Asymmetrical breakup of bubbles at a microfluidic T-junction ...

Microfluid Nanofluid (2012) 13:723–733 DOI 10.1007/s10404-012-0991-x

RESEARCH PAPER

Asymmetrical breakup of bubbles at a microfluidic T-junction divergence: feedback effect of bubble collision Yining Wu • Taotao Fu • Chunying Zhu Yutao Lu • Youguang Ma • Huai Z. Li

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Received: 6 March 2012 / Accepted: 24 April 2012 / Published online: 9 May 2012 Ó Springer-Verlag 2012

Abstract This paper aims at studying the asymmetrical breakup of bubbles at a microfluidic T-junction divergence stemming from the feedback effect of bubble behaviors at the T-junction convergence in a loop with the symmetrical branches by a high-speed digital camera. The experiments were performed under gas/liquid flow rates ratio ranging from 0.084 to 4.333. The microfluidic channels have uniform square cross-section with 400 lm wide and 400 lm deep. Four bubble behaviors (bubble pair asymmetrical collision, bubble pair staggered flow, single bubble flow and dynamic transformation flow) were observed at the T-junction convergence in different gas and liquid flow rates. The feedback effects of asymmetrical collision and staggered flow of bubble pairs at the T-junction convergence on bubble behavior at the T-junction divergence were mainly investigated. The result showed that the feedback effect is negligible at relatively low flow rates when no collision of bubble pairs occurs. And the bubble pair asymmetrical collision at T-junction convergence or an amplified effect of structured blemish of microchannel at relatively high flow rates is primarily responsible for the asymmetric breakup of bubbles at the T-junction divergence. Keywords Feedback Asymmetrical breakup Bubble collision Microfluidics Loop

Y. Wu T. Fu C. Zhu Y. Lu Y. Ma (&) State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, People’s Republic of China e-mail: [email protected] H. Z. Li Laboratory of Reactions and Process Engineering, Lorraine-Universite´, CNRS, 1, rue Grandville, BP 20451, 54001 Nancy Cedex, France

1 Introduction Microfluidic devices are endowed with the power of precisely handling very small volume of fluid in a high degree of controllability and reproducibility (Stone et al. 2004). Moreover, microfluidic technique could facilely generate bubbles (droplets) of desirable sizes; accordingly, it could be conveniently extended to two phases flow or multiphase flow systems. In recent years, much attention has been devoted to the application of microfluidics in chemical reaction (Shao et al. 2010), mixing (Hou et al. 2011), emulsion (Abate et al. 2011; Nisisako and Hatsuzawa 2010), extraction (Kamio et al. 2011), materials and medicine synthesis (Huang et al. 2011; Zhao et al. 2011), biological, chemical analysis (Lien et al. 2009) and coding/ decoding (Maddala et al. 2011b). Successful realization of the above-mentioned assignments usually requires that the microfluidic device could integrate two or multiple operating units, including bubble (droplet) generation (Fu et al. 2011b), transporting (Cubaud and Ho 2004), breakup (Fu et al. 2011a; Leshansky and Pismen 2009), repartition (Belloul et al. 2009; Jousse et al. 2006), coalescence (Jose and Cubaud 2012) and so on. Therefore, some relatively complex configurations such as T-junction divergences/convergences (Fu et al. 2011a), loops (Cybulski and Garstecki 2010; Maddala et al. 2011a) and ladders (Maddala et al. 2011b) have been introduced into microfluidic device family instead of simple-structured microchannel which is impossible to perform so complicated operating and controlling. However, these complex structured configurations lead to many intricate bubble behaviors and interactions between bubbles (droplets). Classificatory, T-junction divergence/convergence is one of the most common and widely applied configuration, many significant works like droplet/bubble formation (Sivasamy

