A phase separation of active colloidal suspension via Quorum-sensing

We present the Brownian dynamics simulation of active colloidal suspension in two dimensions, where the self-propulsion speed of a colloid is regulated according to the local density sensed by it. The role of concentration-dependent motility on the phase-separation of colloids and their dynamics is investigated in detail. Interestingly, the system phase separates at a very low packing fraction ($\Phi\approx 0.125$) at higher self-propulsion speeds ($\text{Pe}$), which coexists with a homogeneous phase and attains long-range crystalline order beyond a transition point. The transition point is quantified here from the local density profiles, local and global-bond order parameters. We have shown that the phase diagram's characteristics are qualitatively akin to the active Brownian particle (ABP) model. Moreover, our investigation reveals that the density-dependent motility amplifies the slow-down of the directed speed, which facilitates phase-separation even at low packing fractions. The effective diffusivity shows a crossover from quadratic rise to a power-law behavior of exponent $3/2$ with $\text{Pe}$ in the phase-separated regime. Furthermore, we have shown that the effective diffusion decreases exponentially with packing fraction in the phase-separated regime while linear decrease in the single phase regime.