Assembling ellipsoidal particles at fluid interfaces using switchable dipolar capillary interactions

Formation of bijels stabilized by magnetic ellipsoidal particles in external magnetic fields

Bicontinuous interfacially-jammed emulsion gels (bijels) are increasingly used as emulsion templates for the fabrication of functional porous materials including membranes, electrodes, and biomaterials. Control over the domain size and structure is highly desirable in these applications. For bijels stabilized by spherical particles, particle size and volume fraction are the main parameters that determine the emulsion structure. Here, we investigate the use of ellipsoidal magnetic particles and study the effect of external magnetic fields on the formation of bijels. Using hybrid Lattice Boltzmann-molecular dynamics simulations, we analyze the effect of the magnetic field on emulsion dynamics and the structural properties of the resulting bijel. We find that the formation of bijels remains robust in the presence of magnetic fields, and that the domain size and tortuosity become anisotropic when ellipsoidal particles are used. We show that the magnetic fields lead to orientational ordering of the particles which in turn leads to alignment of the interfaces. The orientational order facilitates enhanced packing of particles in the interface which leads to different jamming times in the directions parallel and perpendicular to the field. Our results highlight the potential of magnetic particles for fabrication and processing of emulsion systems with tunable properties.

Capillary Assembly of Anisotropic Particles at Cylindrical Fluid-Fluid Interfaces

The unique behavior of colloids at liquid interfaces provides exciting opportunities for engineering the assembly of colloidal particles into functional materials. The deformable nature of fluid-fluid interfaces means that we can use the interfacial curvature, in addition to particle properties, to direct self-assembly. To this end, we use a finite element method (Surface Evolver) to study the self-assembly of rod-shaped particles adsorbed at a simple curved fluid-fluid interface formed by a sessile liquid drop with cylindrical geometry. Specifically, we study the self-assembly of single and multiple rods as a function of drop curvature and particle properties such as shape (ellipsoid, cylinder, and spherocylinder), contact angle, aspect ratio, and chemical heterogeneity (homogeneous and triblock patchy). We find that the curved interface allows us to effectively control the orientation of the rods, allowing us to achieve parallel, perpendicular, or novel obliquely orientations with respect to the cylindrical drop. In addition, by tuning particle properties to achieve parallel alignment of the rods, we show that the cylindrical drop geometry favors tip-to-tip assembly of the rods, not just for cylinders, but also for ellipsoids and triblock patchy rods. Finally, for triblock patchy rods with larger contact line undulations, we can achieve strong spatial confinement of the rods transverse to the cylindrical drop due to the capillary repulsion between the contact line undulations of the particle and the pinned contact lines of the sessile drop. Our capillary assembly method allows us to manipulate the configuration of single and multiple rod-like particles and therefore offers a facile strategy for organizing such particles into useful functional materials.

Assembly and manipulation of responsive and flexible colloidal structures by magnetic and capillary interactions

The long-ranged interactions induced by magnetic fields and capillary forces in multiphasic fluid-particle systems facilitate the assembly of a rich variety of colloidal structures and materials. We review here the diverse structures assembled from isotropic and anisotropic particles by independently or jointly using magnetic and capillary interactions. The use of magnetic fields is one of the most efficient means of assembling and manipulating paramagnetic particles. By tuning the field strength and configuration or by changing the particle characteristics, the magnetic interactions, dynamics, and responsiveness of the assemblies can be precisely controlled. Concurrently, the capillary forces originating at the fluid-fluid interfaces can serve as means of reconfigurable binding in soft matter systems, such as Pickering emulsions, novel responsive capillary gels, and composites for 3D printing. We further discuss how magnetic forces can be used as an auxiliary parameter along with the capillary forces to assemble particles at fluid interfaces or in the bulk. Finally, we present examples how these interactions can be used jointly in magnetically responsive foams, gels, and pastes for 3D printing. The multiphasic particle gels for 3D printing open new opportunities for making of magnetically reconfigurable and "active" structures.

Fluid interfaces laden by force dipoles: towards active matter-driven microfluidic flows

In recent years, nonlinear microfluidics in combination with lab-on-a-chip devices has opened a new avenue for chemical and biomedical applications such as droplet formation and cell sorting. In this article, we integrate ideas from active matter into a microfluidic setting, where two fluid layers with identical densities but different viscosities flow through a microfluidic channel. Most importantly, the fluid interface is laden with active particles that act with dipolar forces on the adjacent fluids and thereby generate flows. We perform lattice-Boltzmann simulations and combine them with phase field dynamics of the interface and an advection-diffusion equation for the density of active particles. We show that only contractile force dipoles can destabilize the flat fluid interface. It develops a viscous finger from which droplets break up. For interfaces with non-zero surface tension, a critical value of activity equal to the surface tension is necessary to trigger the instability. Since activity depends on the density of force dipoles, the interface can develop steady deformation. Lastly, we demonstrate how to control droplet formation using switchable activity.

Mixing properties of bi-disperse ellipsoid assemblies: mean-field behaviour in a granular matter experiment

The structure and spatial statistical properties of amorphous ellipsoid assemblies have profound scientific and industrial significance in many systems, from cell assays to granular materials. This paper uses a fundamental theoretical relationship for mixture distributions to explain the observations of an extensive X-ray computed tomography study of granular ellipsoidal packings. We study a size-bi-disperse mixture of two types of ellipsoids of revolutions that have the same aspect ratio of α ≈ 0.57 and differ in size, by about 10% in linear dimension, and compare these to mono-disperse systems of ellipsoids with the same aspect ratio. Jammed configurations with a range of packing densities are achieved by employing different tapping protocols. We numerically interrogate the final packing configurations by analyses of the local packing fraction distributions calculated from the Voronoi diagrams. Our main finding is that the bi-disperse ellipsoidal packings studied here can be interpreted as a mixture of two uncorrelated mono-disperse packings, insensitive to the compaction protocol. Our results are consolidated by showing that the local packing fraction shows no correlation beyond their first shell of neighbours in the binary mixtures. We propose a model of uncorrelated binary mixture distribution that describes the observed experimental data with high accuracy. This analysis framework will enable future studies to test whether the observed mean-field behaviour is specific to the particular granular system or the specific parameter values studied here or if it is observed more broadly in other bi-disperse non-spherical particle systems.

