PHYSICAL REVIEW E 89, 013003 (2014)

Effect of the fluid injection configuration on droplet size in a microfluidic T junction Odile Carrier, Denis Funfschilling,* and Huai Z. Li Laboratoire R´eactions et G´enie des Proc´ed´es, Universit´e de Lorraine, CNRS, 1 rue Grandville, Boˆıte Postale 20451, 54001 Nancy, France (Received 14 March 2013; revised manuscript received 19 November 2013; published 7 January 2014) The effect of confinement on the droplet formation in T junctions was studied for three configurations of fluid injection. The sizes of the main droplets and the satellite droplets were measured in the squeezing and dripping regimes. The evolution of droplet sizes with capillary number in the continuous phase is similar to that in flow-focusing junctions, i.e., the size of the main droplets decreases with an increase of this capillary number, while the size of the satellite droplets increases with an increase of this capillary number. While in the range of flow rates investigated the injection configuration does not exhibit a significant effect on the main droplet sizes, it does have an effect on the size of the satellite droplets. The latter ones are smaller when the neck rupture of the droplet occurs on an angle of the microsystem. DOI: 10.1103/PhysRevE.89.013003

PACS number(s): 47.61.Jd, 47.61.Fg

I. INTRODUCTION

Two phase flows and in particular droplet manipulations play a main role in microfluidic systems. Indeed, the formation of droplets in microsystems finds wide applications in analysis and screening, for example, each droplet behaving as a microreactor independent from the preceding and following droplets [1,2]. Droplets are, moreover, easy to manipulate and it is easier to control their properties (size, size distribution, temperature, residence time, etc.) [3]. Droplets formed in microfluidic systems are also usually monodispersed, which makes them interesting for improving emulsification processes [4]. Microfluidic droplet production consists of introducing two immiscible fluids in a channel with a more or less complex geometry. Three main geometries were extensively studied for the past decade: coflowing, flow focusing, and T junctions [5]. The geometry is a key factor for the formation of droplets. The choice of the geometry determines the range of flow rates over which droplets are monodispersed [6]. The first studies on T junctions date back to the early 2000’s [7]. Nowadays, studies in T junctions focus on understanding rupture mechanisms of droplets and bubbles, on establishing diagrams for flow regimes [8], often with numerical simulations [9–12], or by measuring experimentally the flow fields around the droplet in formation [13]. Wettability also has an influence on the formation of bubbles and droplets in T junctions. Appropriate wall treatments can change the size of droplets and the regime of the droplets’ formation [14]. The T junction can also be used to break down large droplets into precisely controlled daughter droplets [15]. Sometimes, the generation of droplets in microsystems leads to the formation of one or several satellite droplets besides the main droplet [16–18]. The formation of such satellite droplets has not been often studied in flow-focusing or T junction microsystems. While they can be sorted out to obtain really small droplets, their formation could give rise to some problems, in particular, processes such as emulsification. The path taken by droplets in microsystems depends on their size, especially in complex structured systems, and this

*

Corresponding author: [email protected]

1539-3755/2014/89(1)/013003(6)

provides an opportunity to sort them out [19]. In emulsions such satellite droplets could probably disappear due to Ostwald ripening. They could also accumulate in structured microsystems, leading to flow perturbations. Their formation during two-step emulsification in T junctions [20] could also lead to a faster aging of double emulsions. Obviously, it is important to understand their formation mechanisms and related parameters influencing their sizes to control or avoid their formation. Three possible configurations for fluids injection exist in T junctions: perpendicular flow, opposite flow, and inversed flow (Fig. 1). Most of the time, only one configuration was used and no comparison between different configurations has been made in the literature. Perpendicular flow and inversed flow were compared but the formation of satellites was not observed or studied [6]. The symmetric breakup was studied for bubbles without the formation of satellites [21]. According to [4], droplet formation in a T junction obeys the scaling law d ∝ Ca−1 c for droplets whose diameter is less than the height of otherwise. The intersection the microchannel, and d ∝ Ca−0.3 c of these scaling laws is not exactly located where the diameter is equal to the height of the channel, but is located at Cac ≈ 10−1 . In Ref. [4], only the perpendicular-flow configuration was studied. In the present work, the formation of droplets in T junction was experimentally investigated for the three configurations of fluid injections. The influence of the capillary number in the continuous phase on the size of main and satellite droplets was determined, showing the effect of confinement on these two kinds of droplets. II. EXPERIMENTAL SETUP

