Self-propelled, chemically powered colloidal locomotors are swimmers designed to transverse small scale landscapes in a range of applications involving micropumping, sensing, and cargo transport. Although applications can require precise navigation and onboard steering mechanisms, here we examine by calculation how locomotors through their hydrodynamic interaction can navigate along a boundary. We adopt an engine model consisting of a spherical Janus colloid coated with a symmetrical catalyst cap, which converts fuel into a product solute. The solute is repelled from the colloid through a repulsive interaction, which occurs over a distance much smaller than the swimmer radius. Within this thin interaction layer, a concentration difference develops along the surface, which generates a pressure gradient as pressure balances the interaction force of the solute with the surface. The pressure gradient drives a slip flow towards the high concentration, which propels the particle oppositely, away from product accumulation (self-diffusiophoresis). To study boundary guidance, the motion near an infinite no-slip planar wall that does not adsorb solute is obtained by analytical solution of the solute conservation and the Stokes equations using bispherical coordinates. Several regimes of boundary interaction unfold: When the colloid is oriented with its cap axisymmetrically facing the wall, it is repelled by the accumulation of solute in the gap between the swimmer and the wall. With the cap opposite to the wall, the swimmer moves towards the wall by the repulsion from the solute accumulating on the cap side, but very large caps accumulate solute in the gap, and the motor stops. For oblique approach with the cap opposite to the wall and small cap sizes, the swimmer is driven to the wall by accumulation on the cap side, but rotates as it approaches the wall, and eventually scatters as the cap reorients and faces the wall. For a swimmer approaching obliquely with a larger cap (again facing away from the wall), boundary navigation results as the accumulation of product in the gap suppresses rotation and provides a normal force, which directs the swimmer to skim along the surface at a fixed distance and orientation or to become stationary. We also demonstrate how gravity can force transitions between skimming and stationary states.

We address the question: How does capillarity propel microspheres along curvature gradients? For a particle on a fluid interface, there are two conditions that can apply at the three phase contact line: Either the contact line adopts an equilibrium contact angle, or it can be pinned by kinetic trapping, e.g. at chemical heterogeneities, asperities or other pinning sites on the particle surface. We formulate the curvature capillary energy for both scenarios for particles smaller than the capillary length and far from any pinning boundaries. The scale and range of the distortion made by the particle are set by the particle radius; we use singular perturbation methods to find the distortions and to rigorously evaluate the associated capillary energies. For particles with equilibrium contact angles, contrary to the literature, we find that the capillary energy is negligible, with the first contribution bounded to fourth order in the product of the particle radius and the deviatoric curvature. For pinned contact lines, we find curvature capillary energies that are finite, with a functional form investigated previously by us for disks and microcylinders on curved interfaces. In experiments, we show microsphere migrate along deterministic trajectories toward regions of maximum deviatoric curvature with curvature capillary energies ranging from 6 × 10 3 − 5 × 10 4 kBT . These data agree with the curvature capillary energy for the case of pinned contact lines. The underlying physics of this migration is a coupling of the interface deviatoric curvature with the quadrupolar mode of nanometric disturbances in the interface owing to the particle's contact line undulations. This work is an example of the major implications of nanometric roughness and contact line pinning for colloidal dynamics.

The dynamics and pair trajectory of two self-propelled colloids are reported. The autonomous motions of the colloids are due to a catalytic chemical reaction taking place asymmetrically on their surfaces that generates a concentration gradient of interactive solutes around the particles and actuate particle propulsion. We consider two spherical particles with symmetric catalytic caps extending over the local polar angles θ 1 cap and θ 2 cap from the centers of active sectors in an otherwise quiescent fluid. A combined analytical-numerical technique was developed to solve the coupled mass transfer equation and the hydrodynamics in the Stokes flow regime. The ensuing pair trajectory of the colloids is controlled by the reacting coverages θ j cap and their initial relative orientation with respect to each other. Our analysis indicates two possible scenarios for pair trajectories of catalytic self-propelled particles: either the particles approach, come into contact and assemble or they interact and move away from each other (escape). For arbitrary motions of the colloids, it is found that the direction of particle rotations is the key factor in determining the escape or assembly scenario. Based on the analysis, a phase diagram is sketched for the pair trajectory of the catalytically active particles as a function of active coverages and their initial relative orientations. We believe this study has important implications in elucidation of collective behaviors of auotophoretically self-propelled colloids.

In directed assembly, small building blocks are assembled into an organized structures under the influence of guiding fields. Capillary interactions provide a versatile route for structure formation. Colloids adsorbed on fluid interfaces distort the interface, which creates an associated energy field. When neighboring distortions overlap, colloids interact to minimize interfacial area. Contact line pinning, particle shape and surface chemistry play important roles in structure formation. Interface curvature acts like an external field; particles migrate and assemble in patterns dictated by curvature gradients. We review basic analysis and recent findings in this rapidly evolving literature. Understanding the roles of assembly is essential for tuning the mechanical, physical, and optical properties of the structure.