corresponds to particles that would exhibit sliding states only either at the floor or at the ceiling-or there are no sliding states at all. These predictions are critically compared with the results of previous experimental studies, as well as with our dedicated experiments carried out with Pt-coated, polystyrene-core, or silica-core Janus spheres immersed in aqueous hydrogen peroxide solutions.

Interface-mediated spontaneous symmetry breaking and mutual communication between drops containing chemically active particles

Symmetry breaking and the emergence of self-organized patterns is the hallmark of complexity. Here, we demonstrate that a sessile drop, containing titania powder particles with negligible self-propulsion, exhibits a transition to collective motion leading to self-organized flow patterns. This phenomenology emerges through a novel mechanism involving the interplay between the chemical activity of the photocatalytic particles, which induces Marangoni stresses at the liquid–liquid interface, and the geometrical confinement provided by the drop. The response of the interface to the chemical activity of the particles is the source of a significantly amplified hydrodynamic flow within the drop, which moves the particles. Furthermore, in ensembles of such active drops long-ranged ordering of the flow patterns within the drops is observed. We show that the ordering is dictated by a chemical communication between drops, i.e., an alignment of the flow patterns is induced by the gradients of the chemicals emanating from the active particles, rather than by hydrodynamic interactions.

Complex systems exhibit unique properties like spontaneous symmetry breaking and self-organization. Singh et al. show that catalytically active, non-propelling particles can induce steady vortical flows within a drop, as well as flow alignment between neighboring drops.

Numerical simulations of self-diffusiophoretic colloids at fluid interfaces

The dynamics of active colloids is very sensitive to the presence of boundaries and interfaces which therefore can be used to control their motion. Here we analyze the dynamics of active colloids adsorbed at a fluid-fluid interface. By using a mesoscopic numerical approach which relies on an approximated numerical solution of the Navier-Stokes equation, we show that when adsorbed at a fluid interface, an active colloid experiences a net torque even in the absence of a viscosity contrast between the two adjacent fluids. In particular, we study the dependence of this torque on the contact angle of the colloid with the fluid-fluid interface and on its surface properties. We rationalize our results via an approximate approach which accounts for the appearance of a local friction coefficient. By providing insight into the dynamics of active colloids adsorbed at fluid interfaces, our results are relevant for two-dimensional self assembly and emulsion stabilization by means of active colloids.

Guidance of active particles at liquid-liquid interfaces near surfaces

Artificial microswimmers have the potential for applications in many fields, ranging from targeted cargo delivery and mobile sensing to environmental remediation. In many of these applications, the artificial swimmers will operate in complex media necessarily involving liquid-liquid interfaces. Here, we experimentally study the motion of chemically powered phoretic active colloids close to liquid-liquid interfaces while swimming next to a solid substrate. In a system involving this complex geometry, we find that the active particles have an alignment interaction with both the neighbouring solid and liquid interfaces, allowing for a robust guiding mechanism along the liquid interface. We compare with minimal active Brownian simulations to show that these phoretically active particles stay along the interfaces for much longer times and lengths than expected for standard active Brownian particles. We also track the propulsion speeds of these particles and find a reduced speed close to the liquid-liquid interface. We report an interesting non-linear dependence of this reduction on the particle's bulk speed.

Glucose Oxidase Micropumps: Multi-Faceted Effects of Chemical Activity on Tracer Particles Near the Solid–Liquid Interface

We report the development of glucose oxidase pumps characterized by small lateral dimensions (≈200 μ m). We studied the effects of the activity of the enzyme pump on silica particles (“tracers”) sedimented around the enzyme pump/patch. Once the activity of the pump was turned on (i.e., the glucose substrate was added to the solution), in-plane motion of the tracers away from the enzyme patch, as well as the emergence of an in-plane region around the patch which was depleted by tracers, was observed. The lateral extent of this depletion zone increased in time at a rate dependent both on the glucose concentration and on the areal density of the enzyme in the patch. We argue that, when the tracers were very near the wall, their motion and the emergence of the depletion zone were most likely the result of diffusiophoresis and drag by osmotic flows induced at the wall, rather than that of drag by a solutal buoyancy driven convective flow. We infer that, for the glucose oxidase enzymatic pumps, bulk (solutal buoyancy), as previously reported, as well as surface (osmotic) driven flows coexist and have to be explicitly accounted for. It seems plausible to assume that this is the case in general for enzyme pumps, and these complementary effects should be considered in the design of applications, e.g., stirring or sensing inside microfluidic systems, based on such pumps.

