For partially wetting, ellipsoidal colloids trapped at a fluid interface, their effective, interface--mediated interactions of capillary and fluctuation--induced type are analyzed. For contact angles different from 90$^o$, static interface deformations arise which lead to anisotropic capillary forces that are substantial already for micrometer--sized particles. The capillary problem is solved using an efficient perturbative treatment which allows a fast determination of the capillary interaction for all distances between and orientations of two particles. Besides static capillary forces, fluctuation--induced forces caused by thermally excited capillary waves arise at fluid interfaces. For the specific choice of a spatially fixed three--phase contact line, the asymptotic behavior of the fluctuation--induced force is determined analytically for both the close--distance and the long--distance regime and compared to numerical solutions.
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. [Advanced Materials, 26, 6715 (2014)] 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 Su…
We investigate the equilibrium orientation and adsorption process of a single, ellipsoidal Janus particle at a fluid-fluid interface. The particle surface comprises equally sized parts that are hydrophobic or hydrophilic. We present free energy models to predict the equilibrium orientation and compare the theoretical predictions with lattice Boltzmann simulations. We find that the deformation of the fluid interface strongly influences the equilibrium orientation of the Janus ellipsoid. The adsorption process of the Janus ellipsoid can lead to different final orientations determined by the inte…
Manufacturing new soft materials with specific optical, mechanical and magnetic properties is a significant challenge. Assembling and manipulating colloidal particles at fluid interfaces is a promising way to make such materials. We use lattice-Boltzmann simulations to investigate the response of magnetic ellipsoidal particles adsorbed at liquid-liquid interfaces to external magnetic fields. We provide further evidence for the first-order orientation phase transition predicted by Bresme and Faraudo [Journal of Physics: Condensed Matter 19 (2007), 375110]. We show that capillary interface defor…
The fabrication of novel soft materials is an important scientific and technological challenge. We investigate the response of magnetic ellipsoidal particles adsorbed at fluid-fluid interfaces to external magnetic fields. By exploiting previously discovered first-order orientation phase transitions we show how to switch on and off dipolar capillary interactions between particles, leading to the formation of distinctive self-assembled structures and allowing dynamic control of the bottom-up fabrication of reconfigurable novel-structured materials
Membrane budding and wrapping of particles, such as viruses and nano-particles, play a key role in intracellular transport and have been studied for a variety of biological and soft matter systems. We study nano-particle wrapping by numerical minimization of bending, surface tension, and adhesion energies. We calculate deformation and adhesion energies as a function of membrane elastic parameters and adhesion strength to obtain wrapping diagrams. We predict unwrapped, partially-wrapped, and completely-wrapped states for prolate and oblate ellipsoids for various aspect ratios and particle sizes…
A simulation of ellipsoidal particles inside a fluid flow is presented and validated from our own lab size experiments where data has been recorded using a camera set-up and post-processing of the pictures. The model is based on Jeffery's equation, where the orientation and position of the particles are influenced by the surrounding fluid. Additionally, particle-particle interaction and particle-wall interaction are taken into account.
Based on renormalization group concepts and explicit mean field calculations we study the universal contribution to the effective force and torque acting on an ellipsoidal colloidal particle which is dissolved in a critical fluid and is close to a homogeneous planar substrate. At the same closest distance between the substrate and the surface of the particle, the ellipsoidal particle prefers an orientation parallel to the substrate and the magnitude of the fluctuation induced force is larger than if the orientation of the particle is perpendicular to the substrate. The sign of the critical tor…
Enhanced diffusion of passive tracers immersed in active fluids is a universal feature of active fluids and has been extensively studied in recent years. Similar to microrheology for equilibrium complex fluids, the unusual enhanced particle dynamics reveal intrinsic properties of active fluids. Nevertheless, previous studies have shown that the translational dynamics of spherical tracers are qualitatively similar, independent of whether active particles are pushers or pullers---the two fundamental classes of active fluids. Is it possible to distinguish pushers from pullers by simply imaging th…
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, we report the capillary assembly of magnetic ellipsoidal Janus particles at a fluid-fluid interface. Depending on their tilt angle, i.e. 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 ch…
