Coalescence with Droplets Caused Acceleration of the Liquid

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Droplets coalescence caused acceleration of the liquid movement in microchannels Qiang Liao, Shu-Zhe Li, Rong Chen, Hong Wang, Xun Zhu, Wei Zhang, and Xue-Feng He Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie5044133 • Publication Date (Web): 05 Jan 2015 Downloaded from http://pubs.acs.org on January 13, 2015

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Industrial & Engineering Chemistry Research

Coalescence with droplets caused acceleration of the liquid movement in microchannels

Qiang Liaoa,b, Shuzhe Lia,b, Rong Chena,b*, Hong Wanga,b, Xun Zhua,b, Wei Zhanga,b, Xuefeng Hea,b a

Key Laboratory of Low-grade Energy Utilization Technologies and Systems (Chongqing University), Ministry of Education, Chongqing 400030,China

b

Institute of Engineering Thermophysics, Chongqing University, Chongqing 400030, China

*Corresponding author. Tel.: 0086-23-65102474; fax: 0086-23-65102474; e-mail: [email protected] Abstract The coalescence between the liquid flow and droplets is usually encountered in the liquid filling or some new microdevices, which requires a deep understanding of its underlying mechanism. In this work, therefore, the dynamic behaviors of this atypical phenomenon in micorchannels were visually investigated with the droplets generated by the photothermally induced evaporation and condensation. The effects of the droplet quantity and position, inlet pressure and microchannel size were also explored. Experimental results showed that the coalescence accelerated the liquid movement as a result of lowered pressure at the interface. Parametric studies indicated that large droplet quantity and small distance between the inlet and droplets yielded a large velocity increment ratio as a consequence of lowered liquid pressure at the interface and increased pressure gradient, respectively. A high peak velocity increment but with low velocity increment ratio was obtained at high inlet pressure because of high liquid flow velocity. Moreover, the microchannel with small size yielded a strong

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acceleration rate of the liquid movement because of more obvious capillary action in small channel. Results obtained will be helpful for the design and operation those kinds of microdevices that may face this atypical phenomenon.

Keywords: Coalescence; Two-phase flow; Droplets; Velocity increment ratio


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1. Introduction The past decades have seen rapid development of microfluidics that integrates multi-functions, including delivery 1, on-line analysis 2, sorting 3and so on, due to the advantages of large surface-to-volume ratio, good mass transport property and precise manipulation and control of fluids. In microfluidics, accurately filling into microchannels is usually required to guarantee the precise manipulation and control of fluids in most applications. To this end, many approaches have been proposed, including micro-injection molding delivery technique

8

4, 5

, capillary-driven pumpless system

6, 7

, medical

and electrokinetic pump 9. Despite various strategies have been

developed, the fluid fillings by the hydrostatic pressure difference between inlet and outlet or by capillary action

10-12

are still the most widely-used techniques owing to

easy realization and operation. In these two types of the fluid filling, however, one problem may come out with repetitive use of microfluidic devices, that is, there might exist some residual droplets left in microchannel caused by previous filling. The residual droplets will coalesce with the coming liquid flow. Such coalescence between the droplets and liquid flow will definitely affect the fluid filling rate and stability. In addition to the fluid filling, this phenomenon has also been found in a micro pump based on the liquid phase change at water-air interface by using photothermal nanoparticles (PNPs) suspended in the water to convert the laser power into heat 13. In this design, water was evaporated from the interface and condensed in front of the interface to form droplets. These droplets coalesced with the original liquid flow and then

the

interface

was

advanced.

The

photothermally


induced


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evaporation-condensation-coalescence process realized this new micro pump. The authors believed that the droplet coalescence with the liquid flow played an important role in the water pumping. In addition, our recent works on the infrared (IR) laser assisted condensation in a microchannel also found that the coalescence between the liquid flow and condensed droplets could advance the liquid movement 14. However, the underlying mechanism of this atypical phenomenon is still unknown. Therefore, it is essential to gain insight into the dynamic behaviors between the liquid flow and droplets, which may help optimize these microdevices. As a matter of the fact, the dynamic behaviors regarding the coalescence of droplets have been widely studied in the past. Boreyko and Chen

15

studied

self-propelled droplets condensation on superhydrophobic surfaces and found that when the average droplet diameter reached a threshold value, the coalescence led to out-of-plane jumping motion of the coalesced droplets from the surface due to the surface energy released upon the droplet coalescence. Aryafar and Kavehpour