Interfacially driven transport theory: a way to unify Marangoni and osmotic flows

We show that the solvent behaviour in both diffusio-osmosis and Marangoni flow can be derived from a simple model of colloid-interface interactions. We demonstrate that the direction of the flow is regulated by a single value of the attractive parameter covering the purely repulsive and attractive-repulsive interaction cases. The proposed universality between diffusio-osmosis and Marangoni flow is extended further to include diffusio-phoresis. In particular, an object immersed to a colloidal solution moves towards the low concentration of the colloidal particles in the case of colloid-interface repulsion and towards the high concentration of the colloidal particles in the case of colloid-interface attraction. The approach combines the methods of fluid dynamics, molecular physics and transport phenomena and provides a tractable explanation of how the colloid-interface interactions affect the momentum balance and the transport phenomena (interfacially driven transport).

Dynamics of a fully wetted Marangoni surfer at the fluid-fluid interface

Marangoni flow created by the gradient of surface tension can be used to transport small objects along fluid interfaces. We study lateral motion of a fully wetted self-propelled body (swimmer) at a fluid-fluid interface. The swimmer releases a surfactant at a constant rate inducing a surface tension gradient. The dynamics of the insoluble surfactant is incorporated by taking into account advection by the Marangoni flow, surface diffusion and homogeneous decomposition reaction. We show that the translational speed of a Marangoni swimmer is increased as compared with the self-propulsion speed of a chemically inactive surface-bound swimmer. Flow induced in-plane rotation of the swimmer with an elongated body is generally weak so that its trajectory in the steady state is a straight line. A non-motile thin rod that releases surfactant at one of its ends is capable of surfing on the self-generated surfactant cloud. Steady surfing occurs along the body length with the source of the surfactant at the back end acting as a propulsion engine.

Effective Interactions between Chemically Active Colloids and Interfaces

Chemically active colloids can achieve force- and torque-free motility ("self-propulsion") via the promotion, on their surface, of catalytic chemical reactions involving the surrounding solution. Such systems are valuable both from a theoretical perspective, serving as paradigms for nonequilibrium processes, as well as from an application viewpoint, according to which active colloids are envisioned to play the role of carriers ("engines") in novel lab-on-a-chip devices. The motion of such colloids is intrinsically connected with a "chemical field", i.e., the distribution near the colloid of the number densities of the various chemical species present in the solution, and with the hydrodynamic flow of the solution around the particle. In most of the envisioned applications, and in virtually all reported experimental studies, the active colloids operate under spatial confinement (e.g., within a microfluidic channel, a drop, a free-standing liquid film, etc.). In such cases, the chemical field and the hydrodynamic flow associated with an active colloid are influenced by any nearby confining surfaces, and these disturbances couple back to the particle. Thus, an effective interaction with the spatial confinement arises. Consequently, the particle is endowed with means to perceive and to respond to its environment. Understanding these effective interactions, finding the key parameters which control them, and designing particles with desired, preconfigured responses to given environments, require interdisciplinary approaches which synergistically integrate methods and knowledge from physics, chemistry, engineering, and materials science. Here we review how, via simple models of chemical activity and self-phoretic motion, progress has recently been made in understanding the basic physical principles behind the complex behaviors exhibited by active particles near interfaces. First, we consider the occurrence of "interface-bounded" steady states of chemically active colloids near simple, nonresponsive interfaces. Examples include particles "sliding" along, or "hovering" above, a hard planar wall while inducing hydrodynamic flow of the solution. These states lay the foundations for concepts like the guidance of particles by the topography of the wall. We continue to discuss responsive interfaces: a suitable chemical patterning of a planar wall allows one to bring the particles into states of motion which are spatially localized (e.g., within chemical stripes or along chemical steps). These occur due to the wall responding to the activity-induced chemical gradients by generating osmotic flows, which encode the surface-chemistry of the wall. Finally, we discuss how, via activity-induced Marangoni stresses, long-ranged effective interactions emerge from the strong hydrodynamic response of fluid interfaces. These examples highlight how in this context a desired behavior can be potentially selected by tuning suitable parameters (e.g., the phoretic mobility of the particle, or the strength of the Marangoni stress at an interface). This can be accomplished via a judicious design of the surface chemistry of the particle and of the boundary, or by the choice of the chemical reaction in solution.