A Droplet-Manipulation Method Based on the Magnetic Particle-Stabilized Emulsion and Its Direct Numerical Simulation

Droplet manipulation has found broad applications in various engineering fields, such as microfluidic systems. This work reports a droplet-manipulation method based on particle-stabilized emulsions, where the magnetic particles adsorbed to the droplet surface serve as the actuator. The movement and the release of the droplet can be controlled by applying an external magnetic field. A lattice Boltzmann model for a three-phase system containing liquids and solid particles is adopted, which could provide a full coupling between fluids and particles. The effectiveness of the present droplet-manipulation method is validated through experiments and numerical simulations. Furthermore, the numerical simulation can provide insight into the interactions between the magnetic particles and the droplet during the droplet-driven process. To drive the droplet successfully, the magnetic particle needs to adhere to its surface and act as an "engine" to provide the driving force. As it is a surface-tension-dominant problem, the capillary effect can be considered as an "energy transfer station". The magnetic driving force on the particle is transmitted primarily to the droplet through interfacial capillary forces at the three-phase contact line, which assists the droplet in overcoming the viscous resistance and moving forward. A dimensionless number is proposed as a predictor of droplet transport and particle detachment.

1D Colloidal chains: recent progress from formation to emergent properties and applications

Integrating nanoscale building blocks of low dimensionality (0D; i.e., spheres) into higher dimensional structures endows them and their corresponding materials with emergent properties non-existent or only weakly existent in the individual building blocks. Constructing 1D chains, 2D arrays and 3D superlattices using nanoparticles and colloids therefore continues to be one of the grand goals in colloid and nanomaterial science. Amongst these higher order structures, 1D colloidal chains are of particular interest, as they possess unique anisotropic properties. In recent years, the most relevant advances in 1D colloidal chain research have been made in novel synthetic methodologies and applications. In this review, we first address a comprehensive description of the research progress concerning various synthetic strategies developed to construct 1D colloidal chains. Following this, we highlight the amplified and emergent properties of the resulting materials, originating from the assembly of the individual building blocks and their collective behavior, and discuss relevant applications in advanced materials. In the discussion of synthetic strategies, properties, and applications, particular attention will be paid to overarching concepts, fresh trends, and potential areas of future research. We believe that this comprehensive review will be a driver to guide the interdisciplinary field of 1D colloidal chains, where nanomaterial synthesis, self-assembly, physical property studies, and material applications meet, to a higher level, and open up new research opportunities at the interface of classical disciplines.

Capillary force on an 'inert' colloid: a physical analogy to dielectrophoresis

"Inert" colloids are μm-scale particles that create no distortion when trapped at a planar fluid-fluid interface. When placed in a curved interface, however, such colloids can create interfacial distortions of quadrupolar symmetry - so-called "induced capillary quadrupoles." The present work explores the analogy between capillary quadrupoles and electric dipoles, and the forces exerted on them by a symmetry-breaking gradient. In doing so, we weigh in on an outstanding debate as to whether a curvature gradient can induce a capillary force on an inert colloid. We argue that this force exists, for the opposite would imply that all dielectrophoretic forces vanish in two dimensions (2D). We justify our claim by solving 2D Laplace problems of electrostatics and capillary statics involving a single particle placed within a large circular shell with an imposed gradient. We show that the static boundary condition on the outer shell must be considered when applying the principle of virtual work to compute the force on the particle, as verified by a direct calculation of this force through integration of the particle stresses. Our investigation highlights some of the subtleties that emerge in virtual work calculations of capillary statics and electrostatics, thereby clarifying and extending previous results in the field. The broader implication of our results is that inert particles - including particles with planar, pinned contact lines and equilibrium contact angles - interact through interparticle capillary forces that scale quadratically with the deviatoric curvature of the host interface, contrary to recent claims made in the literature.

Controllable Capillary Assembly of Magnetic Ellipsoidal Janus Particles into Tunable Rings, Chains and Hexagonal Lattices

Colloidal assembly at fluid interfaces has a great potential for the bottom-up fabrication of novel structured materials. However, challenges remain in realizing controllable and tunable assembly of particles into diverse structures. Herein, the capillary assembly of magnetic ellipsoidal Janus particles at a fluid-fluid interface is reported. Depending on their tilt angle, that is, the angle the particle main axis forms with the fluid interface, these particles deform the interface and generate capillary dipoles or hexapoles. Driven by capillary interactions, multiple particles thus assemble into chain-, hexagonal-lattice-, and ring-like structures, which can be actively controlled by applying an external magnetic field. A field-strength phase diagram is predicted in which various structures are present as stable states. Owing to the diversity, controllability, and tunability of assembled structures, magnetic ellipsoidal Janus particles at fluid interfaces could therefore serve as versatile building blocks for novel materials.

