Interdisciplinary Applied Mathematics

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FIGURE 1.9. Summary of results from MD simulations reported in (Thompson

and Troian, 1997). The normalized slip length is plotted against the normalized shear rate. All data collapse into a universal curve as shown; т is a relaxation time scale. (Courtesy of S. Troian.)

ing the surface force apparatus (see Section 10.5) have revealed a slip length much larger than what is predicted by MD simulations, often by an order of magnitude!

The question of validity of the continuum approach arises also in particulate flows, especially in applications involving nanoparticles. A systematic MD study was undertaken by (Drazer et al., 2002) for a colloidal spherical particle through a nanotube containing a partially wetting fluid. They used a generalized Lennard-Jones liquid of the form

Vps(r) = 4e



12    / r

— CFSa


where cFS is an attractive strength that controls the wetting properties of the fluid-wall system. Full wetting corresponds to cFS = 1, while poor wetting corresponds to    cFS    ^ 1.    Drazer    et    al.    demonstrated    that    the    MD

simulations are in good agreement with the continuum simulations of (Bungay and Brenner, 1973) despite the large thermal fluctuations present in the system.    This is    true    even    for    very    small    particles    of    order 2 nm.    In

Figure 1.10 we plot comparisons of MD and continuum simulations, first reported in (Drazer et al., 2002), for different values of the nanotube radius

FIGURE 1.10. Mean sphere velocity in a microtube as a function of the radii ratio. Points correspond to MD simulations of Drazer et al. (2002) and the solid line the continuum results of Bungay & Brenner (1973). The error bars denote temporal fluctuations. (Courtesy of J. Koplik.)

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