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

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.

Equilibrium Orientation and Adsorption of an Ellipsoidal Janus Particle at a Fluid–Fluid Interface

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 interplay of particle aspect ratio and particle wettablity contrast.

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.

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.

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.