Self-propelled running droplets on solid substrates driven by chemical reactions

Kinetic monitoring of molecular interactions during surfactant-driven self-propelled droplet motion by high spatial resolution waveguide sensing

HYPOTHESIS

Self-driven actions, like motion, are fundamental characteristics of life. Today, intense research focuses on the kinetics of droplet motion. Quantifying macroscopic motion and exploring the underlying mechanisms are crucial in self-structuring and self-healing materials, advancements in soft robotics, innovations in self-cleaning environmental processes, and progress within the pharmaceutical industry. Usually, the driving forces inducing macroscopic motion act at the molecular scale, making their real-time and high-resolution investigation challenging. Label-free surface sensitive measurements with high lateral resolution could in situ measure both molecular-scale interactions and microscopic motion.

EXPERIMENTS

We employ surface-sensitive label-free sensors to investigate the kinetic changes in a self-assembled monolayer of the trimethyl(octadecyl)azanium chloride surfactant on a substrate surface during the self-propelled motion of nitrobenzene droplets. The adsorption-desorption of the surfactant at various concentrations, its removal due to the moving organic droplet, and rebuilding mechanisms at droplet-visited areas are all investigated with excellent time, spatial, and surface mass density resolution.

FINDINGS

We discovered concentration dependent velocity fluctuations, estimated the adsorbed amount of surfactant molecules, and revealed multilayer coverage at high concentrations. The desorption rate of surfactant (18.4 s-1) during the microscopic motion of oil droplets was determined by in situ differentiating between droplet visited and non-visited areas.

Spontaneous Rise of Hydrogen Microbubbles in Interfacial Gas Evolution Reaction

Liquid organic hydrogen carrier is a promising option for the transport and storage of hydrogen as a clean energy source. This study examines the stability and behavior of organic drops immobilized on a substrate during an interfacial hydrogen-evolution reaction (HER) at the drop surface and its surrounding aqueous solution. Hydrogen microbubbles form within the drop and rise to the drop apex. The growth rate of the hydrogen in-drop bubble increases with the concentration of the reactant in the surrounding medium. The drop remains stable till the buoyancy acting on the in-drop bubble is large enough to overcome the capillary force and the external viscous drag. The bubble spontaneously rises and carries a portion drop liquid to the solution surface. These spontaneous rising in-drop bubbles are detected in measurements using a high-precision sensor placed on the upper surface of the aqueous solution, reversing the settling phase from phase separation in the reactive emulsion. The finding from this work provides new insights into the behaviors of drops and bubbles in many interfacial gas evolution reactions in clean technologies.

Enzyme-Enriched Condensates Show Self-Propulsion, Positioning, and Coexistence

Enzyme-enriched condensates can organize the spatial distribution of their substrates by catalyzing nonequilibrium reactions. Conversely, an inhomogeneous substrate distribution induces enzyme fluxes through substrate-enzyme interactions. We find that condensates move toward the center of a confining domain when this feedback is weak. Above a feedback threshold, they exhibit self-propulsion, leading to oscillatory dynamics. Moreover, catalysis-driven enzyme fluxes can lead to interrupted coarsening, resulting in equidistant condensate positioning, and to condensate division.

Kinetic analysis of wetting and spreading at high temperatures: A review

The kinetic factors of the liquid-solid interface formation process are extremely useful in the design of composite preparation methods and the manufacture of comprehensive performance-controlled metal- or ceramic-based composites. Here, we review the available spreading dynamic models, focusing on wetting at high temperatures. There is yet to be developed a general spreading dynamic model with complete physical meaning that can accurately describe complicated surface-interface kinetic processes at high temperatures. In this work, we highlight common analysis errors in the description of the spreading dynamics for metal-ceramic and metal-metal systems. By unifying the expressions of the spreading dynamic models as the function f(v, θ_d) and fitting the experimental data reported in the literature, we discovered that the molecular-kinetic model commonly used to describe adsorption-controlled spreading at room temperature and reaction-limited spreading model used at high temperature have a certain range of overlap. When the condition σ_lv(cosθ_e-cosθ_d) < <2nk_BT is satisfied, these models are consistent in terms of mathematical functional expressions. As a result, distinguishing between them when the spreading behavior includes both adsorption and reaction is challenging.