We study the effective interaction between two ellipsoidal particles at the interface of two fluid phases which are mediated by thermal fluctuations of the interface. In this system the restriction of the long--ranged interface fluctuations by particles gives rise to fluctuation--induced forces which are equivalent to interactions of Casimir type and which are anisotropic in the interface plane. Since the position and the orientation of the colloids with respect to the interface normal may also fluctuate, this system is an example for the Casimir effect with fluctuating boundary conditions. In…
In our study we investigate the behaviour of the net force (NF) emerging between an ellipsoidal particle and a thick plate (slab), when the interaction takes place in a near critical fluid medium with account for the omnipresent van der Waals forces (vdWF). Here we consider the case of complete wetting of the objects surfaces by the medium, due to strong adsorbing local surface potentials, exerted by thin solid coating films. The influence of the bulk inner regions of the particle and the slab on the constituents of the fluid results in long-ranged competing dispersion potentials. As a consequ…
We consider a mean field hierarchy of models for large systems of interacting ellipsoids suspended in an incompressible fluid. The models range from microscopic to macroscopic mean field models. The microscopic model is based on three ingredients. Starting from a Langevin type model for rigid body interactions, we use a Jefferys type term to model the influence of the fluid on the ellipsoids and a simplified interaction potential between the ellipsoids to model the interaction between the ellipsoids. A mean field equation and corresponding equations for the marginals of the distribution functi…
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. Fin…
The scaled-particle theory equation of state for the two-dimensional hard-disk fluid on a curved surface is proposed and used to determine the saddle-splay modulus of a particle-laden fluid interface. The resulting contribution to saddle-splay modulus, which is caused by thermal motion of the adsorbed particles, is comparable in magnitude with the saddle-splay modulus of a simple fluid interface.
The energy required to detach a single particle from a fluid-fluid interface is an important parameter for designing certain soft materials, for example, emulsions stabilised by colloidal particles, colloidosomes designed for targeted drug delivery, and bio-sensors composed of magnetic particles adsorbed at interfaces. For a fixed particle volume, prolate and oblate spheroids attach more strongly to interfaces because they have larger particle-interface areas. Calculating the detachment energy of spheroids necessitates the difficult measurement of particle-liquid surface tensions, in contrast …
The kinetics of non-ionic surfactant adsorption at a fluid-fluid interface from a micellar solution is considered theoretically. Our model takes into account the effect of micelle relaxation on the diffusion of the free surfactant molecules. It is shown that non-ionic surfactants undergo either a diffusion or a kinetically limited adsorption according to the characteristic relaxation time of the micelles. This gives a new interpretation for the observed dynamical surface tension of micellar solutions.
The influence of a fluid-fluid interface on self-phoresis of chemically active, axially symmetric, spherical colloids is analyzed. Distinct from the studies of self-phoresis for colloids trapped at fluid interfaces or in the vicinity of hard walls, here we focus on the issue of self-phoresis close to a fluid-fluid interface. In order to provide physically intuitive results highlighting the role played by the interface, the analysis is carried out for the case that the symmetry axis of the colloid is normal to the interface; moreover, thermal fluctuations are not taken into account. Similarly t…
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 inspecti…
Using a fundamental measure density functional theory we investigate both bulk and inhomogeneous systems of the binary non-additive hard sphere model. For sufficiently large (positive) non-additivity the mixture phase separates into two fluid phases with different compositions. We calculate bulk fluid-fluid coexistence curves for a range of size ratios and non-additivity parameters and find that they compare well to simulation results from the literature. Using the Ornstein-Zernike equation, we investigate the asymptotic, r->infinity, decay of the partial pair correlation functions, g_ij(r). A…
Complex fluid-fluid interfaces featuring mesoscale structures with adsorbed particles are key components of newly designed materials which are continuously enriching the field of soft matter. Simulation tools which are able to cope with the different scales characterizing these systems are fundamental requirements for efficient theoretical investigations. In this paper we present a novel simulation method, based on the approach of Ahlrichs and Dünweg [Ahlrichs and Dünweg, Int. J. Mod. Phys. C, 1998, 9, 1429], that couples the "Shan-Chen" multicomponent Lattice Boltzmann technique to off-lattic…
Two-fluid interfaces in porous media, an example of driven disordered systems, were studied by a real time three-dimensional imaging technique with pore scale resolution for a less viscous fluid displacing a more viscous one. With increasing flow rate the interface transforms from flat to fingers and thence to droplets for both drainage and imbibition. The results compare and contrast the effects of randomness, both physical (geometry of the pore space) and chemical (wettability of the fluids), on the dynamical instability and identify the origin of the pore-scale processes that govern them.
