Interdisciplinary Applied Mathematics

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condition with slip length b « 40 nm, while for the cobalt surface the slip was zero. The molecular size of the glycerol molecule is 0.6 nm, so the slip length is about 65 times the molecular diamater of glycerol. Interestingly, at distances smaller than 5 nm, both hydrophobic and hydroplilic surfaces gave the same response and it was assumed that at these small distances the film did not behave like a liquid.

In (Craig et al., 2001), SFA measurements were also used to infer boundary slip for water on sphere-plane surfaces with (advancing) contact angle 70°. The silica sphere and the mica flat surface were coated with a layer of gold and an additional layer of titanium to promote adhesion. Aqueous solutions of sucrose at various concentration levels were used to control the

viscosity magnitude. It was found that at low viscosity and low approach rate of the    surfaces,    the    no-slip condition    was    valid,    whereas    at    higher    vis

cosities and shear rates boundary slip was observed. The corresponding slip length    was    up    to    18    nm,    corresponding to    the    highest    viscosity    of the

aqueous solutions (80.3 mPa s) and varied nonlinearly with the driving rate (up to 22 pm/s). A summary of these results is included in Figure 10.20. In a follow-up experiment in (Bonaccurso et al., 2003), the effect of roughness mounted    on    hydrophilic    surfaces    on    the    slip    length    was    investigated.

Roughness with rms heights of 0.7 nm, 4 nm, and 12.2 nm was tested, and the force curves showed clearly an enhanced slip at the wall as the roughness increased. The particular slip length value depended on the way that the data were fitted, but very large values of b were reported on the order of hundreds of nanometers.

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