Zhuo Chen, Qiqiang Xiong, Shaowei Li, Yundong Wang,*, Jianhong Xu,*

1 The State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China

2 Collaborative Innovation Center of Advanced Nuclear Energy Technology, Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China

Keywords:Droplet formation Micro-LIF measurement Internal circulation Mass transfer model

A B S T R A C T The mass transfer of Rhodamine 6G from the droplet to the continuous phase in a coaxial micro-channel is studied using micro-LIF(Laser-Induced Fluorescence).The mass distribution inside droplet is measured and visualized.The experimental results affirm that there exists the internal circulation inside the droplet and it could enhance the convective mass transfer. The stagnant center of vortices is also observed. The extraction fraction could reach 40%-80%. In order to establish the mass transfer model, different flow rates of the dispersed and continuous phase are adopted. The high continuous phase flow rate and low dispersed phase flow rate are both beneficial to enhance mass transfer by expediting the internal circulation. A modified mass transfer model is found to calculate the extraction fraction. A good agreement between the model and experiment in various conditions demonstrates that the mass transfer model in this work is reliable and feasible.

1. Introduction

Recently, more and more attention has been paid to the microfluidic technology. And microfluidic technology has been supposed to be a promising research direction.Compared with traditional devices, microfluidic devices have many advantages, such as high safety, excellent heat and mass transfer performance and continuous operation [1-3]. Droplet flow in microchannels is one of the most important research directions [4]. The droplet flow could enhance the mass transfer owing to the advantages of high surface to volume ratio,short mass transfer distance and fast mixing [5,6]. It has been widely applied in particle synthesis [7,8],polymer preparation [9,10], biological detection and analysis[11-14], and liquid-liquid extraction [15,16]. Whitmanet al.[17,18]divided the formation of droplets into three stages:growth,free-falling or rising, and coalescence. The formation stage plays a significant role in determining the original size, primitive shape,initial velocity of droplets and mass transfer performance [19].Thus,it is indispensable to study the mechanism of droplet formation in order to control the droplet flow more precisely and enhance the mass transfer performance.

Many studies on the mass transfer during the droplet formation have been conducted by means of extrapolation [20]. The droplet was produced by a nozzle and injected into a stationary continuous phase. Then the droplet was collected and analyzed by gas chromatography, refractometeretc.[21-23]. The studies of Popovichet al.[18],Waliaet al.[24],Lee[25]demonstrated that the extraction efficiency could be up to 3%-50%during the droplet formation stage. However, the mass transfer performance in microchannel was different because the continuous phase was flowing through the forming droplet. When the droplet was generated, the droplet was subjected to the large shear force of the continuous phase flow. Many numerical simulations showed that the internal circulation was observed in droplet when the droplet was generated[26-32]. Accompanied with the timely emergence of microparticle image velocimetry (micro-PIV), researchers could acquire experimental data about internal circulation more expediently.Wanget al.[33] affirmed two vortices were generated inside the droplet during the formation stage by micro-PIV and the mass transfer was enhanced.A pair of symmetrical vortices were corroborated in co-flow junction and cross junction channels when the droplet was produced by Liuet al.[34]. Meanwhile, it was found that the direction of internal circulation was related to the wetting state of dispersed phase on the channel wall.In our previous work[35], the internal circulation in coaxial microchannel was also verified. And the results also demonstrated that the strength of vortices increased with the decrease of interfacial tension and continuous phase viscosity.

A lot of research indicated that the internal circulation inside droplet had a significant impact on mass transfer [36-42]. Das et al. [43] studied the mass transfer of phenol from microscale silicone oil droplet to continuous water flow on the microchip.A pair of vortices were observed,enhancing the mass transfer during droplet formation stage. The internal circulation made mass transfer time reduce to several seconds, which was in accordance with Mary’s research [44]. Xu et al. [2] investigated the mass transfer of succinic acid between n-butanol and aqueous drops containing NaOH.The results demonstrated that the vortex within the droplet accelerated mass transfer greatly during droplet forming stage.The mass transfer coefficients raised one to two orders compared with droplet moving stage.Bai et al.[45]used micro-LIF(Laser-Induced Fluorescence)measurement technique to investigate mass transfer between the water droplet and ionic liquid. It was found that the overall volumetric mass transfer coefficient of droplet formation stage was three to four times than that of moving stage, which was due to the strong internal circulation.This was consistent with the conclusions by Li and Angeli [46] for slug formation stage.

