Interdisciplinary Applied Mathematics

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is close    to    the    case    of    mercury    on    a glass    surface, a flow    configuration

studied in the experiments of (Chuarev et al., 1984) with mercury flowing through glass capillaries. For this hydrophobic case a slip length of about 15 molecules was computed, whereas for the 100° case the no-slip condition was valid all    the    way    to the    wall    boundary.    Taking into    account    that    the

molecule size is about 0.25 nm, the maximum computed slip length in the MD simulations of (Barrat and Bocquet, 1999) is about 4 nm, which is still much smaller than any of the experimental data, especially for hydrophobic surfaces.

10.5.2 Conceptual Models of Slip

We have seen that the MD simulations systematically underpredict the slip length deduced from the various experiments either based on force curves in the surface force apparatus or based on the flowrate measured in capillaries and microchannels. Specifically, the MD simulations predict a slip length roughly ten times smaller than in the experiments, and such a large discrepancy implies that there are some other physical phenomena not included in the simulation. Here we present some of the physical models that have been proposed in the literature that can justify the large values of slip length and the origin of slippage.

1. Molecular slippage: This theory first appeared in the Russian literature    and is    due    to Tolstoi    (1952);    it    was analyzed    more    thoroughly    in

(Blake, 1990). It provides a link between the mobility of the molecules in the first few layers closer to the wall with the interfacial energy associated with the liquid-solid interface. Therefore, it relates directly the contact angle to the slip length.

2. Gaseous film: This model was first suggested by (Ruckenstein and Ra-jora, 1983) and was also discussed by (Vinogradova, 1999). It assumes that there may be a    film    of    gas    at    the    interface    between    the    solid    surface and

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