16

investigated droplet impacting different liquid interface. It was found that droplets would fully coalesce when the Ohnesorge number was greater than 1 and if not, droplets would partially coalesce and a secondary drop was created. Besides, the flow-induced droplet coalescence at a microfluidic T-junction was studied by Christopher etc.17 It was revealed that the capillary number dominated the responses to droplets collision at microfluidic junctions and the critical capillary number for coalescence depended on the local curvature of the colliding droplets at the point of collision. From these studies, it can be found that the capillary action induced by the


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coalescence dominates the droplet coalescence dynamic behaviors. Although these works have given a deep understanding of the coalescence behaviors of the droplets and are beneficial for the design and operation of the droplet microfluidics, how the coalescence of the liquid flow and droplets affects the liquid flow in microchannels remains unclear. Recently, we have simulated the coalescence between the liquid flow and a sessile droplet in hydrophobic microchannel and found that the coalescence can accelerate the original liquid flow movement.18 We also revealed the propulsion mechanism that the large curvature at the interface caused by the coalescence lowered the average liquid pressure at the interface and finally promoted the liquid flow movement. In our simulation, however, there was only a droplet existed in the microchannel, which might be significantly different from the real situations

13

. To

date, experimental works directed to the coalescence between the liquid flow and droplets have not yet been reported. To shed light on the dynamic behavior of this atypical phenomenon, therefore, we are intended to visually and experimentally study the liquid flow coalescing with disperse droplets in a microchannel with taking into account the variation of liquid flow speed and the interfacial dynamic behavior during coalescence process. To do this, a T-shape microchannel was designed and fabricated. The formation of disperse droplets in microchannels to simulate the residual droplets or condensed droplets is a critical problem. In this work, we proposed to use the IR laser to heat up the pre-set liquid segment so as to generate the droplets at the desired locations by condensation, with which the dynamic behaviors of the coalescence



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between the liquid flow and droplets could then be investigated. Variations in the speed of the liquid flow under different conditions were recorded and the interfacial dynamic phenomena were captured. In addition, the effects of the inlet pressure and microchannel size, droplets quantity and position were also discussed in this work.

2

Experimental Since the microchannel with T junction is one of the most frequently used

microchannels to produce immiscible fluid segments, in present study, T-shape microchannel was employed and fabricated by PDMS (polydimethylsiloxane, SYLGARD 184，Dow Corning) with rectangular cross section using standard soft photolithography technique

19-20

. The microchannel was formed by assembling two

PDMS layers and then attached onto a glass plate. In the process of the microchannel fabrication, the T-shape microchannel was firstly patterned in the top layer and then three holes directed to three tanks were drilled through this layer. The bottom layer was made by a thin PDMS film. When assembling these two layers, both of them were completely solidified and then heated at 95 oC for 15 minutes to enhance the bonding between them. Finally the formed T-shape microchannel was fastened onto a glass substrate, as shown in Fig. 1. The total length of the horizontal microchannel was 20 mm and the distances from inlet 1 and inlet 2 to T-junction was 15 mm and 7 mm, respectively. During the experiment, the needles with the diameter of 0.5 mm were fixed with the inlets and outlets and connected with the PTFE tube for supplying water and air, respectively.


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To investigate the dynamic behaviors of the coalescence between the liquid flow and droplets in a microchannel, the droplets should be formed at desired locations prior to the measurement. This is actually a challenging issue because of the difficulty in forming disperse droplets at desired location of a microchannel. Recently, the photothermal effect based optofluidics allowed us to realize non-contact control and manipulation of fluids

21-23

. As a result, our experiment systems were split into

two parts: the first one is the experimental system of the droplets generation by the photothermal effect of IR laser and the other one is the system of the coalescence experiment. The experimental system of the droplets generation is schematically shown in Fig. 2a, where the perpendicular flowing method was used to produce the short liquid segment 24. To do this, the fabricated microchannel was firstly fixed at a three-dimensional

motorized

precision

positioning

platform

(LUGE

M150RX100Y100Z100-3) with the step precision of 1 µm so that the laser would be adjusted to accurately focus on the liquid segment. As illustrated in Fig. 2b, air with the relative humidity of about 60% and distilled water were supplied into the microchannel from the inlet 2 and 3 by a microfluidic flow control system (MFCS, FLUIGENT, France), respectively. After the water-air interface passed through the T-junction and reached at desired position, the air pressure was immediately increased until water was sheared to form a liquid segment with desired volume and a liquid flow. After that, the supply of water was immediately shut down and the liquid flow could then be swept out of the horizontal microchannel from the inlet 2 by air and the liquid segment continuously moved forward. By doing this way, not only the length of



