Fluctuating motion in a homogeneous liquid-liquid dispersed flow at high phase fraction

Abstract

Velocity fluctuations in a dispersed liquid-liquid cocurrent upward flow, statistically homogeneous and gravity driven, have been characterized with the help of a particle image velocimetry technique in a matched refractive index medium. Results first show a strong anisotropy of the fluctuations field in the range of phase fraction investigated (from 0.01 to 0.4), the axial component of the kinetic energy of the continuous phase being 4–5 times larger than the transverse component. The axial component of the fluctuating energy of the continuous phase normalized by the square of the local slip velocity follows a 2∕3 power law as a function of the product of the phase fraction by the local drag coefficient, in the whole range of phase fraction investigated. This remarkable result agrees with the hypothesis of a local equilibrium between the dissipation of these fluctuations at a nonresolved length scale (0.12×drop diameter) and their production rate is induced by the mean drag force. Examination of the local structure of the instant fluctuating velocity field shows that the continuous phase instant fluctuations are locally correlated with the dispersed phase spatial distribution that is found to follow a Poisson law. The characteristic length of this distribution in the direction of the flow is of the order of several drop diameters and is comparable with the integral scale of the fluctuations of the continuous phase (correlation length). These results at high phase fraction are discussed and compared with experimental data and models available in the literature, for most of them in dilute systems.