Fluid flow due to collective non-reciprocal motion of symmetrically-beating artificial cilia

Metachronal Motion of Biological and Artificial Cilia

Cilia are slender, hair-like cell protrusions that are present ubiquitously in the natural world. They perform essential functions, such as generating fluid flow, propulsion, and feeding, in organisms ranging from protozoa to the human body. The coordinated beating of cilia, which results in wavelike motions known as metachrony, has fascinated researchers for decades for its role in functions such as flow generation and mucus transport. Inspired by nature, researchers have explored diverse materials for the fabrication of artificial cilia and developed several methods to mimic the metachronal motion observed in their biological counterparts. In this review, we will introduce the different types of metachronal motion generated by both biological and artificial cilia, the latter including pneumatically, photonically, electrically, and magnetically driven artificial cilia. Furthermore, we review the possible applications of metachronal motion by artificial cilia, focusing on flow generation, transport of mucus, particles, and droplets, and microrobotic locomotion. The overall aim of this review is to offer a comprehensive overview of the metachronal motions exhibited by diverse artificial cilia and the corresponding practical implementations. Additionally, we identify the potential future directions within this field. These insights present an exciting opportunity for further advancements in this domain.

Programmable metachronal motion of closely packed magnetic artificial cilia

Despite recent advances in artificial cilia technologies, the application of metachrony, which is the collective wavelike motion by cilia moving out-of-phase, has been severely hampered by difficulties in controlling closely packed artificial cilia at micrometer length scales. Moreover, there has been no direct experimental proof yet that a metachronal wave in combination with fully reciprocal ciliary motion can generate significant microfluidic flow on a micrometer scale as theoretically predicted. In this study, using an in-house developed precise micro-molding technique, we have fabricated closely packed magnetic artificial cilia that can generate well-controlled metachronal waves. We studied the effect of pure metachrony on fluid flow by excluding all symmetry-breaking ciliary features. Experimental and simulation results prove that net fluid transport can be generated by metachronal motion alone, and the effectiveness is strongly dependent on cilia spacing. This technique not only offers a biomimetic experimental platform to better understand the mechanisms underlying metachrony, it also opens new pathways towards advanced industrial applications.

Miniaturized metachronal magnetic artificial cilia

Biological cilia, hairlike organelles on cell surfaces, often exhibit collective wavelike motion known as metachrony, which helps generating fluid flow. Inspired by nature, researchers have developed artificial cilia as microfluidic actuators, exploring several methods to mimic the metachrony. However, reported methods are difficult to miniaturize because they require either control of individual cilia properties or the generation of a complex external magnetic field. We introduce a concept that generates metachronal motion of magnetic artificial cilia (MAC), even though the MAC are all identical, and the applied external magnetic field is uniform. This is achieved by integrating a paramagnetic substructure in the substrate underneath the MAC. Uniquely, we can create both symplectic and antiplectic metachrony by changing the relative positions of MAC and substructure. We demonstrate the flow generation of the two metachronal motions in both high and low Reynolds number conditions. Our research marks a significant milestone by breaking the size limitation barrier in metachronal artificial cilia. This achievement not only showcases the potential of nature-inspired engineering but also opens up a host of exciting opportunities for designing and optimizing microsystems with enhanced fluid manipulation capabilities.

Mucociliary clearance affected by mucus-periciliary interface stimulations using analytical solution during cough and sneeze

Assessment of mucus velocity variations under different conditions including viscosity variation and boundary conditions is useful to develop mucosal-based medical treatments. This paper deals with the analytical investigation of mucus-periciliary velocities under mucus-periciliary interface movements and mucus viscosity variations. The results for mucus velocity show that there is no difference between the two cases under the free-slip condition. Therefore, power-law mucus can be substituted with a high viscosity Newtonian fluid since the upper boundary of the mucus layer is exposed to the free-slip condition. However, when the upper boundary of the mucus layer is under nonzero shear stress levels, including cough or sneeze, the assumption of a high viscosity Newtonian mucus layer is invalid. Moreover, mucus viscosity variations are investigated for both Newtonian and power-law mucus layers under sneeze and cough to propose a mucosal-based medical treatment. The results indicate by varying mucus viscosity up to a critical value, the direction of mucus movement changes. The critical values of viscosity in sneezing and coughing for Newtonian and power-law mucus layers are 10-4 and 5 × 10-5 and 0.0263 and 006.024 m2 s-1, respectively. Therefore, the pathogen entry into the respiratory system can be prevented by varying mucus viscosity during sneeze and cough.

