Fluid transport at low Reynolds number with magnetically actuated artificial cilia

238

252

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 selfassemble 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.biomimetics | microfluidics | colloids | low Reynold's number | hydrodynamics E fficient pumping and mixing of fluids in microscopic channels is paramount in microfluidic applications (1, 2). Small characteristic dimensions of such devices result in very low Reynolds numbers and one encounters hydrodynamics that is conceptually different from the turbulent macroscopic world. As stated by Purcell's "scallop theorem," nonreciprocal motion is required for generation of fluid flow or directed swimming (3). This is clearly manifested in biological systems, for instance in bending waves of sperm tails or in corkscrew motion of bacterial flagella. Another example are cilia, flexible protrusions on the surface of many eukaryotic cells with a typical length of several micrometers. In humans, ciliated surfaces are found, for example, in the respiratory tract where they sweep mucus, or in the Fallopian tubes where they move an ovum to the uterus. The motion of the fluid above a ciliated surface is generated by periodic beating of cilia. Experimental observations have shown that the beating pattern of an individual cilium is asymmetric and composed of two phases: the effective stroke, during which the outstretched cilium propels the fluid like an oar, followed by the recovery stroke, when the bent cilium returns to the initial position sweeping along the surface in a way that produces as little backward flow as possible (4). Although each cilium can beat independently, cilia densely covering a surface synchronize their cycles and form metachronal waves, thus increasing their fluid pumping efficiency (5). It is believed that the metachronal waves occur as a result of hydrodynamical interactions between the cilia (6, 7).The efficiency of the ciliary pumping mechanism leads to the idea of using the same principle for designing artificial cilia that act as microscale pumps and mixers. An important step towards biomimetic cilia was made by Darnton et al., who created a bacterial carpet by attaching bacteria to a solid surface (8). Due to symmetric rotation and wea...

Section: Materials and Techniquesmentioning

confidence: 99%

“…In the presence of a wall, we follow the approach from ref. 21 and calculate the off-diagonal mobility matrix elements as…”

Section: Materials and Techniquesmentioning

confidence: 99%

Self-assembled artificial cilia

Vilfan

Potočnik²,

Kavčič³

et al. 2010

238

252

“…For many cilia arrays, a wave-like pattern has been found and described, which is called a metachronal wave (MCW) (10). Biomimetic systems of externally actuated semiflexible strings, like chains of magnetic beads, have been proposed to use the cilia propulsion mechanism in artificial nanomachines and microfluidic devices (11)(12)(13)(14)(15)(16)(17).Theoretical approaches to investigate hydrodynamic interactions between cilia and the formation of metachronal waves fall into three categories: (i) highly simplified model systems, designed to elucidate the mechanism of hydrodynamic synchronization of many active agents (18-23); (ii) models of an actively driven semiflexible filament, which mimic the beat of a real cilium (24-27); and (iii) models of a filament, with a beat shape obtained from maximizing the pumping efficiency (28,29).The first class of models consists either of rotors-spheres orbiting on quasi-elliptical trajectories near a wall (19-22)-or rowers-spheres that oscillate on a line with different hydrodynamic radii in the two directions of motion (18, 23)-in both cases under a constant driving force. Two rotors have been found to show asynchronous dynamics-taken as an indication for metachronal coordination-if their distance is close enough or their relative orientation is perpendicular to the beat direction (19).…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Emergence of metachronal waves in cilia arrays

