Microscopic chaos in shear and elongational flows

Abstract

The simulation of atoms and molecules under planar elongational flow in a nonequilibrium steady state for arbitrarily long times has recently been made possible by an appropriate implementation of nonequilibrium molecular dynamics (NEMD) with suitable periodic boundary conditions. We address some fundamental questions regarding the chaotic behaviour of this type of flow and compare its chaotic properties with the behaviour of fluids under planar shear flow. We analyse the spectra of Lyapunov exponents for a number of state points where the energy dissipation is the same for both flows, simulating a nonequilibrium steady state for isoenergetic and isokinetic constrained dynamics. We test the conjugate pairing rule and confirm its validity for planar elongation flow, as is expected from the Hamiltonian nature of the adiabatic equations of motion. Discussion about the chaoticity of the convective part of the flows, the link between Lyapunov exponents and viscosity and phase space contraction will also be presented