Microfluidic devices. The microfluidic T junctions were manufactured by precision milling in polymethylmethacrylate (PMMA). All channels have a 300 μm square cross section. Continuous and dispersed phases were delivered from glass syringes (Gastight Syringes, Hamilton, Switzerland), by syringe pumps (Harvard Apparatus, PHD 2000 Infusion, USA) through flexible Teflon tubing. All experiments were conducted at room temperature and atmospheric pressure. The three possible configurations of fluid injection were studied. Materials. The dispersed phase was silicon oil (Dow Corning, USA). Its density was 0.913 g/cm3 and its viscosity

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©2014 American Physical Society

ODILE CARRIER, DENIS FUNFSCHILLING, AND HUAI Z. LI

PHYSICAL REVIEW E 89, 013003 (2014)

FIG. 2. (a)–(f) Formation of droplets in a T junction for the perpendicular-flow configuration (Qc = 100 μl min−1 ; Qd = 4 μl min−1 ); (g) main droplet and its satellite (Qc = 300 μl min−1 ; Qd = 20 μl min−1 ).

FIG. 1. Injection of fluid configuration: (a) perpendicular flow; (b) opposite flow; (c) inversed flow.

measured by capillary viscosimetry was 5 mPa s−1 at 20 °C. The continuous phase was an aqueous solution of 2 wt % sodium dodecylsulfate (SDS, Amresco, USA) as surfactant. An interfacial tension of 10 mN m−1 between the silicon oil and the aqueous surfactant solution was measured by the pendant drop method (Tracker S, Teclis, France). The contact angle of a drop of distilled water+2% SDS surrounded by silicon oil on Plexiglas is 101°. A drop of silicon oil surrounded by a distilled water+2% SDS solution does not wet the Plexiglas. The flow rate of the continuous phase was varied between Qc = 10 and 2000 μl min−1 and the flow rate of the dispersed phase ranged from Qd = 2 to 100 μl min−1 ; these correspond to a formation of droplets in the squeezing and dripping regime. The flow rate ratios (continuous phase over dispersed phase flow rates) are between 0.5 and 100. Previous studies [21] (confirmed by our experiments), have shown that the dispersed phase flow rate has little effect on the size of the main and satellite droplets, compared to the continuous flow rate. Imaging. Devices were placed on an inverted microscope (10×) (Leica, Germany) and illuminated with a cold fiber light (Schott, KL1500) located on the opposite side of the channel. A high-speed digital camera (CamRecord 600, Optronis, Germany) was used to visualize the formation of droplets in the T junctions. The frame rate was between 50 and 2000 fps and the shutter speed 1/12 500 s. The full resolution of the camera was 1280 × 800 pixels. The volume of droplets was determined by image analysis using MATLAB and assuming the cylindrical symmetry of

droplets along the axis of symmetry of the outlet channel. Each image was divided by the mean image of the sequence (mean image of more than a hundred images). The divided image was then converted into a binary image on which the pixels constituting the droplets were counted. Droplets were constituted of at least a dozen pixels. The dimensionless droplet volumes given in the following parts are the volume of the droplets normalized by the volume of the intersection of the channels. A microparticle image velocimetry technique (μPIV, Dantec Dynamics, Denmark) was employed to measure the flow fields in the continuous phase. The aqueous continuous phase was seeded with latex particles of 1.01 μm diameter (Merck, France). The influence of seeding particles on the interfacial tension was negligible (the measured difference was less than 0.3 mN m−1 ). The flow was illuminated by a Nd:YAG pulsed laser (DualPower 30-15) of 532 nm wavelength. Flow fields were measured in the horizontal plane of symmetry of the microfluidic device. III. RESULTS AND DISCUSSION

