Synchronization of rotating helices by hydrodynamic interactions

Reichert, Michael; Stark, Holger

doi:10.1140/epje/i2004-10152-7

Cited by 140 publications

(144 citation statements)

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“…For a collection of free swimmers, such as microorganisms [8], hydrodynamic interactions have been shown to lead to instabilities [9,10] that can result in complex dynamical behaviors [10,11]. In the context of simple microswimmer models where hydrodynamic interactions coupled to internal degrees of freedom can be studied with minimal complexity, it has been shown that the coupling could result in complex dynamical behaviors such as oscillatory bound states between two swimmers [12], and collective many-body swimming phases [13,14].A particularly interesting aspect of such hydrodynamic coupling is the possibility of synchronization between different objects with cyclic motions [4,5,[15][16][17][18][19][20][21]. This effect has mostly been studied in simple systems such as two interacting objects or linear arrays and very little is known about possible many-body emergent behaviors of a large number of active objects with hydrodynamic coupling.…”

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confidence: 99%

“…A particularly interesting aspect of such hydrodynamic coupling is the possibility of synchronization between different objects with cyclic motions [4,5,[15][16][17][18][19][20][21]. This effect has mostly been studied in simple systems such as two interacting objects or linear arrays and very little is known about possible many-body emergent behaviors of a large number of active objects with hydrodynamic coupling.…”

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Synchronization and Collective Dynamics in a Carpet of Microfluidic Rotors

2010

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We study synchronization of an array of rotors on a substrate that are coupled by hydrodynamic interaction. Each rotor, which is modeled by an effective rigid body, is driven by an internal torque and exerts an active force on the surrounding fluid. The long-ranged nature of the hydrodynamic interaction between the rotors causes a rich pattern of dynamical behaviors including phase ordering and self-proliferating spiral waves. Our results suggest strategies for designing controllable microfluidic mixers using the emergent behavior of hydrodynamically coupled active components. PACS numbers: 87.19.rh,07.10.Cm,47.61.Ne,87.80.Fe,87.85.Qr Introduction. Microorganisms and the mechanical components of the cell motility machinery such as cilia and flagella operate in low Reynolds number conditions where hydrodynamics is dominated by viscous forces [1]. The medium thus induces a long-ranged hydrodynamic interaction between these active objects, which could lead to emergent many-body behaviors. Examples of such cooperative dynamical effects include sperms beating in harmony [2], metachronal waves in cilia [3][4][5], formation of bound states between rotating microorganisms [6], and flocking behavior of red blood cells moving in a capillary [7]. For a collection of free swimmers, such as microorganisms [8], hydrodynamic interactions have been shown to lead to instabilities [9,10] that can result in complex dynamical behaviors [10,11]. In the context of simple microswimmer models where hydrodynamic interactions coupled to internal degrees of freedom can be studied with minimal complexity, it has been shown that the coupling could result in complex dynamical behaviors such as oscillatory bound states between two swimmers [12], and collective many-body swimming phases [13,14].A particularly interesting aspect of such hydrodynamic coupling is the possibility of synchronization between different objects with cyclic motions [4,5,[15][16][17][18][19][20][21]. This effect has mostly been studied in simple systems such as two interacting objects or linear arrays and very little is known about possible many-body emergent behaviors of a large number of active objects with hydrodynamic coupling. For example, in a recent experiment [22], Darnton et al. observed chaotic flow patterns with complex vortices above a carpet of bacteria with their heads attached to a substrate and their flagella free to interact with the fluid (see also [23]). On the other hand, recent advances from micron-scale magnetically actuated tails [24] to synthetic molecular rotors [25] now allow fabrication of arrays of active tails that can stir up the fluid. It is therefore very important to explore the possible complexity of the phase behavior of such an actively stirred microfluidic system.Here, we consider a simple generic model of rotors [26] positioned on a regular 2D array on a substrate and study

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Synchronization and Collective Dynamics in a Carpet of Microfluidic Rotors

2010

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“…Although minimizing dissipation is not a general principle from which to derive dynamics, a growing body of work has identified requirements for synchronization within minimal models involving systems of rotating spheres or helices [4][5][6]. It is now known that oscillators with more than one degree of freedom or those with suitable internal forcing can be synchronized by hydrodynamics [6,7].…”

