REVISITING THE HYDRODYNAMIC BOUNDARY CONDITION: NEW RESULTS ON AN OLD PROBLEM

The no-slip hydrodynamic boundary condition (NSBC) states that there can be no relative motion at the fluid-solid interface. In spite of the lack of first-principles support, either from kinetic theory or otherwise, NSBC has been regarded as a pillar of continuum hydrodynamics for more than a century. However, over the past fifty years, it has been realized that in immiscible two-phase flows, the moving contact line (MCL), defined as the intersection of the fluid-fluid interface with the solid wall, is incompatible with the NSBC. In 1988, molecular dynamic (MD) simulations for the first time explicitly demonstrated the breakdown of NSBC in the vicinity of the MCL. Since that time it was realized that without a new framework to treat the boundary condition(s), continuum hydrodynamics would be unable to accurately model nanoscale or microscale hydrodynamic behavior. This is sometimes described as an example of the "breakdown of continuum.

By applying Onsager's principle of minimum energy dissipation, we have recently derived the boundary conditions that for the first time enabled quantitative prediction of the MD simulation results from continuum hydrodyanmics, and in so doing revised the NSBC [1]. Our results indicate that the hydrodynamic boundary condition(s) should be consistent with the general statistical mechanic principle with underlie all linear response phenomena in dissipative systems. Implications of our results will be presented.

Note from Publisher: This article contains the abstract only.