Although experiments and numerical simulations confirmed the existence of internal circulation, few of them characterized the relationship between internal circulation and mass transfer quantitatively. Most of researches on liquid-liquid mass transfer during the droplet formation adopted offline detective method and lacked of detailed data at each time[47-50].Meanwhile,many models cannot predict the experiments accurately [20]. Wellknown mass transfer models(see Table 1)[51-55]during the droplet formation were established based on the surface stretch theory [56-59], the fresh surface elements theory [60] and flow expansion theory [61-63]. The first model was provided by Newman in order to calculate the dynamic mass transfer in rigid spherical particles without internal circulation [51]. Then, the internal circulation following Hadamard streamlines was introduced and the mass transfer model was modified by Kronig et al. [64]. And it was found that the extraction rate had been doubled owing to the internal circulation. Calderbank and Korchinski used the concept of effective diffusion coefficient. The equation proposed by Kronig et al. was well represented by their empirical correlation if R was set to 2.25. Based on the fruit in modified mass transfer models of the former researches,Henschke and Pfennig[55]established the semi-empirical model to elaborate the mechanism of mass transfer inside droplet with the internal circulation. The Fourier number contained the time t, the droplet diameter dp,the molecular diffusion coefficient D,and a turbulent transfer coefficient ε related to the terminal drop rise velocity Vt, the viscosity ratio μ* and an instability constant CIP adjustable to experimental data.

Table 1 Typical mass transfer equations

A reasonable model which could simulate the droplet formation dynamically has not been established, and few of them characterized the relationship between internal circulation and mass transfer quantitatively. Therefore, further studies are needed on the mass transfer from droplet to the continuous phase during droplet formation stage. In present work, we applied the online micro-LIF to study the mass transfer performance during the droplet formation process in microchannels.Firstly,mass distribution in droplet was revealed and corroborated quantitatively by analyzing the visualization images acquired from the micro-LIF measurement.Then, extraction efficiency was calculated precisely at any time of the droplet formation stage. Furthermore, a modified model was built to characterize the mass transfer during the droplet formation stage. And the experimental results verified the feasibility and reliability of the modified model.

2. Experimental

2.1. Micro-LIF measurement system

Micro-LIF system (Dantec Dynamics A/S, Denmark) equipped with an invert microscope was used to measure mass transfer performance during the droplet formation process.The schematic diagram of micro-LIF was shown in Fig. 1. The continuous phase and dispersed phase(5.0 mg·L-1rhodamine 6G aqueous solution)were injected into the microchannel by two syringe pumps. The 30-mJ double-pulsed Nd:YAG laser with the peak emission wavelength of 532 nm and pulse frequency of 15 Hz was applied to exciting the fluorescence of rhodamine 6G dissolved in the dispersed phase and a 12-bit CCD camera whose resolution was 2048 px×2048 px with 5 × objective lens(numerical aperture NA=0.3) was used to observe and capture the mass transfer process. The exposure time was 1 ns. The measuring area per pixel was 1.5 μm × 1.5 μm,and the smallest resolved length scale was 1.5 μm. Dell workstation was used to process the captured images with system-provided Dynamic Studio software(Dantec Dynamics A/S,Denmark)rapidly and efficiently.

Fig. 1. Schematic diagram fo the experiment setup in this work.

2.2. Working system

n-Butanol (A.R., ≥98%, Sinopharm Chemical Reagent Co., Ltd.,China)and de-ionized water were chosen as the continuous phase and the dispersed phase respectively in our work. And they were both saturated with each other before adding into the microfluidic device. 100 ml of deionized water and 100 ml ofn-butanol were stirred and mixed for 2 h. After 20 minutes’ standing, the phase separation was achieved. The upper layer was water-saturatednbutanol, and the lower layer wasn-butanol-saturated water. The physical properties of working system were presented in Table 2.Rhodamine 6G (A.R. ≥99%, Acros Organics, China) was used as the solute to study the mass transfer from the droplet to the continuous phase. The viscosities of the dispersed and continuous phase were measured by a viscometer (NDJ-5S, Shanghai Jingtian Electronics Instrument Co.), and the interfacial tension was measured by a sessile tensiometer (OCAH200, Data Physics Instruments GmbH, Germany) when two phases reached phase equilibrium state thoroughly. When the concentration of Rhodamine 6G increased from 0 to 5 mg·L-1, the interfacial tension changed slightly from 1.76 mN·m-1to 1.75 mN·m-1.

