Regularized image system for Stokes flow outside a solid sphere

Wróbel, Jacek K.; Cortez, Ricardo; Varela, Douglas; Fauci, Lisa

doi:10.1016/j.jcp.2016.04.043

Cited by 19 publications

(9 citation statements)

References 39 publications

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“…The present model does not account for the long range hydrodynamic effects of viscous fluids. Future extensions of this work will account for the full hydrodynamics, using a combination of slender body theory and regularized Stokeslet formulation, in the presence of the cell body or the cell wall [54,56]. Future work will also focus on the effects of anisotropy in the bending rigidity matrix B, which encodes information about the internal axoneme structure.…”

Section: Discussionmentioning

confidence: 99%

Instability-driven oscillations of elastic microfilaments

Ling

Guo

Kanso

2018

J. R. Soc. Interface.

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Cilia and flagella are highly conserved slender organelles that exhibit a variety of rhythmic beating patterns from non-planar cone-like motions to planar wave-like deformations. Although their internal structure, composed of a microtubule-based axoneme driven by dynein motors, is known, the mechanism responsible for these beating patterns remains elusive. Existing theories suggest that the dynein activity is dynamically regulated, via a geometric feedback from the cilium's mechanical deformation to the dynein force. An alternative, open-loop mechanism based on a 'flutter' instability was recently proven to lead to planar oscillations of elastic filaments under follower forces. Here, we show that an elastic filament in viscous fluid, clamped at one end and acted on by an external distribution of compressive axial forces, exhibits a Hopf bifurcation that leads to non-planar spinning of the buckled filament at a locked curvature. We also show the existence of a second bifurcation, at larger force values, that induces a transition from non-planar spinning to planar wave-like oscillations. We elucidate the nature of these instabilities using a combination of nonlinear numerical analysis, linear stability theory, and low-order bead-spring models. Our results show that away from the transition thresholds, these beating patterns are robust to perturbations in the distribution of axial forces and in the filament configuration. These findings support the theory that an open-loop, instability-driven mechanism could explain both the sustained oscillations and the wide variety of periodic beating patterns observed in cilia and flagella. arXiv:1808.01583v2 [physics.flu-dyn]

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Section: Discussionmentioning

confidence: 99%

Instability-driven oscillations of elastic microfilaments

Ling

Guo

Kanso

2018

J. R. Soc. Interface.

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“…Because inertia is unimportant at this scale, u must satisfy the Stokes equation ∇P = η Δu, where p is pressure; it must also be incompressible ∇ • u = 0. We solved these equations analytically to obtain the velocity field u generated by a regularized Stokeslet force, emulating the effect of the epibiont ciliated crown, located at a distance h/R from the diatom surface and pointing toward the center of the diatom (34). Although not an exact replica of empirically measured flows, the three-dimensional flow field of the regularized Stokeslet captures the main features of the flow observed experimentally: 1) flow directed toward the spherical diatom along the direction normal to its surface, 2) compression of fluid streamlines near the regularized Stokeslet, 3) highest flow speeds around the regularized Stokeslet, and 4) zero flows at the diatom surface (Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Modeling applied forces (known as Stokeslets in viscous fluid) as a general flow solution (61) has been applied to other biological systems (62,63) and is a common practice in studying ciliates attached to flat walls (26,27). Here, we extend these models to ciliates attached to diatoms by representing the epibionts as regularized forces applied to the fluid domain outside a spherical diatom (34). Details of the model, as well as the sinking diatom model, can be found in SI Appendix.…”

Section: Methodsmentioning

confidence: 99%

Teamwork in the viscous oceanic microscale

Kanso

Lopes

Strickler

et al. 2021

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

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Nutrient acquisition is crucial for oceanic microbes, and competitive solutions to solve this challenge have evolved among a range of unicellular protists. However, solitary solutions are not the only approach found in natural populations. A diverse array of oceanic protists form temporary or even long-lasting attachments to other protists and marine aggregates. Do these planktonic consortia provide benefits to their members? Here, we use empirical and modeling approaches to evaluate whether the relationship between a large centric diatom, Coscinodiscus wailesii, and a ciliate epibiont, Pseudovorticella coscinodisci, provides nutrient flux benefits to the host diatom. We find that fluid flows generated by ciliary beating can increase nutrient flux to a diatom cell surface four to 10 times that of a still cell without ciliate epibionts. This cosmopolitan species of diatom does not form consortia in all environments but frequently joins such consortia in nutrient-depleted waters. Our results demonstrate that symbiotic consortia provide a cooperative alternative of comparable or greater magnitude to sinking for enhancement of nutrient acquisition in challenging environments.

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“…Other key areas of methodological development for the method of regularized stokeslets include development of image systems for plane boundaries [13,45,46]; extension to Brinkman/oscillatory Stokes flow [47], triply [48], doubly [49,50] and singly [51] periodic boundary conditions; the use of radial basis functions to represent force distributions [52]; improvement to the near-field regularization error [53], far-field regularization error [54]; Richardson extrapolation in regularization parameter [55]; and perhaps most powerfully, methods based on kernel-independent fast multipole method [56,57] and treecode [58]. Regularization at the level of the boundary integral equation itself combined with asymptotic corrections (a related but different perspective from regularization of the equation from which the fundamental solution is derived) has been shown to provide highly accurate results for problems including near-contact of droplets without the need for specialized quadrature [59,60].…”

Section: Literature Reviewmentioning

confidence: 99%

The Role of the Double Layer Potential in Regularized Stokeslet Models of Self-Propulsion

Smith¹,

Gallagher²,

Schuech³

et al. 2021

Preprint

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The method of regularized stokeslets is widely-used to model microscale biological propulsion. The method is usually implemented with only the single layer potential, with the double layer potential being neglected, despite this formulation often not being justified a priori due to non-rigid surface deformation. We describe a meshless approach enabling inclusion of the double layer which is applied to several Stokes flow problems in which neglect of the double layer is not strictly valid: the drag on a spherical droplet with partial slip boundary condition, swimming velocity and rate of working of a force-free spherical squirmer, and trajectory, swimmer-generated flow and rate of working of undulatory swimmers of varying slenderness. The resistance problem is solved accurately with modest discretization on a notebook computer with the inclusion of the double layer ranging from no-slip to free slip limits; neglect of the double layer potential results in up to 24% error, confirming the importance of the double layer in applications such as nanofluidics, in which partial slip may occur. The squirming swimmer problem is also solved for both velocity and rate of working to within a few percent error when the double layer potential is included, but the error in the rate of working is above 250% when the double layer is neglected. The undulating swimmer problem by contrast produces a very similar value of the velocity and rate of working for both slender and non-slender swimmers, whether or not the double layer is included, which may be due to the deformation’s `locally rigid body’ nature, providing empirical evidence that its neglect may be reasonable in many problems of interest. Inclusion of the double layer enables us to confirm robustly that slenderness provides major advantages in efficient motility despite minimal qualitative changes to the flow field and force distribution.

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Regularized image system for Stokes flow outside a solid sphere

Cited by 19 publications

References 39 publications

Instability-driven oscillations of elastic microfilaments

Instability-driven oscillations of elastic microfilaments

Teamwork in the viscous oceanic microscale

The Role of the Double Layer Potential in Regularized Stokeslet Models of Self-Propulsion

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