Tracer diffusion in active suspensions

Abstract

We study the diffusion of a Brownian probe particle of size R in a dilute dispersion of active Brownian particles of size a, characteristic swim speed U 0 , reorientation time τ R , and mechanical energy k s T s = ζ a U 2 0 τ R /6, where ζ a is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity D P = k B T /ζ P , where k B T is the thermal energy of the solvent and ζ P is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by Pe s = U 0 a/D P . The active contribution to the diffusivity scales as Pe 2 s for weak swimming and Pe s for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale τ R , the active diffusivity scales as k s T s /ζ P : the probe moves as if it were immersed in a solvent with energy k s T s rather than k B T .

A continuous-time persistent random walk model for flocking

“…where D = V 2 0 τ /2 and, as noted earlier, τ = λ −1 is the mean time that a particle spends moving in the same direction. It is interesting to note the similarity with the swimming diffusivity, D swim ∼ V 2 0 τ , obtained in the context of active suspensions 26 . Hence, the telegrapher's equation (8) seems to be a good candidate to emulate the properties of active particles in one dimension.…”

Energy dissipation and fluctuations in a driven liquid

“…Understanding the basis of the increase of D due to the nonconservative forces is important -in the present context, it can help explain how the phase transition depends on the non-equilibrium forces. We note that non-conservative forces need not necessarily lead to an increase in the diffusion constant: in the self-propelled variety of active matter systems, the diffusion constant eventually decreases as a function of the driving force, leading to self-trapping and phase transitions [45,46].…”

Dissipation controls transport and phase transitions in active fluids: mobility, diffusion and biased ensembles

“…The reduction of transport coefficients by activity is then often regarded as a precursor of cluster formation. While several works have strived to predict how internal transport is affected by activity [30][31][32][33][34][35], a recent study has put forward an explicit connection between diffusion and dissipation in a mixture of active and passive particles [36]. Moreover, for generic driven systems, it has been shown recently that the diffusion coefficient is generically bounded by dissipation [37][38][39][40][41].…”