Simple shear flow of a Herschel-Bulkley fluid with wall slip above a threshold stress

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• The simple shear flow of a Herschel-Bulkley fluid in the presence of wall slip is solved. • A slip law with a threshold slip stress is applied. • The apparent flow curve is characterized by two plateaus corresponding to the onset of the sliding and yielding branches. • The resulting apparent flow curves agree with certain rheometric data on yield stress materials. • Analytical solutions are derived for certain values of the flow index and the slip exponent. The simple shear flow of Herschel-Bulkley fluids is analyzed, under the assumption that wall slip occurs at both plates above a characteristic wall shear stress, the slip yield stress. The latter critical value is usually lower than the yield stress of viscoplastic materials exhibiting wall slip. The effects of wall slip and the slip yield stress on the apparent flow curve, i.e. the plot of the shear stress vs the apparent shear rate, are investigated. With non-viscoplastic fluids, the flow curve is gap-independent below the slip yield stress. Above a critical apparent shear rate at which the slip yield stress is exceeded, a plateau zone is encountered, and then the flow curve becomes gap dependent. Viscoplastic materials remain at rest for stresses below the slip yield stress, slide unyielded for stresses between the slip yield stress and the yield stress, at half the velocity of the moving plate, and yield and slip for stresses above the yield stress. Hence, the apparent flow curve exhibits an initial plateau corresponding to slip yield stress, followed by a rapid-growth gap-dependent part and a second plateau corresponding to the yield stress, and then approaches asymptotically its zero-slip-yield-stress counterpart. This behavior describes well certain rheometric experiments on concentrated suspensions and pastes.