An investigation of the effects of various physical properties, drop size, and drop velocity on drop shape was carried out for nonoscillating liquid drops falling through stationary liquid continuous phases. The data of forty-five dispersed-continuous phase systems were studied with continuous phase viscosities varying from 0.3 to 46 centipoise and interfacial tensions varying from 0.3 to 42 dyne/cm. A theoretical relation was obtained from the Taylor and Acrivos analysis which quite accurately predicts drop eccentricities for drop Reynolds numbers less than about 20, but is highly inaccurate at higher Reynolds numbers. Relatively simple empirical relations involving the Weber number, Eotvos number, and viscosity ratio were obtained which enable the prediction of the eccentricity of nonoscillating drops over a wide range of Reynolds numbers (6.0 to 1,354) with average deviations of 6 to 8%. These relations may be useful in the estimation of the interfacial area, velocity, and continuous phase mass transfer coefficient of drops distorted from spherical shape.

Shape of liquid drops moving in liquid media

Empirical correlations for the prediction of mass transfer coefficients for single drops are presented. Published experimental results for both circulating and oscillating drops are considered. Correlation for the individual continuous-phase mass transfer coefficient, which is based on data from 596 measurements taken from 10 different groups of investigators, reproduces the data with an average absolute error of 14.1%. This is then used to determine a correlating equation for the individual dispersed-phase mass transfer coefficient on the basis of data for overall dispersed-phase mass transfer coefficient taken from 21 sources. The average absolute value of the relative error in the predicted values of overall dispersed-phase mass transfer coefficient from the experimental points by using the correlations for individual mass transfer coefficients is 24.5%. It is further shown that by allowing for the effects of power input per unit mass and dispersed-phase hold-up, the correlations for single drops can be extended to extraction columns. The correction factors required for this purpose have been obtained by using simulated values of overall mass transfer coefficients for pulsed perforated-plate, Karr reciprocating-plate, Kuhni, and rotating disc columns.

Correlations for Prediction of Mass Transfer Coefficients in Single Drop Systems and Liquid–Liquid Extraction Columns

https://cyberleninka.org/article/n/994494.pdf

Effect of channel size on mass transfer during liquid–liquid plug flow in small scale extractors

https://hal.archives-ouvertes.fr/hal-01340709/document

Experiments of mass transfer with liquid-liquid slug flow in square microchannels

https://oatao.univ-toulouse.fr/1382/1/prat_1065.pdf

Direct numerical simulations of mass transfer in square microchannels for liquid–liquid slug flow

An experimental investigation of the effects of various physical properties on the dispersedphase mass transfer coefficient was carried out for both nonoscillating and oscillating liquid droplets falling in a single stream through stationary continuous liquid phases. The Colburn and Welsh two-component technique was used to isolate and measure the disperesed-phase resistance to mass transfer. This technique limited the experimental study to systems with low interfacial tensions, between 2.5 and 5.8 dynes/cm. Solute was transferred into the droplets, and the droplet concentration was measured after droplet-fall heights ranging from about 2 cm. to 103 cm. Precautions were taken to minimize end effects.

The experimental mass transfer rates on nonoscillating droplets in general were greater than that predicted by the Kronig and Brink model for nonoscillating circulating droplets. Experimental Sherwood numbers for four liquid systems were correlated in terms of a relationship involving the dispersed-phase Schmidt number, the Weber number, and the time group, 4DLtc/d2e, which allows for the time dependency of the transfer mechanism. The data were correlated with an average absolute deviation of 34%. The Kronig and Brink and Newman relations fitted the experimental data for nonoscillating droplets with an average absolute deviation of 46 and 54%, respectively. The experimental results for the oscillating droplets were correlated by two relationships with an average absolute deviation of 10.5%. The Handlos and Baron model fitted the experimental results for oscillating droplets with an average absolute deviation of 38%.

R. M. Wellek

Papers

Resistance to mass transfer inside droplets