Mesoscopic Descriptions of Fluids

Abstract

Molecular Dynamics simulations of hydrodynamics require an overwhelming computational effort. This motivates the development of mesoscopic descriptions in which the relevant hydrodynamic behavior appears with a number of particles much smaller than those required in conventional Molecular Dynamics. Dissipative Particle Dynamics (DPD) is an attempt for such a mesoscopic approach. The crucial idea behind is that the point particles describing the fluid interact through conservative, dissipative and random forces. In a previous paper we have derived from first principles the DPD for a 1D harmonic chain. Starting from a microscopic description of the harmonic chain in terms of the positions and momenta of the atoms of the chain, we have deduced the equations of motion for a coarse-grained chain constructed by grouping the atoms in clusters of size n. Making use of a projection operator technique we found, in the limit of very long chains and large groupings, that the clusters interact elastically and dissipatively. They are also subject to random delta-correlated forces that take into account the eliminated degrees of freedom. This is how dissipation and noise come out naturally.