Capillary interactions between soft capsules protruding through thin fluid films

When a suspension dries, the suspending fluid evaporates, leaving behind a dry film composed of the suspended particles. During the final stages of drying, the height of the fluid film on the substrate drops below the particle size, inducing local interface deformations that lead to strong capillary interactions among the particles. Although capillary interactions between rigid particles are well studied, much is still to be understood about the behaviour of soft particles and the role of their softness during the final stages of film drying. Here, we use our recently-introduced numerical method that couples a fluid described using the lattice Boltzmann approach to a finite element description of deformable objects to investigate the drying process of a film with suspended soft particles. Our measured menisci deformations and lateral capillary forces, which agree well with previous theoretical and experimental works in case of rigid particles, show that the deformations become smaller with increasing particle softness, resulting in weaker lateral interaction forces. At large interparticle distances, the force approaches that of rigid particles. Finally, we investigate the time dependent formation of particle clusters at the late stages of the film drying.

Optocapillarity-driven assembly and reconfiguration of liquid crystal polymer actuators

Realizing programmable assembly and reconfiguration of small objects holds promise for technologically-significant applications in such fields as micromechanical systems, biomedical devices, and metamaterials. Although capillary forces have been successfully explored to assemble objects with specific shapes into ordered structures on the liquid surface, reconfiguring these assembled structures on demand remains a challenge. Here we report a strategy, bioinspired by Anurida maritima, to actively reconfigure assembled structures with well-defined selectivity, directionality, robustness, and restorability. This approach, taking advantage of optocapillarity induced by photodeformation of floating liquid crystal polymer actuators, not only achieves programmable and reconfigurable two-dimensional assembly, but also uniquely enables the formation of three-dimensional structures with tunable architectures and topologies across multiple fluid interfaces. This work demonstrates a versatile approach to tailor capillary interaction by optics, as well as a straightforward bottom-up fabrication platform for a wide range of applications.

Desorption energy of soft particles from a fluid interface

The efficiency of soft particles to stabilize emulsions is examined by measuring their desorption free energy, i.e., the mechanical work required to detach the particle from a fluid interface. Here, we consider rubber-like elastic as well as microgel particles, using coarse-grained molecular dynamics simulations. The energy of desorption is computed for two and three-dimensional configurations by means of the mean thermodynamic integration method. It is shown that the softness affects the particle-interface binding in two opposing directions as compared to rigid particles. On the one hand, a soft particle spreads at the interface and thereby removes a larger unfavorable liquid-liquid contact area compared to rigid particles. On the other hand, softness provides the particle with an additional degree of freedom to get reshaped instead of deforming the interface, resulting in a smaller restoring force during the detachment. It is shown that the first effect prevails so that a soft spherical particle attaches to the fluid interface more strongly than rigid spheres. Finally, we consider microgel particles both in the swollen and in the collapsed state. Surprisingly, we find that the latter has a larger binding energy. All results are rationalised using thermodynamic arguments and thereby offer detailed insights into the desorption energy of soft particles from fluid interfaces.

Particle dynamics at fluid interfaces studied by the color gradient lattice Boltzmann method coupled with the smoothed profile method

We suggest a numerical method to describe particle dynamics at the fluid interface. We adopt a coupling strategy by combining the color gradient lattice Boltzmann method (CGLBM) and smoothed profile method (SPM). The proposed scheme correctly resolves the momentum transfer among the solid particles and fluid phases while effectively controlling the wetting condition. To validate the present algorithm (CGLBM-SPM), we perform several simulation tests like wetting a single solid particle and capillary interactions in two solid particles floating at the fluid interface. Simulation results show a good agreement with the analytical solutions available and look qualitatively reasonable. From these analyses, we conclude that the key features of the particle dynamics at the fluid interface are correctly resolved in our simulation method. In addition, we apply the present method for spinodal decomposition of a ternary mixture, which contains two-immiscible fluids with solid particles. By adding solid particles, fluid segregation is much suppressed than in the binary liquid mixture case. Furthermore, it has different morphology, such as with the jamming structure of the particles at the fluid interface, and captured images are similar to bicontinuous interfacially jammed emulsion gels in literature. From these results, we confirm the feasibility of the present method to describe soft matters; in particular, emulsion systems that contain solid particles at the interface.

Detachment work of prolate spheroidal particles from fluid droplets: role of viscous dissipation

The force-displacement curve for removal of an elongated solid particle from the surface of liquid droplets or gas bubbles is calculated and compared to our previous reported results for spherical particles. The surface adsorption energy for prolate particles is known to be larger than that for spheres. We show that in fact the minimum possible work done upon removal of an elongated particle from surface can be less than that for a sphere. This result is obtained when the dissipation of interfacial energy, stored in the fluid film, attaching the particles to the surface during their displacement, is properly accounted for. This dissipation is unavoidable, even if the particles are removed infinitely slowly. Once the particle actually leaves the surface, the formed liquid bridge relaxes thus dissipating any stored interfacial energy as the surface returns to its original undistorted state. The difference between the work of removal of a particle from surface and its adsorption energy is seen to become increasingly larger with smaller particle to droplet size ratios. For example, for a size ratio of 1 : 100, the work of removal is 1.93 times greater than the adsorption energy. However, we also find that for any given size ratio, there is a value of particle aspect ratio for which the work of removal of particles (combined dissipated and adsorbed energy) attains its minimum value.

Interactions between polystyrene particles with diameters of several tens to hundreds of micrometers at the oil-water interface

HYPOTHESIS

The charged spherical colloidal particles at the fluid-fluid interface experience considerably strong and long-ranged electrostatic and capillary interactions. The contribution of capillary force becomes more significant as the particle size increases beyond a certain limit. The relative strengths of the two competing interactions between the spherical polystyrene particles at the oil-water interface are quantified depending on their size.