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et al. 2011; Wang et al. 2011), breakup (Fu et al. 2011a; Leshansky and Pismen 2009) and coalescence (Jose and Cubaud 2012), etc. have been completed in this structure. Recently, the droplet behaviors and interactions in microfluidic ladder networks with fore-aft structural symmetry (Prakash and Gershenfeld 2007) and asymmetry (Maddala et al. 2011b) have also been investigated, in which different ladder structures could be used to adjust the interval between two droplets. The loop is another typical and useful configuration in which a channel bifurcates into two branches and then recombines downstream. The loop can be used to tailor the size of formed bubble or droplet, affording great flexibility and controllability in emulsification, crystallization process and other potential process (Bremond et al. 2008; Link et al. 2004; Ralf et al. 2012). But the feedback effect in a loop is obvious. When a bubble/droplet flows into a loop it will choose a branch to flow away if no occurrence of breakup in the inlet node. This behavior will cause the resistance variation of each branch and accordingly influence the choice of subsequent bubble/droplet. In general, this feedback effect is nonlinear (Belloul et al. 2009, 2011; Cybulski and Garstecki 2010; Fuerstman et al. 2007a; Jousse et al. 2006; Parthiban and Khan 2011; Sessoms et al. 2009; Smith and Gaver 2010). Results show that flow patterns of bubble/droplet were mainly affected by operating conditions and the geometry of microchannel (Gupta and Kumar 2010; Timgren et al. 2009). More specifically, Sessoms et al. (2009) studied droplet flows in microfluidic networks both experimentally and numerically. During their experiments, they found two kinds of flow patterns: filtering regime and repartition regime. The transformation of these two regimes depended on the spacing between droplets k before flowing into the loop, excess resistance length Ld resulting from the presence of droplet in the branch and the ratio of two branches length K. When 2Ld [ ðK 1Þk, the droplet flow followed repartition regime, contrarily it fell into filtering regime. The flow of droplets in the loop is simplified in their numerical simulation. Once k, K and Ld are preset, the Fig. 1 a Schematic diagram of the microfluidic device. Bubbles are formed in a microfluidic flow-focusing junction and move towards a loop. b T-junction divergence and T-junction convergence in the loop. Bubbles can break or do not break at the T-junction divergence and exit the T-junction convergence into the single channel. The crosssection of the microchannel is 400 9 400 lm2

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Microfluid Nanofluid (2012) 13:723–733

droplet reaching the loop inlet chooses a channel with lower resistance by logical judgment without knowing the details of flow fields in the loop. Their experimental results could be predicted successfully by the numerical simulation. Furthermore, Cybulski and Garstecki (2010) studied the transformation between sub-regimes within repartition regime utilizing artificial disturbance method. Belloul et al. (2009, 2011) investigated the influence of droplets’ collision on flow patterns, and they proposed two physical mechanisms regulating flow pattern at the bifurcation: collision and collective hydrodynamic feedback affecting droplet, whether collision or hydrodynamic feedback remains dominant relied principally on the droplet confinement (the ratio of droplet radius to microchannel radius) and the distance between two consecutive droplets. Although several experimental efforts have been devoted to the flow behaviors of droplet in a loop (Belloul et al. 2009; Cybulski and Garstecki 2010; Fuerstman et al. 2007a; Sessoms et al. 2009), and similar bubble and droplet behaviors were found at a T-junction divergence (Calderon et al. 2005; Fu et al. 2011a; Jullien et al. 2009; Leshansky and Pismen 2009; Link et al. 2004). To our best knowledge, little attention has been paid to the feedback effect of bubble behaviors at the T-junction convergence on the bubble breakup at the T-junction divergence of a loop. This work is mainly focused on the asymmetric breakup of bubbles at the T-junction divergence, owing to the feedback effect of bubble collision at the T-junction convergence in a loop.

2 Experimental procedures The microfluidic device used in this study is shown in Fig. 1. This microchannel consists of the bubble formation section, snakelike microchannel and a symmetric loop. Bubbles were formed in a microfluidic flow-focusing junction (the left hand diagram of Fig. 1a) and driven into the snakelike microchannel which damped the changes in pressure caused by droplets flowing through the loop to ensure that the process


