Description of interaction processes in agitated liquid-liquid dispersions

A literature review of theoretical models for drop and bubble breakup in turbulent dispersions

A review of statistical models for the break-up of an immiscible fluid immersed into a fully developed turbulent flow

Dynamics of bubble and drop breakup in turbulent flows have been studied in detail, using a high-speed CCD camera. Analysis of breakup times, deformations, deformation velocities, number of fragments, and the resulting daughter size distributions show that there are several important differences in the breakup mechanism of bubbles and drops. It is shown that the increase in interfacial energy prior to breakup exceeds the increase after breakup. The use of an activation barrier that better describes the turbulent structures that can interact with fluid particles and also cause breakup is proposed. Measurements under identical hydrodynamic conditions reveal that an internal flow redistribution mechanism is responsible for generation of unequal-sized bubble fragments. Due to the three orders of magnitude higher density of liquids than of gases, this mechanism does not occur for drops. The measurements also show that assumption of binary breakup is reasonable for bubbles but not for drops.© 2006 American Institute of Chemical Engineers.

On the breakup of fluid particles in turbulent flows

Flow induced emulsification in the flow of two immiscible liquids in horizontal pipes

Drop-size distributions in turbulently flowing dispersion of immiscible liquids were investigated. The observed drop-size distributions were actually a composite of two superimposed distributions. One is the distribution produced by the injection nozzle and the other is that produced by breakup in the turbulent flow field. A mathematical model was developed which predicted both the shape of the observed distributions and kinetics of the droplet breakup process for the distribution produced by the turbulent flow field.

The flowing dispersion composed of water and insoluble organic phase was photographed at 27, 209, 421, and 576 pipe diameters below the mixing jet and at distances of 0.05, 0.1, and 0.4 diam. from the wall. Average flow rates varied from 14 to 20 ft./sec. in the 0.750-in. I.D. tube. Three organic phases were studied at concentrations ranging from 0.6 to 10% by volume. Dispersed phase viscosity and interfacial tension varied from 1 to 18 cp. and 13 to 40 dynes/cm.

No distribution law with any theoretical basis could be found which correlated experimental distributions.

The stochastic model describing the breakup process postulates that each breakup event leads to two daughter drops with uniformly distributed volume ratios and a very small satellite droplet. An empirical correlation exists to predict only one of the three parameters of the model.

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Drop‐size distributions produced by turbulen pipe flow of immiscible liquids

Friction lossess, velocity distributions, and drop size distributions were obtained for unstable liquid-liquid dispersions in turbulent flow. The friction losses and velocity profiles were used to determine effective viscosities which were correlated by the Einstein relation for dispersions in which μd/μc ≤ 15. When μd/μc ≈ 200 the dispersion could not be considered as a single-phase fluid and exhibited non-Newtonian characteristics. Drop size distributions were obtained from photographs of the flowing dispersion. These drop size distributions provided information concerning drop breakup and coalescence in the circulation system. From drop size distribution and effective viscosity measurements a criterion was obtained to determine if a dispersion could be treated as a homogeneous single-phase fluid.

Turbulent flow of unstable liquid‐liquid dispersions: Drop sizes and velocity distributions

Drag coefficients were determined at low Reynolds numbers for cylinders (0.1 ⩽ Re ⩽ 1.0) and flat plates (0.05 ⩽ Re ⩽ 2.0) moving through a viscous medium. The drag coefficient was calculated from the force required to move the immersed body through the fluid, and preliminary work on spheres was used to calibrate the apparatus. For all bodies studied the drag coefficient was inversely proportional to the Reynolds number. The data were analyzed by a least-squares method to obtain the relationship between drag coefficient and Reynolds number.

The diameter of the tank containing the viscous fluid had a very definite effect upon the drag coefficient of the various cylinders and flat plates studied. In the range of DT/D (tank diameter/cylinder diameter) studied the relationships recommended by White involving the wall effect and the end correction agree with experimental data for values of L/D (cylinder length/cylinder diameter) greater than 16. At L/D ratios less than this drag coefficients are lower than those predicted by White's equations, and the experimental curves are recommended for these ratios.

For flat plates in perpendicular flow no effect of the W/L (plate width/plate length) was detected in the range studied. The tank diameter however had a considerable effect, and a curve is proposed to predict drag coefficients for flat plates in perpendicular flow in the range of experimental conditions studied.

Drag coefficients at low Reynolds numbers for flow past immersed bodies

A method utilizing a diffusion controlled electrochemical reaction was used to measure average and instantaneous mass transfer coefficients at the solid-liquid interface in upward gas-liquid climbing film flow in a vertical annular duct. These measurements give some indication of the mechanics of flow of the film, the extent of turbulence at the inner wall, and the effect of film thickness and wave motion on the mass transfer process at the inner wall. Predictions of incipient downflow of the film, shear stress at the inner wall, and interfacial shear stress were obtained from these measurements. Fluctuations in the velocity gradient at the inner wall were also studied. Results of this study are in fair agreement with previous work and with theoretical predictions based on simplified momentum balance concepts.

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J. G. Knudsen

Papers

Drop‐size distributions produced by turbulen pipe flow of immiscible liquids

Turbulent flow of unstable liquid‐liquid dispersions: Drop sizes and velocity distributions

Drag coefficients at low Reynolds numbers for flow past immersed bodies

Mass transfer at the solid-liquid interface for climbing film flow in an annular duct

Note on j factors for turbulent flow in annuli