Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles

Abstract

We construct the hydrodynamic equations for suspensions of self-propelled particles (SPPs) with spontaneous orientational order, and make a number of striking, testable predictions: (i)SPP suspensions with the symmetry of a true nematic are always absolutely unstable at long wavelengths. (ii) SPP suspensions with polar, i.e., head-tail asymmetric, order support novel propagating modes at long wavelengths, coupling orientation, flow, and concentration. (iii) In a wavenumber regime accessible only in low Reynolds number systems such as bacteria, polar-ordered suspensions are invariably convectively unstable. (iv) The variance in the number N of particles, divided by the mean <N>, diverges as <N>^⅔ in polar-ordered SPP suspensions.