Modeling slender bodies with the method of regularized Stokeslets

Bouzarth, Elizabeth L.; Minion, Michael L.

doi:10.1016/j.jcp.2011.02.017

Cited by 29 publications

(39 citation statements)

References 21 publications

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“…With this blob parameter, we discretize each helix into 120 points. It has been shown that when using the method of regularized Stokeslets, a good choice for the discretization is one where the spacing between points is on the order of the size of the blob parameter [3,5,10]. The plot of the blob function with our chosen parameter is shown in Figure 2.…”

Section: Helical Flagellummentioning

confidence: 99%

Flow Induced by Bacterial Carpets and Transport of Microscale Loads

Buchmann

Fauci

Leiderman

et al. 2015

The IMA Volumes in Mathematics and Its Applications

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In this paper we utilize the method of regularized Stokeslets to explore flow fields induced by 'carpets' of rotating flagella. We model each flagellum as a rigid, rotating helix attached to a wall, and study flows around both a single helix and a small patch of multiple helices. To test our numerical method and gain intuition about flows induced by a single rotating helix, we first perform a numerical timereversibility experiment. Next, we investigate the hypothesis put forth in (Darnton et al., Biophys J 86, 1863-1870) that a small number of rotating flagella could produce "whirlpools" and "rivers" a small distance above them. Using our model system, we are able to produce "whirlpools" and "rivers" when the helices are rotating out of phase. Finally, to better understand the transport of microscale loads by flagellated microorganisms, we model a fully coupled helix-vesicle system by placing a finite-sized vesicle held together by elastic springs in fluid near one or two rotating helices. We compare the trajectories of the vesicle and a tracer particle initially placed at the centroid of vesicle and find that the two trajectories can diverge significantly within a short amount of time. Interestingly, the divergent behavior is extremely sensitive to the initial position within the fluid.

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Section: Helical Flagellummentioning

confidence: 99%

Flow Induced by Bacterial Carpets and Transport of Microscale Loads

Buchmann

Fauci

Leiderman

et al. 2015

The IMA Volumes in Mathematics and Its Applications

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“…To reduce computational costs, we do not explicitly discretize the surfaces of the helices. Instead, we place ns -130 regularized Stokeslets along each of the helix centerlines and tune the regularization parameter e to account for the finite filament radius [33]. We find that £ = 0.5L /n s reproduces the behavior for a = R / 16 with high accuracy.…”

Section: A Geometrymentioning

confidence: 91%

Decoupling translational and rotational effects on the phase synchronization of rotating helices

Arcak

Maharbiz

2015

Phys. Rev. E

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The locomotion of swimming microorganisms often relies on synchronized motions; examples include the bundling of flagella and metachronal coordination of cilia. It is now generally accepted that such behavior can result from hydrodynamic interactions alone. In this paper we consider the interactions between two side-by-side rigid helices driven by constant torques. We use the method of regularized Stokeslets to simulate an end-pinned model, in which restoring forces and torques are applied at one end of each helix. This allows us to decouple the respective effects of translation and rotation on phase synchronization. We find that while translational freedom leads to synchrony, rotational freedom can result in either synchrony or antisynchrony, depending on the stiffness of the system. In addition, we characterize the nature of the physical mechanisms driving these behaviors, focusing on the individual effects of each applied force and torque. For translational freedom, there is a single underlying mechanism in which the interaction forces indirectly influence the helix rotation rates. Multiple mechanisms are at play for rotational freedom: the interaction torques may exert either direct or indirect influence depending on stiffness. These characterizations are important to the future development of reduced-order models, which should capture not only the expected end behaviors (synchrony or antisynchrony), but also the nature of the driving mechanisms.

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“…Technical details on how SBT may be applied to a slender spheroid, as well as the choice of spreading parameter to minimize errors, have also been given (Bouzarth and Minion 2011). Here, we give our attention to papers which made comparisons between their analytical or numerical results with experimental observations.…”

Section: Slender Body Theorymentioning

confidence: 99%

“…The simulation by Autrusson et al (2011) using SBT also allows the elastic modulus of biofilm streamers to be computed accurately Page 7 of 27 98 within the measured range (Aravas and Laspidou 2008). It was found that the presence of error arising from the use of SBT can in general be attributed primarily to the fact that Stokeslets are used instead of a collection of singularities, and that imposing centerline boundary conditions correspond to better accuracy when analyzing a slender spheroid (Bouzarth and Minion 2011). SBT can be used not only for micro-sized particles and cells in microfluidics, but also for large but slender-bodied objects such as ships.…”

Section: Slender Body Theorymentioning

confidence: 99%