of bubble generating would not be interrupted (Fuerstman et al. 2007a). And then, the bubble moved towards the loop (the right hand diagram of Fig. 1a). In the loop, the microchannel divides into two symmetric parts at the first T-junction, and then the two channels reconvert to a single channel again at the second T-junction. Each branch of the T-junction is 5 mm in length. The bubble stream is divided into two streams at the T-junction divergence, where bubbles could break or not (Fig. 1b). At the T-junction convergence, the two streams recombine and then exit into the latter single channel. The experiments were mainly focused on the T-junction divergence and convergence in the loop (Fig. 1b). The microfluidic device was fabricated in a polymethyl methacrylate (PMMA) plate by precision milling and sealed by another PMMA plate. The cross-section of all channels is 400 lm wide and 400 lm high. Gas was fed by a N2 cylinder and the flow rate was controlled by a high precision micro-metering valve (KOFLOC, Japan). Liquid was delivered from a 60-mL syringe by a syringe pump (Harvard Apparatus, PHD 22/2000, USA). All of our experiments were conducted at room temperature and atmospheric pressure. The surfactant sodium dodecyl sulfate (SDS) (0.24 wt%) was added into deionized water to prevent the coalescence of bubbles at the T-junction convergence. The Surface tension r, viscosity l and density q are 34.3 mN m-1, 0.92 mPa s and 1,000 kg m-3, respectively. The surface tension was measured using a tensiometer, by the pendant drop technique on a Tracker apparatus (Dataphysics, Germany). An ubbelohde capillary viscometer (Shanghai Qihang Glass Instruments Factory, China) was used to characterize the viscosity of liquid. The density of liquid was measured using a vibrating tuber density meter (Anton Paar DMA-4500-M, Austria). For the present experiment, the microfluidic device was placed under an inverted microscope (Nikon Ti-S, Japan), which was equipped with a high-speed camera (Redlake Motion Pro Y-5, USA). The minimum shutter speed of the camera is 1/1,000,000 s. In this work, the frame rates were between 1,000 and 2,500 fps. The behaviors of bubbles at the T-junction divergence and the T-junction convergence were captured simultaneously by the highspeed camera. Pictures were analyzed in post-processing to quantify the size and velocity of the bubbles. In addition, the movement of bubble caps was measured as a function of time during the bubble flows into the T-junction divergence.

3 Results and discussion 3.1 Bubble behaviors at the T-junction convergence The bubble behaviors at the T-junction convergence and T-junction divergence of the symmetric loop (Fig. 1) were

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systematically investigated. In our experiment, four categories of bubble behaviors at the T-junction convergence were observed (Fig. 2): bubble pair asymmetrical collision, bubble pair staggered flow, single bubble flow and dynamic transformation flow (an alternate presentation of symmetrical and asymmetrical collision of bubble pairs). Whether bubble collision takes place is determined by the relationship between the time for the first one of the two daughter bubbles flowing through the outlet of the loop tL and the time difference of the two daughter bubbles arriving at the T-junction convergence td. The time tL could be estimated as tL ¼ LB =UA , where LB and UA denote the length and the average velocity of the first one of the two daughter bubbles passing through the outlet, respectively. And td ¼ jL=V1 L=V2 j, where L, V1 and V2 denote the branch length of the loop, the velocity of the bubble in the left and right branch, respectively. When td \ tL, the asymmetrical collision of two daughter bubbles occurs. Under this circumstance, one of the two daughter bubbles can slip through another, then the two bubbles flow downstream into the exit channel in a pair end-to-cap (Fig. 2A1), or one bubble first enters into the exit channel and subsequently is sniped into two parts (Fig. 2A2), then the three bubbles travel downstream one after another. When td [ tL, staggered flow occurs without contact between the two bubbles (Fig. 2B). This means that one of the daughter bubble pair passes through the T-junction convergence first, and then the latter one arrives at the exit. As a result, no collision occurs. In this case two subregimes could be found: non-collision of uniform daughter bubbles (Fig. 2B1): non-collision of nonuniform daughter bubbles (Fig. 2B2). Figure. 2C shows the bubble behavior when gas flow rate is relatively low, for instance, less than 1 mL/min in our experiment. In this situation, the mother bubbles enter into the divergence without breakup, then flow into the branch with higher instantaneous flow rate, consequently, no other bubble appears in the opposite channel while the bubble arrives at the exit, this phenomenon is named as single bubble flow. This flow regime has also been systematically studied by theoretical, numerical and experimental investigation (Belloul et al. 2009, 2011; Cybulski and Garstecki 2010; Fuerstman et al. 2007a; Jousse et al. 2006; Parthiban and Khan 2011; Sessoms et al. 2009; Smith and Gaver 2010). In our experiment, dynamic transformation flow is also visualized. In this regime, bubble pair symmetrical collision (Fig. 2D1) and bubble pair asymmetrical collision (Fig. 2D2) present alternately. It is worth noting that the collision of bubbles at the microfluidic T-junction convergence is quite similar to the behavior of droplets at such a device (Christopher et al. 2009). However, late splitting (Fig. 2F in Christopher et al. 2009) was rarely observed in our experiment owing to the lower density and viscosity of bubbles than those of

