Nonlinear rheology of active particle suspensions: Insights from an analytical approach

Heidenreich, Sebastian; Hess, Siegfried; Klapp, Sabine H. L.

doi:10.1103/physreve.83.011907

Cited by 17 publications

(20 citation statements)

References 47 publications

(81 reference statements)

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“…This is supported by the slow-swimming perturbation expansion which shows that the spatial autocorrelation function of the concentration fluctuations is delta-correlated in real space to the first three orders. Recall that it is typically nonlinear effects or near-field effects that are responsible for the substantial concentration fluctuations seen in other studies [25,29,[55][56][57], while near-field effects are neglected here. We consider next the shear component of the active stress, which under the deterministic mean field theory is the driver of the instability of the uniform isotropic state.…”

Section: Microswimmer Fluctuations and Correlationsmentioning

confidence: 99%

Stochastic kinetic theory for collective behavior of hydrodynamically interacting active particles

2017

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Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the hydrodynamic or kinetic equations. By incorporating stochastic fluxes into the mean field kinetic equation, we quantify the dynamics of a suspension of microswimmers in the parameter regime where the deterministic equation is stable. We can thereby compute nontrivial collective phenomena concerning spatial correlations of orientation and stress as well as the enhanced diffusion of tracer particles. Our analysis here focuses primarily on twodimensional systems, though we also show how superdiffusion of tracers in three dimensions can occur by our framework.

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Section: Microswimmer Fluctuations and Correlationsmentioning

confidence: 99%

Stochastic kinetic theory for collective behavior of hydrodynamically interacting active particles

2017

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“…Further investigations include the effect of fluid viscoelasticity [25][26][27][28][29][30][31] , swimming near a fluid interface [32][33][34] or inside a channel [35][36][37][38][39] , and the hydrodynamic interactions between two neighboring microswimmers near a wall 40 . Intriguing collective behavior and spatiotemporal patterns may arise from the interaction of many swimmers, including the onset of propagating density waves [41][42][43][44][45][46][47][48] and laning [49][50][51][52] , the motility-induced phase separation [53][54][55][56][57] and the emergence of active turbulence [58][59][60][61][62][63][64] . Boundaries have also been shown to induce order in collective flows of bacterial suspensions [65][66][67] , leading to potential applications in autonomous microfluidic systems 68 .…”

Section: Introductionmentioning

confidence: 99%

Swimming trajectories of a three-sphere microswimmer near a wall

Daddi-Moussa-Ider

Lisicki

Hoell

et al. 2018

The Journal of Chemical Physics

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The hydrodynamic flow field generated by self-propelled active particles and swimming microorganisms is strongly altered by the presence of nearby boundaries in a viscous flow. Using a simple model three-linked sphere swimmer, we show that the swimming trajectories near a no-slip wall reveal various scenarios of motion depending on the initial orientation and the distance separating the swimmer from the wall. We find that the swimmer can either be trapped by the wall, completely escape, or perform an oscillatory gliding motion at a constant mean height above the wall. Using a far-field approximation, we find that, at leading order, the wall-induced correction has a source-dipolar or quadrupolar flow structure where the translational and angular velocities of the swimmer decay as inverse third and fourth powers with distance from the wall, respectively. The resulting equations of motion for the trajectories and the relevant order parameters fully characterize the transition between the states and allow for an accurate description of the swimming behavior near a wall. We demonstrate that the transition between the trapping and oscillatory gliding states is first order discontinuous, whereas the transition between the trapping and escaping states is continuous, characterized by non-trivial scaling exponents of the order parameters. In order to model the circular motion of flagellated bacteria near solid interfaces, we further assume that the spheres can undergo rotational motion around the swimming axis. We show that the general three-dimensional motion can be mapped onto a quasi-two-dimensional representational model by an appropriate redefinition of the order parameters governing the transition between the swimming states.

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“…This was first noted in a theoretical study by Hatwalne et al, 17 who argued that extensile particles or so-called pushers for which r 0 < 0 should have a negative intrinsic viscosity ½g < 0, whereas contractile particles or pullers for which r 0 > 0 should have ½g > 0. A number of more sophisticated models have been proposed since, [18][19][20][21][22][23][24][25][26] which usually extend theories for the rheology of passive rod suspensions [27][28][29] to account for this active dipole and have led to similar predictions. Of particular relevance to the present study is the model of Saintillan, 20 which calculated the effective viscosity and normal stress differences in a dilute active suspension in uniform shear flow as functions of shear rate.…”

Section: Introductionmentioning

confidence: 99%

Microfluidic rheology of active particle suspensions: Kinetic theory

2016

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We analyze the effective rheology of a dilute suspension of self-propelled slender particles confined between two infinite parallel plates and subject to a pressure-driven flow. We use a continuum kinetic model to describe the configuration of the particles in the system, in which the disturbance flows induced by the swimmers are taken into account, and use it to calculate estimates of the suspension viscosity for a range of channel widths and flow strengths typical of microfluidic experiments. Our results are in agreement with previous bulk models, and in particular, demonstrate that the effect of activity is strongest at low flow rates, where pushers tend to decrease the suspension viscosity whereas pullers enhance it. In stronger flows, dissipative stresses overcome the effects of activity leading to increased viscosities followed by shear-thinning. The effects of confinement and number density are also analyzed, and our results confirm the apparent transition to superfluidity reported in recent experiments on pusher suspensions at intermediate densities. We also derive an approximate analytical expression for the effective viscosity in the limit of weak flows and wide channels, and demonstrate good agreement between theory and numerical calculations.

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Nonlinear rheology of active particle suspensions: Insights from an analytical approach

Cited by 17 publications

References 47 publications

Stochastic kinetic theory for collective behavior of hydrodynamically interacting active particles

Stochastic kinetic theory for collective behavior of hydrodynamically interacting active particles

Swimming trajectories of a three-sphere microswimmer near a wall

Microfluidic rheology of active particle suspensions: Kinetic theory

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