Self-assembled artificial cilia

Abstract

Due to their small dimensions, microfluidic devices operate in the low Reynolds number regime. In this case, the hydrodynamics is governed by the viscosity rather than inertia and special elements have to be introduced into the system for mixing and pumping of fluids. Here we report on the realization of an effective pumping device that mimics a ciliated surface and imitates its motion to generate fluid flow. The artificial biomimetic cilia are constructed as long chains of spherical superparamagnetic particles, which self-assemble in an external magnetic field. Magnetic field is also used to actuate the cilia in a simple nonreciprocal manner, resulting in a fluid flow. We prove the concept by measuring the velocity of a cilia-pumped fluid as a function of height above the ciliated surface and investigate the influence of the beating asymmetry on the pumping performance. A numerical simulation was carried out that successfully reproduced the experimentally obtained data.

Fig. 1.

Artificial cilia were assembled in an external magnetic field. (A) Detail of the experimental setup, which was used for creating and manipulating artificial cilia. Three orthogonal pairs of coils that generated a homogeneous magnetic field of arbitrary direction and varying magnitude were integrated into an optical microscope (not shown) equipped with optical tweezers. (B) Artificial cilia were made by assembling superparamagnetic colloidal particles into chains that were held together and attached to the nickel anchoring points only by the magnetic field. The external field was also used to rotate the cilia along a tilted conical path with the angular frequency ω = ϕ/t and the conical motion resulted in the generation of fluid flow. Tilt angle of the cone ϑ was chosen to be equal to the semi-cone angle ψ. By varying the angle, we were able to change the pumping performance of the artificial cilia.

Fig. 2.

Assembly of artificial cilia. (A) Superparamagnetic beads were individually trapped by optical tweezers and assembled into chains. They were anchored to the surface via nickel anchoring sites. (B) The beads self-assembled into chains in an external magnetic field. Rectangular trenches in a photoresist layer guided the self-assembly process of chain formation and ensured that all chains had approximately the same length and width. The trenches measured 45 μm × 5 μm and had a depth of 5 μm. The bead diameter was 2a = 4.4 μm. Micron-sized non-magnetic spheres, which are visible in both figures, were added to the system as tracer particles to visualize the generated flow and measure its velocity.

Fig. 3.

Visualization of the fluid flow generated by the artificial cilia. (A) Paths of four tracer particles (diameter 1 μm) at the height h = 40 μm. The cilia with length L = 31 μm were rotated in a conical manner at the frequency of 1 Hz and the cone tilt angle ϑ = 30°. The pumping direction was chosen to deviate by α = 30° from the direction of the square array of cilia anchoring points. (B) Paths of tracer particles shown in A projected onto the chosen pumping direction. The net flow velocity is obtained from a linear fit to the obtained data. The average velocity was 3.3 ± 0.2 μm/s. An offset in the coordinate was added for clarity.

Fig. 4.

Induced flow velocity depends on the height h above the ciliated surface. (A) Flow velocity generated by rotating cilia as a function of h for different tilt angles (rotation frequency was 0.5 Hz). Experimental data (sym-bols), and data obtained by a numerical simulation (lines): ϑ= 20° (• and solid line), ϑ = 30° (♦ and dashed line), ϑ = 40° (▪ and dotted line). One should note that there were no free parameters in the simulation. (B) Schematic view of the numerical simulation that was done for exactly the same configuration as in the experiment and for the same parameter values. Tracer particles were randomly distributed through the sample and their average velocity was calculated. The arrow denotes the direction of the external magnetic field.