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

TL;DR

This study investigates the dynamics of active run-and-tumble particles and passive particles in a binary mixture, revealing a crossover from ballistic to diffusive behavior, size-dependent subdiffusion, and establishing an effective equilibrium through temperature measures.

Contribution

It introduces a detailed analysis of active-passive particle mixtures, demonstrating how activity and size influence dynamics and effective temperature, and suggests the emergence of an effective equilibrium.

Findings

Passive particle diffusivity decreases with size.

Passive particles show a transition from diffusive to subdiffusive motion.

Effective temperature increases linearly with activity and aligns across different measurement methods.

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.