Active particles in reactive disordered media: How does adsorption affect diffusion?

Abstract

In this work we study analytically and numerically the transport properties of non-interacting active particles moving on a d-dimensional disordered medium. The disorder is modeled by means of a set of non-overlapping spherical obstacles. We assume that obstacles are reactive in the sense that they react in the presence of the particles in an attractive manner: when the particle collides with an obstacle, it is attached during a random time (adsorption time), i.e., it gets adsorbed by an obstacle; thereafter the particle is detached from the obstacle and continues its motion in a random direction. We give an approximate analytical expression for the effective diffusion coefficient when the mean adsorption time is finite. If the mean adsorption time is infinite the system undergoes a transition from a normal to anomalous diffusion regime. We also show that another transition takes place in the mean number of adsorbed particles: in the anomalous diffusion phase all the particles become adsorbed in the average. We show that the fraction of adsorbed particles, seen as an order parameter of the system, undergoes a second-order-like phase transition, because the fraction of adsorbed particles is not differentiable but changes continuously as a function of a parameter of the model.