Yingjie Fei,Chunying Zhu,*,Taotao Fu,Xiqun Gao,Youguang Ma,*

1 State Key Laboratory of Chemical Engineering,Tianjin University,Tianjin 300072,China

2 Yifang Industry Corporation,Liaoyang Petrochemical Fiber Company,Liaoyang 111003,China

Keywords:Slug bubble Microchannel Bubble deformation Bubble breakup

ABSTRACT The deformation of moving slug bubbles and its influence on the bubble breakup dynamics in microchannel were studied.Three bubble morphologies were found in the experiment:slug,dumbbell and grenade shapes.The viscosity effect of continuous phase aggravates the velocity difference between the fluid near the wall and the bubble,resulting in that the continuous phase near the bubble head flows towards and squeezes the bubble tail,which causes the deformation of bubbles.Moreover,the experimental results show that the deformation of bubbles could significantly prolong the bubble breakup period at the downstream Y-junction.There exists the critical capillary number CaCr for the asymmetric breakup of grenade bubbles, CaCr increases with the rise of flow rate and viscosity of the continuous phase.

1.Introduction

Microfluidic technique has been verified to have various advantages such as small size,large specific area,controllable flow,good transfer performance,uniform reaction conditions,intrinsic safety and easy scale-up,today it has been an important approach for chemical process intensification,chemical synthesis,biological detection and drug delivery [1-4].In recent years,the gas/liquid heterogeneous system in the microreactor has been extensively investigated due to its wide application in the chemical industry[5-7].For microreactor,T-junction,cross-focusing,and coflowing channels are usually used to generate bubbles in a shearing manner [8,9].Since the T-junction has a simple structure and is facile to manufacture,it accordingly is more adopted.In principle,the size of the generated bubbles depends primarily on the channel structure,fluid properties,and two-phase flow rate,the flow regime mainly includes bubbly flow,slug flow,and annular flow patterns,which the slug flow has received more attention in industrial applications and scientific research owing to its uniform bubble size and high radial mass transfer efficiency [10].

Different from the circular microchannel,the cross-section of slug bubble is non-axisymmetric in the rectangular microchannel,similar to a rectangle with rounded corners,and its axial radius(the radius measured by they-axis orz-axis on the cross-section)is smaller than the diagonal radius[11].Consequently,for a rectangular microchannel,the liquid film around the bubble is uneven,and the thickness of liquid film in the corner area is much larger than that at the center of the wall.Kreutzeret al.[12]reported that the diagonal radius is closely related to the capillary numberCawhile the axial radius is insensitive toCa.Liet al.[13]investigated experimentally and numerically the velocity profiles in the aqueous plug phase,and found that the velocity profiles was parabolic in the middle of the bubble,but was Couette-shaped in the surrounding continuous phase film.This indicated that the liquid film thickness in the corner relies dramatically on the viscosity of the continuous phase and bubble velocity,which would affect remarkably the bubble behavior in the microchannel.In practical application,considerable reactions involve high viscosity fluids,such as nitrification,polymer synthesis,and ionic liquid-related reactions[14-16],hence,the study on the effect of viscosity on the flow behavior and breakup of slug bubbles in microchannels is a foundational and imperative requirement.

The regulation of the bubble size and monodispersity could not only be performed at the generation stage but it could also be implemented by changing the geometric structure of the downstream channel to achieve re-intervention.Linket al.[17] pioneered the breakup process of the droplets at the T-junction,and found that the droplets would have two behaviors: breakup and non-breakup.According to the Rayleigh-Plateau theory,they proposed the transition prediction model of the two behaviors.Subsequently,Leshansky and Pismen [18] proposed a new transition model between the two behaviors by combining the lubrication analysis in the gap with the simple geometric construction for the interface shape.Successively,Fuet al.[19] investigated the breakup behavior of bubbles at the symmetric T-junction,and found that the breakup behaviors of bubbles and droplets are quite similar.Furthermore,Wuet al.[20] found that bubbles at Tjunction exist asymmetric breakup behavior,which was stemming from the feedback effect of bubble collision at loop channel.Moreover,Yamadaet al.[21] introduced an ’adjusting flow’ on the subchannel to precisely adjust the size of the sub-droplets by controlling the volume flow distributed to the two branch channels.

