Friction and the Continuum Limit - Where is the Boundary?
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Friction and the Continuum Limit – Where is the Boundary? Yingxi Zhu and Steve Granick Department of Materials Science and Engineering University of Illinois, Urbana, IL 61801 USA ABSTRACT The no-slip boundary condition, believed to describe macroscopic flow of low-viscosity fluids, overestimates hydrodynamic forces starting at lengths corresponding to hundreds of molecular dimensions when water or tetradecane is placed between smooth nonwetting surfaces whose spacing varies dynamically. When hydrodynamic pressures exceed 0.1-1 atmospheres (this occurs at spacings that depend on the rate of spacing change), flow becomes easier than expected. Therefore solid-liquid surface interactions influence not just molecularly-thin confined liquids but also flow at larger length scales. This points the way to strategies for energy-saving during fluid transport and may be relevant to filtration, colloidal dynamics, and microfluidic devices, and shows a hitherto-unappreciated dependence of slip on velocity.
INTRODUCTION The assumption that flowing single-component viscous liquids come to rest within 1-2 molecular dimensions of a solid boundary, so that fluid molecules at the boundary move on average with the same tangential velocity as that boundary, lies at the heart of our understanding of the flow of simple low-viscosity fluids and comprises a bedrock for much sophisticated calculation [1,2]. Its validity has been debated for over 250 years [3] but justified on practical grounds by the fact that its phenomenological predictions appear to agree with experiments, even for flow through thin capillaries [4]. This “stick” contrasts with “slip” characteristic of highly viscous polymers when the shear stress is high [5], gas flowing past solids [6], superfluid helium [7], and moving contact lines of liquid droplets on solids [8]. Recently much interest has been given to sheared films of molecularly-thin simple liquids, where slip is also believed to occur, but these interesting anomalies, which are relevant primarily to friction, disappear when films are thicker than 5-10 molecular dimensions [9]. Any breakdown of the stick boundary condition at larger length scales would have potential implications in areas such as groundwater transport, filtration, colloidal dynamics, and microfluidic devices, and might form the basis of a strategy for saving energy in the transport of fluids such as oil and gasoline. For these practical reasons as well on scientific grounds, failure of the no-slip flow boundary condition for low-viscosity fluids would be of considerable interest. Here we put to direct test recent theoretical predictions [10,11] and molecular dynamics simulations [14] that predict its breakdown when low-viscosity fluids fail to wet a smooth solid boundary. We confirm the generality of a study that found slip of hexadecane based on fluorescence studies [12], of another recent study that found toluene to slip on mica that had been modified with adsorbed C60 [13], as well as of controversial earlier literature [14]. The physics appea
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