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The mobility of externally driven phoretic propulsion of particles is evaluated by simultaneously solving the solute conservation equation, interaction potential equation and the modified Stokes equation. While accurate, this approach is cumbersome, especially when the interaction potential decays slowly compared with the particle size. In contrast to external phoresis, the motion of self-phoretic particles is typically estimated by relating the translation and rotation velocities with the local slip velocity. While this approach is convenient and thus widely used, it is only valid when the interaction decay length is significantly smaller than the particle size. Here, by taking inspiration from Brady (J. Fluid Mech., vol. 922, 2021, A10), which combines the benefits of two approaches, we reproduce their unified mobility expressions with arbitrary interaction potentials and show that these expressions can conveniently recover the well-known mobility relationships of external electrophoresis and diffusiophoresis for arbitrary double-layer thickness. Additionally, we show that for a spherical microswimmer, the derived expressions relax to the slip velocity calculations in the limit of the thin interaction length scales. We also employ the derived mobility expressions to calculate the velocities of an autophoretic Janus particle. We find that there is significant dampening in the translation velocity even when the interaction length is an order of magnitude larger than the particle size. Finally, we study the motion of a catalytically self-propelled particle, while it also propels due to external concentration gradients, and demonstrate how the two propulsion modes compete with each other. 

Diffusiophoresis involves the movement of colloidal-scale entities in response to concentration gradients of a solute. It is broadly categorized into two types: passive and active diffusiophoresis. In passive diffusiophoresis, external concentration gradients drive the motion, while in active diffusiophoresis, the colloidal entity itself assists in generating the gradients. In this perspective, we delve into the fundamental processes underlying passive and active diffusiophoresis and emphasize how prevalent both kinds of diffusiophoresis are in colloidal and natural systems. In particular, we highlight the colloidal focusing feature in passive diffusiophoresis and discuss how it underpins the variety of experimental observations and applications such as low-cost zetasizers, water filtration, and biological pattern formation. For active diffusiophoresis, we emphasize the dependence of particle trajectory on its shape and surface heterogeneity, and discuss how this dictates the applications such as drug delivery, removal of microplastics, and self-repairing materials. Finally, we offer insights and ideas regarding future opportunities in diffusiophoresis. 

Swimming at the microscale typically involves two modes of motion: mechanical propulsion and propulsion due to field interactions. During mechanical propulsion, particles swim by reconfiguring their geometry. When propelled by field interactions, body forces such as phoretic interactions drive mobility. In this work, we employ slender-body theory to explore how a bent rod actuator propels due to a mechanical mode of swimming via hinge articulations and due to a chemical mode of swimming via diffusiophoretic interactions with a solute field. Although previous theoretical studies have examined mechanical and chemical modes of swimming in isolation, the simultaneous investigation of both modes has remained unexplored. For the mechanical mode of swimming, our calculations, both numerical and analytical, recover Purcell’s scallop theorem and show that the bent rod actuator experiences zero net displacement during reciprocal motion. Additionally, we calculate the trajectories traced by a bent rod actuator under a non-reciprocal hinge articulation, revealing that these trajectories are influenced by the amplitude of the hinge articulation, geometric asymmetry, and the angular velocity distribution between the two arms of the bent rod actuator. We provide intuitive explanations for these effects using free-body diagrams. Furthermore, we explore the motion induced by simultaneous hinge articulations and self-diffusiophoresis. We observe that hinge articulations can modify the effective phoretic forces and torques acting on the bent rod actuator, either supporting or impeding propulsion. Additionally, during self-diffusiophoretic propulsion, reciprocal hinge articulations no longer result in zero net displacement. In summary, our findings chart a new direction for designing micron-sized objects that harness both mechanical and chemical modes of propulsion synchronously, offering a mechanism to enact control over trajectories. 

Active particles, or micromotors, locally dissipate energy to drive locomotion at small length scales. The type of trajectory is generally fixed and dictated by the geometry and composition of the particle, which can be challenging to tune using conventional fabrication procedures. Here, we report a simple, bottom-up method to magnetically assemble gold-coated polystyrene Janus particles into “locked” clusters that display diverse trajectories when stimulated by AC electric fields. The orientation of particles within each cluster gives rise to distinct modes of locomotion, including translational, rotational, trochoidal, helical, and orbital. We model this system using a simplified rigid beads model and demonstrate qualitative agreement between the predicted and experimentally observed cluster trajectories. Overall, this system provides a facile means to scalably create micromotors with a range of well-defined motions from discrete building blocks.