MIPS is a Maxwell fluid with an extended and non-monotonic crossover

Understanding the mechanical properties of active suspensions is crucial for their potential applications in materials engineering. Among the various phenomena in active matter that have no analogue in equilibrium systems, motility-induced phase separation (MIPS) in active colloidal suspensions is one of the most extensively studied. However, the mechanical properties of this fundamental active state of matter remain poorly understood. This study investigates the rheology of a suspension of active colloidal particles under constant and oscillatory shear. Systems consisting of pseudo-hard active Brownian particles exhibiting co-existence of dense and dilute phases behave as a viscoelastic Maxwell fluid at low and high frequencies, displaying exclusively shear thinning across a wide range of densities and activities. Remarkably, the cross-over point between the storage and loss moduli is non-monotonic, rising with activity before the MIPS transition but falling with activity after the transition, revealing the subtleties of how active forces and intrinsically out-of-equilibrium phases affect the mechanical properties of these systems.