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Effect of slip boundary conditions on flow homogeneity in cone-and-plate geometries
Phys. Rev. Fluids 11, 074001 – Published 6 July, 2026
DOI: https://doi.org/10.1103/pdp6-zczm
Abstract
Cone-and-plate (CP) viscometry is now widely employed to quantify slip lengths on superhydrophobic surfaces owing to its sensitivity at the micrometer scale; however, the presence of wall slip disrupts its intrinsic flow homogeneity. In this study, we present a combined theoretical and numerical investigation on how different slip boundary formulations affect flow homogeneity and its consequences for non-Newtonian fluid flows. Semianalytical solutions are derived under both constant slip-length and constant wall-stress boundary conditions. Numerical simulations are performed to examine the spatial structure of velocity, shear rate, and apparent viscosity in non-Newtonian fluids. The results demonstrate that a fixed slip length induces pronounced spatial variations in shear rate and radial dependence of viscosity for Carreau fluids, whereas a stress-controlled slip condition restores a nearly uniform shear field despite the presence of slip. The drag reduction and effective slip length for shear-thinning Carreau fluids are shown to depend explicitly on the imposed shear rate, with maximum slip enhancement occurring in the intermediate shear-thinning regime. These findings clarify the fundamental limitations of conventional slip interpretations in CP rheometric systems and provide a physically consistent framework for a homogenous flow field.
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