Propulsion by stiff elastic filaments in viscous fluids

Katsamba, Panayiota; Lauga, Eric

doi:10.1103/physreve.99.053107

Cited by 7 publications

(6 citation statements)

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“…Such a mode transition was experimentally observed by Frka-Petesic et al for a system of a paramagnetic rod driven by a rotating magnetic field, 41 and also in other magnetic systems, such as nano-and micro-swimmers composed of a magnetic spherical head and a non-magnetic helical tail. 42,43 The behaviour of the soft-hard magnetic cilium in the stationary state can be explored in more detail by analyzing the fixed point structure of eqn (10); the results are shown in Fig. 4.…”

Section: Dynamics Of the Simple Magnetic Ciliummentioning

confidence: 99%

Magnetically-actuated artificial cilium: a simple theoretical model

et al. 2019

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Section: Dynamics Of the Simple Magnetic Ciliummentioning

confidence: 99%

Magnetically-actuated artificial cilium: a simple theoretical model

et al. 2019

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“…Khalil et al produced two tailed-microbots that showed frequency dependent back and forth movement through flagellar propulsion [27]. These microbots are still several hundreds of micrometer and might face micromechanical problems when scaling them down, similar to the theoretically proposed equivalent for joint helices [28]. An interesting system was presented by…”

Section: Discussionmentioning

confidence: 99%

Using Shape Diversity on the Way to Structure-Function Designs for Magnetic Micropropellers

et al. 2019

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Synthetic microswimmers mimicking biological movements at the microscale have been developed in recent years. Actuating helical magnetic materials with a homogeneous rotating magnetic field is one of the most widespread techniques for propulsion at the microscale, partly because the actuation strategy revolves around a simple linear relationship between the actuating field frequency and the propeller velocity. However, the full control of the swimmers' motion has remained a challenge. Increasing the controllability of micropropellers is crucial to achieve complex actuation schemes that in turn are directly relevant for numerous applications. The simplicity of the linear relationship though limits the possibilities and flexibilities of swarm control. Using a pool of randomly-shaped magnetic microswimmers, we show that the complexity of shape can advantageously be translated into enhanced control. In particular, directional reversal of sorted micropropellers is controlled by the frequency of the actuating field.2 This directionality change is linked to the balance between magnetic and hydrodynamic forces.We further show an example how this behavior can experimentally lead to simple and effective sorting of individual swimmers from a group. The ability of these propellers to reverse swimming direction solely by frequency increases the control possibilities and is an example for propeller designs, where the complexity needed for many applications is embedded directly in the propeller geometry rather than external factors such as actuation sequences. I. IntroductionMicroswimmers are envisioned for a multitude of applications ranging from solving environmental problems to being used for micro surgery [1][2][3]. Precise, versatile and noninvasive controllability is necessary to cover this broad scope of applications. These requirements are mostly matched by magnetic microswimmers. The fuel-free actuation by weak and homogeneous magnetic fields indeed allows remote controlling in many environments, the synthesis via nanofabrication makes them accessible even on a sub-micrometer scale [4][5][6]. In addition, the ability to functionalize their surface and the limited toxicity of the mostly iron-based propellers makes them appealing for medical applications [2,7]. Many of the current magnetic microswimmers use a helical shape with a fixed magnetic moment to rotate in an externally applied magnetic field, which enables stable propulsion. In this case, a simple linear relationship between the frequency of the actuating magnetic field and the velocity of micropropellers is used to precisely control the propeller [5,[8][9][10]. This leaves the sign of the swimming direction of the propeller to be determined by the rotation direction of the applied magnetic field, which limits the versatility of their actuation capability: when controlling two or more geometrically identical propellers, it is not possible to let them swim in a common propulsion mode respectively in the same direction and, if needed, in opposite directions, simpl...

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“…We note that resistive-force theory is only the leading-order approximation for the hydrodynamic forces in the slenderness of the filaments. More accurate theories such as slenderbody theory [61], or such accounting for elasticity [27] give more accurate though significantly more complicated estimates for F i and G i . However, as we show in §III C, their absolute values do not actually matter when comparing direct and indirect interactions since they both scale linearly with the kinematic quantities.…”

Section: A Hydrodynamics Of Flagellar Propulsionmentioning

confidence: 99%

“…We focus on the model bacterium E. coli, and summarise these values in Table I. We note that there exists considerable spread in the bending moduli of flagellar filaments across species [27,71], as well as specifically for E. coli in the flagellar length [72] and estimates for the motor torque [73]. Nevertheless, these representative values are sufficient to gain an understanding of the general dynamics of bundling.…”

Section: B Computational Modellingmentioning

confidence: 99%

“…the filaments allows for multiple different helical configurations, a phenomenon called polymorphism [24,25], which may change depending on the dynamic load [26]. Moreover, because the flagellar filaments and especially the hook are flexible, and the interaction between these slender elastic structures, the cell body and the fluid lead to non-linearities that are difficult to compute [27]. Despite these challenges, the dynamics of bundling and unbundling have been the subject of numerous theoretical [28][29][30][31], numerical [32][33][34][35][36][37][38][39][40][41][42][43] and experimental [6,13,16,[44][45][46][47][48][49] studies.…”

Section: Introductionmentioning

confidence: 99%

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Direct vs indirect hydrodynamic interactions during bundle formation of bacterial flagella

Chamolly,

Lauga

2020

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Most motile bacteria swim in viscous fluids by rotating multiple helical flagellar filaments. These semi-rigid filaments repeatedly join ('bundle') and separate ('unbundle'), resulting in a two-gait random walk-like motion of the cell. In this process, hydrodynamic interactions between the filaments are known to play an important role and can be categorised into two distinct types: direct interactions mediated through flows that are generated through the actuation of the filaments themselves, and indirect interactions mediated through the motion of the cell body (i.e. flows induced in the swimming frame that result from propulsion). To understand the relative importance of these two types of interactions, we study a minimal singularity model of flagellar bundling. Using hydrodynamic images, we solve for the flow analytically and compute both direct and indirect interactions exactly as a function of the length of the flagellar filaments and their angular separation.We show (i) that the generation of thrust by flagella alone is sufficient to drive the system towards a bundled state through both types of interaction in the entire geometric parameter range; (ii) that for both thrust-and rotation-induced flows indirect advection dominates for long filaments and at wide separation, i.e. primarily during the early stages of the bundling process; and (iii) that, in contrast, direct interactions dominate when flagellar filaments are in each other's wake, which we characterise mathematically. We further introduce a numerical elastohydrodynamic model that allows us to compute the dynamics of the helical axes of each flagellar filament while analysing direct and indirect interactions separately. With this we show (iv) that the shift in balance between direct and indirect interactions is non-monotonic during the bundling process, with a peak in direct dominance, and that different sections of the flagella are affected by these changes to different extents.

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Propulsion by stiff elastic filaments in viscous fluids

Cited by 7 publications

References 67 publications

Magnetically-actuated artificial cilium: a simple theoretical model

Magnetically-actuated artificial cilium: a simple theoretical model

Using Shape Diversity on the Way to Structure-Function Designs for Magnetic Micropropellers

Direct vs indirect hydrodynamic interactions during bundle formation of bacterial flagella

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