We present a technique for analyzing the full three-dimensional density profiles of a planar crystal-fluid interface in terms of density modes. These density modes can also be related to crystallinity order parameter profiles which are used in coarse-grained, phase field type models of the statics and dynamics of crystal-fluid interfaces and are an alternative to crystallinity order parameters extracted from simulations using local crystallinity criteria. We illustrate our results for the hard sphere system using finely-resolved, three-dimensional density profiles from density functional theor…
Particle stabilized emulsions have received an enormous interest in the recent past, but our understanding of the dynamics of emulsion formation is still limited. For simple spherical particles, the time dependent growth of fluid domains is dominated by the formation of droplets, particle adsorption and coalescence of droplets (Ostwald ripening), which eventually can be almost fully blocked due to the presence of the particles. Ellipsoidal particles are known to be more efficient stabilizers of fluid interfaces than spherical particles and their anisotropic shape and the related additional rot…
Hypothesis: Particle-laden fluid interfaces are the central component of many natural and engineering systems. Understanding the mechanical properties and improving the stability of such interfaces are of great practical importance. Janus particles, a special class of heterogeneous colloids, might be utilized as an effective surface-active agent to control the assembly and interfacial rheology of particle-laden fluid interfaces. Experiments: Using a custom-built interfacial stress rheometer, we explore the effect of Janus particle additives on the interfacial rheology and microscopic structure…
We present an extension of the multiparticle collision dynamics method for flows with complex interfaces, including supramolecular near-contact interactions mimicking the effect of surfactants. The new method is demonstrated for the case of (i) short range repulsion of droplets in close contact, (ii) arrested phase separation and (iii) different pattern formation during spinodal decomposition of binary mixtures.
We show theoretically that near a fluid-fluid interface a single active colloidal particle generating, e.g., chemicals or a temperature gradient experiences an effective force of hydrodynamic origin. This force is due to the fluid flow driven by Marangoni stresses induced by the activity of the particle; it decays very slowly with the distance from the interface, and can be attractive or repulsive depending on how the activity modifies the surface tension. We show that, for typical systems, this interaction can dominate the dynamics of the particle as compared to Brownian motion, dispersion fo…
Recent experimental developments showed that the use of the radiation pressure, induced by a continuous laser wave, to control fluid-fluid interface deformations at the microscale, represents a very promising alternative to electric or magnetic actuation. In this article, we solve numerically the dynamics and steady state of the fluid interface under the effects of buoyancy, capillarity, optical radiation pressure and viscous stress. A precise quantitative validation is shown by comparison with experimental data. New results due to the nonlinear dependence of the optical pressure on the angle …
Within the Onsager theory we study free planar isotropic-nematic interfaces in binary mixtures of hard rods. For sufficiently different particle shapes the bulk phase diagrams of these mixtures exhibit a triple point, where an isotropic (I) phase coexists with two nematic phases ($N_1$ and $N_2$) of different composition. For all explored mixtures we find that upon approach of the triple point the $IN_2$ interface shows complete wetting by an intervening $N_1$ film. We compute the surface tensions of isotropic-nematic interfaces, and find a remarkable increase with fractionation, similar to th…
Hypothesis: The collective dynamics and self-assembly of colloids floating at a fluid/fluid interface is a balance between deterministic lateral interaction forces, viscous resistance to colloid motion along the surface and thermal (Brownian) fluctuations. As the colloid size decreases, thermal forces become important and can affect the self assembly into ordered patterns and crystal structures that are the starting point for various materials applications. Numerics: Langevin dynamic simulations involving two particles straddling a liquid/liquid interface with a high viscosity contrast are pre…
We determine the capillary attraction and equilibrium configurations of particles trapped at a liquid-fluid interface due to the pinning of their contact-line. We calculate analytically the asymptotic interaction energy between two particles and, numerically, the multi-body energy landscape for up to four contacting particles. Our results are consistent with recent experiments. We show that a system composed of a large number of such particles behaves as a jammed system.
