Magnetic Cilia with Programmable Beating Patterns for Vortex-Driven Mixing in Microfluidics

Abstract

Artificial cilia are widely employed in microfluidic platforms, where their beating motion is harnessed to emulate the fluid transport capabilities of natural motile cilia. In particular, metachronal beating, characterized by phase-shifted motion among adjacent cilia, has proven to be effective for directional fluid transport. However, its potential for micromixing remains limited due to its inherently planar wave propagation, which offers room for improvement in generating strong vortices. To address this, three magnetically actuated artificial cilia carpets are fabricated with identical structural designs featuring spatially varied cilia orientations to embed controlled orientational asymmetry. To realize distinct motion patterns, each carpet is magnetized with a single, unique magnetization profile such that one carpet corresponds to one beating mode, including synchronous, symplectic metachronal, or antiplectic metachronal, and is actuated externally to generate its respective motion. For demonstration purposes, two different experiments are conducted, including micromixing and photocatalytic dye degradation. The results reveal that metachronal motion alone is insufficient to enhance micromixing, thereby highlighting the need for integration with orientational asymmetry. Compared to the aligned cilia carpet (control), superior mixing efficiency of 87% and a 3-fold enhancement in dye degradation are observed in the inclined cilia carpet actuated with antiplectic metachronal motion. This enhanced hydrodynamic activity is further substantiated through μPIV experiments. These findings define metachrony as a dual-function paradigm for both fluid propulsion and vortex-enabled microfluidic mixing.

1

Design, fabrication, actuation modes, and applications of magnetic cilia arrays for microfluidic flow manipulation. (a) Schematic illustrations of individual magnetic cilia and the fabricated two distinct cilia carpet configurations. (i,ii) Geometric features of a single cilium composed of magnetic (NdFeB-PDMS) and nonmagnetic (PDMS) segments, and (iii,iv) Design I with uniformly vertical cilia and Design II with inclined cilia forming a gradient of inclination angles from 90° to 11.25°. (b) Step-by-step fabrication process of artificial cilia arrays featuring a controlled 1:1 length ratio between magnetic and nonmagnetic (PDMS) segments. (i) CNC micromilling of the mold cavity from an acrylic sheet. (ii) Precise masking of the PDMS segment using an acrylic shutter plate, followed by pouring the magnetic composite into the exposed cavity and partial curing. (iii) Removing the shutter plate and subsequent filling of the remaining cavity with PDMS to form the nonmagnetic segment. (iv) Thermal curing of the complete cilia structure on a hot plate. (v) Final demolding of the bilayer artificial cilia array from the mold. (c) Three distinct actuation modes of two different designs of magnetic cilia array that were encoded during the magnetization process. Specifically, mode Δψ = 0 represents the synchronized beating pattern that was preprogrammed by employing a planar magnetization template. Modes Δψ = +π/4 and Δψ = −π/4 represent the antiplectic and symplectic metachronal beating patterns, respectively, that were encoded by employing a circular template. (d) Schematic of the experimental setup that was employed for the fluid mixing embedded with magnetic cilia carpets. (e) Schematic of the photocatalytic degradation experiment by employing Ti₃C₂ as an adsorbent under cyclic illumination.

2

Characterization of single and collective artificial cilia motion dynamics under three distinct actuation modes. (a) Schematic illustration of the fundamental motion of a single artificial cilium under a rotating magnetic field, comprising (i) the magnetic (effective) stroke, where the cilium was deflected by an external magnetic field, and (ii) the elastic (recovery) stroke, where it was passively returned to its initial configuration due to elastic restoring forces. (b) Experimental quantification of spatiotemporal motion characteristics of three representative cilia (n = 3, 4, and 5) out of eight in the carpet for all different actuation modes. Note that this analysis was performed by employing the aligned cilia configuration as a representative structure for characterizing fundamental motion dynamics. The top panels show the variation in interciliary spacing between adjacent cilia tips (d _x ^tip), while the lower panels present the x-position of cilia tips (x ^tip) during one full actuation cycle. Shaded regions denote the magnetic stroke (gray) and elastic stroke (yellow). Mode Δψ = 0 was observed to exhibit synchronized, nonreciprocal beating with a constant value of d _x ^tip (representing a uniform displacement across cilia). In contrast, mode Δψ = +π/4 demonstrates antiplectic metachronal wave propagation (distal-to-proximal) with temporally staggered tip displacement and a decrease in the value of d _x ^tipduring the elastic stroke. Meanwhile, mode Δψ = −π/4 shows symplectic metachronal motion (proximal-to-distal) with a reversed displacement sequence and an increase in the value of d _x ^tip during the elastic stroke. The error bar represents a unit standard deviation in both directions, calculated from the results of three independent experiments. (c) Representative experimental snapshots of magnetic cilia carpet (aligned cilia configuration) at selected time points during the beating cycle for each mode, which qualitatively validates the observed changes in interciliary spacing (between cilia n = 3 and n = 4) (d _x ^tip) described in panel (b). These images highlight the differences in local cilia density during actuation, with mode Δψ = +π/4 enhancing the fluid-contact area during recovery, while mode Δψ = −π/4 was observed to reduce it. The scale bar represents 1 mm. (d). This figure shows the relationship between the programmed (or magnetized Δφ) and observed phase differences (ΔΦ) for different actuation modes. The error bar represents a unit standard deviation in both directions, calculated from the results of three independent experiments.