Two-dimensional localized states in an active phase-field-crystal model

The active phase-field-crystal (active PFC) model provides a simple microscopic mean field description of crystallization in active systems. It combines the PFC model (or conserved Swift-Hohenberg equation) of colloidal crystallization and aspects of the Toner-Tu theory for self-propelled particles. We employ the active PFC model to study the occurrence of localized and periodic active crystals in two spatial dimensions. Due to the activity, crystalline states can undergo a drift instability and start to travel while keeping their spatial structure. Based on linear stability analyses, time simulations, and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of resting and traveling states. We explore, for instance, how the slanted homoclinic snaking of steady localized states found for the passive PFC model is modified by activity. Morphological phase diagrams showing the regions of existence of various solution types are presented merging the results from all the analysis tools employed. We also study how activity influences the crystal structure with transitions from hexagons to rhombic and stripe patterns. This in-depth analysis of a simple PFC model for active crystals and swarm formation provides a clear general understanding of the observed multistability and associated hysteresis effects, and identifies thresholds for qualitative changes in behavior.

Effect of a product on spontaneous droplet motion driven by a chemical reaction of surfactant

We focus on the self-propelled motion of an oil droplet within an aqueous phase or an aqueous droplet within an oil phase, which originates from an interfacial chemical reaction of surfactant. The droplet motion has been explained by mathematical models, which require the assumption that the chemical reaction increases the interfacial tension. However, several experimental reports have demonstrated self-propelled motion with the chemical reaction decreasing the interfacial tension. Our motivation is to construct an improved mathematical model, which explains these experimental observations. In this process, we consider the concentrations of the reactant and product on the interface and of the reactant in the bulk. Our numerical calculations indicate that the droplet potentially moves in the cases of both an increase and a decrease in the interfacial tension. In addition, the reaction rate and size dependencies of the droplet speed observed in experiments were well reproduced using our model. These results indicate the potential of our model as a universal one for droplet motion.

Kinetics of active water/ethanol Janus droplets

Droplets made of a water/ethanol mixture spontaneously self-propel in an oil/surfactant solution and, depending on the initial ethanol concentration at the time of production, may evolve in up to three stages. Upon self-propulsion the droplets absorb surfactant molecules during their continuous motion in the oily phase. In combination with the continuous loss of ethanol this mass exchange with the ambient phase may lead to a spontaneous phase separation of the water/ethanol mixture, and eventually to the formation of characteristic Janus droplets. Supported by experimental evidence, we propose a simple model that is able to explain the propulsion velocity and its scaling with the droplet radius in the last stage of the droplet evolution.

Physics of active emulsions

Phase separating systems that are maintained away from thermodynamic equilibrium via molecular processes represent a class of active systems, which we call active emulsions. These systems are driven by external energy input, for example provided by an external fuel reservoir. The external energy input gives rise to novel phenomena that are not present in passive systems. For instance, concentration gradients can spatially organise emulsions and cause novel droplet size distributions. Another example are active droplets that are subject to chemical reactions such that their nucleation and size can be controlled, and they can divide spontaneously. In this review, we discuss the physics of phase separation and emulsions and show how the concepts that govern such phenomena can be extended to capture the physics of active emulsions. This physics is relevant to the spatial organisation of the biochemistry in living cells, for the development of novel applications in chemical engineering and models for the origin of life.

