Experimental evidence for convective rolls in finite two-dimensional molecular models

Abstract

Molecular dynamics (MD) techniques, based on explicit numerical solution of the equations of motion of the particles in a molecular system, have been successful in the study of models simulating fluids in equilibrium configurations as well as in stationary states due to the presence of external constraints. The possibility of observing true hydrodynamical behaviour has however been frequently questioned. There has been much recent interest¹ in new computational techniques which might be used to approach the difficult problems of flow and convection². Results from studies of cellular automata^3,4 are very promising. Fluid flows obstructed by plates or cylinders have been studied, using MD techniques, by Rapaport and Clementi⁵, who demonstrated the appearance of vortices, although it was generally argued that such simulations were out of range of the power of present computers. Here, we study finite systems of hard disks⁶ in the presence of both a thermal gradient and an external constant force. For well-chosen geometrical parameters, (density, gradient value and magnitude of the applied force), we observe the appearance of convective flow in these very small two-dimensional systems. Starting from a completely chaotic state, the system evolves to an ordered state after a few million collisions between particles. The vortices remain stable thereafter for at least a few thousand collisions per particle.