Nonequilibrium dynamics of mixtures of active and passive colloidal particles

We develop a mesoscopic field theory for the collective nonequilibrium dynamics of multicomponent mixtures of interacting active (i.e., motile) and passive (i.e., nonmotile) colloidal particles with isometric shape in two spatial dimensions. By a stability analysis of the field theory, we obtain equations for the spinodal that describes the onset of a motility-induced instability leading to cluster formation in such mixtures. The prediction for the spinodal is found to be in good agreement with particle-resolved computer simulations. Furthermore, we show that in active-passive mixtures the spinodal instability can be of two different types. One type is associated with a stationary bifurcation and occurs also in one-component active systems, whereas the other type is associated with a Hopf bifurcation and can occur only in active-passive mixtures. Remarkably, the Hopf bifurcation leads to moving clusters. This explains recent results from simulations of active-passive particle mixtures, where moving clusters and interfaces that are not seen in the corresponding one-component systems have been observed.Comment: 17 pages, 3 figure

Focusing by blocking: repeatedly generating central density peaks in self-propelled particle systems by exploiting diffusive processes

Over the past few years the displacement statistics of self-propelled particles has been intensely studied, revealing their long-time diffusive behavior. Here, we demonstrate that a concerted combination of boundary conditions and switching on and off the self-propelling drive can generate and afterwards arbitrarily often restore a non-stationary centered peak in their spatial distribution. This corresponds to a partial reversibility of their statistical behavior, in opposition to the above-mentioned long-time diffusive nature. Interestingly, it is a diffusive process that mediates and makes possible this procedure. It should be straightforward to verify our predictions in a real experimental system.Comment: 6 pages, 6 figure

Pressure is not a state function for generic active fluids

Pressure is the mechanical force per unit area that a confined system exerts on its container. In thermal equilibrium, it depends only on bulk properties (density, temperature, etc.) through an equation of state. Here we show that in a wide class of active systems the pressure depends on the precise interactions between the active particles and the confining walls. In general, therefore, active fluids have no equation of state, their mechanical pressures exhibit anomalous properties that defy the familiar thermodynamic reasoning that holds in equilibrium. The pressure remains a function of state, however, in some specific and well-studied active models that tacitly restrict the character of the particle-wall and/or particle-particle interactions.Comment: 8 pages + 9 SI pages, Nature Physics (2015

Scalar <i>φ</i>⁴ field theory for active-particle phase separation

Recent theories predict phase separation among orientationally disordered active particles whose propulsion speed decreases rapidly enough with density. Coarse-grained models of this process show time-reversal symmetry (detailed balance) to be restored for uniform states, but broken by gradient terms; hence detailed-balance violation is strongly coupled to interfacial phenomena. To explore the subtle generic physics resulting from such coupling we here introduce `Active Model B'. This is a scalar $\phi^4$ field theory (or phase-field model) that minimally violates detailed balance via a leading-order square-gradient term. We find that this additional term has modest effects on coarsening dynamics, but alters the static phase diagram by creating a jump in (thermodynamic) pressure across flat interfaces. Both results are surprising, since interfacial phenomena are always strongly implicated in coarsening dynamics but are, in detailed-balance systems, irrelevant for phase equilibria.Comment: 15 pages, 7 figure