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