Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model

Abstract

Suspensions of self-propelled particles are studied in the framework of two-dimensional (2D) Stokesean hydrodynamics. A formula is obtained for the effective viscosity of such suspensions in the limit of small concentrations. This formula includes the two terms that are found in the 2D version of Einstein's classical result for passive suspensions. To this, the main result of the paper is added, an additional term due to self-propulsion which depends on the physical and geometric properties of the active suspension. This term explains the experimental observation of a decrease in effective viscosity in active suspensions.

15 pages, 3 figures, submitted to Physical Biology

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• Swimming in Complex Fluids
• Activity-induced clustering in model dumbbell swimmers: The role of hydrodynamic interactions
• Non-equilibrium fluctuations and nonlinear response of an active bath
• Non-linear rheology of active particle suspensions: Insights from an analytical approach
• Focusing of Active Particles in a Converging Flow
• Asymptotic expansion of the solution of the steady Stokes equation with variable viscosity in a two-dimensional tube structure
• Colliding cells: when active segments behave as active particles
• Active gel segment behaving as an active particle
• Effective medium model for a suspension of active swimmers
• Self-sustained patchy turbulence in shear-thinning active fluids
• The zero-shear-rate limiting rheological behaviors of ideally conductive particles suspended in concentrated dispersions under an electric field
• Irreversibility and Chaos in Active Particle Suspensions