Interdisciplinary Applied Mathematics

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is kept    at    1.0    units.    In    Figure    1.8    we    show a snapshot    of    the    flow in    the


near-wall region to demonstrate the layering phenomenon, where the fluid atoms are organized in horizontal layers parallel to the wall atomic layers. This layering is responsible for the large density fluctuations very near to the wall. While in liquids this effect extends only a few atom diameters from the wall, in gases the wall-fluid interaction extends over much greater length, and this has to be accounted for explicitly.


The amount of slip revealed in the above MD simulations depends strongly on the wall type and its modeling, which is determined by the strength of the liquid-solid coupling and the wall-liquid density ratio, among others. A shear-driven (Couette) microflow was simulated by (Thompson and Troian, 1997) in a channel with height h = 24.57a using a truncated Lennard-Jones potential,    which    was set    to zero    for    r >    rc    = 2.2a.    The    wall-liquid


interaction was also modeled with a Lennard-Jones potential but with different energy and length scales ew and aw, respectively. The liquid density was described by p = 0.81a-3, and its temperature was maintained at T = 1.1kB/e. A very wide range of values of shear rate у was investigated in (Thompson and Troian, 1997), leading to both linear and nonlinear responses. The    shear rate    was    scaled    with    the    characteristic    time    of    the


Lennard-Jones potential ma2


т


FIGURE 1.7. Density profile of Lennard-Jones fluid in a channel made of two atomic    walls. The    length    dimensions    are    in molecular    units    (diameter    of    a


molecule is 1.0). (Courtesy of J. Koplik and J. Banavar.)


e


where m is the mass of the molecule. A linear velocity profile was obtained in the bulk of the flow, in accordance with Navier-Stokes solutions, suggesting that the dynamic viscosity was constant (Newtonian fluid).

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