Although the irregular slug bubbles could be also found in the literature [22-24],the bubble deformation and its influence on bubble breakup were less concerned,which were mainly focused on the slug bubble/droplet with standard morphology.In this study,a T-junction structure is used to generate bubbles,and a Y-junction structure is used to break up bubbles.In the experiment,the bubbles generated at the T-junction were all slug-like.For continuous phase fluids with different viscosities,the experiments are mainly focused on the phenomenon and mechanism of the deformation of slug bubbles,and the effect of bubble deformation on its breakup dynamics at the downstream Y-junction.

2.Materials and Methods

2.1.Materials

Glycerol,cetyltrimethylammonium bromide(CTAB)(AR,＞99%),NaBr used in this study were purchased from Shanghai Aladdin Biochemical Technology Co.,Ltd.(China).The ultrapure water with a resistivity of 18.25 MΩ was prepared by a reverse osmosis device(Milli-Q,Millipore,USA).Nitrogen (≥99%) was purchased from Tianjin Liufang Industrial Gas Distribution Co.,Ltd.(China).To visualize the flow of the continuous phase around the bubbles,monodisperse polystyrene microspheres with a diameter of 5 μm were used as tracer particles,which were purchased from Wuxi Green Biotechnology Co.,Ltd.(China).

2.2.Microfluidic device

The material of the microfluidic device used in this study is polymethyl methacrylate (PMMA).The microchannel was manufactured on a PMMA plate by a precision milling process,and then sealed by another PMMA plate with bolts.The channel structure is shown in Fig.1.The cross-section of the exit channel for the two microchips is 0.8 mm × 2 mm,and the remaining channels are 0.8 mm × 0.8 mm.A T-junction structure was adopted to generate bubbles,and a symmetrical Y-junction structure was used for bubble breakup.The outlets of the two branch channels were connected to avoid the influence of the pressure imbalance on the breakup process,and the bubbles flowed out from the same outlet.A chamber was set before the outlet and the diameter of the outlet was enlarged to reduce the feedback effect of the bubble competition in the exit channel on the breakup at the Y-junction.Two microchannels with different length were adopted in this experiment.

The experimental setup is shown in Fig.2.The continuous phase was injected into the microchannel at a flowrateQcthrough a syringe pump (PHD 2000,Harvard Apparatus,USA),and an N2cylinder was connected to a mass flow controller(SLA5800,Brooks,USA) to supply gas at a flow rateQd.The microfluidic device was placed under an inverted microscope (ECLIPSE Ti-CU,Nikon,Japan),and images of the bubble flow and breakup process were captured by a high-speed camera (Fastcam SA1.1,Photron,Japan).

2.3.Physical properties

The density of liquid was measured using a U-shaped vibrating tube density meter (Anton Paar DMA 5000 M,Austria).A falling ball viscometer(Anton Paar Lovis 2000 ME)was used to characterize the viscosity of the continuous phase.The interfacial tension was measured using a surface tensiometer(OCAH200,Dataphysics,Germany).The physical properties data are listed in Table 1.During the measurement of these data,each sample was measured at least 3 times and averaged.The solution was placed in a 20 °C water bath for 30 min before the experiment to preheat,and a custommade thermostatic water jacket was equipped on the syringe to maintain the temperature of the solution at 20 °C during the experiment.

Table 1 Physical properties of test liquids at 20 °C

3.Results and Discussion

3.1.Flow and deformation of bubbles

As shown in Fig.3,three kinds of bubbles with different shapes were found in the experiment: grenade shape,dumbbell shape,and slug shape (including slug shape I and slug shape II).Among them,slug bubble I appears at smallerCadand slug bubble II only appears for the continuous phase with viscosity of 52.82 mPa·s within the experimental range.Flow pattern diagram was drawn based on the dimensionless parameterCa,as shown in Fig.4.With the increase of the disperse phase flow rate at a fixed continuous phase flow rate,the bubble morphology evolves from slug I to dumbbell,then to grenade,and finally to slug shape II.It could be also seen that the transition between deformation and nondeformation of slug bubbles is dominated byCadand is insensitive toCac.The flow range of dumbbell bubble shows an ascending trend with the increase ofCac,and there is a linear relationship betweenCacandCadwhen the bubbles change from dumbbellshaped to grenade-shaped.In addition,whenCad＞0.056,the thickness of the liquid film around the bubble tends to be uniform,and the bubble shape transforms to slug bubble II.

