Two-phase hydrodynamic model of active colloid motion

The paper presents a two-phase hydrodynamic model for the numerical simulation of collective motion in a thin layer of active colloids containing spherical microswimmers. The model accounts for three fundamental mechanisms governing the dynamics of the active colloid: the random motion of the microswimmers, their mutual collisions, and their interaction with the surrounding fluid phase. The accurate resolution of the characteristic time scales associated with each mechanism is crucial for reproducing the different dynamic modes. The model reproduces two primary modes of motion: Brownian and collective, as well as the transition between them. It is demonstrated that hydrodynamic interactions begin to play a significant role when the microswimmer velocity exceeds a critical threshold. At this point, the kinetic energy transferred to the fluid phase is sufficient to generate a noticeable feedback effect on the swimmers' motion. Conversely, a further increase in microswimmers' velocity enhances the role of collisions, causing the system to revert from a collective mode back to a Brownian-like state. A similar transition occurs at higher volume fractions of microswimmers within the colloid.