Spontaneous phase coordination and fluid pumping in model ciliary carpets

Ciliated tissues, such as in the mammalian lungs, brains, and reproductive tracts, are specialized to pump fluid. They generate flows by the collective activity of hundreds of thousands of individual cilia that beat in a striking metachronal wave pattern. Despite progress in analyzing cilia coordination, a general theory that links coordination and fluid pumping in the limit of large arrays of cilia remains lacking. Here, we conduct in silico experiments with thousands of hydrodynamically interacting cilia, and we develop a continuum theory in the limit of infinitely many independently beating cilia by combining tools from active matter and classical Stokes flow. We find, in both simulations and theory, that isotropic and synchronized ciliary states are unstable. Traveling waves emerge regardless of initial conditions, but the characteristics of the wave and net flows depend on cilia and tissue properties. That is, metachronal phase coordination is a stable global attractor in large ciliary carpets, even under finite perturbations to cilia and tissue properties. These results support the notion that functional specificity of ciliated tissues is interlaced with the tissue architecture and cilia beat kinematics and open up the prospect of establishing structure to function maps from cilium-level beat to tissue-level coordination and fluid pumping.

Microscopic artificial cilia - a review

Cilia are microscopic hair-like external cell organelles that are ubiquitously present in nature, also within the human body. They fulfill crucial biological functions: motile cilia provide transportation of fluids and cells, and immotile cilia sense shear stress and concentrations of chemical species. Inspired by nature, scientists have developed artificial cilia mimicking the functions of biological cilia, aiming at application in microfluidic devices like lab-on-chip or organ-on-chip. By actuating the artificial cilia, for example by a magnetic field, an electric field, or pneumatics, microfluidic flow can be generated and particles can be transported. Other functions that have been explored are anti-biofouling and flow sensing. We provide a critical review of the progress in artificial cilia research and development as well as an evaluation of its future potential. We cover all aspects from fabrication approaches, actuation principles, artificial cilia functions - flow generation, particle transport and flow sensing - to applications. In addition to in-depth analyses of the current state of knowledge, we provide classifications of the different approaches and quantitative comparisons of the results obtained. We conclude that artificial cilia research is very much alive, with some concepts close to industrial implementation, and other developments just starting to open novel scientific opportunities.

Morphological Control of Cilia-Inspired Asymmetric Movements Using Nonlinear Soft Inflatable Actuators

Soft robotic systems typically follow conventional control schemes, where actuators are supplied with dedicated inputs that are regulated through software. However, in recent years an alternative trend is being explored, where the control architecture can be simplified by harnessing the passive mechanical characteristics of the soft robotic system. This approach is named “morphological control”, and it can be used to decrease the number of components (tubing, valves and regulators) required by the controller. In this paper, we demonstrate morphological control of bio-inspired asymmetric motions for systems of soft bending actuators that are interconnected with passive flow restrictors. We introduce bending actuators consisting out of a cylindrical latex balloon in a flexible PVC shell. By tuning the radii of the tube and the shell, we obtain a nonlinear relation between internal pressure and volume in the actuator with a peak and valley in pressure. Because of the nonlinear characteristics of the actuators, they can be assembled in a system with a single pressure input where they bend in a discrete, preprogrammed sequence. We design and analyze two such systems inspired by the asymmetric movements of biological cilia. The first replicates the swept area of individual cilia, having a different forward and backward stroke, and the second generates a travelling wave across an array of cilia.

Metachronal motion across scales: current challenges and future directions

Metachronal motion is used across a wide range of organisms for a diverse set of functions. However, despite its ubiquity, analysis of this behavior has been difficult to generalize across systems. Here we provide an overview of known commonalities and differences between systems that use metachrony to generate fluid flow. We also discuss strategies for standardizing terminology and defining future investigative directions that are analogous to other established subfields of biomechanics. Lastly, we outline key challenges that are common to many metachronal systems, opportunities that have arisen due to the advent of new technology (both experimental and computational), and next steps for community development and collaboration across the nascent network of metachronal researchers.