EXPERIMENTS

The studied particles, obtained using the microfluidic method, have diameters of tens to hundreds of micrometers. The scaling behaviors of the commercially available colloidal particles with diameters of ~3 μm are also compared. An optical laser tweezer apparatus is used to directly or indirectly measure the interparticle force. Subsequently, the capillary force that can be attributed to the gravity-induced interface deformation and contact line undulation is calculated and compared with the measured interaction force.

FINDINGS

Regardless of the particle diameter (~3-330 μm), the measured force is observed to decay as r^-4, where r denotes the center-to-center separation, demonstrating that the dipolar electrostatic interaction is important and that the gravity-induced capillary interaction is negligible. Furthermore, numerical calculations with respect to the undulated meniscus confirm that the magnitude of capillary interaction is significantly smaller than that of the measured electrostatic interaction.

Mapping Anisotropic and Heterogeneous Colloidal Interactions via Optical Laser Tweezers

Heterogeneity among particles is an inherent feature that allows nondeterministic prediction of the properties of assembled structures and materials composed of many particles. Here, we report a promising strategy to quantify the heterogeneous and anisotropic interactions between ellipsoid particles using optical laser tweezers. The configuration and separation between two particles at an oil-water interface were optically controlled, and the capillary interaction behaviors were directly observed and measured. As a result, the optimal particle configurations at energetically favorable states were obtained, and the interaction forces between the particles were identified accurately by determining the trap stiffness in the direction of major and minor axes of the particle. Visualization of the capillary field around individual particles confirmed that the capillary interactions were quadrupolar, anisotropic, and heterogeneous. The measurement method presented here can be widely used to quantify interaction fields for various types of anisotropic particles.

Curvature dynamics and long-range effects on fluid-fluid interfaces with colloids

We investigate the dynamics of a phase-separating binary fluid, containing colloidal dumbbells anchored to the fluid-fluid interface. Extensive lattice Boltzmann-immersed boundary method simulations reveal that the presence of soft dumbbells can significantly affect the curvature dynamics of the interface between phase-separating fluids, even though the coarsening dynamics is left nearly unchanged. In addition, our results show that the curvature dynamics exhibits distinct non-local effects, which might be exploited for the design of new soft mesoscale materials. We point out that the inspection of the statistical dynamics of the curvature can disclose new insights into local inhomogeneities of the binary fluid configuration, as a function of the volume fraction and aspect ratio of the dumbbells.

Super-resolution microscopy on single particles at fluid interfaces reveals their wetting properties and interfacial deformations

Solid particles adsorbed at fluid interfaces are crucial for the mechanical stability of Pickering emulsions. The key parameter which determines the kinetic and thermodynamic properties of these colloids is the particle contact angle, θ. Several methods have recently been developed to measure the contact angle of individual particles adsorbed at liquid-liquid interfaces, as morphological and chemical heterogeneities at the particle surface can significantly affect θ. However, none of these techniques enables the simultaneous visualization of the nanoparticles and the reconstruction of the fluid interface to which they are adsorbed, in situ. To tackle this challenge, we utilize a newly developed super-resolution microscopy method, called iPAINT, which exploits non-covalent and continuous labelling of interfaces with photo-activatable fluorescent probes. Herewith, we resolve with nanometer accuracy both the position of individual nanoparticles at a water-octanol interface and the location of the interface itself. First, we determine single particle contact angles for both hydrophobic and hydrophilic spherical colloids. These experiments reveal a non-negligible dependence of θ on particle size, from which we infer an effective line tension, τ. Next, we image elliptical particles at a water-decane interface, showing that the corresponding interfacial deformations can be clearly captured by iPAINT microscopy.

Capillary Interaction and Self-Assembly of Tilted Magnetic Ellipsoidal Particles at Liquid Interfaces

Magnetic ellipsoidal particles adsorbed at a liquid interface provide exciting opportunities for creating switchable functional materials, where self-assembly can be switched on and off using an external field [Davies et al., Adv. Mater., 2014, 26, 6715]. In order to gain a deeper understanding of this novel system in the presence of an external field, we study the capillary interaction and self-assembly of tilted ellipsoids using analytical theory and finite element simulations. We derive an analytical expression for the dipolar capillary interaction between tilted ellipsoids in elliptical polar coordinates, which exhibits a 1/r ² power law dependence in the far field (i.e., large particle separations r) and correctly captures the orientational dependence of the capillary interactions in the near field. Using this dipole potential and finite element simulations, we further analyze the energy landscape of particle clusters consisting of up to eight tilted ellipsoids in contact. For clusters of two particles, we find that the side-to-side configuration is stable, whereas the tip-to-tip configuration is unstable. However, for clusters of more than three particles, we find that circular loops of side-to-side particles become globally stable, whereas linear chains of side-to-side particles become metastable. Furthermore, the energy barrier for the linear-to-loop transition decreases with increasing particle number. Our results explain both thermodynamically and kinetically why tilted ellipsoids assemble side-to-side locally but have a strong tendency to form loops on larger length scales.

Dynamic capillary assembly of colloids at interfaces with 10,000g accelerations

High-rate deformation of soft matter is an emerging area central to our understanding of far-from-equilibrium phenomena during shock, fracture, and phase change. Monolayers of colloidal particles are a convenient two-dimensional model system to visualise emergent behaviours in soft matter, but previous studies have been limited to slow deformations. Here we probe and visualise the evolution of a monolayer of colloids confined at a bubble surface during high-rate deformation driven by ultrasound. We observe the emergence of a transient network of strings, and use discrete particle simulations to show that it is caused by a delicate interplay of dynamic capillarity and hydrodynamic interactions between particles oscillating at high frequency. Remarkably for a colloidal system, we find evidence of inertial effects, caused by accelerations approaching 10,000g. These results also suggest that extreme deformation of soft matter offers new opportunities for pattern formation and dynamic self-assembly.

