Investigation Of Droplet Statistics And Momentum Transport Of Emulsions In A Turbulent Shear Flow

Turbulent emulsions,usually referred to as dispersion systems formed by two im-miscible liquid components(e.g.oil and water)in turbulence,are typical multi-scale nonlinear hydrodynamic systems.They are ubiquitous in nature and also play an impor-tant role in numerous industrial fields,such as oil extraction and transportation,chemical engineering and materials production.This paper combines experimental and theoretical analyses,using high-speed imaging analysis and high-precision torque measurements,to systematically investigate the statistical properties of dispersed droplets and momentum transport characteristics in Taylor-Couette turbulent emulsions,and the results can provide theoretical support for turbulence drag reduction,enhanced mixing,and the regulation of the dispersed droplet size in industrial applications.The statistical properties of the size of dispersed droplets in turbulent fields and the mechanism of droplet fragmentation were investigated at low volume fractions of the dispersed phase.The probability density distribution of the mean droplet size is found to follow a log-normal distribution,indicating that droplet fragmentation is determined by a cascade random fragmentation process,of which the physical model is given.Based on the scalar law relationship between mean droplet size and Reynolds number,it is revealed that the droplet generation occurs within the turbulent boundary layer and is dominated by the dynamic pressure difference due to the mean velocity gradient within the boundary layer,rather than being described by the classical theoretical model of droplet turbulence fragmentation.In addition,we have investigated the fragmentation process of viscous droplets.Based on the revealed mechanism of droplet breakup within the boundary layer,a physical model of viscous droplet breakup is derived and experimentally verified.The model is of great universality and has important application value.The global momentum transport characteristics of the turbulent emulsion are inves-tigated at high dispersed-phase volume fractions.A new method for calculating the effec-tive viscosity of the system is proposed to break through the low Reynolds number limita-tion of conventional rheological viscosity measurements and to enable the measurement and analysis of the effective viscosity of a turbulent emulsion at high Reynolds numbers.It is found that the effective viscosity increases with increasing volume fraction of the dispersed phase but decreases with increasing Reynolds number,showing a shear thin-ning effect,which can be quantitatively described by the classical non-Newtonian fluid model.The asymmetry in droplet size and effective viscosity between the water-in-oil and water-in-oil systems at corresponding volume fractions was identified,and the mech-anism for the formation of the asymmetry was determined by artificially adding a certain concentration of oil-soluble surfactant.By dynamically changing the volume fraction of the dispersed phase,the phase in-version and its physical mechanism were investigated.It is found that the phase inversion corresponds to the abrupt changes in both local droplet size and global drag.Based on the classical Landau mean field theory,we propose a quantitative physical model to describe the critical behavior of the phase inversion.A positive correlation is found between the standard deviation of the torque fluctuation and the standard deviation of the droplet size,revealing a direct link between the macroscopic torque fluctuation and the microscopic droplet dynamic behaviors of breakup and coalescence.This study establishes a direct link between the phase inversion and the phase transition in critical phenomena,provid-ing new ideas for a deeper understanding of phase inversion and its physical mechanisms.