Metachronal μ-Cilia for On-Chip Integrated Pumps and Climbing Robots

Biological cilia often perform metachronal motion, that is, neighboring cilia move out of phase creating a travelling wave, which enables highly efficient fluid pumping and body locomotion. Current methods for creating metachronal artificial cilia suffer from the complex design and sophisticated actuation schemes. This paper demonstrates a simple method to realize metachronal microscopic magnetic artificial cilia (μMAC) through control over the paramagnetic particle distribution within the μMAC based on their tendency to align with an applied magnetic field. Actuated by a 2D rotating uniform magnetic field, the metachronal μMAC enable strong microfluidic pumping and soft robot locomotion. The metachronal μMAC induce twice the pumping efficiency and 3 times the locomotion speed of synchronously moving μMAC. The ciliated soft robots show an unprecedented slope climbing ability (0 to 180°), and they display strong cargo-carrying capacity (>10 times their own weight) in both dry and wet conditions. These findings advance the design of on-chip integrated pumps and versatile soft robots, among others.

Metachronal Actuation of Microscale Magnetic Artificial Cilia

Biological cells often interact with the environment through carpets of microscopic hair-like cilia. These elastic structures are known to beat in a synchronized wavy fashion called metachronal motion to produce fluid transport. Metachronal motion emerges due to a phase difference between beating cycles of neighboring cilia and appears as traveling waves propagating along the ciliary carpet. We demonstrate submerged in water microscale magnetic cilia that are externally actuated to beat in a metachronal fashion. Two approaches are used to induce coordinated phase differences among the beating cilia. In the first case, we fabricate cilia with an imposed gradient of geometrical properties that are subject to a rotating uniform magnetic field. In the second scenario, a ciliary array is composed of identical cilia that experience a magnetic field that varies spatiotemporally. We demonstrate that magnetic cilia can achieve symplectic, antiplectic, and leoplectic metachrony.

Metachronal actuation of microscopic magnetic artificial cilia generates strong microfluidic pumping

Biological cilia that generate fluid flow or propulsion are often found to exhibit a collective wavelike metachronal motion, i.e. neighboring cilia beat slightly out-of-phase rather than synchronously. Inspired by this observation, this article experimentally demonstrates that microscopic magnetic artificial cilia (μMAC) performing a metachronal motion can generate strong microfluidic flows, though, interestingly, the mechanism is different from that in biological cilia, as is found through a systematic experimental study. The μMAC are actuated by a facile magnetic setup, consisting of an array of rod-shaped magnets. This arrangement imposes a time-dependent non-uniform magnetic field on the μMAC array, resulting in a phase difference between the beatings of adjacent μMAC, while each cilium exhibits a two-dimensional whip-like motion. By performing the metachronal 2D motion, the μMAC are able to generate a strong flow in a microfluidic chip, with velocities of up to 3000 μm s^-1 in water, which, different from biological cilia, is found to be a result of combined metachronal and inertial effects, in addition to the effect of asymmetric beating. The pumping performance of the metachronal μMAC outperforms all previously reported microscopic artificial cilia, and is competitive with that of most of the existing microfluidic pumping methods, while the proposed platform requires no physical connection to peripheral equipment, reduces the usage of reagents by minimizing "dead volumes", avoids undesirable electrical effects, and accommodates a wide range of different fluids. The 2D metachronal motion can also generate a flow with velocities up to 60 μm s^-1 in pure glycerol, where Reynolds number is less than 0.05 and the flow is primarily caused by the metachronal motion of the μMAC. These findings offer a novel solution to not only create on-chip integrated micropumps, but also design swimming and walking microrobots, as well as self-cleaning and antifouling surfaces.

Magnetically-actuated artificial cilium: a simple theoretical model

We propose a theoretical model for a magnetically-actuated artificial cilium in a fluid environment and investigate its dynamical behaviour, using both analytical calculations and numerical simulations. The cilium consists of a spherical soft magnet, a spherical hard magnet, and an elastic spring that connects the two magnetic components. Under a rotating magnetic field, the cilium exhibits a transition from phase-locking at low frequencies to phase-slipping at higher frequencies. We study the dynamics of the magnetic cilium in the vicinity of a wall by incorporating its hydrodynamic influence, and examine the efficiency of the actuated cilium in pumping viscous fluids. This cilium model can be helpful in a variety of applications such as transport and mixing of viscous solutions at small scales and fabricating microswimmers.