Resting and traveling localized states in an active phase-field-crystal model

The conserved Swift-Hohenberg equation (or phase-field-crystal [PFC] model) provides a simple microscopic description of the thermodynamic transition between fluid and crystalline states. Combining it with elements of the Toner-Tu theory for self-propelled particles, Menzel and Löwen [Phys. Rev. Lett. 110, 055702 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.055702] obtained a model for crystallization (swarm formation) in active systems. Here, we study the occurrence of resting and traveling localized states, i.e., crystalline clusters, within the resulting active PFC model. Based on linear stability analyses and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of periodic and localized, resting and traveling states in a one-dimensional active PFC model. This allows us, for instance, to explore how the slanted homoclinic snaking of steady localized states found for the passive PFC model is amended by activity. A particular focus lies on the onset of motion, where we show that it occurs either through a drift-pitchfork or a drift-transcritical bifurcation. A corresponding general analytical criterion is derived.

Surface-dependent scenarios for dissolution-driven motion of growing droplets

Nano-droplets on a foreign substrate have received increasing attention because of their technological possible applications, for instance to catalyse the growth of nanowires. In some cases the droplets can move as a result of a reaction with the substrate. In this work we show that the substrate orientation, the surface morphology and the shape of the pits etched in the substrate by the droplets affect the droplet motion, so that a single mechanism (droplet-induced substrate dissolution) may lead to several unexpected droplet dynamics. The experiments are carried out by low energy electron microscopy on Au-Si and Au-Ge, which are model systems for studying liquid droplet alloys. Studying in-situ the behaviour of Au droplets on various Si and Ge surfaces, we describe a subtle interplay between the substrate orientation, the surface defects, and the droplet motion. Our observations allow a deep understanding of the interfacial mechanisms at the origin of the alloy formation and the associated droplet motion. These mechanisms are based on events of substrate dissolution/recrystallization. The outcomes of this work highlight the importance of the etching anisotropy on the droplet-substrate behaviours, and are essential in the perspective of positioning liquid alloy droplets used for instance as nanowire catalysts.

One-step fabricated wettable gradient surface for controlled directional underwater oil-droplet transport

Controlled self-propelling of the underwater oil droplet is achieved by a one-step anodic oxidation method.

Dynamic Chemically Driven Dewetting, Spreading, and Self-Running of Sessile Droplets on Crystalline Silicon

A chemically driven dewetting effect is demonstrated using sessile droplets of dilute hydrofluoric acid on chemically oxidized silicon wafers. The dewetting occurs as the thin oxide is slowly etched by the droplet and replaced by a hydrogen-terminated surface; the result of this is a gradual increase in the contact angle of the droplet with time. The time-varying work of adhesion is calculated from the time-varying contact angle; this corresponds to the changing chemical nature of the surface during dewetting and can be modeled by the well-known logistic (sigmoid) function often used for the modeling of restricted growth, in this case, the transition from an oxidized surface to a hydrogen-terminated silicon surface. The observation of the time-varying contact angle allows one to both measure the etch rate of the silicon oxide and estimate the hydrogenation rate as a function of HF concentration and wafer type. In addition to this, at a certain HF concentration, a self-running droplet effect is observed. In contrast, on hydrogen-terminated silicon wafers, a chemically induced spreading effect is observed using sessile droplets of nitric acid. The droplet spreading can also be modeled using a logistical function, where the restricted growth is the transition from hydrogen-terminated to a chemically induced oxidized silicon surface. The chemically driven dewetting and spreading observed here add to the methods available to study dynamic wetting (e.g., the moving three-phase contact line) of sessile droplets on surfaces. By slowing down chemical kinetics of the wetting, one is able to record the changing profile of the sessile droplet with time and gather information concerning the time-varying surface chemistry. The data also indicates a chemical interface hysteresis (CIH) that is compared to contact angle hysteresis (CAH). The approach can also be used to study the chemical etching and deposition behavior of thin films using liquids by monitoring the macroscopic droplet profile and relating this to the time-varying physical and chemical interface phenomena.

