Solid/liquid interface slippage

Abstract In this chapter we discuss the results of theoretical and experimental studies of the structure and dynamics at solid-liquid interfaces employing the quartz crystal microbalance (QCM). Various models for the mechanical contact between the oscillating quartz crystal and the liquid are described, and theoretical predictions are compared with the experimental results. Special attention is paid to consideration of the influence of slippage and surface roughness on the QCM response at the solid-liquid interface. The main question, which we would like to answer in this chapter, is what information on... 

Mesoscopic roughness at the solid-liquid interface can greatly modify both interfacial flow and static wetting properties leading to two behaviors, either a decrease [45,64,102] or an increase [63,103] of surface slippage with roughness. 

Although the nonslip boundary condition has been remarkably successful in reproducing the characteristics of liquid flow on the macroscopic scale, its application for a description of liquid dynamics in microscopic liquid layers is questionable. A number of experimental [62-64] and theoretical [65,66] studies suggest the possibiility of slippage at solid/liquid interfaces. 

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. 

N. V Churaev, V. D. Sobolev, and A. N. Somov, Slippage of liquids over lyophobic solid surfaces,/ Coiioid Interface Sci, 97, 574-581 (1984). 

In the first part the main fundamental aspects of the description of liquids interfaces at nanometer scale are discussed. In chapters 1 and 2, two essential elements of the liquid-solid interfaces are described, namely, the liquid structuration and the hydrod5mamic slippage that occur at a solid wall. In the case of liquid droplets. 

Basically the same procedure can be applied to the case where the liquid is slipping on the substrate by introducing an extrapolation length (slippage length) b within the substrate (see Fig. 2) where the flow velocity would be zero, i.e., the non-slip boundary would be reached at a virtual interface inside the solid. Thus, one expects /imin b [132]. Slippage is particularly relevant in the case of entangled... 

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. 

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