Microfluidic viscometry using magnetically actuated micropost arrays

Here we describe development of a microfluidic viscometer based on arrays of magnetically actuated micro-posts. Quantitative viscosities over a range of three orders of magnitude were determined for samples of less than 20 μL. This represents the first demonstration of quantitative viscometry using driven flexible micropost arrays. Critical to the success of our system is a comprehensive analytical model that includes the mechanical and magnetic properties of the actuating posts, the optical readout, and fluid-structure interactions. We found that alterations of the actuator beat shape as parameterized by the dimensionless “sperm number” must be taken into account to determine the fluid properties from the measured actuator dynamics. Beyond our particular system, the model described here can provide dynamics predictions for a broad class of flexible microactuator designs. We also show how the model can guide the design of new arrays that expand the accessible range of measurements.

Metachronal motion of artificial magnetic cilia

Organisms use hair-like cilia that beat in a metachronal fashion to actively transport fluid and suspended particles. Metachronal motion emerges due to a phase difference between beating cycles of neighboring cilia and appears as traveling waves propagating along ciliary carpet. In this work, we demonstrate biomimetic artificial cilia capable of metachronal motion. The cilia are micromachined magnetic thin filaments attached at one end to a substrate and actuated by a uniform rotating magnetic field. We show that the difference in magnetic cilium length controls the phase of the beating motion. We use this property to induce metachronal waves within a ciliary array and explore the effect of operation parameters on the wave motion. The metachronal motion in our artificial system is shown to depend on the magnetic and elastic properties of the filaments, unlike natural cilia, where metachronal motion arises due to fluid coupling. Our approach enables an easy integration of metachronal magnetic cilia in lab-on-a-chip devices for enhanced fluid and particle manipulations.

On-chip signal amplification of magnetic bead-based immunoassay by aviating magnetic bead chains

In this work, a Lab-on-a-Chip (LOC) platform is used to electromagnetically actuate magnetic bead chains for an enhanced immunoassay. Custom-made electromagnets generate a magnetic field to form, rotate, lift and lower the magnetic bead chains (MBCs). The cost-effective, disposable LOC platform was made with a polymer substrate and an on-chip electrochemical sensor patterned via the screen-printing process. The movement of the MBCs is controlled to improve the electrochemical signal up to 230% when detecting beta-type human chorionic gonadotropin (β-hCG). Thus, the proposed on-chip MBC-based immunoassay is applicable for rapid, qualitative electrochemical point-of-care (POC) analysis.

Individually Controllable Magnetic Cilia: Mixing Application

This paper introduces a new design for individually controlled magnetic artificial cilia for use in fluid devices and specifically intended to improve the mixing in DNA microarray experiments. The design has been implemented using a low-cost prototype that can be fabricated using polydimethylsiloxane (PDMS) and off-the-shelf parts and achieves large cilium deflections (59% of the cilium length). The device's performance is measured via a series of mixing experiments using different actuation patterns inspired by the blinking vortex theory. The experimental results, quantified using the relative standard deviation of the color when mixing two colored inks, show that exploiting the individual control leads to faster mixing (38% reduction in mixing time) than when operating the device in a simultaneous-actuation mode with the same average cilium beat frequency. Furthermore, the experimental results show an optimal beating pattern that minimizes the mixing time. The existence and character of this optimum is predicted by simulations using a blinking-vortex approach for 2D ideal flow, suggesting that the blinking-vortex model can be used to predict the effect of parameter variation on the experimental system.

Geometric pumping in autophoretic channels

Many microfluidic devices use macroscopic pressure differentials to overcome viscous friction and generate flows in microchannels. In this work, we investigate how the chemical and geometric properties of the channel walls can drive a net flow by exploiting the autophoretic slip flows induced along active walls by local concentration gradients of a solute species. We show that chemical patterning of the wall is not required to generate and control a net flux within the channel, rather channel geometry alone is sufficient. Using numerical simulations, we determine how geometric characteristics of the wall influence channel flow rate, and confirm our results analytically in the asymptotic limit of lubrication theory.