The formation of the droplets in the classical configuration of the T junctions (see Fig. 2) was described by [8]. The finger of the dispersed phase entered into the intersection, filled up [Figs. 2(a)–2(d)], and elongated until its detachment following the neck shrinking [Fig. 2(e)]. A recent work [22] has confirmed the plugging during the droplet formation by in situ pressure measurements. These measurements validate the squeezing mechanism given previously. As already observed in the flow-focusing junction [18,23], a satellite droplet was formed just after the main droplet [Fig. 2(g)] for the three configurations of fluid injection. This satellite resulted from the rupture of the neck, which was pinched at both extremities. A. Size of the main droplets

In all three configurations of fluid injection, oil droplets were formed in distilled water+2% SDS (the concentration of SDS surfactant in the aqueous phase is then ten times the critical micellar concentration). The evolution of the dimensionless volume of the main droplets Vg /a 3 is presented

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continuous-phase and dispersed-phase flow rate, the droplets were almost monodispersed. The polydispersity index [24] was defined as ¯ (1) Ip = 100δ/d,

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FIG. 3. (Color online) Evolution of the dimensionless droplets volume (droplet volume normalized by the volume of the junction) with the capillary number of the continuous phase for the three configurations of fluid injection. (a) Main droplets; the horizontal dotted line corresponds to the limit of confinement, i.e., the largest possible round droplet that exactly touches all walls. The solid line corresponds to the model given in [24]. (b) Satellite droplets for Cad = 1.3 × 10−3 (+) perpendicular flow; (◦) opposite flow; () inversed flow. Error bars correspond to the standard deviation of the measurements.

in Fig. 3(a) in a function of the capillary number in continuous phase Cac = (μv) /σ with μ the viscosity of the continuous phase, v the average velocity of the continuous phase, and σ the interfacial tension between both phases. As the fluids are the same for the three configurations, an evolution of Cac is equivalent to an evolution of the continuous phase flow rate. For the three configurations, droplets of the same mean volume were obtained and the similar evolution of the volume with the capillary number in the continuous phase was observed. The slight dispersion of experimental data at a constant capillary number came mainly from the different flow rates of the dispersed phase. In the range of flow rates studied, the influence of the dispersed flow rate was really low in comparison with the influence of the continuous flow rate, which is why we did not focus on this parameter. For a given

with δ the standard deviation of the droplet diameter and d¯ the average droplet diameter. This polydispersity index was quite low for the three configurations (average Ip is between 1.5 and 3.3) which is in agreement with the literature regarding droplet formation in microfluidic T junctions. The size distribution is thus really narrow and droplets are highly monodispersed. The configuration of fluid injection does not have an influence on the main droplet formation. This first observation differs from what [6] observed for perpendicular-flow and inversed-flow configurations. It is, however, possible that this difference comes from the material configuration of the microsystem. The microchannels used for their study had a mixed material: The bottom plate was in glass and the other three walls were in polydimethylsiloxane. These were treated to be highly hydrophobic. In our case, four walls are in the same materials and PMMA has a mixed affinity for silicon oil and aqueous solution, even if this affinity is higher for the aqueous solution due to the presence of surfactant in great excess. In our microsystem, by switching the continuous and the dispersed phases and accordingly treating the walls to be hydrophobic (Aquapel treatment), the tip streaming regime was reached very quickly because of the important shear stress forces applied by the viscous continuous oil phase on the tip. As a result, the range of Cac where satellite droplets were created was too limited to be significant and it was not possible to compare these results with ours. For the three configurations, the droplet volume decreases with increasing capillary number (i.e., the flow rate of the continuous phase increases in our case) but two different behaviors in different ranges of capillary numbers could be distinguished. For Cac < 10−1 , the decrease of the volume was relatively slow. The decrease was more abrupt when Cac > 10−1 . The following correlations were obtained:  Vg for Cac  10−1 3.510−1 Ca−0.3 c = . (2) −1.2 4.310−2 Cac for Cac  10−1 a3 Several authors have studied the evolution of the volume of the droplet in the function of the capillary number. Liu and Zhang found a scaling V ≈ Ca−0.78 [25]. By lattice-Boltzmann simulations, van der Graaf found a scaling V ≈ Ca−0.75 [11], and De Menech found a scaling as V ≈ Ca−1.2 in the dripping regime [9]. Other publications express a nondimensional d where Qd is the dispersed flow volume in the form of 1 + α Q Qc rate, and Qc the continuous flow rate [8,24]. In [26], the authors give a model which in our geometrical conditions corresponds to Vg /a 3 = 0.841 + 1.18Qd /Qc , which is represented in Fig. 3(a) for the lowest dispersed phase flow rate. If we consider that the volume of the droplet depends only weakly on Qd , we can obtain a scaling law V ≈ Ca−1 , which is in reasonable agreement with our results. The confinement of the droplet can be considered as a parameter that influences the droplet size through the presence of walls near the droplet in formation. The droplet does not “touch” the wall when its diameter is lower than the width of the channel. This threshold between such a droplet and

