Dynamics of active run and tumble and passive particles in binary mixture

Abstract: We study a binary mixture of disk-shaped {\it active run and tumble } particles (${ARNPs}$) and passive particles on a two-dimensional substrate. Both types of particles are athermal. The particles interact through the soft repulsive potential. The activity of $ARNPs$ is controlled by tuning their tumbling rate. The system is studied for various sizes of passive particles keeping size of $ARNPs$ fixed. Hence the variables are, size ratio (S) of passive particles and $ARNPs$, and activity of $ARNPs$ is $v$. The characterstics dynamics of both $ARNPs$ and passive particles show a crossover from early time ballistic to later time diffusive. Furthermore, we observed that passive particles dynamics changes from diffusive to subdiffusive with respect to their size. Moreover, late time effective diffusivity $D_{eff}$ of passive particles decreases with increasing their size as in the corresponding equilibrium Stokes systems. We calculated the effective temperatures, using $D_{eff}$, $T_{a,eff}(\Delta)$ and also using speed distribution $T_{a,eff}(v)$ and compared them. The both $T_{a,eff}(\Delta)$ and $T_{a,eff}(v)$ increases linearly with activity and are in agreement with each other. Hence we can say that an effective equilibrium can be establish in such binary mixture. Our study can be useful to study the various biological systems like; dynamics of passive organels in cytoplasm, colloids etc.