The propulsion of micro- and nanoparticles using ultrasound is an attractive strategy for the remote manipulation of colloidal matter using biocompatible energy inputs. However, the physical mechanisms underlying acoustic propulsion are poorly understood, and our ability to transduce acoustic energy into different types of particle motions remains limited. Here, we show that the three-dimensional shape of a colloidal particle can be rationally engineered to direct desired particle motions powered by ultrasound. We investigate the dynamics of gold microplates with twisted star shape ( C symmetry) moving within the nodal plane of a uniform acoustic field at megahertz frequencies. By systematically perturbing the parametric shape of these "spinners", we quantify the relationship between the particle shape and its rotational motion. The experimental observations are reproduced and explained by hydrodynamic simulations that describe the steady streaming flows and particle motions induced by ultrasonic actuation. Our results suggest how particle shape can be used to design colloids capable of increasingly complex motions powered by ultrasound.

The pursuit of chemically-powered colloidal machines requires individual components that perform different motions within a common environment. Such motions can be tailored by controlling the shape and/or composition of catalytic microparticles; however, the ability to design particle motions remains limited by incomplete understanding of the relevant propulsion mechanism(s). Here, we demonstrate that platinum microparticles move spontaneously in solutions of hydrogen peroxide and that their motions can be rationally designed by controlling particle shape. Nanofabricated particles with n-fold rotational symmetry rotate steadily with speed and direction specified by the type and extent of shape asymmetry. The observed relationships between particle shape and motion provide evidence for a self-electrophoretic propulsion mechanism, whereby anodic oxidation and cathodic reduction occur at different rates at different locations on the particle surface. We develop a mathematical model that explains how particle shape impacts the relevant electrocatalytic reactions and the resulting electrokinetic flows that drive particle motion.

Small autonomous machines like biological cells or soft robots can convert energy input into control of function and form. It is desired that this behavior emerges spontaneously and can be easily switched over time. For this purpose we introduce an active matter system that is loosely inspired by biology and which we term an active colloidal cell. The active colloidal cell consists of a boundary and a fluid interior, both of which are built from identical rotating spinners whose activity creates convective flows. Similarly to biological cell motility, which is driven by cytoskeletal components spread throughout the entire volume of the cell, active colloidal cells are characterized by highly distributed energy conversion. We demonstrate that we can control the shape of the active colloidal cell and drive compartmentalization by varying the details of the boundary (hard vs. flexible) and the character of the spinners (passive vs. active). We report buckling of the boundary controlled by the pattern of boundary activity, as well as formation of core-shell and inverted Janus phase-separated configurations within the active cell interior. As the cell size is increased, the inverted Janus configuration spontaneously breaks its mirror symmetry. The result is a bubble-crescent configuration, which alternates between two degenerate states over time and exhibits collective migration of the fluid along the boundary. Our results are obtained using microscopic, non-momentum-conserving Langevin dynamics simulations and verified via a phase-field continuum model coupled to a Navier-Stokes equation.active matter | emergent pattern | confinement | colloids A ctive matter describes particulate systems with the characteristic that each "particle" (agent) converts energy into motion (1, 2). Active matter covers a range of length scales that include molecular motors in the cytoskeleton (3-5), swimming bacteria (6-8), driven colloids (9, 10), flocks of birds and fish (11)(12)(13)(14), and people and vehicles in motion (15). Over the last decade, studies of active matter have demonstrated behavior not seen in equilibrium systems, including giant number fluctuations (16, 17), emergent attraction and superdiffusion (18)(19)(20), clustering (21, 22), swarming (23-27), and self-assembled motifs (28, 29). These systems provide interesting theoretical and engineering challenges as well as opportunities to explore and target novel behaviors that proceed outside of thermodynamic equilibrium.Of particular interest are systems found in nature or inspired by natural phenomena. Biological systems usually operate in confined regions of space--think of intracellular space, interfaces and membranes, and the crowding of cells near surfaces. The role of hydrodynamics in confinement has been studied for biological swimmers, such as bacteria and sperm, showing accumulation at the walls (30-32) and upstream swimming along surfaces (33) or in a spiral vortex (34-36). Attraction to walls has also been reported in the absence of hydrodynamics for disks (37...

The symmetry and shape of colloidal particles can direct complex particle motions through fluid environments powered by simple energy inputs. The ability to rationally design or "program" the dynamics of such active colloids is an important step toward the realization of colloidal machines, in which components assemble spontaneously in space and time to perform dynamic (dissipative) functions such as actuation and transport. Here, we systematically investigate the dynamics of polarizable particles of different shapes moving in an oscillating electric field via induced-charge electrophoresis (ICEP). We consider particles from each point group in three dimensions (3D) and identify the different rotational and translational motions allowed by symmetry. We describe how the 3D shape of rigid particles can be tailored to achieve desired dynamics including oscillatory motions, helical trajectories, and complex periodic orbits. The methodology we develop is generally applicable to the design of shape-directed particle motions powered by other energy inputs.

Active matter comprised of many self-driven units can exhibit emergent collective behaviors such as pattern formation and phase separation in both biological (e.g., mussel beds) and synthetic (e.g., colloidal swimmers) systems. While these behaviors are increasingly well understood for ensembles of linearly self-propelled "particles", less is known about the collective behaviors of active rotating particles where energy input at the particle level gives rise to rotational particle motion. A recent simulation study revealed that active rotation can induce phase separation in mixtures of counter-rotating particles in 2D. In contrast to that of linearly self-propelled particles, the phase separation of counter-rotating fluids is accompanied by steady convective flows that originate at the fluid-fluid interface. Here, we investigate the influence of these flows on the coarsening dynamics of actively rotating binary liquids using a phenomenological, hydrodynamic model that combines a Cahn-Hilliard equation for the fluid composition with a Navier-Stokes equation for the fluid velocity. The effect of active rotation is introduced though an additional force within the Navier-Stokes equations that arises due to gradients in the concentrations of clockwise and counter-clockwise rotating particles. Depending on the strength of active rotation and that of frictional interactions with the stationary surroundings, we observe and explain new dynamical behaviors such as "active coarsening" via self-generated flows as well as the emergence of self-propelled "vortex doublets". We confirm that many of the qualitative behaviors identified by the continuum model can also be found in discrete, particle-based simulations of actively rotating liquids. Our results highlight further opportunities for achieving complex dissipative structures in active materials subject to distributed actuation.