Biomedical Microdevices

, Volume 13, Issue 3, pp 559–564

The effect of interfacial tension on droplet formation in flow-focusing microfluidic device

Authors

  • Lu Peng
    • Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education, Department of PhysicsSchool of Physics and Technology, Wuhan University
  • Min Yang
    • Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education, Department of PhysicsSchool of Physics and Technology, Wuhan University
  • Shi-shang Guo
    • Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education, Department of PhysicsSchool of Physics and Technology, Wuhan University
    • Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education, Department of PhysicsSchool of Physics and Technology, Wuhan University
    • Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education, Department of PhysicsSchool of Physics and Technology, Wuhan University
Article

DOI: 10.1007/s10544-011-9526-6

Cite this article as:
Peng, L., Yang, M., Guo, S. et al. Biomed Microdevices (2011) 13: 559. doi:10.1007/s10544-011-9526-6
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Abstract

Interfacial tension plays an important role in microfluidic emulsification, which is the process of preparing emulsions. A promising method which controls droplet behavior according to the function of the interfacial tension in the process of microfluidic emulsification is reported. The droplet size and generation frequency changed regularly to obtain appropriate concentrations of surfactant. This method could be of great help for setting up the size-controllable droplet generation systems, and ameliorating the emulsification technology. The interfacial tension effect was first analyzed by computational simulation before the real experiment, which significantly improved the efficiency of the whole research process.

Keywords

MicrofluidicsSimulationInterfacial tensionDropletFlow-focusing

1 Introduction

Since the establishment of the miniaturized total analysis systems (μTAS) half a century ago (Whitesides 2006; Manz et al. 1990), applications of lab-on-a-chip devices (Anna et al. 2003; Xu and Nakajima 2004; Teh et al. 2008) has gradually covered a broad range of fields including biology, chemistry and medicine. Among these, microfluidic emulsification system (Li et al. 2007; Cygan et al. 2005; Köster et al. 2008; Haeberle and Zengerle 2007) is one of the most important μTAS applications and draws attention of modern chemistry analysis. Recently, the lab-on-a-chip systems to generate emulsion droplets, e.g., flow-focusing PDMS channel for water/oil emulsions generation, have been maturely developed and the method to control the droplet size by adjusting the flow rate is widely discussed (Mi et al. 2006; Sugiura et al. 2001; Munshi et al. 2008; Squires and Quake 2005). However, it is a tough job to apply such method to general chemical analysis or biology experiments, as the operation parameters, for example, the best flow rate of the fluid, and the stability of a lab-on-a-chip system is heavily dependent on the inner material characteristics, including interfacial tension σ and viscosities of the liquids to operate with. These characteristics can not be measured and controlled easily.

Nomenclature

σ

Interfacial tension

Ca

Capillary number

hc

Depth of the microchannel

Fs

Sharing force

wc

Width of the microchannel

DH

Hydraulic diameter for the microchannel

φ

Level set function

ηo

Viscosity of the oil

ds

Droplet diameter

Qo

Flow volume of oil

Vs

Volume of the droplet

Qw

Flow volume of water

Ω

The generating zone of a single droplet (φ > 0.5)

uo

Average velocity of oil

The interfacial tension σ is a critical parameter that affects the evolution of the interface of the two phases when the droplets are shaping. Normally, a tensiometer (DSA100) is used to measure σ in an invariable environment. But things can be quite different in a microscale system with dynamic interfacial tension as in microfludic systems. In order to find the best way to build up the size-controllable droplet generation system, researchers tried various methods to figure out the relationship among interfacial tension, surfactant concentration and the droplet properties in μTAS systems (Serra et al. 2007; Wang et al. 2009a). However, the perfect solution never comes out, because the interfacial tension dynamicity was never approached directly.

With developed analysis software, computer simulation is able to play a more and more important role in the physics research and industrial design, especially for prediction and possibility analysis. They can tightly analyze physical domains, act as a validation tool for hypothesis-driven experiments to understand physical mechanisms, validate analytical models, and optimize device design at low cost (Boy et al. 2008). And the explicit visual results of a well setup flow-mechanics model are valuable to the lab-on-a-chip researches.

In this article, we focus on the effect of interfacial tension σ in the microfluidic flow-focusing devices. The same geometry of the microfluidic chip and fluid flow rates are applied, so that the droplet size and generation frequency will only be dependent on the interfacial tension. The droplet size was controlled only by adjusting the concentration of surfactant. During the experiment, the coefficient of variation is approximately 4% and droplet diameter is from 10 to 50 μm. According to the simulation and related experimental results, it can be concluded that the interfacial tension between two immiscible fluids has an important influence on the droplet formation, especially the shape property, at the same flow rate.