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the liquid segment could be precisely controlled but also only the liquid segment with the desired volume could stay in the horizontal microchannel without the liquid flow blocking the microchannel. Finally, the liquid segment was blown to the specified position where the coalescence would take place and in the meantime the air supply was switched off. In this work, the photothermally induced evaporation-condensation of a short liquid segment was then adopted to generate compact multi-droplets 14. As shown in Fig. 2a, the focused infrared laser (wavelength, 1550 nm) with the power ranging from 0.2 mW to 104.6 mW was projected to the center of the liquid segment. Since water can efficiently absorb the infrared light to generate heat, water could be rapidly evaporated. On the other hand, the laser spot diameter was maintained at 30 µm by a focal lens. Such a local heating source only increased the liquid water temperature and the surrounding temperature remained unchanged. In this case, water vapor could immediately condense to disperse droplets in the same region for the coalescence experiment. In this period, a CCD camera (Pointgrey, GS3-U3-41C6C-C) with adjustable zoom lens (Navitar, Zoom 6000) connected to a computer was used to monitor the phase change process. Note that the secondary liquid segment might be formed because of the droplets coalescence during this process. If this happened, the IR laser would be focused on the secondary liquid segment until all original liquid segment was fully transformed to the disperse droplets. Then, the IR laser was shut down and the microchannel with disperse droplets was ready for the coalescence experiment. After the formation of disperse droplets by the photothermal effect induced


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evaporation-condensation method, the microchannel was placed on the stage of the microscope (OLYMPUS, BX63). The experimental system is shown in Fig. 3. A high speed camera (Phantom V5.1) was connected to the microscope for monitoring the coalescence process and obtaining the real-time images. The frame rate was set as 500 fps in our experiments. The MFCS was used to supply water into the microchannel from the inlet 1 with controllable inlet pressure. Simultaneously the FOWELL device in MFCS monitored the flow rate to get the variation of the liquid flow velocity due to the coalescence. In this work, the measured liquid flow velocity by the FOWELL device was the velocity averaged by the cross area of the microchannel. All experiments were repeated for three times.

3

Results and discussion

3.1 The coalescence dynamic behaviors Fig. 4 shows the time-dependent coalescence behavior of the liquid flow and droplets. In this section, we firstly produced a 200 µm liquid segment located in the region of about 10 mm away from the inlet 1. Then the liquid segment was heated by IR laser under the power of 50 mW to generate disperse droplets. As seen, several large droplets with the diameter of about 50 µm were formed in this region. The length of droplets distribution was measured, which was about 560 µm at last. In addition, one question that the droplets were generated by the evaporation and condensation, whose temperature might be higher than that of the coming liquid flow with room temperature. Under such a circumstance, the marrangoni flow driven by



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the surface tension gradient might also contribute to the coalescence process. To identify the marrangoni effect, hence, the droplet temperature was ex-situ measured by assembling thermocouples into the microchannel, which were located at the region of the droplet formation. It was found that the maximum temperature increment of droplets near illuminated region was about 3.5 K. Moreover, after the laser was shut down, the temperature rise of the droplets immediately decreased to less than 1 K in 30 s, which was smaller than the time slot between the droplet generation and coalescence experiments. Therefore it can be concluded that the effect of the temperature difference between liquid flow and droplet can be ignored when studying the coalescence dynamic behaviors. After the droplets were generated, distilled water was then pumped into the microchannel from the inlet 1 by MFCS under the pressure driven. The pressure at the inlet was set at 15 mba relative to atmospheric pressure and the pressures at the other two exits were maintained at atmospheric pressure. It can be seen from Fig. 4 that the water-air interface was a smooth convex surface with an advancing angle of 110° in the hydrophobic microchannel before coalescence owing to the intermolecular forces between liquid, gas and solid phases at the three-phase contact line. After about 6.818 s, the water-air interface came into contact with the droplets and the two front droplets began to coalesce with the coming liquid flow, inducing a fluctuation on the interface. In particular, at the contacting interface region between the liquid flow and droplets, a small concave interface with a large curvature was immediately formed. The non-uniform pressure distribution across the entire interface at this moment resulted


