Viscoplastic displacements in axially rotating pipes

Abstract

We investigate experimentally the effects of a pipe axial rotation on buoyant miscible displacement flows in an inclined pipe. The displacing Newtonian fluid (salt-water solution) is heavier than the displaced viscoplastic one (Carbopol solution). Via image processing techniques and ultrasound Doppler velocity measurements, we analyze the key flow features such as the flow patterns, the velocity and concentration fields, and the leading front velocity (Vˆf) as well as the trailing front velocity (Vˆt) of the displacement flow. The main flow parameters in our experiments are the pipe inclination angle, the small density difference between the two fluids, the yield stress of the displaced fluid, the imposed mean flow velocity (Vˆ0), and most importantly the pipe rotation speed. We find that increasing the pipe rotation speed enhances the transverse mixing between the two fluids and, above a critical transition, leads to a complete removal of the displaced viscoplastic fluid. We classify the flow regimes into efficient and inefficient displacement flows, using appropriate dimensionless groups, i.e. the Rossby number (Rb) and the Froude number (Fr). We find that the critical transition between the two flow regimes can be roughly described by a critical Rossby number (Rbc), as a function of Fr, independent of the other flow dimensionless numbers. For Rb≤Rbc, we find that Vˆf≈1.6Vˆ0 and Vˆt≈Vˆ0, while for Rb>Rbc we propose an empirical relation for the leading front velocity versus the Rossby number. These findings can offer new insight to control viscoplastic displacement flows using rotational motion.