Collective beating of artificial microcilia.

We combine technical, experimental, and theoretical efforts to investigate the collective dynamics of artificial microcilia in a viscous fluid. We take advantage of soft lithography and colloidal self-assembly to devise microcarpets made of hundreds of slender magnetic rods. This novel experimental setup is used to investigate the dynamics of extended cilia arrays driven by a precessing magnetic field. Whereas the dynamics of an isolated cilium is a rigid body rotation, collective beating results in a symmetry breaking of the precession patterns. The trajectories of the cilia are anisotropic and experience a significant structural evolution as the actuation frequency increases. We present a minimal model to account for our experimental findings and demonstrate how the global geometry of the array imposes the shape of the trajectories via long-range hydrodynamic interactions.

Three-dimensional beating of magnetic microrods.

We investigate experimentally and theoretically the dynamics of paramagnetic microrods anchored to a surface and driven by a precessing magnetic field. We identify two distinct regimes, corresponding to extended domains in the (ω,θ(B)) plane, where ω and θ(B) are, respectively, the frequency and inclination of the driving field. At low frequencies, the response of the rod is linear whatever is the inclination of the field, and the rod precesses at ω. However, above a characteristic frequency, two qualitatively different behaviors are distinguished, depending on the inclination θ(B). For small inclinations of the magnetic field, the response of the filament remains linear at all frequencies. Conversely, when θ(B) exceeds a critical value θ(B(c)) ~55°, the response becomes nonlinear, and the tip of the rod follows a complex trajectory exhibiting three-dimensional back-and-forth patterns. A minimal model, which neglects both the flexibility of the rod and the hydrodynamic interaction with the surface, correctly captures the main features of both regimes. We thus show that the complex trajectory patterns are chiefly due to the geometrical nonlinearities in the magnetic dipolar coupling. The critical angle is itself set by a purely geometrical criterium, arising from the magnetic nature of the rod. The paper is closed by a generalization of our results to the case of soft filaments.

Helical beating of an actuated elastic filament.

We investigate the propulsive force resulting from the rotation of a flexible filament in the low Reynolds number regime. Using a simple linear model, we establish the nonlinear torque-force relations for two torque-driven actuation modes. When the rotation of the filament is induced by two perpendicular transverse oscillating torques, the propulsive force increases monotonically with the torque amplitude. Conversely, when a constant axial torque is applied, the torque-force characteristics displays an unstable branch, related to a discontinuous transition in the shape of the filament. We characterize this shape transition using two geometrical parameters, quantifying the wrapping around and the collapse on the axis of the filament. The proposed theoretical description correctly accounts for our experimental observations and reveals a strong dependence of the filament dynamics on the anchoring conditions.

Self-supporting hydrogel stamps for the microcontact printing of proteins.

In this work we explore a new hydrogel stamp material obtained from polymerizing 2-hydroxyethyl acrylate and poly(ethylene glycol) diacrylate in the presence of water for the microcontact printing of proteins directly on gold substrates and by covalent coupling to self-assembled monolayers of alkanethiols. At high cross-link density, the hydrogel is rigid, hydrophilic, and with a high buffer holding capacity to enable the unsupported printing of protein patterns homogeneously and reproducibly, with micrometer-range precision. The stamps were used to print antibodies to human parathyroid hormone, which were shown using immunoassay tests to retain their biological function with binding capacities comparable to those of solution-adsorbed antibodies.