Periodic Motion of Sedimenting Flexible Knots

Gruziel, Magdalena; Thyagarajan, K.; Dietler, Giovanni; Stasiak, Andrzej; Ekiel-Jeżewska, Maria L.; Szymczak, Piotr

doi:10.1103/physrevlett.121.127801

Cited by 23 publications

(27 citation statements)

References 51 publications

(61 reference statements)

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“…The influence of such knots * maximilian.liebetreu@univie.ac.at † christos.likos@univie.ac.at in equilibrium and relaxation properties in the bulk [38][39][40][41][42][43][44][45][46] , under confinement [47][48][49][50][51][52][53][54][55][56] and under tension [57][58][59][60][61][62][63][64] has been thoroughly investigated. Recently, the sedimentation behavior of flexible, non-Brownian knots has been added to the host of counterintuitive phenomena [65] . All polymer architectures (linear, star, dendritic, crosslinked and ring) are known to undergo tumbling under steady shear at sufficiently high shear rates [26,[66][67][68][69][70][71][72][73] .…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic inflation of ring polymers under shear

Liebetreu

Likos

2020

Commun Mater

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Hydrodynamic interactions as modeled by Multi-Particle Collision Dynamics can dramatically influence the dynamics of fully flexible, ring-shaped polymers in ways not known for any other polymer architecture or topology. We show that steady shear leads to an inflation scenario exclusive to ring polymers, which depends not only on Weissenberg number but also on contour length of the ring. By analyzing velocity fields of the solvent around the polymer, we show the existence of a hydrodynamic pocket which allows the polymer to self-stabilize at a certain alignment angle to the flow axis. This self-induced stabilization is accompanied by transitioning of the ring to a non-Brownian particle and a cessation of tumbling. The ring swells significantly in the vorticity direction, and the horseshoe regions on the stretched and swollen ring are effectively locked in place relative to the ring's center-of-mass. The observed effect is exclusive to ring polymers and stems from an interplay between hydrodynamic interactions and topology. Furthermore, knots tied onto such rings can serve as additional "stabilization anchors". Under strong shear, the knotted section is pulled tight and remains well-localized while tank-treading from one horseshoe region to the opposite one in sudden bursts. We find knotted polymers of high contour length behave very similarly to unknotted rings of the same contour length, but small knotted rings feature a host of different configurations. We propose a filtering technique for rings and chains based on our observations and suggest that strong shear could be used to tighten knots on rings.arXiv:1909.00725v2 [cond-mat.soft]

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Section: Introductionmentioning

confidence: 99%

Hydrodynamic inflation of ring polymers under shear

Liebetreu

Likos

2020

Commun Mater

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“…Raymer and Smith [14] studied the formation of knots on string tumbled inside a rotating box and proposed a model based on random braid moves of the free ends to describe the observed distribution of knot types. Studies with entangled granular chains have shown that knots can form on freely hanging chains shaken vertically at a constant frequency [15], considered the knotting and unknotting processes on chains placed on horizontal vibrating plates [16,17], examined the swelling and motion of knots on chains under tension [18], and investigated the oscillatory periodic motion of knots sedimenting in a viscous fluid [19]. Macroscale experiments provide an avenue for exploring the mechanisms of entanglements and can inform our understanding of entanglements on the microscale.…”

Section: Introductionmentioning

confidence: 99%

Self-entanglement of a tumbled circular chain

Soh

Gengaro

Klotz

et al. 2019

Phys. Rev. Research

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The spontaneous knotting of linear chains has been well studied, but little attention has been given to the self-entanglement of chains with more complex topologies. In this work, we perform experiments with granular chains that undergo tumbling motion to investigate the self-entanglement of circular chains, which lack the chain ends essential for forming knots. We study the entanglement probability and types of self-entanglements formed on linear and circular chains, using the well-studied self-entanglements on a linear chain to frame our understanding of self-entanglements on a circular chain. We describe a characterization method that views a self-entangled circular chain as a link of two components and use it to characterize the self-entanglements on circular chains with known topological descriptors from knot theory. Our experimental results show that an increase in circular chain length leads to an increase in entanglement probability and entanglement complexity until a plateau is reached, similar to the trends observed with linear chains. By examining the formation pathway of several self-entanglements, we infer a general mechanism for the self-entanglement of circular chains.

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“…All three modes of motion, namely, rotation and streamwise and cross-streamwise translation, are also present when an asymmetric disk dimer is far away from any side walls as demonstrated by Uspal, Eral, and Doyle ( 22 ). Evidently, screened hydrodynamic interactions give rise to nontrivial behavior not only in particle ensembles ( 40 – 44 ), but also in single-particle systems with broken symmetry ( 45 – 51 ). A first step toward the development of low-cost flow separators requires understanding the relation between the geometry of one such particle and its trajectory in confined Stokes flow.…”

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confidence: 99%

Universal motion of mirror-symmetric microparticles in confined Stokes flow

Georgiev

Toscano

Uspal

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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Comprehensive understanding of particle motion in microfluidic devices is essential to unlock additional technologies for shape-based separation and sorting of microparticles like microplastics, cells, and crystal polymorphs. Such particles interact hydrodynamically with confining surfaces, thus altering their trajectories. These hydrodynamic interactions are shape dependent and can be tuned to guide a particle along a specific path. We produce strongly confined particles with various shapes in a shallow microfluidic channel via stop flow lithography. Regardless of their exact shape, particles with a single mirror plane have identical modes of motion: in-plane rotation and cross-stream translation along a bell-shaped path. Each mode has a characteristic time, determined by particle geometry. Furthermore, each particle trajectory can be scaled by its respective characteristic times onto two master curves. We propose minimalistic relations linking these timescales to particle shape. Together these master curves yield a trajectory universal to particles with a single mirror plane.

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Periodic Motion of Sedimenting Flexible Knots

Cited by 23 publications

References 51 publications

Hydrodynamic inflation of ring polymers under shear

Hydrodynamic inflation of ring polymers under shear

Self-entanglement of a tumbled circular chain

Universal motion of mirror-symmetric microparticles in confined Stokes flow

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