Dynamic Assembly of Small Parts in Vortex–Vortex Traps Established within a Rotating Fluid

Abstract

trapping. Using this arrangement, we demonstrate trapping and dynamic assembly of various particle clusters, cages, and interlocked architectures, as well as jammed colloidal monoliths or colloidal formations on gas bubbles. In these experiments, the shape of the trapping region-and, consequently, the morphology of the assembling structures-can be controlled by adjusting the strengths of one or both vortices and/or the system's global angular velocity, and can switch from a stable equilibrium point to a limit cycle via the so-called supercritical Hopf bifurcation. These findings illustrate how new modalities of dynamic self-assembly [26] and 3D manipulation become possible upon transition from static to noninertial, rotating frames of reference.When a lighter particle of volume V and density ρ P is immersed in a rotating fluid of density ρ L > ρ P , it experiences not only an upward-directed buoyant force F B = (ρ P − ρ L )Vg, but also a centripetal force directed toward the axis of tube's rotation, F C (r) = −(ρ L −ρ P )Vrω 2 , where ω is fluid's angular velocity and vector r specifies particle's radial position (Figure 1a). In other words, the rotation of the tube imposes a confining harmonic potential, E(r) = (ρ L − ρ P )Vr 2 ω 2 /2. As we have shown previously, [27] for polymer beads inside tubes ≈1 cm in diameter, filled with various aqueous salt solutions and rotating at few thousand rpm, centrifugal acceleration is on the order of 10g (allowing us to neglect buoyancy effects in the subsequent discussion), and the beads localize along the fluid's axis of rotation. On the other hand, radially directed forces do not displace the beads along the tube's rotation axis and cannot, by themselves, create a stable trapping region in the axial direction.To enable such lateral confinement, we designed a system (cf. Section S1, Supporting Information) in which two aluminum disks (radius 9.9 mm and thickness 16 mm) are fitted inside and near the two ends of the liquid-filled, rotating tube ≈1 cm in diameter. A permanent neodymium bar magnet (BX088-N52 from KJ Magnetics; w = h = 12.5 mm and l = 25.4 mm, magnetization along the w dimension = 588 mT) is placed at a distance d away from each disk (Figure 1b). The role of the magnets is to act as eddy-current brakes and slow down the rotation of the aluminum disks with respect to the rotation of the liquid-filled tube. Indeed, as the distance d between the disks and the magnets decreases, so does the disks' angular velocity, ω 1 . For a given d, ω 1 increases with but is always smaller than the angular velocity of the tube, ω (Figure 1c). This slowed-down rotation of the disks gives rise to Stable, purely fluidic particle traps established by vortex flows induced within a rotating fluid are described. The traps can manipulate various types of small parts, dynamically assembling them into high-symmetry clusters, cages, interlocked architectures, jammed colloidal monoliths, or colloidal formations on gas bubbles. The strength and the shape of the trapping region can be control...