Fig. 4: Dynamic fluid manipulation by the gel microcilia arrays.

a–c, Fluid control achieved by varying the spatial arrangement and density of gel microcilia within an actuation cell (rotational bending frequency = 40 Hz). a, (1) Programmed motion of a 4 × 4 array with four cilia centred in each cell, all rotating clockwise. a, (2) 2D simulation shows four clockwise vortices and one inter-cell anticlockwise vortex. b, (1) 4 × 4 array with four corner cilia per cell, all rotating clockwise. b, (2) Each cell produces five vortices (four clockwise, one central anticlockwise), forming inter-cell anticlockwise flows. c, (1) 10 × 10 array with 5 × 5 densely packed cilia per cell, all rotating clockwise. c, (2) Hydrodynamic interference cancels intra-cell vortices, leaving peripheral clockwise and central anticlockwise vortices. d–g, Dynamic reprogramming of cilia motion for flow control (20 Hz). d, (1) 5 × 5 individually controlled array with outer 16 cilia generating metachronal waves; inner cilia stationary. d, (2) Simulation shows a central anticlockwise vortex. e, (1) 5 × 5 array with a 3 × 3 top-left subarray rotating clockwise, others anticlockwise. e, (2) Clockwise L-shaped flow forms between these regions. f, (1) Alternating column actuation (columns 1, 3 and 5 clockwise; columns 2 and 4 anticlockwise). f, (2) Downward flows between columns 1–2 and 3–4 and upward flows between columns 2–3 and 4–5. g, (1) 5 × 5 array with outer and central cilia rotating clockwise, middle ring anticlockwise. g, (2) Anticlockwise flow between the outer and middle rings and clockwise flow between the middle ring and the central cilium. Experimental PIV flow fields (a (3)–g (3)), z-stack particle traces (a (4)–d (4)) and particle-trajectory tracking (e (4)–g (4)) all align with simulations a (2)–g (2). Red arrows in e–g highlight that flow directions are consistent with the particle-trajectory-tracking results. The gel microcilia actuators used in the flow experiments have a diameter of 10 µm and a height of 90 µm. The working solution is 0.00769 mol l⁻¹ NaCl. Scale bars, 200 µm (a (4)–c (4)); 150 µm (d (4)–g (4)).