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Fig. 2 Representative regimes observed for N2 bubbles move across the T-junction convergence of the loop. A bubble pair asymmetrical collision with two sub-regimes A1 slipping, A2 splitting. B bubble pair staggered flow with two sub-regimes: B1 noncollision of uniform daughter bubbles, B2 non-collision of non-uniform daughter bubbles. C single bubble flow, D dynamic transformation flow with two sub-regimes, D1 symmetrical collision of bubble pairs, D2 asymmetrical collision of bubble pairs

droplets. More detailed information will be presented in the next section. Figure 3 shows the flow regime diagram for bubbles at the T-junction convergence in SDS solutions (0.24 % w/w), where gas flow rate QG and liquid flow rate QL are chosen as vertical axis and horizontal axis, respectively. In the present experiments the gas flow rate is spanned between 0.44 and 4.2 mL/min, and the liquid flow rate is between 0.3 and 10 mL/min. As shown in Fig. 3, the bubble behaviors depend dramatically on both the gas flow rate and liquid flow rate. When the gas flow rate and liquid flow rate are less than 1.0 and 5.0 mL/min, respectively, dynamic transformation flow occurs. Single bubble flow presents in the gas flow rate ranges from 0.44 to 1 mL/min and the liquid flow rate from 1.6 to 3.6 mL/ min. Bubble pair asymmetrical collision exhibits at a relatively low liquid flow rate over the entire range of gas flow rate, whereas the bubble pair staggered flow occurs at higher liquid flow rate. Asymmetrical collision and staggered flow are the most primary two-flow regimes for bubbles at the T-junction convergence, and could lead to obviously different feedback effects on the bubble breakup at upstream T-junction divergence of the loop. Therefore, these two behaviors are most concerned in this paper.

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Fig. 3 Operating diagram of droplet behaviors by using the gas flow rate QG and liquid flow rate QL as coordinates. Symbols denote the bubble behaviors at the T-junction convergence: square bubble pair asymmetrical collision, circle bubble pair staggered flow, triangle dynamic transformation flow, star single bubble flow

3.2 Degree of asymmetrical breakup of mother bubbles at the T-junction divergence To quantify the feedback effect of bubble pair behaviors at the T-junction convergence on the T-junction divergence


of the loop, we use the absolute value of the length difference between two daughter bubbles jL1 L2 j to express the asymmetry degree of the mother bubble breakup. The dimensionless of the absolute value of length difference between two daughter bubbles jðL1 L2 Þ=Wc j was plotted against the dimensionless of the summation of two daughter bubbles ðL1 þ L2 Þ=Wc , here Wc is the channel width. It is manifested from Fig. 4 that the non-collision region will transform to collision region as the value of ðL1 þ L2 Þ=Wc increases. This results accords with the operating diagram (Fig. 3) because the value of ðL1 þ L2 Þ=Wc is dependent apparently on the flow rate of gas/liquid flow rate. Two distinct domains in non-collision regime were demonstrated in Fig. 4: the asymmetry degree ðL1 þ L2 Þ=Wc decreased remarkably with the increase of ðL1 þ L2 Þ=Wc at first, and then leveled off at a low degree as the size of bubble increased until bubble collision happened. In the collision region, the variation trend of the asymmetry degree is different. The asymmetry degree varied from rising at first to latterly moderate decreasing with fluctuation. These results arouse our curiosity and research interests to seek the mechanism of the feedback effects of the two bubble behaviors at the T-junction convergence on the bubble breakup at the T-junction divergence of the loop. 3.3 Feedback of asymmetrical collision of bubble pair at the T-junction divergence Figure 5 illustrates an example of the temporal evolution of the asymmetric breakup of the mother bubble at the

Fig. 4 Dependence of the asymmetry degree of the bubble breakup at the T-junction divergence on the bubble length. Open circle, solid circle QG = 3.16 mL/min; open square, solid triangle QG = 2.6 mL/ min; open star, solid star QG = 1.43 mL/min; open symbol bubble pair asymmetrical collision; solid symbol bubble pair staggered flow. The inset shows the length L1, L2 of the two daughter bubbles