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a droplet whose diameter is above the width of the channel corresponds to Vg π = ≈ 0.52. 3 a 6

(3)

This induces the change in evolution of droplet volume presented in Fig. 3(a) (dashed line). So, the transition between various size evolutions corresponds then to a change of confinement: If the droplet is not confined, its size decreases faster with the capillary number than if it is confined. When the droplet diameter is higher than the width of the channel, walls have an effect on the rupture. With increasing flow rate of the continuous phase, this parameter dominates the formation mechanism of the droplets over the wall effects. These results are in agreement with the scaling laws observed by [4]. A slight difference was observed for the smaller droplets (power index of −1.2 instead of −1) but the order of magnitude was the same and the range of flow rates studied was slightly higher. The value obtained by these authors can be then extended to the three configurations of fluid injection in T junctions studied here and not only to the perpendicular-flow configuration. B. Size of satellite droplets

As seen in Fig. 2(g), a satellite droplet was formed after the main one in these T junctions. Figure 3(b) presents the evolution of the dimensionless volume of satellite droplets formed after the main droplet. While there is no difference of main droplet volume between the three injection configurations, the volumes of satellite droplets differ from each other. First of all, the polydispersity index for the satellite droplet was higher than that of the main droplets. For the three configurations the average Ip was between 10 and 14. However, it is worth mentioning that the determination of the size of the satellites is less accurate than for the main droplets because of the smaller number of pixels occupied by the satellite. The evolution of the size of the satellite droplets is similar in the three configurations as in flow-focusing junctions [23]: It hardly evolves when Cac  Cacrit = 10−2 and then the satellite size increases with Cac when Cac  Cacrit = 10−2 :  −2 Vsat α for Cac  Cacrit = 10−2 , (4) K ∝ Ca c K Cacrit for Cac  Cacrit = 10 a3

FIG. 4. (Color online) Velocity fields in the continuous phase measured just before the rupture of a droplet in the T junction in the perpendicular-flow configuration: (a) Qc = 100 μl min−1 , Qd = 10 μl min−1 ; (b) Qc = 900 μl min−1 , Qd = 10 μl min−1 .

with K a constant. In flow-focusing junctions, K depends only on the fluid properties (viscosity, interfacial tension). In T junctions it appears to depend on the configurations of fluid injection. For the perpendicular-flow configuration K = 2.5 × 10−4 and for the inversed-flow configuration, K = 7.5 × 10−4 . The power index α is around 1. The critical capillary number of 10−2 , which corresponds to this transition, is the classical critical value that was observed in T junctions [9]. Above this value, shear stress plays an increasing role in the breakup process due to the velocity of the continuous phase. The shape of the curve of the satellite droplets volume is very little influenced by the flow rate ratio in the range of flow rates studied. Indeed, when the flow rate of the dispersed phase is 2 or 20 μl min−1 for constant continuous

