Curvature-driven capillary migration and assembly of rod-like particles

Abstract

Capillarity can be used to direct anisotropic colloidal particles to precise locations and to orient them by using interface curvature as an applied field. We show this in experiments in which the shape of the interface is molded by pinning to vertical pillars of different cross-sections. These interfaces present well-defined curvature fields that orient and steer particles along complex trajectories. Trajectories and orientations are predicted by a theoretical model in which capillary forces and torques are related to Gaussian curvature gradients and angular deviations from principal directions of curvature. Interface curvature diverges near sharp boundaries, similar to an electric field near a pointed conductor. We exploit this feature to induce migration and assembly at preferred locations, and to create complex structures. We also report a repulsive interaction, in which microparticles move away from planar bounding walls along curvature gradient contours. These phenomena should be widely useful in the directed assembly of micro-and nanoparticles with potential application in the fabrication of materials with tunable mechanical or electronic properties, in emulsion production, and in encapsulation.anisotropic particles | colloidal interactions | colloidosome | Pickering | interfacial assemblies F luid interfaces are remarkable sites for directed migration and assembly of particles (1-6). When particles distort an interface, spontaneous, long-range interactions occur owing to capillary energy, given by the product of the surface tension and the area of the distortion. When distortions induced by neighboring particles overlap, the interfacial area decreases, resulting in capillary interactions that cause particles to attract and assemble. This effect, responsible for clustering of cereal in a bowl of milk (7), is now an important means for microparticle assembly at otherwise planar fluid interfaces, in particular for anisotropically shaped objects, which assemble with preferred orientations (4, 6, 8-13). At planar interfaces, the magnitude of the interaction is determined by the particle geometry, size, and surface energies. Hence, once the particles are placed at the interface, the strength of resulting capillary interactions is fixed. Assembly occurs at random locations on the interface determined by sites of initial encounter between the particles. In this work, we show that interface curvature can be employed as an external field to direct the location at which particles assemble. The phenomenon is entirely controlled by the coupling between geometry and capillarity. Therefore, it can be applied to colloids made of any material.When an anisotropic particle is placed on a curved fluid interface, capillary interactions arise, as the area of the interface then depends on the particle's orientation with respect to the principal axes and its location in a curvature gradient, resulting in torques (5, 14) and forces (5) on the particle. Because fluid interfaces can be molded and reconfigured using pinning sites, ...

Curvature capillary migration of microspheres

“…In experiment, microparticles migrate along curvature gradients to sites of high curvature, as has now been observed for microcylinders [2], microspheres [11], and microdisks [12]. Theoretically, the curvature capillary energy driving this migration is simply the sum of the surface energies and pressure work for particles at the interface.…”

“…5.(c)). We impose a curvature field to the host interface using a technique reported previously [2] which we recapitulate briefly. A curved oil-water interface is formed around a micropost which is either circular or square in cross section (see the schematic in Fig.…”

“…They trap particles at the interface [1] and determine their ensuing organization [2][3][4], allowing particles to be widely exploited in technological applications such as stabilization of foams and emulsions [5], and in settings as diverse as the food [6], pharmaceutical [7], mineral recovery [8], and petroleum industries [9]. For microparticles of radius a at planar interfaces of tension γ, gravity is irrelevant, as the Bond number Bo = ∆ρga 2 γ 1, where g is the gravitational acceleration constant, and ∆ρ is the density difference between the two fluids on either side of the interface.…”

Deformation of a free interface pierced by a tilted cylinder: Variation of the contact angle

“…In future work it will be interesting to change the shape of the object that pierces the interface [21,22], and to characterize the interaction between several objects [20], again varying systematically both the contact angle and the angle of inclination. In principle, the method could be applied to a wide range of systems in which gravity does not play a role.…”

“…These include mesh-free finite difference methods [20]; boundary-element simulations [21]; Surface Evolver simulations coupled to finitedifference simulations [22]; and an ordinary differential equation solver (MATLAB) [3].…”