Interdisciplinary Applied Mathematics

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Results from these MD simulations showed an intriguing response. In

FIGURE 1.8. Snapshot of the Lennard-Jones fluid near a wall. The wall atoms are denoted by crosses, and fluid atoms by circles. This layered structure of the fluid molecules in close proximity with the wall is responsible for the density fluctuations shown in the previous figure. (Courtesy of J. Koplik and J. Banavar.)



particular, at low values of the shear rate, a slip velocity proportional to у was obtained with corresponding values of the slip length b ranging from 0 to about 17a. The slip length increases as the wall energy ew decreases or the wall density pw increases. This is the linear response, and it is consistent with previous investigations. However, beyond 17a a strongly nonlinear response was observed with the slip length b diverging beyond a critical value of    the    shear    rate    yc.    The    results    of MD simulations    of    (Thompson


and Troian, 1997) are summarized in Figure 1.9 in a normalized form and for various conditions. The dashed line represents a best fit to the data in the form



bs_


b2



l-l



Y



c



a



(1.2)


where the exponent a = —1/2 is specific for the conditions that were tested in (Thompson and Troian, 1997), but may be different for other conditions. Such results suggest that at high shear rates and even for Newtonian fluids the liquid behavior in the near-wall vicinity is non-Newtonian; see also equation (10.7). At values of shear rate close to a critical value, such nonNewtonian behavior may propagate into the flow, and in that case even small variations in the wall surface may have a significant effect. It is not clear whether the conditions employed in MD simulations can match the experimental conditions. Experiments in submicron channels and gaps us-

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