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Emergence of Synchronized Beating during the Regrowth of Eukaryotic Flagella

2011

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A fundamental issue in the biology of eukaryotic flagella is the origin of synchronized beating observed in tissues and organisms containing multiple flagella. Recent studies of the biflagellate unicellular alga Chlamydomonas reinhardtii provided the first evidence that the interflagellar coupling responsible for synchronization is of hydrodynamic origin. To investigate this mechanism in detail, we study here synchronization in Chlamydomonas as its flagella slowly regrow after mechanically induced self-scission. The duration of synchronized intervals is found to be strongly dependent on flagellar length. Analysis within a stochastic model of coupled phase oscillators is used to extract the length dependence of the interflagellar coupling and the intrinsic beat frequencies of the two flagella. Physical and biological considerations that may explain these results are proposed. DOI: 10.1103/PhysRevLett.107.148103 PACS numbers: 87.16.Qp, 05.45.Xt, 47.63.Àb, 87.18.Tt From unicellular organisms as small as a few microns to the largest vertebrates on Earth, we find groups of beating flagella or cilia that exhibit striking spatiotemporal organization. This may take the form of precise frequency and phase locking, as frequently found in the swimming of green algae [1], or beating with long-wavelength phase modulations known as metachronal waves, seen in ciliates such as Paramecium [2] and in our own respiratory systems. The remarkable similarity in the underlying molecular structure of flagella across the whole eukaryotic world leads naturally to the hypothesis that a similarly universal mechanism might be responsible for synchronization. Although this mechanism is poorly understood, one appealing hypothesis is that it results from hydrodynamic interactions between flagella.The role of hydrodynamics in synchronization has been the subject of intense theoretical investigation in the half century since the seminal work of Taylor [3] showed that phase synchronization of nearby undulating sheets minimizes viscous dissipation. Although minimizing dissipation is not a general principle from which to derive dynamics, a growing body of work has identified requirements for synchronization within minimal models involving systems of rotating spheres or helices [4][5][6]. It is now known that oscillators with more than one degree of freedom or those with suitable internal forcing can be synchronized by hydrodynamics [6,7]. Various levels of coordination are also found with more realistic models of flagella [8], which rely necessarily on simplified internal driving of the filaments. Nevertheless, these complex models yield important clues to the generation and regulation of flagellar motion [9].Experimental progress has lagged behind that of theory, due in large part to the challenge of finding a sufficiently simple model system that can be studied under an appropriately broad set of experimental conditions. But recent work [10] on Chlamydomonas reinhardtii (CR, Fig. 1), a biflagellate green alga well developed as a model to stud...

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“…A thin nanotube or a thicker microrod will both experience a similar drag force, which will depend mainly on the body length while thickness only appears in logarithmic terms [1]. While there's a huge amount of work on single slender body dynamics, especially in the context of bacterial motility [2], investigation of hydrodynamic interactions between slender bodies is almost only limited to the phenomenology of syncronization [3,4]. One reason could be that, as opposed to spheres, which have been studied extensively [5][6][7], hydrodynamic couplings between anisotropic bodies are a complex function of both relative distance and orientation.…”

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Three-Dimensional to Two-Dimensional Crossover in the Hydrodynamic Interactions between Micron-Scale Rods

et al. 2011

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Moving micron scale objects are strongly coupled to each other by hydrodynamic interactions. The strength of this coupling decays as the inverse particle separation when the two objects are sufficiently far apart. It has been recently demonstrated that the reduced dimensionality of thin fluid layer gives rise to longer ranged, logarithmic coupling. Using holographic tweezers we show that microrods display both behaviors interacting like point particle in 3D at large distance and like point particles in 2D for distances shorter then their length. We derive a simple analytical expression that fits remarkably well our data and further validate it with finite element analysis.

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Synchronization of rotating helices by hydrodynamic interactions

Cited by 140 publications

References 23 publications

Synchronization and Collective Dynamics in a Carpet of Microfluidic Rotors

Synchronization and Collective Dynamics in a Carpet of Microfluidic Rotors

Emergence of Synchronized Beating during the Regrowth of Eukaryotic Flagella

Three-Dimensional to Two-Dimensional Crossover in the Hydrodynamic Interactions between Micron-Scale Rods

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