On particle motion in a confined square domain filled with active fluids

The motion of passive particles in a confined square domain filled with active fluids has been numerically simulated using a direct-fictitious domain method. The ratio of particle diameter to the side length of the square domain (d_p/L) is adopted to classify the degree of confinement (i.e., strong or weak confinement). The translational mean-squared displacement (MSD_T) of weakly-confined particles scales well with the reported theoretical and experimental results in a short time and eventually reaches a plateau because of the confined environment. Additionally, the radial probability densities of the particle positions gradually increase with increasing distance from the center of the square domain at relatively high activity levels, displaying an apparent rise near the boundary and maximize near the corner. Conversely, the strongly confined particles migrate toward the center of the square domain or approach the corner with continuous rotation. In addition, the localized minima of the angular velocity of the particles show a periodic behavior, with the vortices periodically becoming more organized. Moreover, with increasing activity, two distinct linearly correlated regimes emerge in the relationship between the particle's rotational velocity and the activity. A comprehensive analysis of the collective dynamics reveals that the cutoff length is R_c ≈ 0.19(2.375d_p), pointing to the distance at which the velocities of two particles are uncorrelated. Moreover, the spatial correlation function (I_p) shows a small peak at R_r ≈ 0.12(1.5d_p), suggesting a relatively strong correlation between a given particle and another particle located at a distance R from it. Interestingly, both R_c and R_r are smaller than those observed in an unbounded flow, which indicates that boundary confinement significantly influences the ability of the particles to form coherent structures.