Effective squirmer models for self-phoretic chemically active spherical colloids

Various aspects of self-motility of chemically active colloids in Newtonian fluids can be captured by simple models for their chemical activity plus a phoretic-slip hydrodynamic boundary condition on their surface. For particles of simple shapes (e.g., spheres) --as employed in many experimental studies-- which move at very low Reynolds numbers in an unbounded fluid, such models of chemically active particles effectively map onto the well studied so-called hydrodynamic squirmers (S. Michelin and E. Lauga, J. Fluid Mech. 747, 572 (2014)). Accordingly, intuitively appealing analogies of "pusher/puller/neutral" squirmers arise naturally. Within the framework of self-diffusiophoresis we illustrate the above-mentioned mapping and the corresponding flows in an unbounded fluid for a number of choices of the activity function (i.e., the spatial distribution and the type of chemical reactions across the surface of the particle). We use the central collision of two active particles as a simple, paradigmatic case for demonstrating that in the presence of other particles or boundaries the behavior of chemically active colloids may be qualitatively different, even in the far field, from the one exhibited by the corresponding "effective squirmer", obtained from the mapping in an unbounded fluid. This emphasizes that understanding the collective behavior and the dynamics under geometrical confinement of chemically active particles necessarily requires to explicitly account for the dependence of the hydrodynamic interactions on the distribution of chemical species resulting from the activity of the particles.

Surface swimmers, harnessing the interface to self-propel

In the study of microscopic flows, self-propulsion has been particularly topical in recent years, with the rise of miniature artificial swimmers as a new tool for flow control, low Reynolds number mixing, micromanipulation or even drug delivery. It is possible to take advantage of interfacial physics to propel these microrobots, as demonstrated by recent experiments using the proximity of an interface, or the interface itself, to generate propulsion at low Reynolds number. This paper discusses how a nearby interface can provide the symmetry breaking necessary for propulsion. An overview of recent experiments illustrates how forces at the interface can be used to generate locomotion. Surface swimmers ranging from the microscopic scale to typically the capillary length are covered. Two systems are then discussed in greater detail. The first is composed of floating ferromagnetic spheres that assemble through capillarity into swimming structures. Two previously studied configurations, triangular and collinear, are discussed and contrasted. A new interpretation for the triangular swimmer is presented. Then, the non-monotonic influence of surface tension and viscosity is evidenced in the collinear case. Finally, a new system is introduced. It is a magnetically powered, centimeter-sized piece that swims similarly to water striders.

Phase coexistence in a monolayer of active particles induced by Marangoni flows

Thermally or chemically active colloids generate thermodynamic gradients in the solution in which they are immersed and thereby induce hydrodynamic flows that affect their dynamical evolution. Here we study a mean-field model for the many-body dynamics of a monolayer of spherically symmetric active particles located at a fluid-fluid interface. Due to the spherical symmetry, the particles do not self-propel. Instead, the dynamics is driven by the long-ranged Marangoni flows, due to the response of the interface to the activity of the particles, which compete with the direct interaction between particles. We demonstrate analytically that, in spite of the intrinsic out-of-equilibrium character of the system, the monolayer evolves to a "pseudoequilibrium" state, in which the Marangoni flows force the coexistence of the thermodynamic phases associated to the direct interaction. In particular, we study the most interesting case of a r-3 soft repulsion that models electrostatic or magnetic interparticle forces. For a sufficiently large average density, two-dimensional phase transitions (freezing from liquid to hexatic, and melting from solid to hexatic) should be observable in a radially stratified, "onion-like" structure within the monolayer. Furthermore, the analysis allows us to conclude that, while the activity may be too weak to allow direct detection of such induced Marangoni flows, it is relevant as a collective effect in the emergence of the experimentally observable spatial structure of phase coexistences noted above. Finally, the relevance of these results for potential experimental realizations is critically discussed.

