Diffusive behaviors of circle-swimming motors

Marine, Nathan A.; Wheat, Philip M.; Ault, Jesse T.; Posner, Jonathan D.

doi:10.1103/physreve.87.052305

Cited by 26 publications

(35 citation statements)

References 40 publications

(76 reference statements)

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“…Apart from that, near surfaces bent self-propelled objects tend to follow circular trajectories [42,43]. In modeling approaches, circle swimmers are often realized by simply imposing an effective torque or rotational drive in addition to the self-propulsion mechanism [15,31,35,[44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59].…”

Section: Introductionmentioning

confidence: 99%

Dynamical density functional theory for circle swimmers

et al. 2017

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The majority of studies on self-propelled particles and microswimmers concentrates on objects that do not feature a deterministic bending of their trajectory. However, perfect axial symmetry is hardly found in reality, and shape-asymmetric active microswimmers tend to show a persistent curvature of their trajectories. Consequently, we here present a particle-scale statistical approach to circle-swimmer suspensions in terms of a dynamical density functional theory. It is based on a minimal microswimmer model and, particularly, includes hydrodynamic interactions between the swimmers. After deriving the theory, we numerically investigate a planar example situation of confining the swimmers in a circularly symmetric potential trap. There, we find that increasing curvature of the swimming trajectories can reverse the qualitative effect of active drive. More precisely, with increasing curvature, the swimmers less effectively push outwards against the confinement, but instead form high-density patches in the center of the trap. We conclude that the circular motion of the individual swimmers has a localizing effect, also in the presence of hydrodynamic interactions. Parts of our results could be confirmed experimentally, for instance, using suspensions of L-shaped circle swimmers of different aspect ratio.

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Section: Introductionmentioning

confidence: 99%

Dynamical density functional theory for circle swimmers

et al. 2017

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“…Examples of circular motion close to surfaces include sperms [6][7][8][9], and bacteria [10][11][12][13][14][15][16], whereas a special type of algae, Chlamydomonas reinhardtii, exhibits a helical swimming trajectory due to an asymmetry in its flagella beat [17][18][19]. As a consequence of an either simple asymmetric shape or two internal motors propelling into different directions, also artificial microswimmers such as asymmetric Janus particles [20,21], bimetallic micromotors [22][23][24], and self-assembled doublets of spherical Janus particles [25] display circular motion. Moreover, particles, that perform chemotaxis along their self-generated gradient, are expected to follow circular trajectories in a strong chemical field [26].…”

Section: Introductionmentioning

confidence: 99%

Intermediate scattering function of an anisotropic Brownian circle swimmer

Kurzthaler

Franosch

2017

Soft Matter

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Microswimmers exhibit noisy circular motion due to asymmetric propulsion mechanisms, their chiral body shape, or by hydrodynamic couplings in the vicinity of surfaces. Here, we employ the Brownian circle swimmer model and characterize theoretically the dynamics in terms of the directly measurable intermediate scattering function. We derive the associated Fokker-Planck equation for the conditional probabilities and provide an exact solution in terms of generalizations of the Mathieu functions. Different spatiotemporal regimes are identified reflecting the bare translational diffusion at large wavenumbers, the persistent circular motion at intermediate wavenumbers and an enhanced effective diffusion at small wavenumbers. In particular, the circular motion of the particle manifests itself in characteristic oscillations at a plateau of the intermediate scattering function for wavenumbers probing the radius.

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“…Nevertheless, as stated in our Letter [2], effective forces and torques [3][4][5][6][7] can be used together with the grand resistance matrix (GRM) [8] to describe the self-propulsion of forceand torque-free swimmers [9]. To prove this, we perform a hydrodynamic calculation based on slender-body theory for Stokes flow [10,11].…”

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Kümmelet al.Reply:

et al. 2014

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Kümmel et al. Reply: In a Comment [1] on our Letter on self-propelled asymmetric particles [2], Felderhof claims that our theory based on Langevin equations would be conceptually wrong. In this Reply we show that our theory is appropriate, consistent, and physically justified.The motion of a self-propelled particle (SPP) is forceand torque-free if external forces and torques are absent. Nevertheless, as stated in our Letter [2], effective forces and torques [3][4][5][6][7] can be used together with the grand resistance matrix (GRM) [8] to describe the self-propulsion of forceand torque-free swimmers [9]. To prove this, we perform a hydrodynamic calculation based on slender-body theory for Stokes flow [10,11]. This approach has been applied successfully to model, e.g., flagellar locomotion [12,13] and avoids a general Faxén theorem for asymmetric particles. A key assumption of slender-body theory is that the width 2ϵ of the arms of the L-shaped particle is much smaller than the total arc length L ¼ a þ b, where a and b are the arm lengths.The centerline position of the slender particle is xðsÞHere, r is the center-of-mass position of the particle in the laboratory frame of reference and r S ¼ ða∥ Þ=ð2LÞ is a vector in the particle's framedefined by the unit vectorsû ∥ ,û ⊥ -such that r − r S is the point where the two arms meet at right angles. The fluid velocity on the particle surface is approximated by _ x þ v sl with a prescribed slip velocity v sl ðsÞ. According to the leading-order slender-body approximation [10], the fluid velocity is related to the local force per unit length fðsÞ on the particle surface byÞf with c ¼ logðL=ϵÞ=ð4πηÞ, the solvent viscosity η, the identity matrix I, x 0 ¼ ∂x=∂s, and the dyadic product ⊗. The force density f satisfies the integral constraints of vanishing net force, R a −b fds ¼ 0, and vanishing net torque relative to the center of mass,T . First, we consider a passive particle driven by an external force F ext , which is constant in the particle's frame, and torque M ext . For this case, we assume no-slip conditions for the fluid on the entire particle surface. Then the integral constraints with net force F ext and torque M ext givewhereÞ=ð12L 2 Þ is the GRM that depends on the particle shape [8,14].In the self-propelled case, motivated by the slip flow generated near the Au coating in the experiments, we setthe arm of length b and no slip (v sl ¼ 0) along the other arm. This results inWe emphasize that the tensor H in Eq. (3) is identical to the GRM in Eq. (1). Formally, both equations are exactly the same ifû ∥ · F ext ¼ 0,û ⊥ · F ext ¼ bV sl =c, and M ext ¼ −ab 2 V sl =ð2cLÞ. This shows that the motion of a SPP with v sl ¼ −V slû⊥ along the arm of length b is identical to the motion of a passive particle driven by a net external force F ext ¼ Fû ⊥ and torque M ext ¼ lF with the effective self-propulsion force F ¼ bV sl =c and effective lever arm l ¼ −ab=ð2LÞ. By transforming Eq. (3) from the particle's frame to the laboratory frame and introducing the generalized diffusi...

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Diffusive behaviors of circle-swimming motors

Cited by 26 publications

References 40 publications

Dynamical density functional theory for circle swimmers

Dynamical density functional theory for circle swimmers

Intermediate scattering function of an anisotropic Brownian circle swimmer

Kümmelet al.Reply:

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