2 Materials and methods

2.1 Device design

The flow-focusing devices were fabricated by soft lithography (Xia and Whitesides 1998), using SU8 2100 photoresist. The channel was made by bonding PDMS to glass through oxygen plasma treatments and later baked in 120°C for 3 days for totally hydrophobic. The schematics of the flow-focusing device and microfluidic chip are shown in Fig. 1. The channel has three inlets and a subsequent rectangular expansion which was designed to relax the water and oil streams and easily observe the droplet status easily. The depth hc and width wc of the microchannel were calibrated by the Imaging Pro Plus 5.1 to be approximately 40 μm and 50 μm respectively and the expansion has a width of 100 μm.
https://static-content.springer.com/image/art%3A10.1007%2Fs10544-011-9526-6/MediaObjects/10544_2011_9526_Fig1_HTML.gif
Fig. 1

Fabrication of flow-focusing emulsions in microfluidic devices. (a) Schematic of the droplet generation channel geometry. The water stream enters from the middle channel and is sheared by two oil streams at the orifice of subsequent rectangular expansion. The depth of channel is 40 μm; (b) Image of the PDMS microfluidic chip

2.2 Materials and measurement

Soybean oil was used as the continuous phase and 0%, 0.005%, 0.01%, 0.2%, and 1% tween20 water solution were chosen as the disperse phase, respectively. The viscosity of the sample was measured by Rheometrics ARES (TA Instruments Inc.), and the temperature was controlled by Julabo FS18 (A heating and refrigerator circulation).

It is generally accepted that a tiny portion of surfactant can significantly lower the interfacial tension (thereby facilitating breakup) and prevent coalescence (Hu et al. 2000). In this study, a common surfactant tween20 (Garstecki et al. 2004) was used to decrease the interfacial tension between the two phases, because it was an efficient nonionic surfactant which could be dissolved in both water and organic solvent, remarkably change the interfacial tension with negligible influence on the viscosity and material density, and be of little harm to the biological environment. The surfactant was of greatest efficiency in a low range of concentration and less efficient closer to Critical Micelle Concentration (CMC). The CMC of tween20 was 8.04 × 10−5 M at 20°C, approximately 0.008% concentration. However, this data was relatively high at the microscale due to the much higher ratio of the surface to the volume than the normal standard. Consequently, the concentrations of the surfactants were determined from the preliminary experiment.

In order to test the efficiency of tween20, two separate measurements were made: First, the tension for the interface between oil and pure water was measured, and the result was 29.8 mN/m; then 1% concentration (much higher than the CMC to make sure the interfacial tension was invariable in the saturated state) tween20 was added to the water and another measurement value as 8.2 mN/m was derived. All these values were obtained from a KRUSS tensiometer (Drop Shape Analyzer DSA100, KRUSS GmbH, Hamburg, Germany).

2.3 Numerical method

Before the experiment, a numerical simulation of the droplet formation was conducted by COMSOL Multiphysics software, version 3.4 COMSOL . During this simulation, all geometries were created two-dimensional based on the dimensions of the designed microfluidic devices. The momentum and mass balances were modeled by the Navier–Stokes equations and the position of the fluid interface was tracked by a level set method (Osher and Sethian 1988; Sethian and (Cambridge University Press, Cambridge 1999). This method was extremely successful on uniform Cartesian grids as well as in the study of physical problems such as compressible flows, epitaxial growth and imaging processing. The method described the evolution of the interface between the two fluids tracing an isocontour curve of the level set function φ. Here, the interface was defined as φ = 0.5 and disperse phase corresponded to water where φ > 0.5, continuous phase corresponded to oil where φ < 0.5. The droplet diameter was calculated using the following formula:
$$ {d_s} = 2\sqrt {{\int_{\Omega } {d\Omega /\pi } }} $$
(1)
The water contact angle of 108° was a conservative estimate for PDMS devices. Six groups of cases with increasing values of interfacial tension between the two measured values, which were 8.2 mN/m, 10 mN/m, 15 mN/m, 20 mN/m, 25 mN/m and 29.8 mN/m, were simulated. The parameters used in the simulations on the basis of the measurement results are listed in Table 1.
Table 1

