Interdisciplinary Applied Mathematics

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covery after photobleaching and total internal reflection at the solid-liquid interface was employed to directly probe the velocity within 80 nm of a solid wall. The surface was made of modified sapphire treated with OTS (y > 21 mJ/m2) and FDS (perfluorodecanetrichlorosilane, j < 13 mJ/m2) in order to change the interfacial energy in a controlled manner. It was found that for the bare sapphire surface a slip length of 175 nm (±50 nm) was obtained, while for a dense OTS layer the slip length was 400 nm (±100 nm) independent of the shear rate in the range from 200 s-1 to 2000 s-1. For the FDS    surface    no    boundary    slip    was    observed.    In    agreement    with

most of    the    other    investigators, (Pit    et    al.,    2000)    also    hypothesized    that

roughness decreases slip, and thus it is in competition with the strength of the fluid-surface interaction.

With regard to microfluidic applications directly involving microchannels, it    is not    clear    how    much    the    slip    boundary    condition depends    on    the

way that the flow is driven, although the majority of the experimental work clearly points to a strong dependence on the shear rate (an exception is the    work    of    (Pit    et    al.,    2000)). In the work    of Bau    and    collaborators

(Urbanek et al., 1993), a pressure-driven flow was considered, and boundary slip    was reported    for    channels    with the    smallest    height    of 20    p,m    and

silicone oil    as    well    as isopropol    alcohol    (see Figure    1.16 in    Section    1.2).    A

comprehensive study of pressure-driven flows was undertaken in (Cheng and Giordano, 2002), with several fluids for very small microchannels fabricated lithographically down to 40 nm. The channel width was 20 pm, and the length was in the range of 100 to 900 pm; the roughness was about 0.5 nm. The flowrate was measured using a macroscopic capillary in series with the outlet side of the sample, but for smaller flowrate values a microchannel was fabricated and the flow was measured with photomicroscopy. One of the surfaces of the channel was glass, and the other one was coated with photoresist; no measurements of the contact angle were made.

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