  The ability to predict and/or control wall slip is a fundamental problem in
the hydrodynamics of yield stress fluids, which is poorly understood to date
and has important applications in bio- and micro-fluidic systems. Systematic
measurements of steady flows of a simple yield stress fluid (Carbopol Ultrez
10) in a plane acrylic micro-channel are used to establish rigorous scaling
laws for the wall velocity gradient and the slip velocity. By means of
epi-fluorescent microscopy combined with a custom developed Digital Particle
Image Velocimetry (DPIV) technique, times series of velocity fields were
measured within a wide range of flow rates and three distinct flow regimes were
identified: full plug, partial plug and fully yielded. Corresponding to each
flow regime, wall velocity gradients and slip velocities were obtained by
extrapolating the velocity profiles using a smoothing spline function. By
combining the flow field measurements with the macro-rheological measurements,
scaling laws for the wall velocity gradient and the slip velocity with the wall
shear stress were identified, and compared with results from the literature.
Detailed microscopic measurements of the velocity field enabled an assessment
of the effectiveness of a chemical treatment of the channel walls meant to
suppress wall slip proposed by Metivier and coworkers in Ref. [1].