Amphiphile-Induced Anisotropic Colloidal Self-Assembly

Spherical colloidal particles typically self-assemble into hexagonal lattices when adsorbed at liquid interfaces. More complex assembly structures, including particle chains and phases with square symmetry, were theoretically predicted almost two decades ago for spherical particles interacting via a soft repulsive shoulder. Here, we demonstrate that such complex assembly phases can be experimentally realized with spherical colloidal particles assembled at the air/water interface in the presence of molecular amphiphiles. We investigate the interfacial behavior of colloidal particles in the presence of different amphiphiles on a Langmuir trough. We transfer the structures formed at the interface onto a solid substrate while continuously compressing, which enables us to correlate the prevailing assembly phase as a function of the available interfacial area. We observe that block copolymers with similarities to the chemical nature of the colloidal particles, as well as the surface-active protein bovine serum albumin, direct the colloidal particles into complex assembly phases, including chains and square arrangements. The observed structures are reproduced by minimum energy calculations of hard core-soft shoulder particles with experimentally realistic interaction parameters. From the agreement between experiments and theory, we hypothesize that the presence of the amphiphiles manipulates the interaction potential of the colloidal particles. The assembly of spherical colloidal particles into complex assembly phases on solid substrates opens new possibilities for surface patterning by enriching the library of possible structures available for colloidal lithography.

Capillary interactions between dynamically forced particles adsorbed at a planar interface and on a bubble

We investigate the dynamic interfacial deformation induced by micrometric particles exerting a periodic force on a planar interface or on a bubble, and the resulting lateral capillary interactions. Assuming that the deformation of the interface is small, neglecting the effect of viscosity, and assuming point particles, we derive analytical formulas for the dynamic deformation of the interface. For the case of a planar interface the dynamic point force simply generates capillary waves, while for the case of a bubble it excites shape oscillations, with a dominat deformation mode that depends on the bubble radius for a given forcing frequency. We evaluate the lateral capillary force acting between two particles, by superimposing the deformations induced by two point forces. We find that the lateral capillary forces experienced by dynamically forced particles are non monotonic and can be repulsive. The results are applicable to micrometric particles driven by different dynamic forcing mechanisms such as magnetic, electric or acoustic fields.

Magnetocapillary self-assemblies: Locomotion and micromanipulation along a liquid interface

This paper presents an overview and discussion of magnetocapillary self-assemblies. New results are presented, in particular concerning the possible development of future applications. These self-organizing structures possess the notable ability to move along an interface when powered by an oscillatory, uniform magnetic field. The system is constructed as follows. Soft magnetic particles are placed on a liquid interface, and submitted to a magnetic induction field. An attractive force due to the curvature of the interface around the particles competes with an interaction between magnetic dipoles. Ordered structures can spontaneously emerge from these conditions. Furthermore, time-dependent magnetic fields can produce a wide range of dynamic behaviours, including non-time-reversible deformation sequences that produce translational motion at low Reynolds number. In other words, due to a spontaneous breaking of time-reversal symmetry, the assembly can turn into a surface microswimmer. Trajectories have been shown to be precisely controllable. As a consequence, this system offers a way to produce microrobots able to perform different tasks. This is illustrated in this paper by the capture, transport and release of a floating cargo, and the controlled mixing of fluids at low Reynolds number.

Interaction anisotropy and the KPZ to KPZQ transition in particle deposition at the edges of drying drops

The deposition process at the edge of evaporating colloidal drops varies with the shape of suspended particles. Experiments with prolate ellipsoidal particles suggest that the spatiotemporal properties of the deposit depend strongly on particle aspect ratio. As the aspect ratio increases, the particles form less densely-packed deposits and the statistical behavior of the deposit interface crosses over from the Kardar-Parisi-Zhang (KPZ) universality class to another universality class which was suggested to be consistent with the KPZ plus quenched disorder. Here, we numerically study the effect of particle interaction anisotropy on deposit growth. In essence, we model the ellipsoids, at the interface, as disk-like particles with two types of interaction patches that correspond to specific features at the poles and equator of the ellipsoid. The numerical results corroborate experimental observations and further suggest that the deposition transition can stem from interparticle interaction anisotropy. Possible extensions of our model to other systems are also discussed.

Elastocapillary Driven Assembly of Particles at Free-Standing Smectic-A Films

Colloidal particles at complex fluid interfaces and within films assemble to form ordered structures with high degrees of symmetry via interactions that include capillarity, elasticity, and other fields like electrostatic charge. Here we study microparticle interactions within free-standing smectic-A films, in which the elasticity arising from the director field distortion and capillary interactions arising from interface deformation compete to direct the assembly of motile particles. New colloidal assemblies and patterns, ranging from 1D chains to 2D aggregates, sensitive to the initial wetting conditions of particles at the smectic film, are reported. This work paves the way to exploiting LC interfaces as a means to direct spontaneously formed, reconfigurable, and optically active materials.

Self-assembly of smart mesoscopic objects

Self-assembly due to capillary forces is a common method for generating 2D mesoscale structures made of identical particles floating at some liquid-air interface. We show herein how to create soft entities that deform or not the liquid interface as a function of the strength of some applied magnetic field. These smart floating objects self-assemble or not depending on the application of an external field. Moreover, we show that the self-assembling process can be reversed opening ways to rearrange structures.