Table 2 Physical properties of working system

2.3. Microfluidic device

The schematic diagram of microfluidic device for producing droplets was shown in Fig.2.The coaxial micro-channel was fabricated on 40 mm × 20 mm × 3 mm polymethyl methacrylate(PMMA) plates. The computerized numerical control (CNC)machine was employed to manufacture the cross-junction channels, and the inlet and the outlet were both 2 mm wide × 2.1 m m deep.A 24 mm×14 mm rectangle and 6 mm×3 mm rectangle was hollowed out from PMMA plate with channels.The former was used to add water, which could reduce the measurement error resulted from the refractive difference of glass capillary and air.The latter was used to fix the capillary and prevent the fluorescent tracer from entering the gap between channel and capillary.Then,another 40 mm×20 mm×3 mm PMMA plate was covered on the micro-channels directly by a solvent sealing technique with hot press. A glass capillary with 1.56 mm inner diameter (ID) and 2.0 mm outer diameter(OD)was imbedded into the main channel as the outlet.In order to form the coaxial structure,a finer capillary whose internal and external diameters were 0.9 mm and 1.2 mm with the tapered orifice was inserted into the capillary. The diameter and length of the tapered orifice were approximately 150 μm and 2.5 mm respectively.The continuous phase was delivered into side channels and the dispersed phase was delivered into the finer capillary through two polytetrafluoroethylene(PTFE)pipes by syringe pumps. In this work, the volumetric flow rates of continuous phaseQc, changed from 600 to 1200 μl·min-1and the dispersed phaseQd, changed from 2 to 8 μl·min-1.

Fig. 2. Schematic of microfluidic device in this work.

2.4. Calibration of micro-LIF measurement

The micro-LIF measurement system has been widely used to obtain concentration or temperature information in various circumstances owing to the advantages of less disturbance,high sensitivity and rapid measurement. The monotonous relationship between the fluorescence intensity and the fluorescence tracer concentration or temperature under illumination was the basis of micro-LIF measurement.However,some obstacles should be overcome when micro-LIF was employed to measure the mass or concentration information at the droplet formation stage. Firstly, the laser was selected to illuminate the microfluidic device and the fluorescence intensity distribution was obtained as shown in Fig. 3.The results demonstrated that the fluorescence intensity depended on the position of fluorescence tracer in microfluidic device. That was due to the source of light and the structure of microfluidic device. The light source was volume illuminant. In addition, the glass circular capillary was embedded in a rectangular channel engraved in PMMA plate, and this curved surface of circular capillary caused different refraction of light, thus leading to the different intensity of different positions. Therefore, the fluorescence intensity was calibrated for each pixel. Then, the depth of measured samples should be constant in general micro-LIF measurement. However, when the technique was adopted to measure the concentration distribution inside droplet,the depths varied in various positions of the droplet in the vertical direction. In order to tackle this obstacle, three capillaries whose internal diameters were 1.56 mm, 1.10 mm and 0.9 mm respectively were selected to study the relationship between the fluorescence intensity and the depth when the fluorescence tracer concentration was constant. The intensity distributions on capillary axis were shown in Fig.4.When the concentration of the tracer was fixed but the capillary diameter(depth)was different,it was found that the fluorescence intensity was increased as the depth of capillary increased,which demonstrated that the tracer concentration cannot reflect the fluorescence intensity accurately. In addition, the results showed that the fluorescence intensity was linear with the depth in each position. Therefore, the mass chose as calibration parameter was feasible and reliable.

In the micro-LIF measurement,the fluorescence intensity information was obtained and it could be converted to mass information by the relationship between fluorescence intensity and fluorescence tracer mass. In order to obtain the calibration curve,the standard solution was prepared with the concentration of 0 mg·L-1,1.0 mg·L-1,2.0 mg·L-1,3.0 mg·L-1,4.0 mg·L-1,5.0 mg·L-1respectively. Each pixel was calibrated separately. The slope and intercept is shown in Fig. 5.

