Molecular Dynamics Simulations of Benchmark Geometries Representing a Flow Through Porous Media

Fluid Dynamics Simulations are often based on continuum assumptions that, for micro- or nano-flows, are extended by models that take into account special phenomena (e. g. wall slip) that occour in these dimensions. On the nano-scale not only the near wall layers show peculiarities. Especially for liquids the bulk flow deviates from smooth profiles and thus strongly differs from continuum theory. So far mainly the flow in straight channels has been investigated with Molecular Dynamics Simulations. In real porous media such perfectly flat channels do not appear. Thus, to analyze the applicability of the continuum assumption for the simulation of fluid flow on the pore-scale the type of geometries that are evaluated has to be extended. Therefore in this paper we present the results of Molecular Dynamics Simulations of a liquid in a Couette flow, the flow through a straight channel, a bend and through an array of cylinders. We present the results for varying wall-fluid potentials, shear rates, and temperatures and compare the results to the validated data from a finite volume solution of the Navier-Stokes-Equations for the same geometries. As a result we show the difficulties due to complex geometries for the simulation with Molecular Dynamics. Also the boundary conditions for Molecular Dynamics Simulations, like the thermostat or the wall model are discussed. We show that for some parameter sets, a critical behaviour can be observed for the more complex geometries. Such results are evaluated to show the differences between MD and FVM simulations. It turns out however, that the limits of the continuum assumptions are very different for different geometries. In complex geometries the minimum characteristic size can be much smaller than in straight channels. Hence the scope of continuum methods for the simulation of fluid flow through porous media on the pore scale is larger than expected.