Surfactant induced autophobing

Surfactant adsorption in a three-phase system and its influence on wetting properties are relevant in various applications. Here, we report a hitherto not observed phenomenon, namely the retraction of an aqueous drop on hydrophilic solid substrates (which we refer to as 'autophobing') in ambient oil containing water-insoluble fatty acids, caused by the deposition of these fatty acids from the ambient oil onto the solid substrate. AFM measurements confirm that the surfactant is deposited on the solid by the moving contact line. This leads to a more hydrophobic substrate, the retraction of the contact line and a concomitant increase in the contact angle. The deposition process is enabled by the formation of a reaction product between deprotonated fatty acids and Ca(2+) ions at the oil/water interface. We investigate how the transition to a new equilibrium depends on the concentrations of the fatty acids, the aqueous solute, the chain lengths of the fatty acid, and the types of alkane solvent and silica or mica substrates. This phenomenon is observed on both substrates and for all explored combinations of fatty acids and solvents and thus appears to be generic. In order to capture the evolution of the contact angle, we develop a theoretical model in which the rate of adsorption at the oil-water interface governs the overall kinetics of autophobing, and transfer to the solid is determined by a mass flux balance (similar to a Langmuir Blodgett transfer).

Mathematical model for self-propelled droplets driven by interfacial tension

We propose a model for the spontaneous motion of a droplet induced by inhomogeneity in interfacial tension. The model is derived from a variation of the Lagrangian of the system and we use a time-discretized Morse flow scheme to perform its numerical simulations. Our model can naturally simulate the dynamics of a single droplet, as well as that of multiple droplets, where the volume of each droplet is conserved. We reproduced the ballistic motion and fission of a droplet, and the collision of two droplets was also examined numerically.

Radial wettable gradient of hot surface to control droplets movement in directions

A radial wettable gradient was fabricated on the surface of graphite plate by a simple one-step anodic oxidation process. It was found that the direction and value of the wettable gradient could be easily controlled by adjusting current and oxidation time gradient. With the increase of surface temperature, droplets on surface not only exhibited the transition of boiling mode, but also showed the controlled radial spreading, evaporation and movement behaviors. These phenomena could be attributed to the cooperation of wettability force, hysteresis force and vapor pressure (Leidenfrost effect). Especially, the controlled radial convergence or divergence of droplets with high velocity were realized on the surfaces with either inside or outside radial gradient, which would have crucial applications in the design of microfluidic devices and the exploration of the biotechnology.

Self‑propelled droplets on heated surfaces with angled self‑assembled micro/nanostructures

Directional and ratchet-like functionalized surfaces can induce liquid transport without the use of an external force. In this paper, we investigate the motion of liquid droplets near the Leidenfrost temperature on functionalized self-assembled asymmetric microstructured surfaces. The surfaces, which have angled microstructures, display unidirectional properties. The surfaces are fabricated on stainless steel through the use of a femtosecond laser-assisted process. Through this process, mound-like microstructures are formed through a combination of material ablation, fluid flow, and material redeposition. In order to achieve the asymmetry of the microstructures, the femtosecond laser is directed at an angle with respect to the sample surface. Two surfaces with microstructures angled at 45° and 10° with respect to the surface normal were fabricated. Droplet experiments were carried out with deionized water and a leveled hot plate to characterize the directional and self-propelling properties of the surfaces. It was found that the droplet motion direction is opposite of that for a surface with conventional ratchet microstructures reported in the literature. The new finding could not be explained by the widely accepted mechanism of asymmetric vapor flow. A new mechanism for a self-propelled droplet on asymmetric three-dimensional self-assembled microstructured surfaces is proposed.

Endothelial cell motility, coordination and pattern formation during vasculogenesis

How vascular networks assemble is a fundamental problem of developmental biology that also has medical importance. To explain the organizational principles behind vascular patterning, we must understand how can tissue level structures be controlled through cell behavior patterns like motility and adhesion that, in turn, are determined by biochemical signal transduction processes? We discuss the various ideas that have been proposed as mechanisms for vascular network assembly: cell motility guided by extracellular matrix alignment (contact guidance), chemotaxis guided by paracrine and autocrine morphogens, and multicellular sprouting guided by cell-cell contacts. All of these processes yield emergent patterns, thus endothelial cells can form an interconnected structure autonomously, without guidance from an external pre-pattern.