flow rate, i.e., for tenfold flow rate ratios, the same two-step evolution of the satellite droplet size is observed. This result is consistent with the numerical simulations of [25]. Flow fields measured in the continuous phase are illustrated in Figs. 4(a) and 4(b) for different continuous phase capillary numbers for the perpendicular-flow configuration, respectively, for Cac  Cacrit = 10−2 and Cac  Cacrit = 10−2 . Flow patterns are clearly different in both cases. At low flow rates just before the rupture, the continuous phase flow is directed towards the neck of the droplet reinforcing the effect of the presence of an angle. The dispersed phase plugs the exit channel, leading thus to a marked rupture on the neck. At high flow rates, the flow before the rupture exerts significant shear stresses on the

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FIG. 5. Step of droplet formation just before rupture for the three configurations of fluid injection: (a) perpendicular flow; (b) opposite flow; (c) inversed flow.

forming droplet. These shear stresses prevent the droplet from occupying the whole section of the junction, leading thus to such a rupture, slightly shifted downstream in comparison with the rupture at lower flow rates. This evolution is similar to that observed in a flow-focusing junction [23] for PMMA microsystems and silicon glass treated to be hydrophobic systems. These systems have different wetting properties towards both fluids. However, the evolution of the size of satellite droplets is the same: even at low capillary number, the wetting properties of the wall do not affect the evolution of the satellite droplet size, contrary to shear stresses and inertia. Concerning the configuration of fluid injection, satellite droplets have the same size for perpendicular- and oppositeflow configurations while the satellites are bigger (five times for low capillary numbers) in the inversed-flow configuration. This difference comes from the difference of rupture mechanisms leading to the satellite droplet between these configurations. The size of the satellite depends on the flow rate as well as on the rupture mechanism. For the perpendicularand opposite-flow configuration, the rupture occurs on an angle of the microfluidic system [see, respectively, Figs. 5(a) and 5(b)]. For the inversed-flow configuration, the rupture is longitudinal and the neck does not properly touch the channel’s walls when the rupture takes place [Fig. 5(c)]. To some extent, the rupture mechanism in this configuration is comparable to that in the flow-focusing geometry.

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At low values of capillary number, the neck is pressed against an angle whose presence contributes to facilitate the rupture, limiting then the development of the neck and the size of the satellite droplet. This latter one is thus smaller than for the inversed-flow configuration. When the capillary number increases, we saw previously that the rupture is slightly shifted away from the angle on which rupture occurs for the perpendicular- and opposite-flow configuration. It results in an increase of the size of the satellite droplet as it evolves towards a longitudinal rupture with a Rayleigh-Plateau instability mechanism for the latest step (less effect of the angle of the microsystem). As for flow-focusing geometries, the longitudinal rupture becomes asymmetric when the capillary number rises, resulting usually in a bigger satellite droplet [21]. When the capillary number increases, the difference of sizes between the three configurations fades out progressively: The shift of the rupture brings a longitudinal rupture for the three configurations. IV. CONCLUSION

The influence of fluid injection on the size of the main and satellite droplets was experimentally investigated for the three possible configurations in a T junction microchannel of square cross section. The configuration does not have a significant influence on the size of the main droplet, but the confinement of the droplet determines its size. On the contrary, the configuration of fluid injection shows an effective influence on the size of the satellite droplet. It is interpreted as the effect of the presence of the angle of the system on which the rupture can occur: The size of the satellite is smaller. If the rupture is longitudinal, the satellite is bigger (inversed-flow configuration). When the capillary number increases, the difference between the configurations vanishes: The shear stresses applied by the continuous phase lead to a longitudinal rupture for all configurations. ACKNOWLEDGMENT

The French Minist`ere de l’Enseignement Sup´erieur et de la Recherche is gratefully acknowledged for the financial support.

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Effect of the fluid injection configuration on droplet size in a microfluidic T junction.

The effect of confinement on the droplet formation in T junctions was studied for three configurations of fluid injection. The sizes of the main dropl...
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