Corresponding author: lsw@tsinghua.edu.cn Tel: (8610) 80194037 Fax: (8610) 62771740

Abstract

Interfacial tension is an essential physical property in two-phase flow, and it changes due to the mass transfer. The measurement of dynamic interfacial tension (DIFT) in such a condition is a difficult problem. In the previous study (Zhou et al., Chem Eng Sci. 2019; 197:172-183), we presented the quantitative relation between the droplet breakup frequency function (DBFF) and interfacial tension. It is found that the DBFF is highly depended on interfacial tension. Therefore, the DBFF is a suitable parameter to quantitatively characterize the interfacial tension. Based on this concept, the DIFT in the column is determined by regression method after the DBFF under mass transfer condition is measured. It is found that the DIFT is smaller than the static interfacial tension. This result indicates that interphase mass transfer leads to decreasing of the interfacial tension. The decreasing extent of the DIFT has a positive correlation with the mass transfer flux.

Introduction

Liquid-liquid two-phase flow, a classical but complicated process, is widely used in aromatics extraction, hydrometallurgy, wastewater treatment, nuclear fuel cycle and other processes 1, 2. In the above processes, production needs are satisfied by different types of equipment such as pulsed column 3, pump-mixer4, centrifugal contactor 5, micro-fluidic device 6, etc. Among them, the pulsed column is often used in solvent extraction process for it has high mass transfer efficiency 7. Droplet size is an important parameter affecting mass transfer. It has been found that interfacial tension between the two liquids is a key physical property affecting the droplet size in the pulsed column 8. In the solvent extraction process, mass transfer between the two fluids occurs, thus the interfacial tension changes dynamically with the process, which is usually referred as dynamic interfacial tension (DIFT). The value of DIFT changes at different location of the pulsed column. Nevertheless, the interfacial tension is usually treated as a constant parameter in most reported works 9-12. In order to accurately describe the two-phase flow behavior, it is important to quantitatively determine the DIFT in the pulsed column.
As early as the mid-19th century, researchers discovered the Marangoni effect of interfacial liquid flow caused by interfacial tension gradient. By the mid-20th century, Sternling 13 and Maroudas 14 first studied the interfacial instability caused by interfacial mass transfer. In the study of pulsed extraction column, Sawistowski et al. 15, 16 found that the interface area between two liquids was increased due to the instability of the interface under mass transfer conditions. The mass transfer was also strengthened by the convection effect caused by the dynamic interfacial tension. Kleczek et al. 17 found that for some extraction systems, the behavior of droplets in different regions of the extraction column varies greatly: in some regions, droplets are easily broken into small droplets; in some regions, droplet size is relatively large; in some regions, the degree of droplet sphericity is very high; and in some regions, droplet deformation is serious, even the shape of “liquid filament” and “liquid belt” may be discovered. One of the main reasons for these phenomena is the spatial and temporal distribution of interfacial tension caused by mass transfer, that is, the existence of dynamic interfacial tension. However, these reports have not involved the quantitative characterization of the dynamic interfacial tension. So far, the effect of mass transfer on interfacial tension is rarely considered in the studies on extraction columns18-21.
In recent years, some researchers have carried out DIFT measurement in microfluidic devices. There are mainly three different categories: (A) The interfacial tension is correlated with the droplet diameter22-26. The correlation between interfacial tension and droplet diameter is first determined through a series of experiments. When the interfacial tension changes, the DIFT can be calculated through the correlation once the diameters of droplets are measured. (B) The interfacial tension is calculated by pressure fluctuation27-29. In microchannel, pressure fluctuations occur during droplet formation process. The pressure fluctuation was measured by researchers and brought into the Laplace formula to calculate the DIFT. (C) The interfacial tension is calculated by the degree of droplet deformation 30-35. The deformation of droplets is recorded when they pass through a suddenly enlarged or narrowed microchannel. The interfacial tension in this process can be calculated by using the magnitude of deformation. As a summary, the three DIFT measurement methods based on different principles are developed in the field of microfluids and the measurement is carried out under simple flow conditions. It is difficult to apply these methods into classical mass transfer equipment because DIFT is strongly depending on the flow field, especially for the equipment with complex flow conditions such as pulsed column. The measuring method for DIFT in such equipment is still not discovered.
Since the DIFT changes with locations in a pulsed column, the main problem to measure the DIFT is to search for a local parameter that is a monotone function of interfacial tension. The traditionally measured parameters, such as holdup and average droplet diameter, do not compliant with this requirement because they are influenced by the upstream or downstream conditions. Comparatively, the droplet breakup frequency function (DBFF), which is defined as the breakup probability of a droplet in unit time, is just such a parameter monotonically related with the interfacial tension. The measurement method for the DBFF in a pulsed disc and doughnut column (PDDC) has been developed in our previous work36. This makes it possible to quantitatively characterize the DIFT in the PDDC. Focusing on a location in the PDDC, once the DBFF under mass transfer condition is measured, the DIFT at this location can be determined by regression method. Moving the measuring location one can obtain the spatial distribution of the DIFT. The monotonic relation between the interfacial tension and the DBFF has been provided in our previous study 37.
Based on the above concept, a DIFT measurement method in PDDC under mass transfer condition is developed in this work. To the best of our knowledge, this is the first method to measure the DIFT in the macro-scale two-phase flow. The DITF is measured at different height of the PDDC. Since the mass transfer condition varies with column height, the DITF value is also changed. The main influencing factors that affect DIFT are also discussed. Furthermore, the breakup behavior under mass transfer condition is investigated and compared to that without mass transfer.

Experiments and methods

Experimental setup