the kinetic theory of lane formation


We develop the kinetic theory based on Enskog equation to describe the lane formation process for counter driven dissipative particles. We have derived a set of hydrodynamic equations for the density, the momentum current, and the kinetic temperature for a binary mixture got counter driven particles, and characterized the interface between two stable phases of driven particles. Such a microscopic derivation of the driven particles is quite new, and thus, the derived equations are completely different from the conventional hydrodynamic equations. We will also try to discuss the instability for the straight interface between two phases in terms of hydrodynamic equations derived from the kinetic theory. This research enable us to understand the mechanism of various phenomena observed in our former numerical study of the lane formation, M. Ikeda, H. Wada and H. Hayakawa, EPL 99, 68005 (2012).

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