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in the liquid flow inside, finally making original convex interface to be transformed into a concave interface. Such behaviors lowered the liquid pressure at the interface, increasing the pressure gradient between the inlet and interface. As a result, the liquid flow could be accelerated at this moment. Besides the simultaneous coalescence between the liquid flow and two droplets, another important phenomenon, that is, the sequential coalescences between the liquid flow and single droplet, was also frequently observed. As shown in Fig. 4, at t=6.822 s and 6.824 s, the liquid flow sequentially coalesced with two droplets. Unlike forming a clear concave interface in the case of the simultaneous coalescence between the liquid flow and two droplets, in this situation, the first contacting interface of the liquid flow was firstly advanced as a result of the lowered liquid pressure and the other side was then pulled forward. This process would be repeated, depending on the droplet locations. However, although a clear concave interface was not formed in this situation, induced large curvature still existed, which lowered the liquid pressure and thereby led to increasing the flow velocity. During the coalescence process, an interesting phenomenon was also observed in this study. When the front interface of the liquid flow was in contact with droplets, air bubbles marked with red circles were easily entrapped in the liquid flow and then attached on the wall as a result of the hydrophobicity of the PDMS nature. This phenomenon can be attributed to the following reasons. During the coalescence between the original liquid flow and droplets, the interfaces in the central regions of the microchannel were easy to firstly contact with each other, meaning that more space occupied by air between them existed. Because the coalescence time was rather



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short, air could not be fully and rapidly drained out in the process of the coalescence. Consequently, some air would be entrapped in water to form air bubbles. Air bubbles may change the flow characteristics of microchannel, thereby influencing the precise control of microfluidics. In particular, if the air bubbles flow with the coming liquid fluids, the terrible effects on the sample diagnosis may be unavoidable. It is known that the air bubble formation is inherently associated with the droplet size. Hence, when the droplets are relatively large, the air bubble formation should be avoided when operating such kinds of microdevices. As mentioned above, the coalescence between the liquid flow and droplets may accelerate the movement of original liquid flow. To verify this point, the velocity of the liquid flow was measured and compared with the case without the coalescence. The results are presented in Fig. 5. As seen, before the coalescence, both cases showed the almost same velocity and the liquid velocity slightly decreased from about 1.2 mm/s to about 0.7 mm/s. The decrease in the liquid flow velocity can be attributed to the viscous dissipation. However, it is interesting to find that when the coalescence occurred, the liquid flow velocity was immediately increased. In less than 0.5 s, the liquid flow velocity was rapidly increased from about 0.7 mm/s to about 4 mm/s. It should be noted that because the coalescence was finished in a critically short time and the velocity monitor frequency of the equipment was limited, the velocity fluctuation could not be monitored and only once velocity increment was observed. This actually reflects the overall effect of the coalescence on the liquid velocity. The following experimental results have the same situation. To more clearly show the


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increase of velocity, we defined a velocity increment ratio, ∆v ∗ = (v p − v ) / v , where v p and v represented the peak liquid velocity during the coalescence and the liquid

velocity without coalescence at the same moment respectively. In this case, the velocity increment ratio was measured as 3.95. The reasons leading to increasing the speed of the flow have been addressed above. The coalescence resulted in the formation of a small concave interface with a large curvature in the first contacting region, which caused the original convex interface to be fully transformed to a concave interface. The liquid pressure at the interface was then lowered to increase the pressure gradient, thereby increasing the liquid flow velocity. Hence, the coalescence can immediately increase the liquid flow velocity. After that, the velocity became the almost same as the case without the coalescence and the water-air interface was also restored to a convex shape. Therefore, the residual droplets show a significant on the fluid filling rate. It should be mentioned that in three times repeated experiments, though the distribution of droplets illustrated in Fig. 6a was relatively random, the values of the liquid flow velocity appeared almost the same as shown in Fig. 6b. The average velocity increment ratio for three times repeated experiments of 3.74 with the deviation of 5.88% was obtained. The results indicate the droplets generated by the same length liquid segment can still give the repeated results. On the other hand, if such droplets can be always generated in front of the interface of the original liquid body, continuous coalescence may pump liquid without external power input. This process is similar to the reported work on the photothermal effect based micro pump

12

. It is also indicated that the coalescence dominates the pumping



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mechanism. In summary, the coalescence would contribute to actuate the liquid flow due to the interface behavior, which highly depends on the droplet quantity and position, inlet pressure and microchannel size. Since the variation in the velocity is the most straightforward parameter to characterize the effect of the coalescence in this work, parametric studies of these factors in terms of the velocity change was carried out.

