Transport and Collective Dynamics in Suspensions of Confined Swimming Particles

Hernández-Ortiz, Juan P.; Stoltz, Christopher; Graham, Michael D.

doi:10.1103/physrevlett.95.204501

Cited by 389 publications

(439 citation statements)

References 24 publications

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“…Such a model is in a coarse grained level and without hydrodynamic interactions [69,70]. The model is composed of self-propelled particles moving with constant speed v 0 in two dimensions.…”

Section: Microscopic Modelmentioning

confidence: 99%

Gaussian theory for spatially distributed self-propelled particles

2016

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Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting selfpropelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatio-temporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.

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Section: Microscopic Modelmentioning

confidence: 99%

Gaussian theory for spatially distributed self-propelled particles

2016

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“…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].…”

mentioning

confidence: 99%

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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“…10,11 For instance, flagellates propelled from behind by a rotating helical bundle are "pushers" while those swimming towards the bundle are "pullers." These are the examples of dipole swimmers, so-called because the disturbance flow generated by the swimmer has the form of that due to a force dipole.…”

Section: Pushers and Pullers-the Implicit Swimming Gaitmentioning

confidence: 99%

“…Analytical simplifications to the latter process are possible for very slender or nearly spherical bodies. [9][10][11] It is these simplifications that we leverage to achieve a general technique for modeling swimming animalcules.…”

Section: Introductionmentioning

confidence: 99%

Modeling hydrodynamic self-propulsion with Stokesian Dynamics. Or teaching Stokesian Dynamics to swim

et al. 2011

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We develop a general framework for modeling the hydrodynamic self-propulsion (i.e., swimming) of bodies (e.g., microorganisms) at low Reynolds number via Stokesian Dynamics simulations. The swimming body is composed of many spherical particles constrained to form an assembly that deforms via relative motion of its constituent particles. The resistance tensor describing the hydrodynamic interactions among the individual particles maps directly onto that for the assembly. Specifying a particular swimming gait and imposing the condition that the swimming body is force-and torque-free determine the propulsive speed. The body's translational and rotational velocities computed via this methodology are identical in form to that from the classical theory for the swimming of arbitrary bodies at low Reynolds number. We illustrate the generality of the method through simulations of a wide array of swimming bodies: pushers and pullers, spinners, the Taylor=Purcell swimming toroid, Taylor's helical swimmer, Purcell's three-link swimmer, and an amoeba-like body undergoing large-scale deformation. An open source code is a part of the supplementary material and can be used to simulate the swimming of a body with arbitrary geometry and swimming gait.

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Transport and Collective Dynamics in Suspensions of Confined Swimming Particles

Cited by 389 publications

References 24 publications

Gaussian theory for spatially distributed self-propelled particles

Gaussian theory for spatially distributed self-propelled particles

Synchronization and Collective Dynamics in a Carpet of Microfluidic Rotors

Modeling hydrodynamic self-propulsion with Stokesian Dynamics. Or teaching Stokesian Dynamics to swim

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