# Interdisciplinary Applied Mathematics

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In MD simulations the slip length predicted is typically much lower due to the substantial pressure imposed, which can modify the wetting properties of the surface. Specifically, MD simulations with hexadecane were performed in (Stevens et al., 1997), and dependence on the strength of the liquid-wall interaction was established similar to that in the experiments. However, a realistic representation of the surface, i.e., to account accurately for the glass or sapphire or other surfaces tested experimentally, is not available. In (Cieplak et al., 2001), MD simulations were performed for a simple molecule as well as a chainlike molecule. They were described by a shifted Lennard-Jones potential for two atoms for the former and for ten atoms for the latter. The consecutive atoms along the chain were tethered by the finitely extensible nonlinear elastic potential (FENE) used often in polymer modeling; it has the form

Vfene = k/2t2 log[1 — (r/ro)2],    (10.6)

where к = 30e and r0 = 1.5a. The crucial wall-fluid interaction was modeled by a distinct Lennard-Jones potential of the form

Vw = 16e[(r/a)~12 — CFs(r/a)~6],

where cFS determines the wall type, so that cFS = 1 corresponds to a thermal (attractive) wall and cFS = 0 corresponds to a specular (repulsive) wall. The narrowest channel simulated had dimensions of 13.6a x 5.1a x 12.75a, with the the last dimension denoting the distance between the two walls (channel height).

The results for Couette flow in (Cieplak et al., 2001), suggest that the slip length is independent of the type of flow or the channel height, but that it is a strong function of the wall type. When cFS = 0 there is a relatively large slip (about 10a), but for cFS = 1 the slip length is equal to the negative of the distance between the    wall    and    the    second    layer    (about    -1.7a).    In    the

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