Fig. 3. Fluorescence intensity distribution in microfluidic device.

Fig. 4. Fluorescence intensity on axis for different capillary diameters.

Fig. 5. (a) Slope and (b) intercept of the calibration curve at each pixel.

3. Results and Discussion

3.1. Visualization of mass distribution

The liquid-liquid mass transfer performance in microfluidic devices has been investigated a lot as stated in the introduction.However, the limited studies on the dynamic process of mass transfer at the droplet stage have been in progress. The micro-LIF technique enables us to track the formation process of droplets and obtain abundant information on mass transfer. The typical image acquired by the micro-LIF measurement is shown in Fig. 6,where the flow ratio of continuous phase to dispersed phase was 600 μl·min-1:2 μl·min-1.From our previous study[35]of velocity field inside and outside droplet,the fluid on the surface of the droplet was in a creeping state. Thus, the tracer transferring to the continuous phase at the surface gradually accumulated at the tip of the droplet, leading to a tail of tracer in front of the droplet. A pair of vortices were revealed clearly which were also verified in our previous work [35]. Meanwhile, we found that the mass at the center of vortex and the axis of droplets were greater than that at the other parts,while the mass at the edge of droplet was about 0 mg. Corresponding to the micro-PIV experiment [35], it was firstly found that mass was about the same for all locations of a streamline. It could be also demonstrated that the mass transfer occurred in very thin layers near the droplet surface. The concentration of fluorescence tracer in the continuous phase was approximately 0 mg·L-1due to high phase ratio.

Fig. 6. Typical image during the droplet formation.

The motivation of our experiment was to study the mechanism of mass transfer during the droplet formation process by analyzing information of mass (concentration) distribution inside droplet.The information of mass distribution of the continuous phase was screened by a mask. The mass distribution inside the droplet within a droplet growth cycle changed over time, as shown in Fig. 7. It could be concluded that the center of vortices was stagnant [65] and the mass at the center of vortices decreased over time. It could be explained that mass at the center of vortices was primarily inflected by mass transfer. In the prophase of the droplet growth, the droplet was small and its specific area was large which was in favor of mass transfer at the interface.However,the internal circulation strength was weak[35]so that the convective mass transfer at the center of vortices was low. With the growth of droplet, the convective mass transfer was enhanced owing to stronger internal circulation. Therefore, the mass at the center of vortices was dwindled.It was consistent with our experimental results.

Fig. 7. Mass distribution in droplet during the droplet formation.

3.2. Mass transfer during droplet formation process

There are many factors that could influence the mass transfer during the droplet formation, such as operating conditions, physical properties and so on[22,23].In this work,the effect of the flow rates of continuous and dispersed phase on the mass transfer was mainly investigated by changing flow ratio.Firstly,the flow rate of dispersed phase was retained at 2 μl·min-1and the flow rates of continuous phase were changed from 600 μl·min-1to 1200 μl·min-1by 200 μl·min-1stepwise. Then, the flow rates of the dispersed phase increased from 2 μl·min-1to 8 μl·min-1with increment of 2 μl·min-1stepwise while the flow rate of continuous phase was kept at 800 μl·min-1. The capillary number,Ca=μu/γ,for both the two phases could be used to characterize the twophase flow pattern region. TheCa(c)for the continuous phase was 0.004-0.02 and theCa(d)for the continuous phase was 0.0005-0.003. The mass and extraction fraction in droplet were studied in order to clarify the mechanism of mass transfer at the droplet formation stage.

3.2.1. Fluorescence tracer mass inside droplet

The integral mass of fluorescence tracer for each moment was calculated as shown in Fig.8 in order to quantify the mass transfer inside droplet. Three droplets were considered to calculate the average mass of tracer.The experiment has been repeated for three times.It is shown that the fluorescence tracer mass increased with time during the droplet formation.In the early stage of droplet formation, the fluorescence tracer mass increased rapidly due to weaker convective mass transfer compared with mass injected into the droplet. Nevertheless, as the droplet grew, the mass transfer from the droplet to the continuous phase was accelerated so much by the stronger internal circulation that solute mass increased slowly or even decreases. It could be clarified that the shearing action of the continuous phase flow on the droplet surface was promoted because increasing droplet diameter leaded to the narrower continuous phase fluid channel and the continuous phase flow rate was expedited as the droplet grew.Therefore,the internal circulation and mass transfer were both enhanced.