Spinning motion of a deformable self-propelled particle in two dimensions

We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from symmetry arguments for three kinds of variable. One is a vector which represents the velocity of the center of mass. The second is a traceless symmetric tensor representing deformation. The third is an antisymmetric tensor for spinning degree of freedom. By numerical simulations, we have obtained a variety of dynamical states due to interplay between the spinning motion and the deformation. The bifurcations of these dynamical states are analyzed by the simplified equations of motion.

Invasion from a cell aggregate--the roles of active cell motion and mechanical equilibrium

Cell invasion from an aggregate into a surrounding extracellular matrix (ECM) is an important process during development disease, e.g., vascular network assembly or tumor progression. To describe the behavior emerging from autonomous cell motility, cell-cell adhesion and contact guidance by ECM filaments, we propose a suitably modified cellular Potts model. We consider an active cell motility process in which internal polarity is governed by a positive feedback from cell displacements, a mechanism that can result in highly persistent motion when constrained by an oriented ECM structure. The model allows us to explore the interplay between haptotaxis, matrix degradation and active cell movement. We show that for certain conditions the cells are able to both invade the ECM and follow the ECM tracks. Furthermore, we argue that enforcing mechanical equilibrium within a bulk cell mass is of key importance in multicellular simulations.

Applications of bio-inspired special wettable surfaces

In this review we focus on recent developments in applications of bio-inspired special wettable surfaces. We highlight surface materials that in recent years have shown to be the most promising in their respective fields for use in future applications. The selected topics are divided into three groups, applications of superhydrophobic surfaces, surfaces of patterned wettability and integrated multifunctional surfaces and devices. We will present how the bio-inspired wettability has been integrated into traditional materials or devices to improve their performances and to extend their practical applications by developing new functionalities.

Schemes for the fragmentation and merging of droplets resting on a solid substrate using a patterned wettability gradient

A methodology has been proposed for the breakup and joining of water drops over a solid surface by varying its wettability gradient. A computational scheme using diffuse interface based smoothed particle hydrodynamics has been employed to simulate the droplet dynamics as the proof of the concept. For both the joining and breakup of drops, Y shaped patterns with the same or different wettability gradient along its different arms have been proposed. The breakup of a drop at the junction of the Y joint may be achieved if it is subjected to pulling forces along both of the branch arms. The pulling force can be brought into existence by providing an appropriate wettability gradient along the branches. By a proper selection of the branch orientation and the wettability gradient along them, it is possible to break a drop into two droplets of equal or unequal size. It has also been demonstrated that a drop can be broken into three small droplets by a specially designed four junction pattern of wettability on the solid surface. A Y junction has also been used for the merger of two drops. For this, two water drops placed at the end of the two branches are made to move toward the junction due to the gradient of contact angle. At the junction, they collide and merge into a single drop. A scheme has also been described where a combination of Y patterns can be exploited to generate a multitude of drops of different size.

Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth

In the present contribution we review basic mathematical results for three physical systems involving self-organizing solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting, evaporation/condensation or epitaxial growth, respectively. We highlight similarities and differences of the three systems based on the observation that in certain limits all of them may be described using models of similar form, i.e. time evolution equations for the film thickness profile. Those equations represent gradient dynamics characterized by mobility functions and an underlying energy functional. Two basic steps of mathematical analysis are used to compare the different systems. First, we discuss the linear stability of homogeneous steady states, i.e. flat films, and second the systematics of non-trivial steady states, i.e. drop/hole states for dewetting films and quantum-dot states in epitaxial growth, respectively. Our aim is to illustrate that the underlying solution structure might be very complex as in the case of epitaxial growth but can be better understood when comparing the much simpler results for the dewetting liquid film. We furthermore show that the numerical continuation techniques employed can shed some light on this structure in a more convenient way than time-stepping methods. Finally we discuss that the usage of the employed general formulation does not only relate seemingly unrelated physical systems mathematically, but does allow as well for discussing model extensions in a more unified way.