Elgeti

Gompper

2013

340

374

Propulsion by cilia is a fascinating and universal mechanism in biological organisms to generate fluid motion on the cellular level. Cilia are hair-like organelles, which are found in many different tissues and many uni-and multicellular organisms. Assembled in large fields, cilia beat neither randomly nor completely synchronously-instead they display a striking self-organization in the form of metachronal waves (MCWs). It was speculated early on that hydrodynamic interactions provide the physical mechanism for the synchronization of cilia motion. Theory and simulations of physical model systems, ranging from arrays of highly simplified actuated particles to a few cilia or cilia chains, support this hypothesis. The main questions are how the individual cilia interact with the flow field generated by their neighbors and synchronize their beats for the metachronal wave to emerge and how the properties of the metachronal wave are determined by the geometrical arrangement of the cilia, like cilia spacing and beat direction. Here, we address these issues by large-scale computer simulations of a mesoscopic model of 2D cilia arrays in a 3D fluid medium. We show that hydrodynamic interactions are indeed sufficient to explain the self-organization of MCWs and study beat patterns, stability, energy expenditure, and transport properties. We find that the MCW can increase propulsion velocity more than 3-fold and efficiency almost 10-fold-compared with cilia all beating in phase. This can be a vital advantage for ciliated organisms and may be interesting to guide biological experiments as well as the design of efficient microfluidic devices and artificial microswimmers.active matter | mesoscale hydrodynamics | dynamical self-organization F luid transport and locomotion due to motile cilia are ubiquitous phenomena in biological organisms on the cellular level (1, 2). Motile cilia are found in many different tissues-from the brain (3) to the lung and the oviduct-and in many uni-and multicellular organisms-from Clamydomonas (4) and Volvox (5, 6) algae to Paramecium. Motile cilia on the surface of a cell perform an active whip-like motion, which propels the fluid along the surface of cells and tissues. In motile cilia, the beat consists of a fast power stroke in which the cilium has an elongated shape and a slower recovery stroke in which the cilium is curved and closer to the cell surface (Fig. 1A). Due to their typical size in the range of 5-20 μm length and 0.25-1.0 μm thickness, the dynamics of cilia in a fluid are dominated by the balance of force generated by motor proteins (7,8) and fluid viscosity and are thus characterized by small-Reynolds-number hydrodynamics (9). Cilia sometimes act together in pairs, such as in the breast-stroke-like motion of Clamydomonas (4), but much more often in large arrays, such as on the surface of Paramecium and Opalina or the tissue lining the airways of the lung. In all these cases, the beat of different cilia is not random, but strongly synchronized. For many cilia arrays, a wave-like pa...

“…Microfluidics is a rapidly developing field with great potential significance, promising a miniaturized "lab-ona-chip" for biological analysis and the synthesis of chemicals. Achieving this goal will require innovative technologies for the effective manipulation of fluids in microfluidic systems.A number of methods for the propulsion of fluids with artificial cilia systems have been the subject of recent computational studies (15)(16)(17)(18)(19). Experimentally, a variety of systems at different scales have demonstrated cilia-like actuation based on piezo-driven stage motion (20), substrate swelling (21), linked magnetic beads (22), liquid crystal elastomers (23), self-oscillating gels (24), and electron beam deflection (25).…”

mentioning

confidence: 99%

Biomimetic cilia arrays generate simultaneous pumping and mixing regimes

Shields

Fiser

Evans

et al. 2010

218

227

Living systems employ cilia to control and to sense the flow of fluids for many purposes, such as pumping, locomotion, feeding, and tissue morphogenesis. Beyond their use in biology, functional arrays of artificial cilia have been envisaged as a potential biomimetic strategy for inducing fluid flow and mixing in lab-on-a-chip devices. Here we report on fluid transport produced by magnetically actuated arrays of biomimetic cilia whose size approaches that of their biological counterparts, a scale at which advection and diffusion compete to determine mass transport. Our biomimetic cilia recreate the beat shape of embryonic nodal cilia, simultaneously generating two sharply segregated regimes of fluid flow: Above the cilia tips their motion causes directed, long-range fluid transport, whereas below the tips we show that the cilia beat generates an enhanced diffusivity capable of producing increased mixing rates. These two distinct types of flow occur simultaneously and are separated in space by less than 5 μm, approximately 20% of the biomimetic cilium length. While this suggests that our system may have applications as a versatile microfluidics device, we also focus on the biological implications of our findings. Our statistical analysis of particle transport identifying an enhanced diffusion regime provides novel evidence for the existence of mixing in ciliated systems, and we demonstrate that the directed transport regime is Poiseuille-Couette flow, the first analytical model consistent with biological measurements of fluid flow in the embryonic node.biomimetics | embryonic nodal cilia | hydrodynamics | low Reynold's number T he cilium is a biological structure unique in its ability to manipulate and sense its fluid environment (1, 2). Research in the last decade has implicated cilia dysfunction in a wide range of human pathologies (3) and has shown that cilia perform an array of unexpected biological functions (4-6) beyond traditional roles such as the clearance of mucus and pathogens from the airways. For example, embryonic nodal cilia drive a fluid flow that plays a key role in the embryogenesis of vertebrate organisms by generating an asymmetric morphogen concentration (7), and cerebrospinal flows produced by arrays of cilia direct cell traffic in the brain (8). Yet, while the role of directed transport within such systems is being explored, the presence of cilia-generated mixing has only recently engendered speculation (9, 10).Flagellar mixing has been shown to be essential to the health of some microorganisms (11,12). More broadly, cilia-induced mixing could alter rates and efficacies of diverse fluid-mediated processes such as biochemical signaling, regulation, chemotaxis, and chemosensation. In addition, the relationship between vortical flows near the cilia and the directed transport they produce is not well understood for ciliated systems, such as the embryonic node where mixing could affect biochemical signaling that has been shown critical to the establishment of vertebrate left-right body asymmetry ...