A particle placed in soft matter distorts its host and creates an energy landscape. This can occur, for example, for particles in liquid crystals, for particles on lipid bilayers or for particles trapped at fluid interfaces. Such energies can be used to direct particles to assemble with remarkable degrees of control over orientation and structure. These notes explore that concept for capillary interactions, beginning with particle trapping at fluid interfaces, addressing pair interactions on planar interfaces and culminating with curvature capillary migration. Particular care is given to the s…
The dynamics of spherical particles driven along an interface between two immiscible fluids is investigated asymptotically. Under the assumptions of a pinned three-phase contact line and very different viscosities of the two fluids, a particle assumes a tilted orientation. As it moves, it causes a deformation of the fluid interface which is also computed. The case of two interacting driven particles is studied via the Linear Superposition Approximation. It is shown that the capillary interaction force resulting from the particle motion is dipolar in terms of the azimuthal angle and decays with…
We study the linear stability of an isotropic active fluid in three different geometries: a film of active fluid on a rigid substrate, a cylindrical thread of fluid, and a spherical fluid droplet. The active fluid is modeled by the hydrodynamic theory of an active nematic liquid crystal in the isotropic phase. In each geometry, we calculate the growth rate of sinusoidal modes of deformation of the interface. There are two distinct branches of growth rates; at long wavelength, one corresponds to the deformation of the interface, and one corresponds to the evolution of the liquid crystalline deg…
Molecular anatomy of the pressure anisotropy in the interface of one and two component fluids: local thermodynamic description of the interfacial tension
The reconfiguration of soft, deformable particles upon adsorption at the interface between two fluids underpins many aspects of their dynamics and interactions, ultimately controlling the macroscopic properties of particle monolayers of relevance for materials, such as particle-stabilized emulsions and foams, and processes, e. g. particle-based lithography. In spite of its importance, experimentally determining the three-dimensional shape of soft particles at fluid interfaces with high resolution remains an elusive task. In this work, we take poly(N-isopropylacrylamide) (pNIPAM) microgels as m…
Bacteria at fluid interfaces endure physical and chemical stresses unique to these highly asymmetric environments. The responses of Pseudomonas aeruginosa PAO1 and PA14 to a hexadecane-water interface are compared. PAO1 cells form elastic films of bacteria, excreted polysaccharides and proteins, whereas PA14 cells move actively without forming an elastic film. Studies of PAO1 mutants show that, unlike solid-supported biofilms, elastic interfacial film formation occurs in the absence of flagella, pili, or certain polysaccharides. Highly induced genes identified in transcriptional profiling incl…
The problem presented involves the development of a new analytical model for the general fluid-solid temperature jump. To the best of our knowledge, there are no analytical models that provide the accurate predictions of the temperature jump for both gas and liquid systems. In this paper, a unified model for the fluid-solid temperature jump has been developed based on our adsorption model of the interfacial interactions. Results obtained from this model are validated with available results from the literature.
We investigate the liquid-vapor interface of the restricted primitive model for an ionic fluid using a density functional approach. The applied theory includes the electrostatic contribution to the free energy functional arising from the bulk energy equation of state and the mean spherical approximation for a restricted primitive model, as well as the associative contribution, due to the formation of pairs of ions. We compare the density profiles and the values of the surface tension with previous theoretical approaches.
Chemically active colloids generate changes in the chemical composition of their surrounding solution and thereby induce flows in the ambient fluid which affect their dynamical evolution. Here we study the many-body dynamics of a monolayer of active particles trapped at a fluid-fluid interface. To this end we consider a mean-field model which incorporates the direct pair interaction (including also the capillary interaction which is caused specifically by the interfacial trapping) as well as the effect of hydrodynamic interactions (including the Marangoni flow induced by the response of the in…
We study the oscillation spectrum and acoustic properties of a liquid drop in the phase-separated fluid when the interfacial dynamics of phase conversion can be described in terms of the kinetic growth coefficient. For a readily mobile interface, i.e., as the growth coefficient becomes comparable with a reciprocal of the acoustic impedance, anomalous behavior is found in the oscillation spectrum of a drop as well as in the velocity and absorption of a sound wave propagating through a suspension of drops in the two-phase system. Compared with the known case of two immiscible fluids, the high in…
Soft particles can be better emulsifiers than hard particles because they stretch at fluid interfaces. This deformation can increase adsorption energies by orders of magnitude relative to rigid particles. The deformation of a particle at an interface is governed by a competition of bulk elasticity and surface tension. When particles are partially wet by the two liquids, deformation is localized within a material-dependent distance $L$ from the contact line. At the contact line, the particle morphology is given by a balance of surface tensions. When the particle radius $R \ll L$, the particle a…
Fluctuations of the interface between coexisting colloidal fluid phases have been measured with confocal microscopy. Due to a very low surface tension, the thermal motions of the interface are so slow, that a record can be made of the positions of the interface. The theory of the interfacial height fluctuations is developed. For a host of correlation functions, the experimental data are compared with the theoretical expressions. The agreement between theory and experiment is remarkably good.
We study the boundary conditions at a fluid-solid interface using molecular dynamics simulations covering a broad range of fluid-solid interactions and fluid densities, and both simple and chain-molecule fluids. The slip length is shown to be independent of the type of flow, but rather is related to the fluid organization near the solid, as governed by the fluid-solid molecular interactions.
