Microscopic origin and macroscopic implications of lane formation in mixtures of oppositely driven particles

Abstract

Colloidal particles of two types, driven in opposite directions, can segregate into lanes [Vissers et al. Soft Matter 7, 2352]. This phenomenon can be reproduced by two-dimensional Brownian dynamics simulations of model particles [Dzubiella et al. Phys. Rev. E 65, 021402 (2002)]. Here we use computer simulation to assess the generality of lane formation with respect to variation of particle type and dynamical protocol. We find that laning results from rectification of diffusion on the scale of a particle diameter: oppositely-driven particles must, in the time taken to encounter each other in the direction of the drive, diffuse in the perpendicular direction by about one particle diameter. This geometric constraint implies that the diffusion constant of a particle, in the presence of those of the opposite type, grows approximately linearly with Péclet number, a prediction confirmed by our numerics over a range of model parameters. Such environment-dependent diffusion is statistically similar to an effective interparticle attraction; consistent with this observation, we find that oppositely-driven non-attractive colloids display features characteristic of the simplest model system possessing both interparticle attractions and persistent motion, the driven Ising lattice gas [Katz, Leibowitz, Spohn, J. Stat. Phys. 34, 497 (1984)]. These features include long-ranged correlations in the disordered regime, and a critical regime characterized by a change in slope of the particle current with Péclet number and by fluctuations that grow with system size. By analogy, we suggest that lane formation in the driven colloid system is in the macroscopic limit a phase transition, but that macroscopic phase separation would not occur in finite time upon starting from disordered initial conditions.

Optimizing active work: Dynamical phase transitions, collective motion, and jamming

“…These particles expend energy to propel themselves, driving active matter out of equilibrium at microscopic scales and causing rich dynamical behaviors. Some of these are universal, whereby systems that differ microscopically show similar emergent physics [8], such as motility induced phase separation (MIPS) [9][10][11][12][13][14][15], collective motion [6,[16][17][18][19][20][21], lane formation [22,23] or motile defects [24][25][26][27][28][29].…”

Universal Long Ranged Correlations in Driven Binary Mixtures

“…For a large enough driving force, such systems undergo an out-of-equilibrium transition into a state in which the particles moving in the same direction spontaneously form lanes, thereby increasing their average velocity [9,10]. The nature of the laning transition remains unclear [10][11][12][13][14][15][16] and still little is known about the correlations-which are key observables to quantify the transition-and in particular about their decay at large distances [14].…”

Lane formation in a driven attractive fluid

“…For such systems, laning has been investigated concerning the impact of density [12], the role of hydrodynamic interactions [13], and the accompanying microscopic dynamics (particularly, the so-called dynamical locking) [2]. More recently studied issues are the impact of anisotropic friction [14] and of environment-dependent diffusion [11].…”

“…Theoretically, lane formation has been studied extensively in model systems composed of hard or soft spheres, where the pair interactions are solely repulsive (see, e.g., [10,11]). A realistic example are suspensions of charged colloids.…”