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T-junction divergence under the influence of bubble pair asymmetrical collision at the T-junction convergence. The origin of time is taken when the mother bubble reaches the entrance of the loop. When bubble behaviors at exit are into consideration, the whole process of asymmetric bubble breakup can be described as follows: (1) the first section is from t = 0 ms to t = 6 ms, a mother bubble penetrates into the loop from the inlet channel and the front cap begins to expand both radially and axially, until the cap reaches the upper wall; (2) the second section is from t = 6 ms to t = 12 ms, the bubble comes through onedimensional axial symmetric expansion to two downstream branches; (3) the third section is from t = 12 ms to t = 30 ms. The daughter bubble in the left branch reaches the exit first and then slips through another one in the right branch which is almost motionless during this time. Afterward the one-dimensional axial expansion of the mother bubble at the entrance becomes asymmetric, it is obvious that the part in the left branch is bigger than that in the right part; (4) the fourth section is from t = 30 ms to t = 45 ms. The daughter bubble in the right branch passes the exit and during this time the mother bubble breaks up into two new daughter bubbles. The dynamical evolution processes of bubble breakup are quantified by measuring several parameters as sketched in Fig. 6a, b. Figure 6a, b shows the penetration and breakup process of a mother bubble, respectively. These two processes determine the length difference between the two daughter bubbles. The increased lengths of the breaking bubble in downstream branches are denoted as DX1 and DX2 , the subscript 1, 2 represent left branch and right branch, respectively. The increased length of the breaking bubble is normalized by the microchannel width Wc. The time is normalized by the characteristic residence time within the T-junction divergence tc ¼ Wc =U where U ¼ ðQG þ QL Þ=Wc2 is the average two-phase flow speed in the main channel. As shown in Fig. 6c, at first, the dimensionless increased length DX1 =Wc , DX2 =Wc increased linearly with the dimensionless time Ut=Wc and the value of DX1 =Wc and DX2 =Wc almost equaled to each other. Corresponding to Fig. 5 (t = 0 ms to t = 9 ms) during this time, the radial and axial expanding process of the front cap evolved into axial expanding and there was no bubble blocked. Then the dimensionless increased length approached to a constant value for a period of time and DX1 =Wc almost equaled to DX2 =Wc . After that DX1 =Wc exceeded DX2 =Wc , the difference between DX1 =Wc and DX2 =Wc appeared. During this time, referring to Fig. 5 (t = 12 ms to t = 30 ms), we found the exit was occupied by the daughter bubble coming from the left branch and the daughter bubble in the right hand was blocked by the left one. This process went on until the left daughter bubble drove away from the

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Fig. 5 Temporal evolution of asymmetric breakup of bubbles at the T-junction divergence. QG = 0.4 mL/min

exit. Finally, the penetration section ended. Then the value of DX2 =Wc exceeded DX1 =Wc as the daughter bubble in the right side flowing away from the exit. When there was no bubble at the T-junction convergence, DX1 =Wc and DX2 =Wc reached the same level again (t = 33 ms to t = 45 ms in Fig. 5). Compared to the penetration period, the breakup section is short. Accordingly, the breakup process of the mother bubble is asymmetric. The above-mentioned results indicated that the different states (moving or being blocked) of daughter bubbles at the T-junction exit have different effects on flow fields in the branches and on the breakup of the mother bubble. To illustrate the mechanism leading to the difference between DX1 =Wc and DX2 =Wc , it is needful to understand the Taylor flow behavior in square cross-section microchannel. In the experiment, a straight microchannel is used for obtaining necessary dynamical information. The Taylor flow is quantified by measuring the length of the bubble and the bubble speed. The bubble length is normalized by the channel width Wc and the bubble speed is normalized by the average two-phase flow speed U, as shown in Fig. 7. As can be seen from Fig. 7a, in low average two-phase flow U, the speed of the bubble in SDS solution with critical colloid concentration is less somewhat than U, and then the bubble speed approaches gradually the superficial