3.2 Effect of droplet quantity and position The coalescence is taking place between the liquid flow and droplets. Therefore, the resulting increase of the velocity is highly affected by the quantity of droplets as well as the droplets position. For this reason, the effects of the droplets quantity and position were firstly investigated with the inlet pressure of 15 mba in this work. As the formation of droplets by the photothermally induced evaporation and condensations was random, the quantity of droplets was characterized by the length of liquid segments. The liquid segment length l was ranged from 100 µm to 400 µm in this study. The centers of the liquid segments were located at about 10 mm away from the inlet 1. As shown in Fig. 7, after the IR laser heating, all liquid segments could be transformed to be disperse droplets with the similar droplet size distribution. Larger liquid segment yielded more droplets. The region of droplets was also wider. Hence, large quantity of droplets indicates that more frequent coalescence will take place, which can be a positive factor leading to an increase in the velocity. The measured liquid velocity changes with time under different liquid segment lengths are shown in


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Fig. 8a. It can be seen that before the coalescence, all cases showed a slight reduction in the liquid velocity because of increasing viscous dissipation loss with increasing the length of the liquid flow. Once the liquid flow started to coalesce with the droplets, the velocity of the original liquid flow was immediately increased as a result of the induced concave-shaped interface. More importantly, the increment of the liquid flow velocity increased with the length of the liquid segment. The velocity increment ratio under different liquid segment length are presented in Fig. 8b. It can be seen that the velocity increment ratio increased with the length of the liquid segment. The maximal value reached 6.15 at the liquid segment of 400 µm. This fact further indicates that a large liquid segment can generate a large velocity increment because of more droplets generated for the coalescence. The liquid pressure at the interface could be dramatically lowered, which resulted in the rapid increase of the liquid velocity at large liquid segment. In addition to the quantity of droplets, the position of the droplets has also effect on the liquid velocity increment. This is because the length of the liquid flow before the occurrence of the coalescence will vary with the droplets position, which will in turn affect the pressure drop from the inlet to the interface. For this reason, the effect of the droplets position was also investigated in this work. The inlet pressure and liquid segment were maintained at 15 mba and 200 µm, respectively. The centers of the liquid segments were set at 4, 7, 10 and 13 mm away from the inlet 1. The results are given in Fig. 9. Clearly, short length resulted in a large increment of the liquid velocity. As shown in Fig. 9b, with increasing the droplets position from 4 mm



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to 13 mm, the velocity increment ratio appearing in the whole coalescence process decreased from 4.58 to 3.23. Two main reasons may contribute to this reduction of the velocity increment ratio with increasing the distance between the inlet 1 and the droplets. The first one is that short distance between the inlet 1 and droplets led to large pressure gradient. As the liquid segment lengths were the same in all case, the formed droplets were rather similar. In this context, the lowered liquid pressures at the interface due to the coalescence were also rather close. For given inlet pressure, short distance between the inlet and droplets means large pressure gradient so that the increment of the liquid velocity was increased. On the other hand, large distance means large viscous dissipation loss and large flow resistance. As a result, the increment of the liquid velocity caused by the coalescence was weakened. Eventually, the velocity increment ratio showed a reduction trend with increasing the distance between the inlet 1 and droplets.

3.3 Effect of the inlet pressure The liquid flow was driven by the pressure. It becomes necessary to know how the inlet pressure affects the velocity increment induced by the coalescence. To do this, the liquid segment with a length of 200 µm was set at 10 mm away from the inlet 1. The inlet pressure ranged from 12.5 to 20 mba. The variations of the liquid flow velocity with time under different inlet pressures are shown in Fig. 10a. Increasing the inlet pressure dramatically increased the liquid flow velocity as a result of larger pressure driving force. For given droplets quantity and position, increased liquid flow


