Interdisciplinary Applied Mathematics

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FIGURE 10.21. Effect of roughness and flow rate (or driving rate) on boundary slip. Plots (a), (b) and (c) show images of roughness at 6 nm, 3.5 nm, and 2 nm, respectively. Plot (d) shows the correction factor in the Reynolds-Vinogradova theory (equation (10.11)), and plot (e) the corresponding slip length. Filled symbols correspond to deionized water and open symbols to tetradecane. The various curves correspond to roughness of: squares — 6 nm; circles — 3.5 nm; triangles — 2 nm; and diamonds — atomically smooth. (Courtesy of S. Granick.)

of 105 s-1 is required to cause onset of boundary slip. These results are in disagreement with the results of (Bonaccurso et al., 2003) for hydrophilic surfaces.

There has been some skepticism regarding the findings of boundary slip based on the SFA measurements. However, similar conclusions were obtained in (Bonaccurso et al., 2002), using a colloidal probe technique to measure forces between hydrophilic surfaces (mica and glass) for water. In particular, spherical borosilicate glass particles of radius 10 p,m were sintered to atomic force microscope (AFM) cantilevers. The hydrophilic surface was periodically moved up and down, and the cantilever deflection was measured optically. A slip length of up to 9 nm was measured for shear

FIGURE 10.22. Normalized flowrate (left) and slip length versus channel height for several fluids. (Courtesy of N. Giordano.)

rates of 104 s-1. Electrokinetic effects, which could render the data erroneous by causing an increase of the effective viscosity in the electric double layer    (EDL),    were    found    insignificant.    In    another study    in (Pit    et    al.,

2000), a novel technique was employed to test boundary slip for hexadecane flowing over a hydrocarbon/lyophobic smooth surface. This technique was adapted from an experimental setup used to investigate boundary slip in polymers. In particular, fluorescent probes of the size of the hexadecane molecules were used as traces in a capillary formed between two parallel disks, only    one    of    which    was    rotating. A    combination    of    fluorescence    re

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