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speed U with its increase. Fuerstman et al. (2007b) also reported similar phenomena. As shown in Fig. 7b, when the dimensionless bubble length is relatively small, the dimensionless bubble speed dramatically decreases with the increase of dimensionless bubble length. Subsequently, the dimensionless speed Ub/U decreases slightly. When the dimensionless bubble length is less than one, the value of dimensionless bubble speed is larger than one. The other way round, the dimensionless bubble speed is less than one, and under this circumstance, the liquid phase flows more rapidly than the bubble, thus a portion of liquid flows through the four gutters (the areas bounded by the curved body of the bubble and the corners of the channel as shown in Fig. 8b). When the bubbles are small enough and are not confined by walls of the channel, the liquid phase flows much slower than the bubble. This phenomenon has also been reported by Luo and Wang (2011), and can be understood by taking the velocity profile of Poiseuille flow into consideration. When the bubbles are small, they flow downstream in the center of the channel, where the speed approaches twice the average two-phase flow speed (Sessoms et al. 2009). While the bubble is confined by the channel, the dynamic resistance of the bubble is larger than the liquid phase in the same length (Fuerstman et al. 2007b).


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Fig. 6 Sketch of the asymmetric breakup of bubbles at the T-junction divergence and definition of the two parameters used to characterize the evolution of asymmetric breakup of bubble: a the penetration process, b the breakup process. c The increased length of breaking bubble DX1,2 in downstream as a function of Ut/Wc (the subscript 1, 2 represent left and right branches, respectively)

Obviously the difference of DX reflects the difference of total two-phase flow rates between two branches in downstream channels. Equation (1) correlates the volumetric rate of flow Q between two given points in a channel, the difference in pressure between those two points DP and the fluidic resistance R. DP ¼ QR

ð1Þ

The pressure drop in the two branches is the same at all time, because the two branches start from the same entrance and recombine at the same exit. In each channel, the law of conservation of mass leads to the following relation:

Fig. 7 a Plot of the velocity of the bubbles versus the superficial velocity in the straight channel. b The dimensionless bubble velocity as a function of the dimensionless bubble length. Liquid phase: SDS 0.24 %

Fig. 8 a Scheme for the determination of Wf in square microchannel, Wc = 400 lm. b Liquid film shape in square microchannel at low capillary number Ca with non-circle bubble

QG þ QL ¼ UAc ¼ Ub Ab þ Ug Ag :

ð2Þ

Q g ¼ U g Ag

ð3Þ

where QG and QL are the volumetric flow rates of the gas and the liquid phase, respectively, and Qg is the volumetric flow rates in gutters Ac ; Ab ; Ag are the cross-sectional area of the microchannel, the bubble and the gutter, respectively,

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Ub and Ug are the velocities of the bubble and the liquid in gutter. We assume the liquid flowing through a thin film is negligible in the presence of gutters (Ransohoff and Radke 1988). In our experiment, capillary number Ca ¼ ll Ub =r is less than 0.01 under bubble pair collision circumstance. Here ll is the viscosity of the liquid phase, r is the surface tension. As shown in Fig. 8b the cross-section of the bubble geometry is non-circle. The bubble surface is curved in the corner and becomes flat far away from the corner at low Ca\0:04 (Thulasidas et al. 1995) and the value of d=Wc is about 0.02, here d is the thickness of liquid film between bubble surface and microchannel wall (Fries et al. 2008). In the bubble collision scope, the width of liquid film (Fig. 8a) Wf 0:48Wc is nearly unchanged. According to these, we calculated that the value of Ab =Ac is about 0.9. Figure 7b distinctly shows that the value of Ub =U is between 0.825 and 0.950. By substituting these two values into Eq. (2), it could be found Qg does not exceed 0.2575 ðQG þ QL Þ. The value of 0.2575 is close to 0.24 measured during the formation of long bubbles by micro-Particle Image Velocimetry (l-PIV) system (van Steijn et al. 2007), in consideration of that the value could range from 0 (when the speed of bubble equal to the speed of average two-phase flow) to 1 (when the bubble was totally blocked, the speed of bubble equal to 0). And the difference between 0.2575 and 0.24 is probably caused by different cross-sections of microchannels employed (square vs. rectangular) (Ransohoff and Radke 1988; van Steijn et al. 2007; Thulasidas et al. 1995). It means that the bulk of liquid phase follows with the bubble synchronously, and only a small portion of liquid flows through the gutters. At critical micelle concentration (0.24 % w/w) of the SDS solution, the liquid preferentially flows through the four gutters rather than the thin films (Fig. 8b), and the pressure drop in channel is dominated by the total bubble length (Fuerstman et al. 2007b). A straightforward derivation demonstrates that the pressure drop across gutter DPg is the main part of the pressure drop across bubble DPb . According to Eq. (1) it is easy to show that DPg ¼ Qg Rg ð4Þ Here Rg denotes hydrodynamic resistance of gutter. The pressure drop DPg is relatively large, compared to that in liquid slugs of the same length at the critical micelle concentration (Fuerstman et al. 2007b) and Qg is small compared to ðQG þ QL Þ, so Rg is larger compared to the resistance of liquid flow in the microchannel. Once a daughter bubble is held up by the other at the exit, the liquid phase has no other choice but to flow through the gutters; thus, Qg increases remarkably. As a result, DPg also increases significantly. To balance the pressure drop, the flow rate of the branch in which bubble is held up has to

