Rheology of Active-Particle Suspensions

Abstract

We study the interplay of activity, order and flow through a set of coarse-grained equations governing the hydrodynamic velocity, concentration and stress fields in a suspension of active, energydissipating particles. We make several predictions for the rheology of such systems, which can be tested on bacterial suspensions, cell extracts with motors and filaments, or artificial machines in a fluid. The phenomena of cytoplasmic streaming, elastotaxis and active mechanosensing find natural explanations within our model. PACS numbers: 87.16.Ac, 87.15.Ya, 87.10.+e An active particle [1, 2] absorbs energy from its surroundings or from an internal fuel tank and dissipates it in the process of carrying out internal movements usually resulting in translatory or rotary motion. This broad definition includes macroscopic machines and organisms, living cells, and their components such as actin-myosin and ion pumps [3]. In this paper, we consider the interplay of activity, order and flow via coarse-grained equations governing the hydrodynamic velocity, concentration and stress fields in a suspension containing active particles of linear size ℓ, at concentration φ, each particle exerting a typical force f on the ambient fluid, with the activity of an individual particle correlated over a time τ 0 (say the 'run' time of a bacterium), and collective fluctuations in the activity correlated over length scales ξ and timescales τ . Rather than focussing on ordered phases [4], instabilities [4,5], or patterns (asters, vortices, spirals) formed in such assemblies [6] which our equations are of course capable of predicting, we apply them in the isotropic phase, with a view to understanding how a system such as a biological cell, composed of active elements, responds to deformation or mechanical stress. In addition to throwing light on full-cell rheometry [7,8], our equations form the framework for an analysis of any experiment probing the mechanical consequences of biological activity.Our simple model makes rather interesting predictions: An orientationally ordered state of active particles has a nonzero, macroscopic, anisotropic stress in contrast with thermal equilibrium nematics. Activity contributes an amount δη ∼ f ℓc 0 τ to the viscosity, with a sign determined by the type of active particle, and always enhances the apparent (noise) temperature. The latter greatly enhances the amplitude of the t −d/2 long-time tails [9] in the velocity autocorrelation. On approaching an orientationally ordered state, active suspensions with δη > 0 behave like passive systems near translational freezing, showing strong shear thickening and Maxwelllike viscoelasticity. Nonlinear fluctuation corrections give a dynamic modulusobservable over a large dynamic range, since τ is large. Cytoplasmic streaming [10], in which material flows from the depolymerising trailing edge to the polymerising leading edge of a crawling amoeboid cell, finds a natural explanation in our model, as do elastotaxis [11] and active mechanosensing [12], where cells orient t...

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