Direct Assembly of Magnetic Janus Particles at a Droplet Interface

Self-assembly of nanoparticles at fluid-fluid interfaces is a promising route to fabricate functional materials from the bottom-up. However, directing and controlling particles into highly tunable and predictable structures, while essential, is a challenge. We present a liquid interface assisted approach to fabricate nanoparticle structures with tunable properties. To demonstrate its feasibility, we study magnetic Janus particles adsorbed at the interface of a spherical droplet placed on a substrate. With an external magnetic field turned on, a single particle moves to the location where its position vector relative to the droplet center is parallel to the direction of the applied field. Multiple magnetic Janus particles arrange into reconfigurable hexagonal lattice structures and can be directed to assemble at desirable locations on the droplet interface by simply varying the magnetic field direction. We develop an interface energy model to explain our observations, finding excellent agreement. Finally, we demonstrate that the external magnetic field allows one to tune the particle deposition pattern obtained when the droplet evaporates. Our results have implications for the fabrication of varied nanostructures on substrates for use in nanodevices, organic electronics, or advanced display, printing, and coating applications.

Dynamic Design of Spatial Patterns of Colloidal Suspensions

We study the collective dynamics of colloidal suspensions in the presence of a time-dependent potential by means of dynamic density functional theory. We consider a nonlinear diffusion equation for the density and show that spatial patterns emerge from a sinusoidal external potential with a time-dependent wavelength. These patterns are characterized by a sinusoidal density with the average wavelength and a Bessel-function envelope with an induced wavelength that depends only on the amplitude of the temporal oscillations. As a generalization of this result, we propose a design strategy to obtain a family of spatial patterns using time-dependent potentials of practically arbitrary shape.

Nano- and microparticles at fluid and biological interfaces

Systems with interfaces are abundant in both technological applications and biology. While a fluid interface separates two fluids, membranes separate the inside of vesicles from the outside, the interior of biological cells from the environment, and compartmentalize cells into organelles. The physical properties of interfaces are characterized by interface tension, those of membranes are characterized by bending and stretching elasticity. Amphiphilic molecules like surfactants that are added to a system with two immiscible fluids decrease the interface tension and induce a bending rigidity. Lipid bilayer membranes of vesicles can be stretched or compressed by osmotic pressure; in biological cells, also the presence of a cytoskeleton can induce membrane tension. If the thickness of the interface or the membrane is small compared with its lateral extension, both can be described using two-dimensional mathematical surfaces embedded in three-dimensional space. We review recent work on the interaction of particles with interfaces and membranes. This can be micrometer-sized particles at interfaces that stabilise emulsions or form colloidosomes, as well as typically nanometer-sized particles at membranes, such as viruses, parasites, and engineered drug delivery systems. In both cases, we first discuss the interaction of single particles with interfaces and membranes, e.g. particles in external fields, non-spherical particles, and particles at curved interfaces, followed by interface-mediated interaction between two particles, many-particle interactions, interface and membrane curvature-induced phenomena, and applications.

Adsorption of Ellipsoidal Particles at Liquid-Liquid Interfaces

The adsorption of particles at liquid-liquid interfaces is of great scientific and technological importance. In particular, for nonspherical particles, the capillary forces that drive adsorption vary with position and orientation, and complex adsorption pathways have been predicted by simulations. On the basis of the latter, it has been suggested that the timescales of adsorption are determined by a balance between capillary and viscous forces. However, several recent experimental results point out the role of contact line pinning in the adsorption of particles to interfaces and even suggest that the adsorption dynamics and pathways are completely determined by the latter, with the timescales of adsorption being determined solely by particle characteristics. In the present work, the adsorption trajectories of model ellipsoidal particles are investigated experimentally using cryo-SEM and by monitoring the altitudinal orientation angle using high-speed confocal microscopy. By varying the viscosity and the viscosity jump across the interfaces, we specifically interrogate the role of viscous forces.

Direct numerical simulation of gas-solid-liquid flows with capillary effects: An application to liquid bridge forces between spherical particles

In this study, a numerical method is developed to perform the direct numerical simulation (DNS) of gas-solid-liquid flows involving capillary effects. The volume-of-fluid method employed to track the free surface and the immersed boundary method is adopted for the fluid-particle coupling in three-phase flows. This numerical method is able to fully resolve the hydrodynamic force and capillary force as well as the particle motions arising from complicated gas-solid-liquid interactions. We present its application to liquid bridges among spherical particles in this paper. By using the DNS method, we obtain the static bridge force as a function of the liquid volume, contact angle, and separation distance. The results from the DNS are compared with theoretical equations and other solutions to examine its validity and suitability for modeling capillary bridges. Particularly, the nontrivial liquid bridges formed in triangular and tetrahedral particle clusters are calculated and some preliminary results are reported. We also perform dynamic simulations of liquid bridge ruptures subject to axial stretching and particle motions driven by liquid bridge action, for which accurate predictions are obtained with respect to the critical rupture distance and the equilibrium particle position, respectively. As shown through the simulations, the strength of the present method is the ability to predict the liquid bridge problem under general conditions, from which models of liquid bridge actions may be constructed without limitations. Therefore, it is believed that this DNS method can be a useful tool to improve the understanding and modeling of liquid bridges formed in complex gas-solid-liquid flows.

Interactions of rod-like particles on responsive elastic sheets

What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive-repulsive rod-rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed.