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decrease, finally leading to a remarkable difference of the dimensionless increased length between DX1 =Wc and DX2 =Wc . It is worth noting that the fluctuation of jðL1 L2 Þ=Wc j in Fig. 4, stems probably from the small fluctuation of timing difference between two daughter bubbles flowing away from the exit and the mother bubble penetrating to the loop. Under some circumstances, the daughter bubbles reached the exit before the mother bubble’s penetration. So when one of the daughter bubbles named A passes the exit first, the mother bubble’s penetration process is tilted towards the branch with bubble A. The other daughter bubble named B from the opposite side passing the exit next will affect the rest of penetration. And during this time, the mother bubble’s penetration process tilted towards the branch with bubble B. Both of the two daughter bubbles affected the breakup of the mother bubble at the T-junction divergence, so the influences of the two bubbles offset each other. As a result, the sizes of new daughter bubbles are approximately the same. Conversely, the mother bubble penetrated into the loop before the daughter bubbles reached the exit. Under this circumstance (Fig. 5), the daughter bubble reaching the exit first would affect the penetration of the mother bubble at the T-junction divergence while the other bubble of the bubble pair hardly affected the penetration. As a result, the sizes of new daughter bubbles are different. 3.4 Feedback of staggered flow of bubble pair at T-junction divergence As can be seen from Fig. 4, the staggered flow region could be divided into two distinct parts: (1) u 1:5 %, where u ¼ jðL1 L2 Þ=ðL1 þ L2 Þj 100 %, (2) u [ 1:5 %. It is obvious that when u 1:5 %, the exit feedback effect of bubbles in the T-junction convergence on divergence is negligible. Figure 9 shows the evolution sequence of the periodic mother bubble breakup under no occurrence of collision. The process of mother bubble breakup can be divided into three sections: (1) from t = 0 ms to t = 6 ms the expanding of the mother bubble in the radial and axial direction; (2) from t = 6 ms to t = 10 ms the symmetric expanding of mother in the axial direction and the daughter bubble in the right branch driving away from the exit; (3) from t = 10 ms to t = 22 ms the mother bubble broke up into two new daughter bubbles, and during this time the daughter bubble in the left branch passed the exit. During the entire process, the daughter bubbles passed the exit one by one without collision. The quantitative evolution of the breakup of the mother bubble is presented in Fig. 10. The parameters are the same as defined in Fig. 6b. The increased length of the breaking


bubble DX and time t are normalized by the Wc, tc ¼ Wc =U, respectively. As shown in Fig. 10, the dimensionless increased length DX1 =Wc , DX2 =Wc increased linearly with dimensionless time and their increment is approximate. Referring to Fig. 9 (t = 0 ms to t = 6 ms), the radial and axial expanding process of the front cap evolved into axial expanding and there was no bubble passing the exit. Subsequently, both DX1 =Wc and DX2 =Wc decreased moderately, but DX2 =Wc exceeded DX1 =Wc slightly. Corresponding to Fig. 9 (t = 6 ms to t = 14 ms), in this period, the right daughter bubble passed away from the exit and no collision occurred. Latter on DX1 =Wc exceeded DX2 =Wc at first, and then, DX1 =Wc and DX2 =Wc reached the same level. In contrast to t = 14 ms to t = 22 ms (Fig. 9), the daughter bubble in the left branch drove away from the exit. Because there was no collision between the daughter bubbles during the entire process, the

