Abstract
Evidence suggests that the transport rate of a passive particle at long timescales is enhanced due to interactions with the surrounding active ones in a size- and composition-dependent manner. Using a system of particles with different temperatures, we probe these effects in dilute solutions and derive long-time friction and self-diffusion coefficients as functions of volume fractions, sizes and temperatures of particles in $d=2$ and 3 dimensions. Thus, we model excluded-volume interactions for nonequilibrium systems but also extend the scope to short-range soft potentials and compare our results to Brownian-dynamics simulations. Remarkably, we show that both viscosity and energy flux display a nonlinear dependence on size. The simplicity of our formalism allows to discover various interesting scenarios that can be relevant for biological systems and active colloids.
Highlights
A particle in a solvent is constantly bombarded by the solvent molecules which push the particle, while the particle dissipates the excess energy through dynamical friction exerted by the solvent at longer time scales
The detailed derivations are included in Supplemental Material [41], which we hope to be useful for further studies in nonequilibrium systems as we extend the scope of microrheology approaches developed in equilibrium systems and simplify the framework
We have identified the effect of energy flux and friction on the long-time self-diffusion constant of colloidal particles
Summary
A particle in a solvent is constantly bombarded by the solvent molecules (receiving random kicks at a rate ∼ τs−1) which push the particle, while the particle dissipates the excess energy through dynamical friction exerted by the solvent at longer time scales. At long time scales t τc, the dynamics converges to diffusive motion where direct collisions dominate and the effect of the hydrodynamic field is decreased in the long-time selfdiffusion coefficient Ds [18,19] This allows for a consistent separation of time scales to implement a multiple-temperature model for studying the long-time transport properties in outof-equilibrium systems. We constructed a theory of phase separation for these systems, and showed that the three-body correlations lead to nonreciprocal interactions upon coarse-graining [28] and a shift from an effective equilibrium construction This reflects similar governing principles and peculiarities observed in polar active models [29,30]. The detailed derivations are included in Supplemental Material [41], which we hope to be useful for further studies in nonequilibrium systems as we extend the scope of microrheology approaches developed in equilibrium systems and simplify the framework
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