An experimental study on single drop rising in a low interfacial tension liquid–liquid system

Highlights

• Drop rising in low interfacial tension system was investigated by high speed camera.

• Terminal velocity influenced by salt addition is mainly due to density difference.

• C_D calculated from We–Re correlation shows good agreement with experimental data.

Abstract

Terminal velocity of liquid drops is one of the key parameters in liquid–liquid extraction column design. It is important in determining residence time, droplet lifetime, and mass transfer rate. In present paper, the rising behavior of a single drops were investigated in a low interfacial tension system by high speed camera. An n-butanol/water system was used as test system. Correlations for terminal velocity were evaluated and compared, both explicitly and implicitly. Moreover, the influence of salt addition in aqueous phase was also studied, including salt concentrations and types. A Weber–Reynolds correlation was derived on the basis of experimental data. Drag coefficient was then calculated and showed a good agreement compared to the correlations in literatures.

Introduction

Liquid–liquid extraction plays an important role in petrochemical, pharmaceutical, hydrometallurgical, as well as post-processing in nuclear industry (Müller et al., 2008). It is a complicated process due to dynamic behavior of droplets, including drop rising, breakage, coalescence and mass transfer characteristics (Kopriwa et al., 2012). One of the most fundamental behaviors is single drop rising in an ambient fluid, which influences the residence time of droplet in an extraction apparatus and affects the overall mass transfer rate subsequently (Kalem et al., 2010). This process is governed by physical properties of the two immiscible phases and is sensitive to contaminations, like ions, surfactants (Edge and Grant, 1972; Griffith, 1962; Leven and Newman, 1999; Li et al., 2003) or solid particles, which are usually unavoidable in industrial operations.

Terminal velocity and drag coefficient of a rising drop are the important parameters. Unlike rigid particles, fluid droplets rise with fully mobile interface, which can be divided into several periods (Wegener et al., 2014). When diameters are relatively small, drops behave like rigid spheres. As the droplets become larger, inner circulation within droplets occurs, then the droplets enter in a transition stage. During this stage, droplets change their shape and reach maximum terminal velocity and minimum drag coefficient as the diameter increase. As diameters increase further, droplets begin to oscillate and deform. In this stage, droplets shows more resistance to motion, therefore slightly reduce the terminal velocity.

In order to determine the terminal velocity of a rising drop, an analytical solution for Navier–Stokes equations was derived by Hadamard (1911) and Rybczynski (1911) which was applicable only for creeping flows ($Re$ <1). For higher $Re$, correlations or models have been developed to evaluate terminal velocity for a given system. There are several options:

(1) Explicit correlation for terminal velocity. In an explicit expression, the terminal velocity is derived by dimensional analysis based on experimental data. Hu and Kintner (1955) investigated ten organic liquids drops in water. A correlation to predict terminal velocity was proposed based on these test systems except one with very low interfacial tension. Klee and Treybal (1956) measured the terminal velocity in eleven organic-water systems, covering a wide range of physical properties. By considering velocity-diameter curve as two separate regions, the terminal velocities were predicted for each region. Thorsen et al. (1968) proposed an equation for terminal velocity of circulating and oscillating liquid drops on the basis of seven high interfacial tension systems with extreme care to avoid contamination. A comparison was made with Hu–Kintner correlation, it was found that the previous one was not generally valid for system for highly purified liquids. Grace et al. (1976) presented an explicit equations for terminal velocity based on a large number of experimental data. This correlation was suggested to be applied in the situation where surface-active contamination was inevitable. Henschke (2003) considered different correlations for all droplet rising regions and combined them by crossover functions. A single model was proposed to predict terminal velocities over the entire diameter range. These crossover functions add more complexity to the equations and at least three parameters need to be determined based on experimental data for a given system.

(2) Implicit correlation for terminal velocity. Unlike explicit correlation which presents a direct way to calculate terminal velocity, implicit correlation is a relationship between drag coefficient ($C_D$) and Reynolds number ($Re$). It always in the form of $C_D=f\left(Re\right).$ A large number of correlations have been proposed in the past few decades, including Hamielec et al. (1963), Saboni and Alexandrova (2002), Brauer (1979), Polyanin et al. (2001) and so on. However, these correlations were confined into certain range of Reynolds number and some were restricted to spherical drop only, which limit their application. In practice, the terminal velocity has to be calculated by an iteration way (Wegener et al., 2014).

(3) Generalized graphical correlation in terms of Eötvös–Reynolds–Morton number. These can be applied for preliminary rough estimation of terminal velocity as well as the shape regime. However, as suggested by Clift et al. (1978), since the viscosity of dispersed phase is not considered in any of these three dimensionless numbers, very pure systems or larger fluid particles in high Morton liquids are not covered in the diagram.

Although different approaches have been adopted for predicting the terminal velocity, few of them are valid in low interfacial tension system. In addition, contaminations like surfactants have been taken into consideration, but limited work has been done to determine the influence caused by simple ions such as sodium chloride. Gebauer (2018) investigated five different types of salts with 0.1 M in continuous phase. His work revealed that a toluene drop was slowed down because of salt addition. Also in toluene-water test system, Chen et al. (2010) found that the terminal velocity was increased as the salt concentration increased from 0.01 M to 2 M. Zameek et al. (2016) derived the same trend as Chen et al., they studied the single crude oil drop rising in electrolytes with low, moderate and high concentration. It seems that opposite conclusions were derived for addition of salt. Therefore, further work is needed to investigate the salt effects, especially in low interfacial tension system.

In this study, single drop rising in low interfacial tension system (i.e. butanol-water system) was recorded by high speed camera to obtain terminal velocity. Then the terminal velocities were compared to the predictions by correlations from literature, both explicitly and implicitly. Furthermore, salt effects were determined by adding different salts with various concentrations into continuous phase. Finally, $Re-We-Mo$ correlation was developed on the basis of experimental data, which was applied to predict drag coefficient for the low interfacial system.