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velocity shortened the time of the liquid flow travelling from the inlet to the droplets. Therefore, the coalescence took place earlier at large inlet pressure. As shown in Fig. 10a, at the inlet pressure of 20 mba, the coalescence occurred after about 1.4 s while it come out after about 76 s at the inlet pressure of 12.5 mba. More importantly, the coalescence led to an increase in the liquid flow velocity as a result of the above-mentioned lowered liquid pressure at the interface. Higher inlet pressure resulted in larger increment of the liquid velocity. For 20 mba, the maximal liquid velocity reached 7.64 mm/s but only 1.73 mm/s of the maximal liquid velocity was obtained at 12.5 mba. The possible reason might be that high inlet pressure yielded a large liquid velocity. With the fixed liquid segment and droplets position, large velocity made the coalescence to be completed in a rather short time. As seen, the coalescence was finished in about 0.3 s at 20 mba but it took 1.1 s for 12.5 mba to finish. In this case, the lowered pressure at the interface due to the coalescence could immediately take effect to accelerate the liquid movement. As a result, a larger liquid flow velocity increment was produced at high inlet pressure. However, although the peak liquid velocity increment was large at high inlet pressure, the peak liquid velocity increment ratio was low, as illustrated in Fig. 10b. This is because high inlet pressure led to a large liquid velocity at the moment when the coalescence started, which reduced the velocity increment ratio in spite of large peak liquid velocity. In summary, high inlet pressure could yield a large peak liquid velocity increment but with small velocity increment ratio.



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3.4 Effect of the microchannel size In this work, the effect of the microchannel size was also studied. To this end, the inlet pressure was kept at 15 mba. The position of the liquid segment was maintained at 10 mm away from the inlet 1. The dimensions of four microchannels were 100 µm × 100 µm, 200 µm × 200 µm, 300 µm × 300 µm and 400 µm × 300 µm, respectively. To ensure the total liquid segment volumes in all cases were the same, the lengths of the liquid segments in correspondence with these four microchannels were 600, 150, 70 and 50 µm, respectively. The results are given in Figs. 11 and 12. Fig. 11 shows the formed droplets with different microchannel sizes. It can be seen that the amount of large droplets relative to the microchannel slightly decreased with increasing the microchannel size. This is because the droplets were generated by the photothermally induced evaporation and condensation in this work, increasing the microchannel size resulted in more space for water vapor to be transported, extending the condensation area. Under such a circumstance, condensed droplets were easier to coalesce with each other to form a large droplet in small microchannel but not for large microchannel. Therefore, a significant amount of small droplets in the microchannel with large size was observed. After generating the droplets in microchannels, water was then supplied into microchannels from the inlet 1 for studying the dynamic coalescence behaviors. It is interesting to find that before coalescence, the liquid flow velocities in the microchannels with 300 µm × 300 µm and 400 µm × 300 µm were the almost same and then decreased with decreasing the channel size. Large microchannel size creates low flow resistance to the liquid flow such that the liquid flow velocity


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reduced with decreasing the microchannel size. Since the difference between 300 µm × 300 µm and 400 µm × 300 µm microchannels were small and the flow resistances were possibly equal, the liquid flow velocities of them were quite close. Similarly, the coalescence also accelerated the liquid movement. As mentioned earlier, the acceleration of the liquid flow was observed due to the induced concave interface during the coalescence process. Such behavior is definitely a capillary action, which is affected by the microchannel size. Large microchannel size could weaken the capillary action so that the velocity increment of liquid movement was enhanced at small microchannel. This can be more clearly seen from the variation of the velocity increment ratio with the microchannel size shown in Fig. 12b. When microchannel size increased, the velocity increment ratio dramatically reduced from about 12 to less than 1. This fact indicates that the microchannel size has a significant effect on the dynamic coalescence behavior.

4. Conclusions In this work, the dynamic behaviors of the coalescence between the liquid flow and disperse droplets in microchannels were visually studied under different conditions. The disperse droplets were generated by the photothermal effect induced evaporation-condensation process by an infrared laser with the wavelength of 1550 nm. Experimental results showed that during the coalescence process, two atypical

coalescence phenomena were observed, including simultaneous contact with two droplets and sequential contact with single droplet, both of which could induce a



