Active ploughing through a compressible viscoelastic fluid

We study the dynamics of a dilute suspension of active Brownian particles in a dense compressible viscoelastic fluid, as a function of the magnitude $f$ and orientational decorrelation time $\tau$ of the active force, using agent-based simulations and hydrodynamic theory. We first demonstrate a crossover in the transport of the motile particles, from activity dominated to cage-hopping dominated to eventual dynamical arrest, as a function of the density of the medium. In the process, the compressible medium is actively churned up -- for low $\tau$, the active particle gets self-trapped in a spherical cavity of its own making, for large $\tau$, the movement of the active particle is accompanied by an anisotropic wake, while for large $f$, the active particle ploughs through the medium rendering it porous. We derive hydrodynamic equations describing how the motile particles drive the compressible fluid, and show within a linearised approach, that the active particle generates a long range density wake which breaks fore-aft symmetry, consistent with the simulations. The back reaction of the compressible medium leads to (i) dynamical jamming of the active particle, and (ii) a dynamical {\it non-reciprocal} attraction between two active particles moving along the same direction, with the trailing particle catching up with the leading one in finite time.