Interdisciplinary Applied Mathematics

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The effective use of the surface force apparatus (SFA) in the 1990s has led to many interesting experimental results and detailed studies of boundary slip with water and other substances. SFA employs a sphere in close proximity to a plane, but other configurations are also possible, e.g., two crossed cylinders. The two surfaces are approaching at a controlled speed, causing drainage of the liquid placed within the sphere-plane gap; see sketch of figure 10.19. Typically, an oscillation of small amplitude is imposed on the sphere (or the plane), and the response force on the plane is recorded. The

FIGURE 10.20. Slip length versus driving rate obtained in SFA experiments. Sucrose solutions of different concentrations are used to change the viscosity: 19.2 mPa s (crosses); 38.9 mPa s (diamonds); 80.3 mPa s (triangles); taken from (Craig et al., 2001). (Courtesy of V. Craig.)


ratio of the    force    component    in-phase with    the    oscillation    to    the    amplitude


of the oscillation gives the normal stiffness coefficient, while the corresponding ratio for the out-of-phase component gives the damping coefficient.


In (Baudry et al., 2001), a drop of glycerol was placed between the two surfaces with roughness of about 1 nm. The surfaces of the plane and the sphere    were    coated    with    thiol and    gold,    respectively,    in a first    set    of


experiments, and with thin cobalt film (for both sphere and plane) in a second set of experiments; cobalt makes the surface hydrophilic, while thiol makes it hydrophobic. The measured (advancing) contact angles for thiol and cobalt were 94° and 62°, respectively. The main finding, based on the measured damping coefficient, was that at sphere-plane distances less than 300 nm    the    hydrophobic    surface    gave    a large    deviation    from    the    no-slip

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