Biaxial nematic phase stability and demixing behaviour in monolayers of rod-plate mixtures

We theoretically study the phase behaviour of monolayers of hard rod-plate mixtures using a fundamental-measure density functional in the restricted-orientation (Zwanzig) approximation. Particles can rotate in 3D but their centres of mass are constrained to be on a flat surface. In addition, we consider both species to be subject to an attractive potential proportional to the particle contact area on the surface and with adsorption strengths that depend on the species type. Particles have board-like shape, with sizes chosen using a symmetry criterion: same volume and same aspect ratio κ. Phase diagrams were calculated for κ = 10, 20 and 40 and different values of adsorption strengths. For small adsorption strengths the mixtures exhibit a second-order uniaxial nematic-biaxial nematic transition for molar fraction of rods 0 ≤x≲ 0.9. In the uniaxial nematic phase the particle axes of rods and plates are aligned perpendicular and parallel to the monolayer, respectively. At the transition, the orientational symmetry of the plate axes is broken, and they orient parallel to a director lying on the surface. For large and equal adsorption strengths the mixture demixes at low pressures into a uniaxial nematic phase, rich in plates, and a biaxial nematic phase, rich in rods. The demixing transition is located between two tricritical points. Also, at higher pressures and in the plate-rich part of the phase diagram, the system exhibits a strong first-order uniaxial nematic-biaxial nematic phase transition with a large density coexistence gap. When rod adsorption is considerably large while that of plates is small, the transition to the biaxial nematic phase is always of second order, and its region of stability in the phase diagram considerably widens. At very high pressures the mixture can effectively be identified as a two-dimensional mixture of squares and rectangles which again demixes above a certain critical point. We also studied the relative stability of uniform phases with respect to density modulations of smectic, columnar and crystalline symmetry.

Translational viscous drags of an ellipsoid straddling an interface between two fluids

We study the dynamics of individual polystyrene ellipsoids of different aspect ratios trapped at the air-water interface. Using particle tracking and in situ vertical scanning interferometry techniques we are able to measure translational drags and the protrusion in air of the ellipsoids. We report that translational drags on the ellipsoid are unexpectedly enhanced: despite the fact that a noticeable part of the ellipsoid is in air, drags are found larger than the bulk one in water.

Controlled capillary assembly of magnetic Janus particles at fluid-fluid interfaces

Capillary interactions can be used to direct assembly of particles adsorbed at fluid-fluid interfaces. Precisely controlling the magnitude and direction of capillary interactions to assemble particles into favoured structures for materials science purposes is desirable but challenging. In this paper, we investigate capillary interactions between magnetic Janus particles adsorbed at fluid-fluid interfaces. We develop a pair-interaction model that predicts that these particles should arrange into a side-side configuration, and carry out simulations that confirm the predictions of our model. Finally, we investigate the monolayer structures that form when many magnetic Janus particles adsorb at the interface. We find that the particles arrange into long, straight chains exhibiting little curvature, in contrast with capillary interactions between ellipsoidal particles. We further find a regime in which highly ordered, lattice-like monolayer structures form, which can be tuned dynamically using an external magnetic field.

Magnetic cylindrical colloids at liquid interfaces exhibit non-volatile switching of their orientation in an external field

We study the orientation of magnetic cylindrical particles adsorbed at a liquid interface in an external field using analytical theory and high resolution finite element simulations. Cylindrical particles are interesting since they possess multiple locally stable orientations at the liquid interface so that the orientational transitions induced by an external field will not disappear when the external field is removed, i.e., the switching effect is non-volatile. We show that, in the absence of an external field, as we reduce the aspect ratio α of the cylinders below a critical value (αc≈ 2) the particles undergo spontaneous symmetry breaking from a stable side-on state to one of two equivalent stable tilted states, similar to the spontaneous magnetisation of a ferromagnet going through the Curie point. By tuning both the aspect ratio and contact angle of the cylinders, we show that it is possible to engineer particles that have one, two, three or four locally stable orientations. We also find that the magnetic responses of cylinders with one or two stable states are similar to that of paramagnets and ferromagnets respectively, while the magnetic response of systems with three or four stable states are even more complex and have no analogs in simple magnetic systems. Magnetic cylinders at liquid interfaces therefore provide a facile method for creating switchable functional monolayers where we can use an external field to induce multiple non-volatile changes in particle orientation and self-assembled structure.

Effect of orientational restriction on monolayers of hard ellipsoids

The effect of out-of-plane orientational freedom on the orientational ordering properties of a monolayer of hard ellipsoids is studied using the Parsons-Lee scaling approach and replica exchange Monte Carlo computer simulation. Prolate and oblate ellipsoids exhibit very different ordering properties, namely, the axes of revolution of prolate particles tend to lean out, while those of oblate ones prefer to lean into the confining plane. The driving mechanism of this is that the particles try to maximize the available free area on the confining surface, which can be achieved by minimizing the cross section areas of the particles with the plane. In the lack of out-of-plane orientational freedom the monolayer of prolate particles is identical to a two-dimensional hard ellipse system, which undergoes an isotropic-nematic ordering transition with increasing density. With gradually switching on the out-of-plane orientational freedom the prolate particles lean out from the confining plane and destabilisation of the in-plane isotropic-nematic phase transition is observed. The system of oblate particles behaves oppositely to that of prolates. It corresponds to a two-dimensional system of hard disks in the lack of out-of-plane freedom, while it behaves similar to that of hard ellipses in the freely rotating case. Solid phases can be realised by lower surface coverage due to the out-of-plane orientation freedom for both oblate and prolate shapes.

Non-Brownian diffusion in lipid membranes: Experiments and simulations

The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Remote control of self-assembled microswimmers

Physics governing the locomotion of microorganisms and other microsystems is dominated by viscous damping. An effective swimming strategy involves the non-reciprocal and periodic deformations of the considered body. Here, we show that a magnetocapillary-driven self-assembly, composed of three soft ferromagnetic beads, is able to swim along a liquid-air interface when powered by an external magnetic field. More importantly, we demonstrate that trajectories can be fully controlled, opening ways to explore low Reynolds number swimming. This magnetocapillary system spontaneously forms by self-assembly, allowing miniaturization and other possible applications such as cargo transport or solvent flows.