Interaction of Pure Marangoni Convection with a Propagating Reactive Interface under Microgravity

A reactive interface in the form of an autocatalytic reaction front propagating in a bulk phase can generate a dynamic contact line upon reaching the free surface when a surface tension gradient builds up due to the change in chemical composition. Experiments in microgravity evidence the existence of a self-organized autonomous and localized coupling of a pure Marangoni flow along the surface with the reaction in the bulk. This dynamics results from the advancement of the contact line at the surface that acts as a moving source of the reaction, leading to the reorientation of the front propagation. Microgravity conditions allow one to isolate the transition regime during which the surface propagation is enhanced, whereas diffusion remains the main mode of transport in the bulk with negligible convective mixing, a regime typically concealed on Earth because of buoyancy-driven convection.

State diagram of a three-sphere microswimmer in a channel

Geometric confinements are frequently encountered in soft matter systems and in particular significantly alter the dynamics of swimming microorganisms in viscous media. Surface-related effects on the motility of microswimmers can lead to important consequences in a large number of biological systems, such as biofilm formation, bacterial adhesion and microbial activity. On the basis of low-Reynolds-number hydrodynamics, we explore the state diagram of a three-sphere microswimmer under channel confinement in a slit geometry and fully characterize the swimming behavior and trajectories for neutral swimmers, puller- and pusher-type swimmers. While pushers always end up trapped at the channel walls, neutral swimmers and pullers may further perform a gliding motion and maintain a stable navigation along the channel. We find that the resulting dynamical system exhibits a supercritical pitchfork bifurcation in which swimming in the mid-plane becomes unstable beyond a transition channel height while two new stable limit cycles or fixed points that are symmetrically disposed with respect to the channel mid-height emerge. Additionally, we show that an accurate description of the averaged swimming velocity and rotation rate in a channel can be captured analytically using the method of hydrodynamic images, provided that the swimmer size is much smaller than the channel height.

Theory of anomalous collective diffusion in colloidal monolayers on a spherical interface

A planar colloidal monolayer exhibits anomalous collective diffusion due to the hydrodynamic interactions. We investigate how this behavior is affected by the curvature of the monolayer when it resides on the interface of a spherical droplet. It is found that the characteristic times of the dynamics still exhibit the same anomalous scaling as in the planar case. The spatial distribution, however, shows a difference due to the relevance of the radius of the droplet. Since for the droplet this is both a global magnitude, i.e., pertaining to the spatial extent of the spherical surface, and a local one, i.e., the radius of curvature, the question remains open as to which of these two features actually dominates in the case of a generically curved interface.

Self-diffusiophoresis induced by fluid interfaces

The influence of a fluid-fluid interface on self-phoresis of chemically active, axially symmetric, spherical colloids is analyzed. Distinct from the studies of self-phoresis for colloids trapped at fluid interfaces or in the vicinity of hard walls, here we focus on the issue of self-phoresis close to a fluid-fluid interface. In order to provide physically intuitive results highlighting the role played by the interface, the analysis is carried out for the case that the symmetry axis of the colloid is normal to the interface; moreover, thermal fluctuations are not taken into account. Similarly to what has been observed near hard walls, we find that such colloids can be set into motion even if their whole surface is homogeneously active. This is due to the anisotropy along the direction normal to the interface owing to the partitioning by diffusion, among the coexisting fluid phases, of the product of the chemical reaction taking place at the colloid surface. Different from results corresponding to hard walls, in the case of a fluid interface the direction of motion, i.e., towards the interface or away from it, can be controlled by tuning the physical properties of one of the two fluid phases. This effect is analyzed qualitatively and quantitatively, both by resorting to a far-field approximation and via an exact, analytical calculation which provides the means for a critical assessment of the approximate analysis.