Chemocapillary instabilities of a contact line

Equilibrium and motion of a contact line are viewed as analogs of phase equilibrium and motion of an interphase boundary. This point of view makes evident the tendency to minimization of the length of the contact line at equilibrium. The concept of line tension is, however, of limited applicability, in view of a qualitatively different relaxation response of the contact line, compared to a two-dimensional curve. Both the analogy and qualitative distinction extend to a nonequilibrium situation arising due to coupling with reversible substrate modification. Under these conditions, the contact line may suffer a variety of chemocapillary instabilities (fingering, traveling, and oscillatory), similar to those of dissipative structures in nonlinear nonequilibrium systems. The preference order of the various instabilities changes, however, significantly due to a different way the interfacial curvature is relaxed.

Surfactant-enhanced rapid spreading of drops on solid surfaces

We study the surfactant-enhanced spreading of drops on the surfaces of solid substrates. This work is performed in connection with the unique ability of aqueous trisiloxane solutions to wet highly hydrophobic substrates effectively, which has been studied for nearly two decades. We couple a lubrication model to advection-diffusion equations for surfactant transport. We allow for micelle formation and breakup in the bulk and adsorptive flux at both the gas-liquid and liquid-solid interfaces and use appropriate equations of state to model variations in surface tension and wettability. Our numerical results show the effect of basal adsorption, kinetic rates, and the availability of surfactant on the deformation of the droplet and its spreading rate. We demonstrate that this rate is maximized for intermediate rates of basal adsorption and the total mass of surfactant.

Deformation of a self-propelled domain in an excitable reaction-diffusion system

We formulate a theory for a self-propelled domain in an excitable reaction-diffusion system in two dimensions where the domain deforms from a circular shape when the propagation velocity is increased. In the singular limit where the width of the domain boundary is infinitesimally thin, we derive a set of equations of motion for the center of gravity and two fundamental deformation modes. The deformed shapes of a steadily propagating domain are obtained. The set of time-evolution equations exhibits a bifurcation from a straight motion to a circular motion by changing the system parameters.

Deformable self-propelled particles

A theory of self-propelled particles is developed in such a way that the particles can be deformed from a circular shape when the propagating velocity is finite. A coupled set of equations in terms of the velocity and a tensor variable is introduced to represent the motion of a deformed particle. It is shown that there is a bifurcation from a straight motion to a circular motion by increasing the propagating velocity. The dynamics of assembly of the particles is studied numerically in two dimensions imposing a global interaction such that the elongated particles tend to undergo an orientational order.

Self-motion of an oil droplet: a simple physicochemical model of active Brownian motion

The self-motion of an oil droplet in an aqueous phase on a glass surface is reported. The aqueous phase contains a cationic surfactant, which tends to be adsorbed onto the glass surface. The oil droplet contains potassium iodide and iodine, which prefers to make an ion pair with the cationic surfactant. Since the ion pair is soluble in the oil droplet, dissolution of the surfactant into the oil droplet is promoted, i.e., the system is far from equilibrium with regard to surfactant concentration. The oil droplet is self-driven in a reactive manner by the spatial gradient of the glass surface tension. We discuss the intrinsic nature of this self-motion by developing a simple mathematical model that incorporates adsorption and desorption of the surfactant on the glass surface. Using this mathematical model we were able to construct an equation of motion that reproduces the observed self-motion of an oil droplet. This equation describes active Brownian motion. Theoretical considerations were used to predict the generation of the regular mode of oil-droplet motion, which was subsequently confirmed by experiments.