The effects of the flow rates of the continuous and the dispersed phase on mass were different.With the increase of flow rates of the continuous phase,the mass decreased at the same droplet volumes(the same droplet formation time). However, the change of mass was consistent with that of the dispersed phase flow rates at the same time.It could be understood that the mass depended on mass transfer and the injection of the dispersed phase.The mass transfer could be influenced by the internal circulation which relied on the shear force.The high continuous phase flow rate could enhance the shearing action while the high dispersed phase flow rate would weaken it. Therefore, the higher continuous phase flow rate was,the less mass was. However, for the higher dispersed phase flow rate, the injection of the dispersed phase dominated the change of mass.

3.2.2. Extraction fraction inside droplet

Mass transfer performance during the droplet formation is further investigated based on the extraction efficiency.The extraction fraction is defined as:

whereCandC0are the average concentration of droplet at each moment and the initial concentration, and hereC*=0 because it is the equilibrium concentration with the initial concentration of continuous phase which is supposed to maintain zero [62].

In our work, it could be seen that the extraction fraction could reach 40% to 80% as shown in Fig. 9 which verified the significant contribution of droplet formation stage to mass transfer from the droplet to the continuous phase [45]. It could also be concluded that the formation time and two-phase flow rates both have effects on the extraction fraction. It was obvious that longer formation time was beneficial to increase the extraction fraction. The higher continuous phase flow rate and lower dispersed flow rate could boost the shearing action as our previous work [35]. The internal circulation was promoted so that the mass transfer was enhanced.

Fig. 8. Effects of the (a) continuous phase flow rate and (b) dispersed phase flow rate on the mass.

Fig. 9. Effects of the (a) continuous phase flow rate and (b) dispersed phase flow rate on the extraction fraction (point: experimental data, line: model prediction data).

In summary,that up to 40%-80%of mass transfer occurred during the droplet formation.It was vital to assess the mass transfer at the droplet formation stage compared with the droplet moving stage.

3.2.3. Modified mass transfer model to predict mass transfer during droplet formation

In the prophase(initial 20%stage)of the formation,the droplet was smaller, and it was more difficult to capture clear image of droplet. Meanwhile, the droplet would be elongated and deviated from the sphere in our experiments.Not only that,in our previous work[35],it was found that the internal circulation was negligible at the initial 20% stage of droplet formation. Therefore, a diffusion model is established in the initial stage as follows:

In the later stage of droplet formation,the internal circulation is very intense that cannot be ignored,and thus a model considering internal circulation is established. For Henschke and Pfennig’s model,CIPis a fixed value at 3400 for all the experiments. In our work, Henschke and Pfennig’s model is modified andCIPis associated with internal circulation.CIPis numerically equal to the absolute value of internal circulation, and the calculation of internal circulation has been reported in our previous work [35]. In addition, it was supposed that droplet was spherical and thedpchanged with time. The velocity v adopted the average velocity of the continuous phase at the maximum radial position of the droplet.The extraction fractions calculated by this modified model are shown in Fig. 9. It could be seen that the model could predict the extraction fraction well.

4. Conclusions

In this paper,the micro-LIF measurement was adopted to study mass transfer of Rhodamine 6G from the droplet to continuous phase during the droplet formation stage online in a coaxial microchannel. Firstly, in order to tackle two obstacles when the micro-LIF was applied to the measurement of the droplet formation process, the mass was adopted as calibration parameter and the mass of Rhodamine 6G at each pixel was calibrated individually. It was affirmed that the micro-LIF measurement is reliable and feasible. Then, the mass distribution inside droplet was obtained and visualized. The results also demonstrated that there exists a pair of vortices in the droplet and the center of the vortex is stagnant by analyzing the information of mass distribution. The high continuous phase flow rate and low dispersed phase flow rate are beneficial to promote the mass transfer.The extraction fraction during the droplet formation could reach as high as 40%-80%.Finally, a modified mass transfer model was proposed to successfully predict the dynamic mass transfer performance during the droplet formation stage. In the future, more experimental and numerical work are needed to study the dynamic mass transfer performance during droplet formation process in microchannels.

Acknowledgements

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors gratefully acknowledge the supports of the National Natural Science Foundation of China (21991100,21991101) for this work.