Generalized hydrodynamic model for fluid flows: From nanoscale to macroscale

At the macroscale, the hydrodynamics of a fluid can be well described by conventional hydrodynamic models such as the Navier-Stokes equations. However, as the flow passage is shrunk down to the nanometer size, the micro-interaction between the fluid and the confined solid walls becomes significant, and the conventional hydrodynamic model will become insufficient for describing such a flow system. In this work, we propose a generalized hydrodynamic model that is derived from a recently developed kinetic model for strong inhomogeneous fluid systems [Guo, Zhao, and Shi, Phys. Rev. E 71, 035301(R) (2005)]. We show that the present model can reduce to other hydrodynamic models in certain limits, and can be used for flows ranging from nanoscale to macroscale. Based on this generalized model, the static and dynamic behaviors of several simple fluid systems are studied. It is shown that at a small scale, the results predicted by the generalized hydrodynamic model are in agreement with those simulated by the molecular dynamic and the Monte Carlo methods, while for flow systems at a large scale, the results agree with those by the Navier-Stokes equations.