Viscosity and effective temperature of an active dense system of self-propelled particles

Abstract

We obtain a nonequilibrium theory for a simple model of a generic class of active dense systems consisting of self-propelled particles with a self-propulsion force, $f_0$, and persistence time, $τ_p$, of their motion. We consider two models of activity and find the system is characterized by an evolving effective temperature $T_{eff}(τ)$, defined through a generalized fluctuation-dissipation theorem. $T_{eff}(τ)$ is equal to the equilibrium temperature at very short time $τ$ and saturates to $T_{eff}=T_{eff}(τ\to\infty)$ at long times; The transition time $t_{trans}$ when $T_{eff}(τ)$ goes to the long-time limit depends on $τ_p$ alone and $t_{trans}\sim τ_p^{0.85}$ for both models. $f_0$ reduces the viscosity with increasing activity, $τ_p$ on the other hand, may increase or decrease viscosity depending on the details of how the activity is included. However, as a function of $T_{eff}$, viscosity shows the same behavior for different models of activity and $η\sim (T_{eff}-T)^{-γ}$ with $γ=1.74$. Our theory gives reasonable agreement when compared with experimental data and is consistent with several experiments on diverse systems.