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By Jaap M J den Toonder, Patrick R Onck
The Royal Society of ChemistryCopyright © 2013 The Royal Society of Chemistry
All rights reserved.
JAAP DEN TOONDER AND PATRICK ONCK
1.1 Natural Cilia
Nature has devised many different ways of creating fluid flow, most of them for animal propulsion, that is, for flying or swimming. At larger scales, examples are the flapping wings of birds, and the waving tails of fishes. Flapping wings are also found at smaller scales in insects. At really small scales, typically for sub-millimetre sizes, a fluid manipulation mechanism used by nature is that by cilia or flagella.
Cilia can be viewed as small hairs or flexible rods, with a typical length between 2 and 15 µm. They cover the outer surface of micro-organisms, such as Paramecia, shown in Figure 1.1a. The length of Paramecia is about 100 µm, and its surface contains over 4000 cilia. These cilia move back and forth in a concerted manner, and are very effective in generating flow: the swimming speed of Paramecium, for example, can be approximately 1 mm s-1 (i.e. it can travel a distance of 10 times its own body length in a second).
An individual cilium moves in a particular, asymmetric manner, as illustrated in Figure 1.1b. It has a so-called effective stroke, during which the cilium is more or less straight, and its effect on the fluid is maximized. During the recovery stroke, its effect on the surrounding fluid is minimized since the cilium has a more curved shape. The micro-organism propulsion is in the direction opposite to the effective stroke. The movement of the cilium is always in a plane perpendicular to the surface during the effective stroke. The recovery stroke movement may lie in the same plane, but also in a plane perpendicular to the effective-stroke plane, so that the movement of a cilium may be truly three-dimensional (the latter is, in fact, the case for Paramecium). The beating frequency of the cilia, typically, is tens of hertz.
The collective movement of the cilia seems to occur in a concerted fashion. Neighbouring cilia move somewhat out of phase, so that a collective wave-like motion, going over the micro-organism's surface, takes place. It is interesting that this wave may travel either in the same direction as the swimming direction of the micro-organism (but opposite to the effective stroke; this is called an antiplectic metachronic wave, and occurs for Paramecium) or in the opposite direction (called symplectic metachronic wave behaviour). This is illustrated in Figure 1.1c. The origin, as well as the physiological reason, for this metachronic co-ordination is not yet completely understood.
Flagella have the same internal structure as cilia, but they are usually longer, typically between 20 and 100 µm, and they do not cover surfaces in large quantities, such as cilia, but as a single flagellum or with a few. Also, their movement is usually different from those of cilia. Instead of having an effective and a recovery stroke, a flagellum mostly makes a helical (cork-skrew) or wave-like motion. The best known example is the flagellum of spermatozoa. A microorganism that is classified as a flagellate by most authors, but as a ciliate by others, is Chlamydomonas (or green algae), shown in Figure 1.2. The length of its body is 10 µm, and it has two flagellates with a length of 10–15 µm. The flagella make an effective recovery stroke, beating with a frequency of about 50 Hz, giving the organism a swimming speed of 100 µm s-1. Interestingly, the beating pattern in Chlamydomonas can change from a typical ciliary beating to flagellar beating upon an external trigger such as intense light or Ca2+.
There are many different micro-organisms that make use of ciliary propulsion or fluid manipulation. Figure 1.3 depicts some of those that can be found in lakes and rivers. Note the scale bar on the right, representing a length of 1 mm.
Next to active cilia, which are used to induce movement, cilia are also used for sensing, for example of fluid flow, but also for detecting other physical and chemical signals. Both motile and non-motile cilia and flagella are present in the human body, at various locations and with various functions, as shown in Figure 1.4. For example, there are cilia in the cochlear, the inner ear, that contribute in detection of vibration caused by sound. As already mentioned, each spermatozoon swims by beating a flagellum. Also, the Fallopian tubes of females are covered with cilia that move the fertilized ovum from the ovary to the uterus, where the ovum attaches itself. Motile cilia are also present in the lining of human lungs and the windpipe (trachea), to sweep mucus and dirt out of the airways in order to avoid infections. More examples of cilia within the human body can be found in Ibanez-Tallon et al.
Motile cilia and flagella both have the same characteristic internal structure. The skeleton of a cilium (or flagella) is made up by a flexible cylindrical structure that is called the axoneme. Figure 1.5a schematically depicts the constituents of the axoneme, showing the structure that is so characteristic for all motile cilia and flagella. An electron micrograph of the cross section of a cilium can be seen in Figure 1.5b. Nine pairs of micro-tubules are arranged along the periphery, and one pair of micro-tubules is situated at the centre. Micro-tubules are biopolymer filaments, which, for example, can also be found in the cytoskeleton (the internal skeleton of cells). They are hollow rods approximately 25 nm in outer diameter and 14 nm inner diameter. For obvious reasons, the axoneme structure shown is known as the 9 + 2 axoneme.