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Analysis of mixing performance associated with aligned cilia array configuration and its respective hydrodynamic behavior. (a) A comparison of mixing efficiency associated with aligned cilia under different actuation modes. (i) Illustration of the temporal evolution of mixing efficiency over 60 s for aligned cilia that was actuated under all the modes. Mode Δψ = 0 was observed to reach the highest mixing efficiency (84% at 60 s) compared to mode Δψ = +π/4 (75%) and mode Δψ = −π/4 (71%), suggesting that synchronized motion was more effective for mixing in this configuration. The error bar represents a unit standard deviation in both directions, calculated from the results of three independent experiments. (ii) Representative snapshots of the dye distribution within the mixing chamber at t = 0 s (initial condition) and at t = 60 s for each actuation mode. The scale bar represents 5 mm. (b) The ensemble-averaged shear stress distribution maps for selected actuation modes. (i) Shear stress distribution map for aligned cilia/Δψ = 0, representing the ensemble average over 18 actuation cycles. The maximum shear stress for mode Δψ = 0 was observed to reach 35 mPa. (ii) The maximum shear stress for mode Δψ = −π/4 was observed to be 22 mPa.

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Analysis of mixing performance associated with inclined cilia array configuration and its respective hydrodynamic behavior. (a) The temporal evolution of mixing efficiency over 60 s for inclined cilia array configuration, actuated under mode Δψ = 0 and mode Δψ = +π/4, is illustrated. It was observed that after 60 s, inclined cilia/Δψ = +π/4 achieved a maximum mixing efficiency of 87%, whereas inclined cilia/Δψ = 0 reached 78%. Until 30 s, aligned cilia/Δψ = 0 was observed to exhibit superior performance compared to inclined cilia, however, beyond this point, inclined cilia/Δψ = +π/4 was observed to exhibit a modest improvement, ultimately surpassing the performance of aligned cilia. The error bar represents a unit standard deviation in both directions, calculated from the results of three independent experiments. Further, the representative experimental snapshots that were captured at 60 s are provided in the inset. The scale bar represents 5 mm. (b) Based on μPIV measurements, circulation values were computed over a circular region of interest (inset). A circulation range of 1.73 × 10³ mm²/s to 1.95 × 10³ mm²/s, with a mean of 1.85 × 10³ mm²/s, was measured for inclined cilia/Δψ = +π/4 actuation. In comparison, an average circulation of 1.6 × 10³ mm²/s was obtained for aligned cilia/Δψ = 0.

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The photocatalytic dye degradation performance under different ciliary configurations and actuation modes. (a) The temporal evolution of the normalized MB dye concentration (C/C ₀) is depicted over 150 min under various artificial cilia configurations and actuation modes, as well as for a control group (Ti₃C₂ without artificial cilia). The combination of inclined cilia/Δψ = +π/4 was observed to demonstrate the highest degradation efficiency, with the C/C₀ value reduced to 0.53 ± 0.01 after 120 min of illumination (47% degradation). In contrast, the least dynamic actuation (mode Δψ = −π/4) applied to both designs resulted in comparatively lower degradation. The control group exhibited the lowest degradation efficiency (C/C ₀ = 0.83 ± 0.02 after 120 min, 17% degradation). The error bar represents a unit standard deviation in both directions, calculated from the results of three independent experiments. (b) The temporal evolution of (−ln­(C/C ₀)) is plotted against time to analyze the reaction kinetics based on a pseudo-first-order model. Linear regression analysis was performed to determine the apparent rate constant “k” for each experimental condition. The lowest rate constant (0.0013 min^–1) was determined for the control case. The highest rate constant (0.0046 min^–1) was exhibited by inclined cilia/Δψ = +π/4, which was approximately 3.5 times greater than the control. Aligned cilia/Δψ = 0 yielded a slightly lower rate constant (0.0042 min^–1). The least dynamic actuation (mode Δψ = −π/4) applied to both designs resulted in relatively reduced degradation rates. These kinetic findings were consistent with the observed degradation efficiencies in (a), highlighting the significant enhancement in the reaction rate achieved by the idealized cilia configuration and actuation mode.