Parameters used for simulations

Parameter

Value

Unit

Density of water

1000

kg/m3

Viscosity of water

0.001

Pa·s

Density of oil

880

kg/m3

Viscosity of oil

0.075

Pa·s

Contact angle

108

°

Flow volume of water

78.4

μL/h

Flow volume of oil

274.4

μL/h

2.4 Chip experiment

The disperse phase fluid and the continuous phase fluid were injected into the PDMS channel at constant flow rates respectively using syringe pumps. A thread of water broke up and released droplet in the orifice. The process was observed with an inverted optical microscope (IX71, Olympus, Japan) and video images were captured by a CCD camera (Evolution VF Cooled Monochrome Camera, Media Cybernetics, Inc.) coupled to the microscope. Image analysis software (Imaging Pro Plus 5.1, Media cybernetics, Inc.) was used to measure the sizes of the droplets. Droplets were squeezed between the top and bottom walls, and had a disc-like geometry when the diameter of the droplets was beyond 40 μm. The volume of the droplets was calculated approximately by
$$ Vs = \pi d{s^3}/6 $$
(2)
where ds represents the diameter of the droplet when it is a pellet.

3 Result and discussion

It is generally accepted that interfacial tension is a significant element in the process of emulsification where one or more immiscible liquid intimately disperse in another insolvable liquid in the form of droplets. When two immiscible liquids contact with each other, they tend to maintain as small an interface as possible, this is due to the nature that a substance tends to maintain the smallest energy on the surface.

To analyze and interpret the droplet formation under different interfacial tensions exported from measurement listed in Table 1, COMSOL was used to simulate the processes. Two phase flow simulation with constant input flow rate were exhibited in Fig. 2. The snapshot showed the volume fraction and the interface between the oil and water were stable. From the colorbar and contour curve of φ = 0.5 depicted in Fig. 2, we can identify the shape of water-in-oil (w/o) droplets corresponding to the area of φ < 0.5. Compared with Fig. 3(a–e), it is observed that the size of droplets generated varied with interfacial tension. The diameters of droplets were calculated by formula (1), and plotted in line as Fig. 3 shows. There is a trend in the figure that the diameters of monodispersed droplets ds increase with the interfacial tension σ, and Fig. 4 shows that the generation frequency decreases with σ at the fixed flow rate, approximately proportional to 1/ds.
https://static-content.springer.com/image/art%3A10.1007%2Fs10544-011-9526-6/MediaObjects/10544_2011_9526_Fig2_HTML.gif
Fig. 2

Simulation results of six groups of cases with various values of interfacial tension: (a) 8.2 mN/m;(b)10 mN/m (c)15 mN/m; (d)20 mN/m; (e)25 mN/m;(f) 29.8 mN/m.The colorbar specifies the oil phase as the area where color distinction is from 0 to 0.5. and water phase the area from 0.5 to 1.0. Contour of 0.5 specifies the interface where the water-in-oil droplet is identified as solid black line

https://static-content.springer.com/image/art%3A10.1007%2Fs10544-011-9526-6/MediaObjects/10544_2011_9526_Fig3_HTML.gif
Fig. 3

Diameter of droplet ds increases with the increasing interfacial tension when it is between the 8.2 mN/m and 29.8 mN/m

https://static-content.springer.com/image/art%3A10.1007%2Fs10544-011-9526-6/MediaObjects/10544_2011_9526_Fig4_HTML.gif
Fig. 4

Generation frequency decreased with the increasing interfacial tension when it is between the 8.2 mN/m to 29.8 mN/m

In the flow-focusing design of water-in-oil emulsions, the shearing comes from the relative magnitude of the co-flowing streams of oil and water.The shearing force is usually expressed by the product of the average velocity and the viscosity of the continuous phase (Fs = ηouo) (Thorsen et al. 2001; Wang et al. 2009b). According to the previous studies (Cristini and Tan 2004), the droplet size is mainly determined by the force balance of shearing force and interfacial tension. Capillary number Ca, the ratio of viscous stress to interfacial tension, has been commonly used to express this force balance. The identification of the Ca is given by (Wang et al. 2009b)
$$ Ca = \eta_ou_o/\sigma = \eta_oQ_o/h_cw_c\sigma $$
(3)
When Ca = O(1), viscous stresses deform the droplet significantly and breakup may occur.In the flow-focusing microchannel, the value of droplet size can be seen as a function of interfacial tension and shearing force: (Cristini and Tan 2004)
$$ {d_{s} \sim \sigma DH^{3} } \mathord{\left/ {\vphantom {{d_{s} \sim \sigma DH^{3} } {\eta _{o} Q_{o} }}} \right. \kern-\nulldelimiterspace} {\eta _{o} Q_{o} } $$
(4)
Where DH is the hydraulic diameter for the flow-focusing microchannel, which determined by geometrical parameters. Formula (4) gives a simple relationship between generated droplet size and the interfacial tension:
$$ {d_s}\sim \sigma $$
(5)
Thus, with the variation of the surfactant concentration at low concentration of Tween 20, lower than CMC, the varied property of the system is the interfacial tension, which causes the variation of the droplet size at the same flow rate. The lower interfacial tension σ leads to the smaller droplet size and higher generation frequency. And this was in agreement with the simulation results.

