Molecular dynamics techniques are used to study the microscopic aspects of several slow viscous flows past a solid wall, where both fluid and wall have a molecular structure. Systems of several thousand molecules are found to exhibit reasonable continuum behavior, albeit with significant thermal fluctuations. In Couette and Poiseuille flow of liquids it is found that the no-slip boundary condition arises naturally as a consequence of molecular roughness, and that the velocity and stress fields agree with the solutions of the Stokes equations. At lower densities slip appears, which can be incorporated into a flow-independent slip-length boundary condition. The trajectories of individual molecules in Poiseuille flow are examined, and it is also found that their average behavior is given by Taylor-Aris hydrodynamic dispersion. An immiscible two-fluid system is simulated by a species-dependent intermolecular interaction. A static meniscus is observed whose contact angle agrees with simple estimates and, when motion occurs, velocity-dependent advancing and receding angles are observed. The local velocity field near a moving contact line shows a breakdown of the no-slip condition and, up to substantial statistical fluctuations, is consistent with earlier predictions of Dussan [AIChE J. 23, 131 (1977)].
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