Continuum Theory for Wet Active Matter: Self-Propelled Rods in Stokes Fluids via Boltzmann-Ginzburg-Landau

Active systems, ensembles of active particles capable of expending energy at the individual level to produce motion or other forms of mechanical work, are present at all scales in biology. Bacteria are a paradigmatic example of such out-of-equilibrium systems, as they can convert chemical energy into motion through structures such as pili or flagella. Active turbulence is one possible state of collective motion exhibited by species of elongated and flagellated bacteria. Their rod-shaped bodies promote nematic alignment, leading to a so-called active nematics where nematic order is disrupted by the turbulent motion of topological defects. A crucial ingredient to produce such collective motion is the effect of the fluid surrounding the bacteria. Indeed, even if they are too packed to swim, they set the fluid in motion which in turn lead to their chaotic swirling motion. Such behavior is well-reproduced by microscopic models of particles coupled to a fluid but, so far, we lack a coarse-grained continuum theory that would express the large-scale behavior in terms of the microscopic parameters. In this work, we derive such a hydrodynamic theory for self-propelled rods embedded in a Stokes fluid by adapting the Boltzmann-Ginzburg-Landau approach, previously used in the dry case to obtain a continuum theory from a wet microscopic model, including explicitly the fluid. This framework accounts for the complex interplay between self-propulsion, nematic alignment, and fluid dynamics. Finally, we analyze the derived model by performing a linear stability analysis of the nematically ordered stationary homogeneous solution and numerically integrating the PDEs. This allows us to investigate the effects of the fluid on both the phase diagram and the non-linear dynamics, providing new insights into the behavior of this wet active matter model.