Axial annular flow of a viscoplastic microgel with wall slip

The fully developed velocity distributions of a viscoplastic Carbopol microgel [0.12 wt. % poly(acrylic acid) in water] flowing axially in the annular gap between two long concentric cylinders were determined. The ratios of the length over the gap and the inner over the outer radii, κ, of the annulus were 442 and 0.78, respectively. The particle image velocimetry, PIV, measurements revealed that the viscoplasticity of the microgel in axial annular flow is manifested via the formation of plug flow and wall slip. The plug flow region spanned the entire or part of the annular gap depending on whether the absolute values of the shear stresses at the two walls were below or above the yield stress of the microgel, respectively. For all flow rates, the velocities at the two walls were similar indicating that the absolute values of the wall shear stress were also similar. Equality of the shear stresses at the two walls suggested that axial annular flow at a relatively high κ can be used as a viscometric flow for which the shear stresses at the two walls can be obtained directly from the fully developed pressure gradient and the annulus dimensions. The velocity distributions compared favorably with the predictions of the analytical solutions of the equation of motion for the axial annular flow of Herschel-Bulkley fluid subject to wall slip. The agreement between the experimental data and the predictions of the analytical model further validates the use of viscoplastic constitutive equations in conjunction with the wall slip condition for the analysis of steady and fully developed shear flows of viscoplastic fluids.