Hydrodynamic boundary condition at the fluid-solid interface

While the no-slip boundary condition (no relative motion at the fluid-solid interface) has been universally accepted as a cornerstone of hydrodynamics, it was known for some time that it is incompatible with the moving contact line, defined as the motion of the line of intersection of the immiscible (two phase) fluid-fluid interface with the solid wall. By employing Onsager's principle of minimum energy dissipation, we show in this work that a continuum hydrodynamics, comprising the equations of motion as well as the relevant boundary conditions, can be obtained which resolves the moving contact line problem. Our derivation reveals that just as other dissipative system dynamics, the fluid-solid interfacial boundary condition should be consistent with the framework of linear response theory. Implications of our results are discussed.