Differential equations for continuum fields describe many macroscopic phenomena. Hydrodynamics, for example, is described by the Navier-Stokes equations, and their solutions depend on boundary conditions. However, boundary conditions are set by the interactions at the atomistic or molecular scale. We introduce a "hybrid model" that permits a continuum description in one region to be coupled to an atomistic description in another region. The coupling is symmetric in the sense that the fluxes of the conserved quantities are continuous across the particle-field interface. As an example, we couple a Lennard-Jones liquid and the compressible Navier-Stokes equations and show that the hybrid model is consistent with hydrodynamic predictions.

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A general scheme to patch together discrete and continuous descriptions of diffusion within the same physical space is studied. In the discrete description, diffusion is described by microscopic random walkers on a lattice; in the continuous description, diffusion is described through the macroscopic diffusion equation. The coupling scheme is based on the mutual exchange of mass flux across the discrete-continuous interface. Detailed tests of the scheme, coupling particle, and field descriptions are particularly illustrative for the diffusion problem. Both the nonequilibrium transport behavior and the equilibrium fluctuations of the combined discrete-continuous system are in agreement with theoretical predictions.

Abstract. The slow displacement of a wetting fluid by a nonwetting fluid in models of a single fracture was studied experimentally and by computer simulations on identical geometries. The fracture was modeled by the gap between a rough plate and a smooth transparent plate, both oriented horizontally. Two different rough plates were used, a textured glass plate and a polymethyl methacrylate plate with a computer-generated pattern. A nonwetting fluid (air) was injected slowly through an inlet into the model and displaced a wetting fluid (water) initially filling the model. The aperture fields of the artifical fractures were measured using a light absorption technique. The experiments were simulated using modified invasion percolation models, making use of the measured aperture fields. The simulation models captured invasion bursts and fragmentation and redistribution of the invading air. Experiments and simulations were compared step by step, and good qualitative and quantitative agreement was found.

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