Interdisciplinary Applied Mathematics

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Comparison of velocity obtained from MD simulation and continuum

FIGURE 12.7. Velocity profile across the channel for case 5 (W = 0.95 nm, as = +0.124 C/m2). The negative velocity close to the channel wall is statistical noise.


flow theory for case 4, where the channel width is 2.22 nm, also indicates that though the continuum flow theory based on a constant viscosity overestimates the velocity in the entire channel, it can be used to study the flow behavior in the central part of the channel, provided that the velocity at a position 6 away from the channel wall is given. It is also observed that the no-slip plane is located at approximately 0.14 nm from the channel wall. This is similar to what (Travis and Gubbins, 2000) had observed for Poiseuille flow of Lennard-Jones atoms in various channel widths where the no-slip plane is located at the position closest to the channel wall that a fluid atom can approach and is independent of the channel width.


Figure 12.7    shows    the    velocity    profile    of    water    across    the    channel    for


case 5, where the channel width is 0.95 nm and the surface charge density is 0.124 C/m2. The characteristics of the velocity profile are significantly different from those of case 1 (channel width: 3.49 nm) and case 4 (channel width: 2.22 nm). Specifically:


1. The strain rate du/dy goes to zero at z « 0.09 nm and z « 0.14 nm, and


2. The velocity at z « 0.14 nm is higher than the velocity at z « 0.09 nm, and the velocity decreases from z « 0.14 nm to z « 0.09 nm. Similar behavior was also observed by (Travis and Gubbins, 2000) and (Travis et al., 1997) for Poiseuille flow of Lennard-Jones atoms when the channel width approaches 4 to 5.1 times the diameter of the fluid molecules.

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