Swimming with stiff legs at low Reynolds number

Locomotion at low Reynolds number is not possible with cycles of reciprocal motion, an example being the oscillation of a single pair of rigid paddles or legs. Here, I demonstrate the possibility of swimming with two or more pairs of legs. They are assumed to oscillate collectively in a metachronal wave pattern in a minimal model based on slender-body theory for Stokes flow. The model predicts locomotion in the direction of the traveling wave, as commonly observed along the body of free-swimming crustaceans. The displacement of the body and the swimming efficiency depend on the number of legs, the amplitude, and the phase of oscillations. This study shows that paddling legs with distinct orientations and phases offers a simple mechanism for driving flow.

Microscale flow propulsion through bioinspired and magnetically actuated artificial cilia

Recent advances in microscale flow propulsion through bioinspired artificial cilia provide a promising alternative for lab-on-a-chip applications. However, the ability of actuating artificial cilia to achieve a time-dependent local flow control with high accuracy together with the elegance of full integration into the biocompatible microfluidic platforms remains remote. Driven by this motive, the current work has constructed a series of artificial cilia inside a microchannel to facilitate the time-dependent flow propulsion through artificial cilia actuation with high-speed (>40 Hz) circular beating behavior. The generated flow was quantified using micro-particle image velocimetry and particle tracking with instantaneous net flow velocity of up to 10(1 ) μm/s. Induced flow patterns caused by the tilted conical motion of artificial cilia constitutes efficient fluid propulsion at microscale. This flow phenomenon was further measured and illustrated by examining the induced flow behavior across the depth of the microchannel to provide a global view of the underlying flow propulsion mechanism. The presented analytic paradigms and substantial flow evidence present novel insights into the area of flow manipulation at microscale.

Emergence of polar order and cooperativity in hydrodynamically coupled model cilia

As a model of ciliary beat, we use two-state oscillators that have a defined direction of oscillation and have strong synchronization properties. By allowing the direction of oscillation to vary according to the interaction with the fluid, with a timescale longer than the timescale of synchronization, we show in simulations that several oscillators can align in a direction set by the geometrical configuration of the system. In this system, the alignment depends on the state of synchronization of the system, and is therefore linked to the beat pattern of the model cilia. By testing various configurations from two to 64 oscillators, we deduce empirically that, when the synchronization state of neighbouring oscillators is in phase, the angles of the oscillators align in a configuration of high hydrodynamic coupling. In arrays of oscillators that break the planar symmetry, a global direction of alignment emerges reflecting this polarity. In symmetric configurations, where several directions are geometrically equivalent, the array still displays strong internal cooperative behaviour. It also appears that the shape of the array is more important than the lattice type and orientation in determining the preferred direction.

Generic flow profiles induced by a beating cilium

We describe a multipole expansion for the low-Reynolds-number fluid flows generated by a localized source embedded in a plane with a no-slip boundary condition. It contains 3 independent terms that fall quadratically with the distance and 6 terms that fall with the third power. Within this framework we discuss the flows induced by a beating cilium described in different ways: a small particle circling on an elliptical trajectory, a thin rod and a general ciliary beating pattern. We identify the flow modes present based on the symmetry properties of the ciliary beat.

High-performance microfluidic rectifier based on sudden expansion channel with embedded block structure

A high-performance microfluidic rectifier incorporating a microchannel and a sudden expansion channel is proposed. In the proposed device, a block structure embedded within the expansion channel is used to induce two vortex structures at the end of the microchannel under reverse flow conditions. The vortices reduce the hydraulic diameter of the microchannel and, therefore, increase the flow resistance. The rectification performance of the proposed device is evaluated by both experimentally and numerically. The experimental and numerical values of the rectification performance index (i.e., the diodicity, Di) are found to be 1.54 and 1.76, respectively. Significantly, flow rectification is achieved without the need for moving parts. Thus, the proposed device is ideally suited to the high pressure environment characteristic of most micro-electro-mechanical-systems (MEMS)-based devices. Moreover, the rectification performance of the proposed device is superior to that of existing valveless rectifiers based on Tesla valves, simple nozzle/diffuser structures, or cascaded nozzle/diffuser structures.

Fluid flow due to collective non-reciprocal motion of symmetrically-beating artificial cilia

Using a magneto-mechanical solid-fluid numerical model for permanently magnetic artificial cilia, we show that the metachronal motion of symmetrically beating cilia establishes a net pressure gradient in the direction of the metachronal wave, which creates a unidirectional flow. The flow generated is characterised as a function of the cilia spacing, the length of the metachronal wave, and a dimensionless parameter that characterises the relative importance of the viscous forces over the elastic forces in the cilia.