Theory for controlling individual self-propelled micro-swimmers by photon nudging I: directed transport

Photon nudging is a new experimental method which enables the force-free manipulation and localization of individual self-propelled artificial micro-swimmers in fluidic environments.

Active Janus Particles at Interfaces of Liquid Crystals

We report an investigation of the active motion of silica-palladium Janus particles (JPs) adsorbed at interfaces formed between nematic liquid crystals (LCs) and aqueous phases containing hydrogen peroxide (H₂O₂). In comparison to isotropic oil-aqueous interfaces, we observe the elasticity and anisotropic viscosity of the nematic phase to change qualitatively the active motion of the JPs at the LC interfaces. Although contact line pinning on the surface of the JPs is observed to restrict out-of-plane rotational diffusion of the JPs at LC interfaces, orientational anchoring of nematic LCs on the silica (planar) and palladium (homeotropic) hemispheres biases JP in-plane orientations to generate active motion almost exclusively along the director of the LC at low concentrations of H₂O₂ (0.5 wt %). In contrast, displacements perpendicular to the director exhibit the characteristics of Brownian diffusion. At higher concentrations of H₂O₂ (1-3 wt %), we observe an increasing population of JPs propelled parallel and perpendicular to the LC director in a manner consistent with active motion. In addition, under these conditions, we also observe a subpopulation of JPs (approximately 10%) that exhibit active motion exclusively perpendicular to the LC director. These results are discussed in light of independent measurements of the distribution of azimuthal orientations of the JPs at the LC interfaces and calculations of the elastic energies that bias JP orientations. We also contrast our observations at LC interfaces to past studies of self-propulsion of particles within and at the interfaces of isotropic liquids.

Assembly and Speed in Ion-Exchange-Based Modular Phoretic Microswimmers

We report an experimental study on ion-exchange-based modular microswimmers in low-salt water. Cationic ion-exchange particles and passive cargo particles assemble into self-propelling complexes, showing self-propulsion at speeds of several micrometers per second over extended distances and times. We quantify the assembly and speed of the complexes for different combinations of ion-exchange particles and cargo particles, substrate types, salt types and concentrations, and cell geometries. Irrespective of the experimental boundary conditions, we observe a regular development of the assembly shape with increasing number of cargo. Moreover, the swimming speed increases stepwise upon increasing the number of cargo and then saturates at a maximum speed, indicating the active role of cargo in modular swimming. We propose a geometric model of self-assembly to describe the experimental observations in a qualitative way. Our study also provides some constraints for future theoretical modeling and simulation.

Chemically active colloids near osmotic-responsive walls with surface-chemistry gradients

Chemically active colloids move by creating gradients in the composition of the surrounding solution and by exploiting the differences in their interactions with the various molecular species in solution. If such particles move near boundaries, e.g. the walls of the container confining the suspension, gradients in the composition of the solution are also created along the wall. This give rise to chemi-osmosis (via the interactions of the wall with the molecular species forming the solution), which drives flows coupling back to the colloid and thus influences its motility. Employing an approximate 'point-particle' analysis, we show analytically that-owing to this kind of induced active response (chemi-osmosis) of the wall-such chemically active colloids can align with, and follow, gradients in the surface chemistry of the wall. In this sense, these artificial 'swimmers' exhibit a primitive form of thigmotaxis with the meaning of sensing the proximity of a (not necessarily discontinuous) physical change in the environment. We show that the alignment with the surface-chemistry gradient is generic for chemically active colloids as long as they exhibit motility in an unbounded fluid, i.e. this phenomenon does not depend on the exact details of the propulsion mechanism. The results are discussed in the context of simple models of chemical activity, corresponding to Janus particles with 'source' chemical reactions on one half of the surface and either 'inert' or 'sink' reactions over the other half.

