Microscopic field-theoretical approach for mixtures of active and passive particles

We consider a phase field crystal modeling approach for mixtures of interacting active and passive particles in two dimensions. The approach allows us to describe generic properties for such heterogeneous systems within a continuum model. We validate the approach by reproducing experimental results, as well as results obtained with agent-based simulations. The approach is valid for the whole spectrum from highly dilute suspensions of passive particles and interacting active particles in a dense background of passive particles. However, we concentrate only on the extreme cases, because for the situation with similar fractions of active and passive particles emerging structures are hard to analyze and experimental results are missing. We analyze in detail enhanced crystallization due to the presence of active particles, how collective migration is affected by a disordered environment, and laning states, which are globally nematic but polar within each lane.