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concave interface and thereby lower the liquid pressure at the interface. As a result, the liquid movement was accelerated. In addition, the effects of the droplets quantity and position, inlet pressure and microchannel size on the coalescence were also investigated. It was found that large quantity of droplets generated by a large length of liquid segment could yield a high velocity increment ratio as a result of more droplets to be contributed to lower the liquid pressure at the interface. Large distance between the inlet and droplets showed a low velocity increment ratio because of large travelling distance of the liquid flow, which led to small pressure gradient and high viscous dissipation and thereby weakened the acceleration effect. Results on the inlet pressure effect indicated that although high inlet pressure could show a large peak velocity increment, the velocity increment ratio was low due to large initial flow velocity. Regarding the microchannel size, it was shown that small microchannel size could exhibit a large increment ratio as a result of stronger capillary action. In summary, this work reveals how the coalescence of the liquid flow and droplets in microchannels affects the liquid flow as well as the underlying mechanism. The results obtained are beneficial for the design and operation of microdivices that are encountered in such an atypical phenomenon.

Acknowledgements The authors gratefully acknowledge the financial supports of National Natural Science Foundation of China (No.51222603), Natural Science Funds for


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Distinguished Young Scholar of Chongqing, China (No. CSTC2012JJJQ90003), National Natural Science Foundation of China (No. 51106188 and No. 51325602), the Fundamental Research Funds for the Central Universities (No. CDJZR12 14 88 01) and Program for New Century Excellent Talents in University (NCET-12-0591).

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Figure captions Figure 1 Image of the fabricated T-shape microchannel Figure 2 (a) Experimental system of the droplet generation; (b) Illustration of the liquid segment formation Figure 3 Experimental system of the coalescence Figure 4 Dynamic interfacial behavior of the coalescence Figure 5 Variation of the liquid velocity with and without the coalescence; Figure 6 (a) Images of the droplets distribution in three repeated experiments; (b) Variation of the liquid velocity in the corresponding cases. Figure 7 Images of the droplets generated by changing the liquid segment length; Figure 8 (a) Variations of the liquid velocity under different droplet quantities; (b) Effect of the droplet quantity on the velocity increment ratio Figure 9 (a) Variations of the liquid velocity under different droplet positions; (b) Effect of the droplet position on the velocity increment ratio Figure 10 (a) Variations of the liquid velocity under different inlet pressures; (b) Effect of the inlet pressure on the velocity increment ratio Figure 11 Images of the droplets generated in microchannels with different sizes Figure 12 (a) Variations of the liquid velocity under different microchannel sizes; (b) Effect of the microchannel size on the velocity increment ratio



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Fig. 1


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(a)

(b)

Fig. 2



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 3


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Fig. 4



5

coalescence with droplets without coalescence

4

3

v (mm/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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2

1

0 0

2

4

t (s)

6

8

Fig. 5


10

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(a)

(b) Fig. 6



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 7


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6

l= 100µm l = 200µm l = 300µm l = 400µm without coalescence

5

v (mm/s)

4

3

2

1

0 0

2

4

6

8

10

t (s)

(a)

7

6

5

∆v*

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4

3

2 100

200

300

l (µm)

(b) Fig. 8


400


s = 4 mm s = 7 mm s = 10 mm s = 13 mm without coalescence

5

v (mm/s)

4

3

2

1

0 0

2

4

t (s)

6

8

10

(a)

4.8

4.4

4.0

∆v*

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3.6

3.2

2.8 4

6

8

10

12

s (mm)

(b) Fig. 9


14

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0

2

4

t (s)

6

8

10

8 p = 12.5mba p = 12.5mba-no droplets p = 15mba p = 15mba -no droplets p = 17.5mba p = 17.5mba-no drople ts p = 20mba p = 20mba -no droplets

7 6

v (mm/s)

5 4 3 2 1 0 0

20

40

60

80

100

120

t (s)

(a)

12

10

8

6

∆v*

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4

2

0 12

14

16

18

p (mba)

(b) Fig. 10


20


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 11


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0

2

t (s)

4

6

8

10

6 d d d d d d d d

5

3

= 100µm = 100µm-no drople ts = 200µm = 200µm-no droplets = 300µm = 300µm-no droplets = 400µm = 400µm-no droplets

2

1

0

0

20

40

60

80

100

120

t (s)

(a) 14 0.40

12 0.35

10

? v*

v (mm/s)

4

0.30

8

? v*

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.25

6

200

250

300

350

400

d (µm)

4 2 0 100

150

200

250

300

350

d (µm)

(b) Fig. 12


400

Coalescence with Droplets Caused Acceleration of the Liquid

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