Perils of ad hoc approximations for the activity function of chemically powered colloids

Colloids can achieve motility by promoting at their surfaces chemical reactions in the surrounding solution. A well-studied case is that of self-phoresis, in which motility arises due to the spatial inhomogeneities in the chemical composition of the solution and the distinct interactions of the solvent molecules and of the reaction products with the colloid. For simple models of such chemically active colloids, the steady-state motion in an unbounded solution can be derived analytically in closed form. In contrast, for such chemically active particles moving in the vicinity of walls, the derivation of closed-form and physically intuitive solutions of the equations governing their dynamics turns out to be a severe challenge even for simple models. Therefore, recent studies of these phenomena have employed numerical methods as well as approximate analytical approaches based on multipolar expansions. We discuss and clarify certain conceptual aspects concerning the latter type of approach, which arise due to ad hoc truncations of the underlying so-called activity function, which describes the distribution of chemical reactions across the surface of the particle.

Collective dynamics of chemically active particles trapped at a fluid interface

Chemically active colloids generate changes in the chemical composition of their surrounding solution and thereby induce flows in the ambient fluid which affect their dynamical evolution. Here we study the many-body dynamics of a monolayer of spherically symmetric active particles trapped at a fluid-fluid interface. To this end we consider a model for the large-scale spatial distribution of particles which incorporates the direct pair interaction (including also the capillary interaction which is caused specifically by the interfacial trapping) as well as the effect of hydrodynamic interactions (including the Marangoni flow induced by the response of the interface to the chemical activity). The values of the relevant physical parameters for typical experimental realizations of such systems are estimated and various scenarios, which are predicted by our approach for the dynamics of the monolayer, are discussed. In particular, we show that the chemically-induced Marangoni flow can prevent the clustering instability driven by the capillary attraction.

Active colloids at fluid interfaces

If an active Janus particle is trapped at the interface between a liquid and a fluid, its self-propelled motion along the interface is affected by a net torque on the particle due to the viscosity contrast between the two adjacent fluid phases. For a simple model of an active, spherical Janus colloid we analyze the conditions under which translation occurs along the interface and we provide estimates of the corresponding persistence length. We show that under certain conditions the persistence length of such a particle is significantly larger than the corresponding one in the bulk liquid, which is in line with the trends observed in recent experimental studies.

Wetting and orientation of catalytic Janus colloids at the surface of water

Janus colloidal particles show remarkable properties in terms of surface activity, self-assembly and wetting. Moreover they can perform autonomous motion if they can chemically react with the liquid in which they are immersed. In order to understand the self-propelled motion of catalytic Janus colloids at the air–water interface, wetting and the orientation of the catalytic surface are important properties to be investigated. Wetting plays a central role in active motion since it determines the contact between the fuel and the catalytic surface as well as the efficiency of the transduction of the chemical reaction into motion. Active motion is not expected to occur either when the catalytic face is completely out of the aqueous phase or when the Janus boundaries are parallel to the interfacial plane. The design of a Janus colloid possessing two hydrophilic faces is required to allow the catalytic face to react with the fuel (e.g. H₂O₂ for platinum) in water and to permit some rotational freedom of the Janus colloid in order to generate propulsion parallel to the interfacial plane. Here, we discuss some theoretical aspects that should be accounted for when studying Janus colloids at the surface of water. The free energy of ideal Janus colloidal particles at the interface is modeled as a function of the immersion depth and the particle orientation. Analytical expressions of the energy profiles are established. Energetic aspects are then discussed in relation to the particle’s ability to rotate at the interface. By introducing contact angle hysteresis we describe how the effects of contact line pinning modifies the scenario described in the ideal case. Experimental observations of the contact angle hysteresis of Janus colloids at the interface reveal the effect of pinning; and orientations of silica particles half covered with a platinum layer at the interface do not comply with the ideal scenarios. Experimental observations suggest that Janus colloids at the fluid interface behave as a kinetically driven system, where the contact line motion over the defects decorating the Janus faces rules the orientation and rotational diffusion of the particle.