The interesting discovery from the simulation actually proposed a method to obtain different droplet behavior by changing the interfacial tension. And in practice, various droplet shape and frequency could be achieved by adjusting the surfactant concentration in the fluid.

In the experiment section, the flow rate of the water phase with surfactant and oil phase were fixed as Table 1 shows, the ratio of flow rate Qo/Qw was kept at 3.5, corresponding to the same velocity in the simulation. If any change of the parameters like the flow rate takes place, 30 min was set to be the minimum time to equilibrate the system. Microphotograph images obtained in experiments are exhibited in the Fig. 5: Immediately after the liquid thread grows pass the orifice, the neck of the thread (located at the orifice) decreases until a sharp point is developed to allow the thread to detach. (Bottom) Generated droplets are not spherical until reaching the reservoir. In the reservoir, the droplet is not restricted by the channel walls and the shape of droplet relaxes into spherical form. From Fig. 5(a–f), the droplet size decreased corresponding to the concentration of tween20, which matched the simulation results. Considering the viscosity was also a parameter to determine the droplet shaping, so the variation of the viscosity of DI water added with 0%, 0.5% and 1% concentration of tween20 was investigated. At room temperature, the results of viscosity measurement were 0.891 mPa·s, 0.921 mPa·s and 0.952 mPa·s, respectively. The variation was less than 6%, and could be ignored. Consequently, it could be concluded that interfacial tension was the factor to determine the droplet size and frequency, the trend was plotted as line in Figs. 6 and 7. It shows that as more tween20 added, the interfacial tension would decreased and the droplet would be with smaller size and higher frequency at fixed flow rate, which shares the same result with the simulation.
https://static-content.springer.com/image/art%3A10.1007%2Fs10544-011-9526-6/MediaObjects/10544_2011_9526_Fig5_HTML.gif
Fig. 5

Microphotograph images of droplet generation in the experiment with water phase adding various concentration tween20: (a)1%;(b)0.2%;(c)0.01%;(d)0.005%;(e)0.001%;(f)0%, respectively

https://static-content.springer.com/image/art%3A10.1007%2Fs10544-011-9526-6/MediaObjects/10544_2011_9526_Fig6_HTML.gif
Fig. 6

Diameter of droplet ds increases with the increasing of interfacial tension when the selected concentration is below the saturated level. As for microfluidic system, saturation concentration of surfactant is much higher than the macro scale, consequently, the 0% to 1% concentration was chosen in the experiment. All the data were collected by operating on a same chip

https://static-content.springer.com/image/art%3A10.1007%2Fs10544-011-9526-6/MediaObjects/10544_2011_9526_Fig7_HTML.gif
Fig. 7

The droplet generation frequency increases with the decreasing of interfacial tension

In the experiment, the coefficient of variation(CV) for the droplet size was lower than 4%, which was good for the experiment analysis, and the simulation showed steady results.

Both the experimental and simulation results agreed at the same point that the interfacial tension apparently affected on the characters of microfluidic droplet formations. Although results were still qualitative, the simulation results matched the experimental results well and exhibited the same trends. It could be confirmed that the simulation used as a prediction and validation tool for experimental could be adequately refined to describe the interfacial tension dependence in droplet formation. The experimental results demonstrated the initial assumption in this paper.

4 Conclusions

In this research, the effect of interfacial tension on the droplet formation within the microfluidic flow-focusing devices was illustrated. Monodisperse droplets of different size were obtained by adjusting the concentration of surfactant. Interfacial tension can be expected to decrease with decrease in droplet size and generation rate in a wide range of circumstances from both simulation and experimental results. The results were of interest in view of the important role of interfacial tension in determining the behavior of small droplets in microfluidic emulsification. The effect of wide range of parameters referred to droplet formation in lab-on-a-chip systems could be also explored, e.g. viscosity of fluids and channel hydrophoblicity, in order to study dynamics in microfluidics based on the behavior of droplets prepared.

Acknowledgments

We thank the financial support of National Natural Science Foundation of China under Grant No. 10804087.

Copyright information

© Springer Science+Business Media, LLC 2011