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difference between DX1 =Wc and DX2 =Wc was small. As a result, the breakup of the mother bubble was symmetric. In this study, the lengths of two daughter bubbles were measured, it could be found that the difference between them is neglectable as u\1:5 %. As expected, as long as no collision, bubbles would not be held up and occupy the entire exit for a long time, thus the resistance and flow rates in two branches would also not be changed markedly. The timing difference between the arrivals of the two bubbles at the exit is owing to the accumulation effect of the slight speed difference (the bubble speed in the left branch is always moderately faster than that in the right branch) between two branches caused by small structured imperfection of the microchannel (Baroud et al. 2006; Calderon et al. 2005, 2010). As shown in Fig. 4, there is a critical flow rate Qc, when the flow rate exceeds the Qc the structured blemish effects

Fig. 9 Temporal evolution of symmetric breakup of bubbles at the T-junction divergence. QG = 0.94 mL/min, QL = 1.4 mL/min

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Fig. 10 The increased length of breaking bubble in downstream DX1 and DX2, the subscript 1, 2 represent left branch, right branch, respectively, as a function of Ut/Wc

could be strongly amplified (Baroud et al. 2006), which leads to the occurrence of asymmetric breakup as shown in Fig. 2B2. The small bubble flowing through the right branch arrives at the exit earlier than that in the left one, but this does not mean that the continuous phase flow rate in the right branch is larger than that in the left branch. This is because the small bubbles in the right branch are usually centralized in the channel center region, where it is well known that the flow speed of continuous phase approaches about twice the average flow speed.

4 Conclusions In this paper, the behaviors of bubbles in the symmetrical loop in a microfluidic device were experimentally investigated by using a high-speed digital camera. Four categories of behaviors such as bubble pair asymmetrical collision, bubble pair staggered flow, single bubble flow and dynamic transformation flow (an alternate presentation of symmetrical and asymmetrical collision of bubble pairs) at the T-junction convergence were observed. The feedback effect of bubble collision at the T-junction convergence on the asymmetric breakup of bubbles at the T-junction divergence in the loop was investigated. Due to the asymmetric accumulation of pressure caused by bubble pair asymmetrical collision, the asymmetry degree of bubble breakup always exceeds 1.5 %. The influence of bubble pair staggered flow on the breakup of the mother bubble is different: when the average two-phase flow speed is relatively low, the asymmetry degree of bubble breakup is less than 1.5 %; while when the flow rates exceed a certain value the asymmetry degree of bubble breakup increases significantly owing to the amplified hydrodynamic resistance caused by structured blemish in the

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microchannel fabrication. This study gives quantitative data and qualitative analysis of asymmetric breakup of bubbles at the T-junction divergence owing to the feedback of bubble collision at the T-junction convergence in the loop. Full understanding of this phenomenon would be helpful to manipulate bubble or droplet by designing complex geometries such as a loop in microfluidic devices (Bremond et al. 2008; Belloul et al. 2011; Fuerstman et al. 2007a; Hou et al. 2011; Huang et al. 2011; Lien et al. 2009; Link et al. 2004; Maddala et al. 2011a; Prakash and Gershenfeld 2007). Moreover, our experimental results suggest that the three-dimensional numerical simulation is an urgent task for modeling bubble/droplet behaviors in square cross-sectional microchannels with complex geometries owing to the existence of gutters (Fuerstman et al. 2007b; Talimi et al. 2012; Wo¨rner 2012). Therefore, this paper is helpful to further experimental and numerical investigations on microfluidics and the design of microfluidic devices for application in the future (Calderon et al. 2010; Cybulski and Garstecki 2010; Luo and Wang 2011; Maddala et al. 2011a; Mark et al. 2010; Ralf et al. 2012; Stone et al. 2004; Wo¨rner 2012; Zhao et al. 2011). Acknowledgments The financial supports for this project from the National Natural Science Foundation of China (Nos. 21106093, 20911130358), the Research Fund for the Doctoral Program of Higher Education (No. 20110032120010) and the Program of Introducing Talents of Discipline to Universities (Grant No. B06006) are gratefully acknowledged.

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