Ratchet-driven fluid transport in bounded two-layer films of immiscible liquids

We present a two-layer thin film model allowing us to study the behavior of a general class of 'wettability ratchets' that can be employed to transport a continuous phase. Brownian ratchets, in contrast, are normally used to transport particles or molecules within a continuous carrier fluid without transporting the fluid itself. The wettability ratchet is based on a switchable, spatially asymmetric, periodic interaction of the free surface of the film and the walls. To illustrate the general concept, we focus on an electrical dewetting mechanism based on the effective force exercised by a static electric field on the liquid-liquid interface between two dielectric liquids. In particular, we analyse (i) an on-off ratchet with a constant lateral force resulting in a dewetting-spreading cycle, (ii) a ratchet switching between two shifted potentials that shows a transition between oscillating and sliding drops, and (iii) a flashing external force ratchet. For the three cases, the macroscopic transport is studied in its dependence on spatial and temporal characteristics of the ratchet, and physical properties and volume of the liquids.

Surface-bound soft matter gradients

This feature article describes the progress realized over the past half century in the field of surface-bound gradient structures created on or from soft materials (oligomers and/or polymers), or those enabling the study of the behavior of soft materials. By highlighting our work in the field and accounting for the contribution of other groups, we emphasize the exceptional versatility of gradient assemblies in facilitating fast screening of physicochemical phenomena, acting as "recording media" for monitoring a process, and playing a key role in the design and fabrication of surface-bound molecular and macromolecular motors capable of directing a transport phenomenon.

Modeling microcapsules that communicate through nanoparticles to undergo self-propelled motion

Using simulation and theory, we demonstrate how nanoparticles can be harnessed to regulate the interaction between two initially stationary microcapsules on a surface and promote the self-propelled motion of these capsules along the substrate. The first microcapsule, the "signaling" capsule, encases nanoparticles, which diffuse from the interior of this carrier and into the surrounding solution; the second capsule is the "target" capsule, which is initially devoid of particles. Nanoparticles released from the signaling capsule modify the underlying substrate and thereby initiate the motion of the target capsule. The latter motion activates hydrodynamic interactions, which trigger the signaling capsule to follow the target. The continued release of the nanoparticles sustains the motion of both capsules. In effect, the system constitutes a synthetic analogue of biological cell signaling and our findings can shed light on fundamental physical forces that control interactions between cells. Our findings can also yield guidelines for manipulating the interactions of synthetic microcapsules in microfluidic devices.

On autophobing in surfactant-driven thin films

Recent experiments (Afsar-Siddiqui, A. B.; Luckham, P. F.; Matar, O. K. Langmuir 2004, 20, 7575-7582) on the spreading of aqueous droplets containing cationic surfactants over thin aqueous films supported by negatively charged substrates demonstrated trends in the spreading behavior with either increasing surfactant concentration or increasing film thickness. Although the substrate is initially hydrophilic and the droplet spreads, surfactant adsorption at the substrate renders it hydrophobic leading to droplet retraction. We generate a model here using lubrication theory that allows the effect of the surfactant on the wettability to be taken into account. Our numerical results show that due to basal adsorption of surfactant at the interface, the initially hydrophilic solid substrate is rendered hydrophobic. This then drives droplet retraction and dewetting, which is in agreement with the experimentally observed trends.

Driven drops on heterogeneous substrates: onset of sliding motion

Pinning and depinning of driven drops on heterogeneous substrates is studied as a function of the driving and heterogeneity amplitude. Two types of heterogeneity are considered: a "hydrophobic" defect that blocks the drop in front and a "hydrophilic" one that holds it at the back. Two different types of depinning leading to sliding motion are identified, and the resulting stick-slip motion is studied numerically.

Perturbation theory for traveling droplets

The motion of chemically driven droplets is analyzed by applying a solvability condition of perturbed hydrodynamic equations affected by the adsorbate concentration. Conditions for traveling bifurcation analogous to a similar transition in activator-inhibitorsystems are obtained. It is shown that interaction of droplets leads to either scattering of mobile droplets or the formation of regular patterns, respectively, at low or high adsorbate diffusivity. The same method is applied to droplets running on growing terrace edges during surface freezing.