Effective viscosity of puller-like microswimmers: a renormalization approach

Gluzman, S.; Karpeev, Dmitry; Berlyand, Leonid

doi:10.1098/rsif.2013.0720

Cited by 14 publications

(24 citation statements)

References 35 publications

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“…For example, it was suggested that pushers become hydrodynamically attracted to boundary surfaces by an inward flow perpendicular to the axis of net swimming [1]. Swimmer type further determines active rheological responses such as shear thinning in dense suspensions of microswimmers [14,15].…”

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Flagellar swimmers oscillate between pusher- and puller-type swimming

Klindt

Friedrich

2015

Phys. Rev. E

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Self-propulsion of cellular microswimmers generates flow signatures, commonly classified as pusher and puller type, which characterize hydrodynamic interactions with other cells or boundaries. Using experimentally measured beat patterns, we compute that the flagellated green alga Chlamydomonas oscillates between pusher and puller, rendering it an approximately neutral swimmer, when averaging over its full beat cycle. Beyond a typical distance of 100μm from the cell, inertia attenuates oscillatory microflows. We show that hydrodynamic interactions between cells oscillate in time and are of similar magnitude as stochastic swimming fluctuations. From our analysis, we also find that the rate of hydrodynamic dissipation varies in time, which implies that flagellar beat patterns are not optimized with respect to this measure.

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Flagellar swimmers oscillate between pusher- and puller-type swimming

Klindt

Friedrich

2015

Phys. Rev. E

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“…The active stress tensor σ represents the forcing of the fluid by the swimmers [8,16,17]. For dense suspensions, the bulk viscosity μ contains contributions from the solvent as well as passive and active contributions from the microswimmers [23][24][25][26][27][28]. For simplicity, we assume that the passive contribution is approximately given by the Batchelor-Einstein relation for spherical colloids, μ = μ 0 (1 + k 1 φ + k 3 φ 2 ), where μ 0 is the "bare" solvent viscosity, φ is the volume fraction, and k i are positive constants [23,[29][30][31].…”

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Hydrodynamic length-scale selection in microswimmer suspensions

et al. 2016

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A universal characteristic of mesoscale turbulence in active suspensions is the emergence of a typical vortex length scale, distinctly different from the scale invariance of turbulent high-Reynolds number flows. Collective length-scale selection has been observed in bacterial fluids, endothelial tissue, and active colloids, yet the physical origins of this phenomenon remain elusive. Here, we systematically derive an effective fourth-order field theory from a generic microscopic model that allows us to predict the typical vortex size in microswimmer suspensions. Building on a self-consistent closure condition, the derivation shows that the vortex length scale is determined by the competition between local alignment forces, rotational diffusion, and intermediate-range hydrodynamic interactions. Vortex structures found in simulations of the theory agree with recent measurements in Bacillus subtilis suspensions. Moreover, our approach yields an effective viscosity enhancement (reduction), as reported experimentally for puller (pusher) microorganisms. DOI: 10.1103/PhysRevE.94.020601 A universal feature shared by many living systems is the emergence of characteristic length and time scales that arise from the nonequilibrium dynamics of their microscopic constituents. Examples range from circadian oscillations in individual cells [1] to multicellular gene-expression patterns in embryos [2] and vortex structures in microbial suspensions, endothelial tissue, and active colloids [3][4][5][6]. Yet, despite their broad biological relevance, it has proved difficult to predict quantitatively how such emergent scales arise from the underlying chemical or physical parameters. In the past decade, bacterial and other active suspensions [4,5,7] have emerged as important biophysical model systems that can help bridge the gap between large-scale spatiotemporal pattern formation and microscopic nonequilibrium dynamics [8]. At high densities, bacterial fluids form coherent vortex structures, spanning several cell lengths in diameter [5,7,9] and persisting for several seconds [9] or even minutes [10][11][12]. Although a number of insightful theoretical models have been proposed [13][14][15][16][17][18], a theory connecting microswimmer properties to the experimentally observed vortex patterns has been lacking.Here, we present such a theory by drawing guidance from the recent observation [5,9] that an effective fourth-order continuum model can provide a quantitative phenomenological description of dense bacterial suspensions [19]. This model, which combines the seminal Toner-Tu description of flocking [20] with the Swift-Hohenberg equation from pattern formation [21], describes the effective bacterial velocity field w(t,x) bywhere the bacterial pressure field q(t,x) accounts for incompressibility, ∇ · w = 0. Although a direct fit of Eq. (1) (1) directly from a generic model for polar microswimmers. The derivation specifies each parameter in the continuum theory in terms of microscopic swimmer parameters and yields direct theoretical ...

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“…With or without such addition, the value of the critical index is of the order of 2. The higher order coefficients c i appear to be redundant as long as one is concerned with the correct estimates for the critical index S [51].…”

Section: Effective Viscosity Of Passive Suspensionsmentioning

confidence: 99%

Optimized Factor Approximants and Critical Index

Gluzman¹

2021

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Based on expansions with only two coefficients and known critical points, we consider a minimal model of critical phenomena. The method of analysis is both based on and inspired with the symmetry properties of functional self-similarity relation between the consecutive functional approximations. Factor approximants are applied together with various natural optimization conditions of non-perturbative nature. The role of control parameter is played by the critical index by itself. The minimal derivative condition imposed on critical amplitude appears to bring the most reasonable, uniquely defined results. The minimal difference condition also imposed on amplitudes produces upper and lower bound on the critical index. While one of the bounds is close to the result from the minimal difference condition, the second bound is determined by the non-optimized factor approximant. One would expect that for the minimal derivative condition to work well, the bounds determined by the minimal difference condition should be not too wide. In this sense the technique of optimization presented above is self-consistent, since it automatically supplies the solution and the bounds. In the case of effective viscosity of passive suspensions the bounds could be found that are too wide to make any sense from either of the solutions. Other optimization conditions imposed on the factor approximants, lead to better estimates for the critical index for the effective viscosity. The optimization is based on equating two explicit expressions following from two different definitions of the critical index, while optimization parameter is introduced as the trial third-order coefficient in the expansion.

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Effective viscosity of puller-like microswimmers: a renormalization approach

Cited by 14 publications

References 35 publications

Flagellar swimmers oscillate between pusher- and puller-type swimming

Flagellar swimmers oscillate between pusher- and puller-type swimming

Hydrodynamic length-scale selection in microswimmer suspensions

Optimized Factor Approximants and Critical Index

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