Dilute suspensions of motile microorganisms are not active liquid crystals

Recent years witnessed a significant interest in physical, biological and engineering properties of self-propelled particles, such as bacteria or microtubule-kinesin mixtures, and the associated simple theoretical models that capture the main features of these systems. The most popular theory of self-propelled particles embedded in a continuum fluid is the active gel theory (AGT) that treats active agents as a liquid crystal capable of applying local force dipoles to its surroundings.

In this work, we address the question whether dilute suspensions of motile microorganisms can be adequately described by AGT. Starting from a kinetic theory that is known to correctly incorporate long-range hydrodynamic interactions that play a crucial role in the collective behaviour of such systems, we perform a systematic reduction of their equation of motion. Although the resulting continuum PDE's appear to be similar to AGT formulated for an isotropic active liquid crystal, no mapping between them exists even at the mean-field level. While AGT has an intrinsic active lengthscale, our continuum theory is scale-free, with the pattern size being selected by the size of the system. We further discuss the relationship between the two theories in two dimensions, and confirm our findings through direct numerical simulations.