We present a model treating the kinetics of adsorption of soluble surface-active molecules at the interface between an aqueous solution and another fluid phase. The model accounts for both the diffusive transport inside the solution and the kinetics taking place at the interface using a free-energy formulation. In addition, it offers a general method of calculating dynamic surface tensions. Non-ionic surfactants are shown, in general, to undergo a diffusion-limited adsorption, in accord with experimental findings.
The dynamics of active colloids is very sensitive to the presence of boundaries and interfaces which therefore can be used to control their motion. Here we analyze the dynamics of active colloids adsorbed at a fluid-fluid interface. By using a mesoscopic numerical approach which relies on an approximated numerical solution of the Navier-Stokes equation, we show that when adsorbed at a fluid interface, an active colloid experiences a net torque even in the absence of a viscosity contrast between the two adjacent fluids. In particular, we study the dependence of this torque on the contact angle …
We study the orientational and translational dynamics of spherical microswimmers trapped at fluid interfaces, in terms of the force dipole and source dipole components of their flow field. Using numerical simulations and analytical calculations, we show that the force dipole exerts a torque, orienting pushers parallel to the interface, and pullers in normal direction. The source dipole results in particle rotation only for a finite viscosity contrast between the two fluids, in agreement with previous studies. The superposition of these two contributions leads to an rotational dynamics with a s…
The active motion of phoretic colloids leads them to accumulate at boundaries and interfaces. Such an excess accumulation, with respect to their passive counterparts, makes the dynamics of phoretic colloids particularly sensitive to the presence of boundaries and pave new routes to externally control their single particle as well as collective behavior. Here we review some recent theoretical results about the dynamics of phoretic colloids close to and adsorbed at fluid interfaces in particular highlighting similarities and differences with respect to solid-fluid interfaces.
We present large-scale molecular dynamics simulations of a nematic-isotropic interface in a system of repulsive ellipsoidal molecules, focusing in particular on the capillary wave fluctuations of the interfacial position. The interface anchors the nematic phase in a planar way, i.e., the director aligns parallel to the interface. Capillary waves in the direction parallel and perpendicular to the director are considered separately. We find that the spectrum is anisotropic, the amplitudes of capillary waves being larger in the direction perpendicular to the director. In the long wavelength limit…
The presence of even small amount of surfactant at the particle-laden fluid interface subjected to shear makes surface flow incompressible if the shear rate is small enough [T. M. Fischer et al, J. Fluid Mech. 558, 451 (2006)]. In the present paper the effective surface shear viscosity of a flat, low-concentration, particle-laden incompressible interface separating two immiscible fluids is calculated. The resulting value is found to be 7.6% larger than the value obtained without account for surface incompressibility.
We consider the behaviour of a dielectric fluid-fluid interface in the presence of a strong electric field from a point charge and line charge, respectively, both statically and, in the latter case, dynamically. The fluid surface is elevated above its undisturbed level until balance is reached between the electromagnetic lifting force, gravity and surface tension. We derive ordinary differential equations for the shape of the fluid-fluid interface which are solved numerically with standard means, demonstrating how the elevation depends on field strength and surface tension coefficient. In the …
If an active Janus particle is trapped at the interface between a liquid and a fluid, its self-propelled motion along the interface is affected by a net torque on the particle due to the viscosity contrast between the two adjacent fluid phases. For a simple model of an active, spherical Janus colloid we analyze the conditions under which translation occurs along the interface and we provide estimates of the corresponding persistence length. We show that under certain conditions the persistence length of such a particle is significantly larger than the corresponding one in the bulk liquid, whic…
Computer simulations of bi-continuous two-phase fluids with intersparsed dumbbells show that, unlike rigid colloids, soft dumbbells do not lead to arrested coarsening. However, they significantly alter the curvature dynamics of the fluid-fluid interface, whose probability density distributions are shown to exhibit (i) a universal spontaneous transition from an initial broad-shape distribution towards a highly localized one and (ii) super-diffusive dynamics with long-range effects. Both features may prove useful for the design of novel families of soft porous materials.
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 utili…
We present a Monte Carlo method to simulate asymmetric binary mixtures in the grand canonical ensemble. The method is used to study the colloid-polymer model of Asakura and Oosawa. We determine the phase diagram of the fluid-fluid unmixing transition and the interfacial tension, both at high polymer density and close to the critical point. We also present density profiles in the two-phase region. The results are compared to predictions of a recent density functional theory.
