Slip velocity and drag law in a liquid-liquid homogeneous dispersed flow

Local measurements of phase velocities and phase fraction in a dense liquid-liquid homogeneous flow were done based on an application of PIV with a refractive index matching technique. This technique allowed to measure simultaneously both phase velocities and phase fraction fields, as well as the drop mean diameter in a vertical cocurrent flow of n-heptane dispersed in an aqueous solution of glycerin. The evolution of the relative velocity as a function of the phase fraction (0–0.4) was studied with moderate particle Reynolds numbers (10–100) for drops behaving as spherical rigid particles. A local drag coefficient was derived from these measurements. The calculated mean relative velocity as a function of the local phase fraction with existing classical drag coefficient laws showed significant discrepancies with the measurements overestimated. Thus, the drag coefficient variation rate as a function of the phase fraction was underestimated by the models. The evolution of the normalized velocity (by the terminal velocity) as a function of the phase fraction was predicted correctly with mixture viscosity models in a creeping flow regime.