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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 , diverges as (2/3 ) in polar-ordered SPP suspensions.
Simha et al. (Mon,) studied this question.
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