The nine outer pairs of micro-tubules are connected by nexin links. Also, each of the outer pairs is linked to the central pair by a radial spoke. A closer inspection of the outer micro-tubules shows that they have side arms of proteins, called dyneins. These proteins are actually mechanical motors, and they are instrumental in the movement of the cilia.
Dyneins convert energy, which is released in the body by hydrolysis of ATP (adenosine triphosphate), into mechanical work by changing their molecular conformation. These successive conformational changes allow the molecule to take 'steps' along the micro-tubules in a certain direction. The outer dynein arms attached to the micro-tubule pairs are different in molecular structure than the inner dynein arms. The molecular structures are shown in Figure 1.6.
In the absence of ATP, the dyneins fixed to each peripheral micro-tubule pair are also attached to the adjacent micro-tubule pair. The presence and hydrolysis of ATP provokes the detachment, movement and re-attachment of the dyneins in such a way that the pairs of neighbouring micro-tubule pairs slide along each other, see Figure 1.6 (the dyneins indeed take steps along the micro-tubules). Since the micro-tubules are connected, through the nexin links and radial spokes, this gliding motion results in an overall bending of the cilium.
The details of the control of the beating of cilia are still not completely understood, and this is a topic of ongoing research. It is the combination of the properties of the molecular motors, their interaction with the elastic properties of the axoneme, as well as the hydrodynamic coupling with the surrounding fluid, that determines the typical ciliary movement characterized by their asymmetry in motion, their beat frequency, and their metachronic behaviour.
1.2 Low Reynolds Number Flows
The Reynolds number is the most important dimensionless number in fluid mechanics. It represents the ratio of the inertial forces to viscous forces in the flow, and is defined by:
Re = ρIL/μ (1.1)
in which U is a characteristic velocity scale, L is a characteristic length scale, ρ is the density of the fluid and m is its dynamic viscosity. The characteristic velocity and length scales are different for different problems. For a relatively simple and well defined flow, such as the flow through a cylindrical tube, the characteristic scales are easily defined: U is the mean flow velocity in the pipe and L is the pipe diameter. For more complex problems, the definition of the characteristic scales may be more difficult, and sometimes, the problem even cannot be described by just one single Reynolds number.
'Inertia' is the property of an object to remain at a constant velocity, unless an outside force acts on it. An object with a large inertia will resist strongly to a change in velocity, or in other words, it is difficult to start or stop its movement. An object with a small inertia, on the other hand, will almost instantaneously start or stop when acted upon by some external or internally generated force. Inertia of fluid flows is caused by nonlinear interactions within the flow field. These nonlinearities may cause instabilities in the flow to grow, and therefore the flow can become turbulent when inertial effects are dominant, that is, for large Reynolds numbers. For small Reynolds numbers, on the other hand, the flow will always be laminar. For pipe flow, the critical Reynolds number above which turbulence may exist is about 2000.
'Viscosity' is the resistance of a fluid to flow under the influence of an applied external force. It is the source of drag on objects moving through the fluid. For such an object, inertia strives to keep the object going, whereas viscosity tries to stop it.
Some characteristic Reynolds numbers for self-propelled organisms from nature are shown in Table 1.1. The characteristic length scale is the size of the organism, the characteristic velocity is its swimming speed. The density and viscosity are those of water, i.e. ρ = 1000 kg m-3 and μ = 1 mPa s or air, i.e. ρ = 1.2 kg m-3 and μ = 0.018 mPa s. We can see that the Reynolds numbers range from very large values, for a swimming whale, to extremely small values for swimming bacteria. That means that for a whale, inertial effects dominate, and thus, after stopping to swim, the whale will continue to move further, or 'coast' for a substantial distance and time. For a bacterium, on the other hand, inertial effects will not be important at all and viscous effects dominate, so that a bacterium will stop almost instantaneously.
Due to their small sizes, cilia in nature operate under low Reynolds number conditions, which are also called the Stokes flow regimes. This means that inertial effects are not important and the flow is dominated by viscous effects. Consequently, to generate any net flow, the motion of the cilia must be asymmetric, i.e. having a different forward trajectory compared to the backward trajectory during one beat cycle. This is the reason for the presence of an effective and a recovery stroke in natural cilia, as shown in Figure 1.1. If the motion was symmetric, fluid would just be displaced back and forth without any net flow, even in the case of temporal asymmetry (moving faster forwards than backwards).
