Microrollers flow uphill as granular media

Article https://doi.org/10.1038/s41467-023-41327-1 Microrollers flow uphill as granular media Received: 5 September 2022 Accepted: 25 August 2023 1234567890():,; 1234567890():,; Check for updates Samuel R. Wilson-Whitford1, Jinghui Gao William E. Buckley1 & James F. Gilchrist 1 , Maria Chiara Roffin1,2, 1 Pour sand into a container and only the grains near the top surface move. The collective motion associated with the translational and rotational energy of the grains in a thin flowing layer is quickly dissipated as friction through multibody interactions. Alternatively, consider what will happen to a bed of particles if one applies a torque to each individual particle. In this paper, we demonstrate an experimental system where torque is applied at the constituent level through a rotating magnetic field in a dense bed of microrollers. The net result is the grains roll uphill, forming a heap with a negative angle of repose. Two different regimes have been identified related to the degree of mobility or fluidisation of the particles in the bulk. Velocimetry of the near surface flowing layer reveals the collective motion of these responsive particles scales in a similar way to flowing bulk granular flows. A simple granular model that includes cohesion accurately predicts the apparent negative coefficient of friction. In contrast to the response of active or responsive particles that mimic thermodynamic principles, this system results in macroscopic collective behavior that has the kinematics of a purely dissipative granular system. When passive granular matter is poured onto a substrate, it forms a heap of material consisting of a near surface flow of grains and an underlying pile of nearly static particles1–3 (Fig. 1a). Within this flowing layer, grain motion is correlated as it transfers potential energy into translation and rotation and eventual frictional dissipation through multibody collisions4. This flowing layer is generally characterized by its angle of repose, θ, which is related to the friction interactions of the particles. This trivial dinner table experiment is analogous to a wide range of natural phenomena such as avalanches and dune formation and is ubiquitous with industrial processes for powder handling that follow scaling laws related to their rheology5. Rather than letting particles passively fall, heap, and flow down an incline driven by gravity, we explore a system where energy is input at the constituent-level through magnetic activation of torque on each particle. This is coupled with magnetically-tunable attractions that alter their interparticle interactions. When activated, a dense bed of these microrollers spontaneously generates a steady heap against a static wall. This is a result of an uphill flowing layer characterized by a negative angle of repose. Grains are recirculated through the underlying bed (Fig. 1b). This negative dynamic angle of repose is not to be confused with negative static angles of repose measured in cohesive or interlocking granular packings6. For stronger magnetic interactions, rather than imparting stronger cohesion7, the entire bed is fluidised by overcoming the weight of the bed and breaking the static force chains associated with a granular heap8. The experimental realisation of this system, where granular flow is driven by torque imparted at the particle level and friction, results in the emergence of collective dynamics that scale as gravity driven granular flows. Results and discussion The microrollers used in this study are non-colloidal Janus particles synthesized from polydisperse polymethyl methacrylate microbeads of radius 19 μm < a < 26 μm (Supplementary Fig. 1) and half coated with a 100 nm layer of iron using physical vapour deposition (PVD)9 (Supplementary Fig. 2). The microrollers are dispersed in ethanol where the iron cap undoubtedly becomes iron oxide and has a weak, single vector, off-centre permanent dipole with poles located at opposite points along the edge of the cap. The phenomenon described herein has also been observed in air, with no substantial change in the observed behaviour, but advantageously the use of a viscous fluid instead of air is helpful in avoiding electrostatic build-up on the particles or the container surface. The emergence of self- 1 Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, PA 18015, USA. 2Department of Physics, School of Science and e-mail: Technology, Nottingham Trent University, Nottingham NG11 8NS, UK. Nature Communications | (2023)14:5829 1 Article Fig. 1 | Gravity-driven and magnetically-driven flowing layer of ferromagnetic Janus particles. Intensity average images of (a) a gravity driven flow in a granular heap of unactuated Janus particles and, in contrast, (b) an uphill flow of the Janus microrollers driven by magnetic actuation, including an illustration of the direction of particle rotation. Movies of uphill granular flow are available (see Supplementary Information). The relative magnetic field strength is (β/β0)2 = 3.5 and the granular bed depth is Δ/2a = 26.0. The dotted white line is an approximate representation of the flowing layer. organized structures that mirror thermodynamic properties10 and instabilities11 have been characterized in dilute, quasi-2D microroller systems that differ significantly from this dense 3D flow. Without imparted magnetic torque, a dense bed of these particles flows under the influence of gravity similar to unfunctionalized microbeads. A set of rotating permanent magnets is mounted on a rotating wheel horizontal in the plane and perpendicular to the sidewall of the cuvette and subsequently positioned below the cuvette. The magnetic field imparts both the particle-level torque and the interparticle cohesion influencing the degree of friction. The magnets are much wider than the 1 cm2 square-bottomed cuvette holding the particles and spaced out such that the particles experience a relatively uniform field across the container, resulting in a near sinusoidal modulated magnetic field as each magnet rotates past the bottom of the cuvette. The amplitude of the magnetic field is a function of the distance of the particle bed above the rotating magnets, h, where the field strength varies proportionately as β ∝ 1/h2, (See Supplementary Figs. 4 and 5). A minimum field strength exists, β0, where the weaker magnetic field generates no discernible particle motion and the particle bed is essentially static, in this case when h = 60 mm. Below β0, the magnetic torque felt by individual particles is insufficient to overcome static friction and the force network within the particle bed. Interparticle interactions are influenced by magnetic dipoles Nature Communications | (2023)14:5829 https://doi.org/10.1038/s41467-023-41327-1 induced by the applied field, where F ∝ β2, as seen in the literature.12 Therefore, magnetic field is scaled as (β/β0)2, where (β/β0)2 = 1 generates no substantial particle motion. Note that dipole (...truncated)