Tangential annular (Couette) flow of a viscoplastic microgel with wall slip

Abstract

The tangential annular or Couette flow of a viscoplastic microgel, i.e., 0.12 wt. % aqueous solution of poly(acrylic acid), Carbopol® 940, under isothermal and creeping flow conditions was investigated by simultaneous particle image velocimetry and rheometrical measurements (Rheo-PIV). A wide range of ratios of the inner over the outer radii of the annuli, i.e., κ = 0.329, 0.749, and 0.933, were used. The PIV measurements revealed the viscoplasticity of the microgel in Couette flow via the formation of plug flow (rigid body motion) and slip at the two walls. A procedure that relied on the characterization of the wall slip behavior was developed for the determination of the yield stress of the microgel, in turn leading to other parameters of the shear viscosity of the viscoplastic fluid. The wall slip velocity versus wall shear stress behavior of the microgel was overall consistent with the mechanism of apparent slip for all three gaps. However, the apparent slip layer thicknesses were dependent on the wall shear stress and were generally greater under deformation conditions, in comparison to those under which plug flow occurred. For all three Couette gaps, the experimental velocity distributions compared favorably with the predictions of the analytical solutions of the equation of motion for the tangential annular flow of the Herschel–Bulkley fluid subject to apparent wall slip.