Dipolar capillary interactions between tilted ellipsoidal particles adsorbed at fluid-fluid interfaces

Capillary interactions have emerged as a tool for the directed assembly of particles adsorbed at fluid-fluid interfaces, and play a role in controlling the mechanical properties of emulsions and foams. In this paper, following Davies et al. [Adv. Mater., 2014, 26, 6715] investigation into the assembly of ellipsoidal particles at interfaces interacting via dipolar capillary interactions, we numerically investigate the interaction between tilted ellipsoidal particles adsorbed at a fluid-fluid interface as their aspect ratio, tilt angle, bond angle, and separation vary. High-resolution Surface Evolver simulations of ellipsoidal particle pairs in contact reveal an energy barrier between a metastable tip-tip configuration and a stable side-side configuration. The side-side configuration is the global energy minimum for all parameters we investigated. Lattice Boltzmann simulations of clusters of up to 12 ellipsoidal particles show novel highly symmetric flower-like and ring-like arrangements.

Detachment force of particles from fluid droplets

We calculate the deformation of a spherical droplet, resulting from the application of a pair of opposite forces to particles located diametrically opposite at the two ends of the droplet. The free-energy analysis is used to calculate the force-distance curves for the generated restoring forces, arising from the displacement of the particles relative to each other. While the logarithmic dependence of the "de Gennes-Hooke" constant on the particle to droplet size ratio, ν, is rather well known in the limit of very small ν, we find that for more realistic particle to droplet size ratios, i.e. ν = 0.001 to 0.01, the additional constant terms of O(1) constitute a significant correction to previously reported results. We derive the restoring force constant to be 2πγ[0.5 - ln (ν/2)](-1), in perfect agreement with the exact semi-numerical analysis of the same problem. The deviation from the linear force-displacement behaviour, occurring close to the point of detachment, is also investigated. A study of the energy dissipated shows it to be an increasingly dominant component of the work done during the detachment of the particles, as ν decreases. This indicates the existence of a significantly higher energy barrier to desorption of very small particles, compared to the one suggested by their adsorption energy alone. The influence of the line tension on the detachment force is also considered. It is shown that where line tension is important, the contact angle is no longer a constant but instead alters with the displacement of the particles from their equilibrium positions.

Tunable dipolar capillary deformations for magnetic Janus particles at fluid-fluid interfaces

Janus particles have attracted significant interest as building blocks for complex materials in recent years. Furthermore, capillary interactions have been identified as a promising tool for directed self-assembly of particles at fluid-fluid interfaces. In this paper, we develop theoretical models describing the behaviour of magnetic Janus particles adsorbed at fluid-fluid interfaces interacting with an external magnetic field. Using numerical simulations, we test the models predictions and show that the magnetic Janus particles deform the interface in a dipolar manner. We suggest how to utilise the resulting dipolar capillary interactions to assemble particles at a fluid-fluid interface, and further demonstrate that the strength of these interactions can be tuned by altering the external field strength, opening up the possibility to create novel, reconfigurable materials.

Soft repulsive interactions, particle rearrangements and size selection in the self-assembly of nanoparticles at liquid interfaces

In the adsorption of nanoparticles at liquid interfaces, soft and short ranged repulsive effective interactions between the nanoparticles at the interface may eventually induce crowding, slow dynamics and jamming at high surface coverage. These phenomena can interfere during the adsorption process, significantly slowing down its kinetics. Here, by means of numerical simulations, we find that modifying the effective interactions, which can be achieved for example by grafting differently functionalized polymer shells on the bare nanoparticles, may qualitatively change such interplay. In particular our results suggest that, in the presence of ultrasoft particle interactions such as the ones described by a Gaussian Core Model potential, a small size polydispersity can be sufficient to decouple the adsorption kinetics from the slow dynamics that develops at the interface, due to a qualitative change from an irreversible adsorption controlled by particle rearrangements at the interface to one dominated by size selection mechanisms. These findings may be useful to achieve higher surface coverages and faster adsorption kinetics.

Influence of magnetic field on the orientation of anisotropic magnetic particles at liquid interfaces

We study theoretically the influence of an external magnetic field on the orientation of an ellipsoidal magnetic particle adsorbed at a liquid interface. Using the finite element program Surface Evolver, we calculate the equilibrium meniscus shape around the ellipsoidal particle and its equilibrium tilt angle with respect to the undeformed interface θt when a magnetic field B is applied perpendicular to the interface. We find that as we increase field strength, θt increases and at a critical magnetic field Bc1 and tilt angle θc1, the particle undergoes a discontinuous transition to the 'perpendicular' orientation (θt = 90°). Our results agree qualitatively with the simplified theory of Bresme and Faraudo [F. Bresme and J. Faraudo, J. Phys.: Condens. Matter, 2007, 19, 375110] which assumes that the liquid interface is flat, while they agree quantitatively with recent lattice-Boltzmann simulations of Davies et al. [G. Davies et al., Soft Matter, 2014, 10, 6742] which account for the deformation of the liquid meniscus. We also show for the first time that upon reducing the external magnetic field, at a critical magnetic field Bc2 < Bc1, the particle undergoes a second discontinuous transition from the perpendicular orientation to a finite tilt angle θc2 < θc1. In other words, for micron-sized particles where the thermal energy kBT is negligible compared to the interfacial energy, the tilt angle vs. magnetic field curve exhibits hysteresis behaviour. Due to the higher degree of accuracy of the Surface Evolver method, we are able to analyse the behaviour of the particles near these orientational transitions accurately and study how the critical quantities Bc1, Bc2, θc1 and θc2 vary with particle aspect ratio and contact angle.