1.3 Artificial Cilia: Micro-fluidics Applications
Micro-fluidics is the science and technology of manipulating and analysing fluid flow in structures of sub-millimetre dimensions. This field is particularly relevant for the development of lab-on-chip devices, which can be pictured as credit-card-sized fluidic systems containing tiny channels and chambers in which processes such as mixing and routing of the liquids, and separation, reaction, and detection of individual components (DNA, proteins, cells) present in these liquids are integrated. In this way, a conventional large-scale biomedical analysis laboratory is miniaturized and combined on a single chip. The typical cross-sectional dimensions of the micro-fluidic channels and structures are between 10 and 100 µm. An artist's impression of a lab-on-chip device is depicted in Figure 1.7.
Many different physical phenomena can be used to manipulate fluids on submillimetre scales. Small droplets can be manipulated by actively changing their surface tension, for instance using electrical potentials. Fluid can be transported through micro-channels by electro-osmosis, in which a spontaneously occurring charged surface layer is set into motion by an applied electrical field. Other physical principles that can be exploited in micro-fluidics are acoustic streaming, optical manipulation, dielectrophoresis, magnetophoresis and thermophoresis. Use has also been made of micro-fabricated valves to control flow in micro-fluidic channels.
A special challenge in micro-fluidic systems is to create efficient mixing flows. Due to the small channel sizes, the Reynolds number is generally small and flows are non-turbulent. On the other hand, the channel size is often too large for molecular diffusion to be effective in mixing within a reasonable time. To obtain efficient mixing, special strategies must therefore be followed. An approach is to create repeatedly stretching and folding flow patterns, leading to so-called chaotic advection that causes effective mixing. Nguyen and Wu have reviewed and classified the relatively large number of micro-mixers proposed in the literature. The existing micro-mixers can be divided into two general classes, namely passive and active micro-mixers. Passive micro-mixers do not require external energy, and the mixing process relies entirely on chaotic advection or diffusion. The effect is often achieved by special geometrical features like channel shape or corrugations on the channel walls. A well-known and elegant concept uses specially designed grooves or ridges on the channel walls, as described by Stroock et al. Active micro-mixers use the disturbance generated by an external field for the mixing process, and thus require external energy. Examples are the use of micro-machined magnetic-bar mixers, sinusoidal pressure pulses, electro-hydrodynamic forcing, AC electro-osmotic flow, and acoustic streaming.
A recent development, inspired by nature, is the use of artificialcilia to create pumping and/or mixing in micro-fluidic devices. Microscopic actuators resembling cilia, actuated to move under the influence of a number of different stimuli such as electric fields, magnetic fields, and even light, have been developed by a number of groups and shown to be capable of generating flow and mixing in micro-fluidic environments. The research on artificial cilia started about a decade ago, and is rapidly expanding. Next to being relevant for potential application in lab-on-a-chip devices, the work on artiticial cilia forms a beautiful example of how a biological system can form the successful basis for both scientific research and for technological applications.
1.4 This Book: An Overview of Artificial Cilia Research and Technologies
This book will give an overview of the research field of artificial cilia, a novel technology for controlling and sensing fluid flow at microscopic scales. The various chapters are clustered in three sections.
Section 1, 'Theoretical and numerical descriptions of artificial cilia', contains three chapters that describe various approaches to model artificial cilia and their interaction with the surrounding fluid. In each of the chapters, particular questions are addressed using the models. In Chapter 2, 'Numerical modelling for artificial cilia' by Holger Stark, a numerical model is introduced for artificial cilia based on a bead-spring chain with bending rigidity whose beads interact hydrodynamically. This is used to describe a super-paramagnetic filament actuated by an external magnetic field. The influence of two-dimensional versus three-dimensional motion of the cilium is investigated, as well as the effect of metachrony on the pumping performance of an array of artificial cilia.
Another approach is taken in Chapter 3, 'Computational design of magnetic artificial cilia' by Syed Khaderi, Jaap den Toonder and Patrick Onck. Using a coupled magneto-mechanical solid–fluid numerical model, artificial cilia are designed that can be realized using thin films consisting of a polymer matrix filled with magnetic nanoparticles, so that they can be actuated using an external magnetic field. The model is used to establish under what conditions (geometrical/mechanical/magnetic design, magnetic field control) a magnetic film will mimic the asymmetric motion of natural cilia and how the flow rates can be maximized using fluid inertia and out-of-phase beating.
Chapter 4, 'Modelling the interaction of active cilia with species in solution: from chemical reagents to microscopic particles' by Pratyush Dayal, Olga Kuksenok, Amitabh Bhattacharya, Gavin A. Buxton, O. Berk Usta and Anna C. Balazs, focuses on a different topic. A computational model is introduced that is used to study cilia formed from chemo-responsive gels, and assess their sensing and communication behaviour. As a second example, the transport of a microscopic particle is modelled via a regular array of beating elastic cilia, whose tips experience an adhesive interaction with the particle's surface. Conditions under which the particle can be 'released', 'propelled' or 'trapped' by the cilia array are investigated.
Excerpted from Artificial Cilia by Jaap M J den Toonder, Patrick R Onck. Copyright © 2013 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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