Slip characteristics, liquid-solid interface

The boundary condition is controlled by the extent to which the liquid feels a spatial corrugation in the surface energy of the solid. This depends on a number of interfacial parameters, including the strength of the liquid-liquid and liquid-solid interactions, the commensurability of the substrate and the liquid densities, characteristic sizes, and also the roughness of the interface. In order to quantify the slippage effect, the slip length. 

The nature of boundary conditions in hydrodynamics was widely debated in the nineteenth century, and many of the great names in fluid dynamics have expressed an opinion on the subject, as discussed in a recent review. The linear slip boundary condition was introduced by Navier, and this remains a standard characteristic of the slip used today. Helmholtz and von Piotrowski were probably the first to report some evidence of slippage at the solid-liquid interface. We refer the reader to a comprehensive review for detailed accounts of early experimental work. The significance of hydrophobicity for the slip phenomenon does not seem to be recognized at this early stage. 

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