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Slip Boundary conditions for water flows in hydrophobic nanoscale geometries

J. H. Walther , R. L. Jaffe , T. Werder , and P. Koumoutsakos
Swiss Federal Institute of Technology, CH

Keywords: nanofluidics, slip condition , hydrophobic surfaces,

In a collaboration with experimental groups at NASA and ETH Zurich we conduct computational studies towards the development of biosensors in aqueous environments. Examples include arrays of carbon nanotubes that may operate as artificial stereocillia (Noca et al., 2000) or as molecular sieves. Here we present novel results assesing the validity of the no-slip boundary condition in nanofluidics for prototypical geometries such as flow past a carbon nanotube and flow between two graphite plates. The role of the geometry on the slip length is investigated. The results show significant slip lengths (in disagreement with the macroscale notion of no-slip at wall-fluid interfaces) and are consistent with relevent experimental works of water flows over other hydrophobic surfaces. First we report results from large scale non-equilibrium molecular dynamics (NEMD) simulations of water flow past graphite surfaces in a setting equivalent to a nanoscale planar Couette flow (Figure 1). A graphite surface is known to be hydrophobic(Adamson:1997), and to exhibit physiochemical similarity with carbon nanotubes in aqueous environments (Balavoine:1999). The validity of the no-slip condition employed in macroscale Navier-Stokes modeling has been questioned by experiments of water in hydrophobic capillaries (Churaev:1984, Baudry:2001). In these experiments, the water is found to exhibit a finite fluid velocity at the fluid-solid interface, with a slip length of 28--30nm.The present NEMD simulations use the SPC/E water model and the graphite-water interaction is modeled using a Lennard-Jones potential calibrated to match the experimentally measured macroscopic contact angle of water on graphite, cf. (Werder:2002). The average density profile in the channel displays the well-known peaks in the vicinity of the interface and bulk properties at the center of the channel cf. Figure 2a. Setting the upper walll in motion with speeds of 50 to 100m/s drives the water and a linear velocity profiles is established after 1-2ns as shown in Figure 2. The velocity profiles indicate a slip length approximately Ls = 30nm in good agreement with the relevant experimental values(Churaev:1984, Baudry:2001). In order to examine geometry effects on the no-slip condition we conduct also simulations of flows past carbon nanotubes (with diameters of 1 to 2 nm) whose axis is placed perpedincular to the mean flow (Figure 1). In this case a slip length of 1nm is observed. A systematic study is conducted where the effects of geometry and driving mean velocity are assesed and a boundary condition for macroscale simulations of water flows past hydrophobic surfaces is proposed.

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