Hydrodynamic Fluctuations and Instabilities in Ordered Suspensions of Self-Propelled Particles

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)Nematic SPP suspensions are always absolutely unstable at long wavelengths. (ii)SPP suspensions support novel propagating modes at long wavelengths, coupling orientation, flow, and concentration. (iii)In a wave number 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 >^2/3 in polar-ordered SPP suspensions.