Fig.1.Schematic diagram of the microfluidic device: (a) channel 1;(b) channel 2.

Fig.2.Schematic diagram of experimental setup:1-collector;2-computer;3-highspeed camera;4-microscope;5-microinjection pump;6-N2 cylinder;7-mass flow controller;8-microchip.

Fig.3.Bubble morphology: (a) slug bubble I;(b) dumbbell bubble;(c) grenade bubble;(d) slug bubble II.

The experimental results also show that both viscosity and gas/liquid flow rate are determining factors.The increase in viscosity could reduce the needed flow rate for bubble deformation.When the viscosity of the continuous phase is 10.52 mPa·s,the bubble deformation occurs only whenQdis larger than 2.5 ml·min-1,and the deformation is insignificant.However,when the viscosity is 57.82 mPa·s,obvious deformation appears at a smallQd,about 0.4 ml·min-1.The increase of the continuous phase viscosity facilitates bubble deformation.Up to now,although the effect of viscosity on gas-liquid two-phase flow in the microchannel has been widely investigated,which was usually focused more on the flow pattern of the dispersed phase and the thickness of the liquid film[22-26],for instance,the similar bubble shapes of tail contraction were also observed in the literature [22-24],it’s just that they were not particularly concerned.

Bubble velocity is a very important parameter in fluid mechanics,so it is necessary to investigate the effect of deformation on it.The superficial velocity of fluids in microchannels can usually be represented byuS=(Qc+Qd)/A,whereQcis the continuous phase flow rate,Qdis the dispersed phase flow rate,Ais the crosssectional area of channel.But in higher viscosity fluids,the velocity of the bubble flowing in the channeluBis higher thanuS.uBatx=59 mm under different viscosity conditions was compared,as shown in Fig.5(a).It has been found that the velocity profile of continuous phase around the bubbles in the gas/liquid two-phase flow follows Couette flow,and the velocity profile in the middle of bubbles abides by Poiseuille flow [13].The rise in the viscosity of the continuous phase would increase the internal friction between adjacent fluid layers,thereby leading to the increase of the thickness of the fluid layer for Couette flow and the decrease of the thickness of the fluid layer for Poiseuille flow.According to the momentum conservation in the microchannel,when the viscosity of the continuous phase elevates,the maximum flow velocity in the Poiseuille flow increases,behaving as an increase of theuB.As can be seen from Fig.5,at all viscosities,uBis larger thanuS.However,it is interesting that when the viscosity of the continuous phase increases from 21.77 to 32.82 mPa·s,uBdoes not increase significantly due to the significant deformation of the bubbles,and even becomes smaller.Furthermore,the evolution of the deformed and undeformed bubble velocity along the microchannel is shown in Fig.5(b).Theoretically,due to mechanical friction or viscous losses,the flow velocity would slow down along the channel.But deformed bubbles exhibit a different phenomenon of getting faster.Both of these indicate that the deformation could affect the flow characteristic of bubbles.

The shape of the bubble at the positionxfrom T-junction is shown in Fig.6.It could be seen that the shape of the bubbles is gradually changing.Firstly,the tail of the bubble begins to shrink,and then the shrinking section gradually increases.Before entering the Y-junction,the middle and rear sections of the bubble break away from the wall and evolve from a non-axisymmetric cylinder to an axisymmetric cylinder.Yuet al.[27] reported the phenomenon of gradual variation of bubble morphology,they thought that the phenomenon resulted from the adsorption of nanoparticles on the gas-liquid interface.Obviously,the mechanism of morphological change of bubbles in this experiment is different from that reported in the literature.

Fig.4.The flow pattern diagram:(a)Cac-Cad;(b)Qc-Qd.▲,slug bubble I;●,dumbbell bubble;■,grenade bubble;◆,slug bubble II.Dash lines are transition lines from slug bubble I to dumbbell bubble;dot-dash lines are transition lines from dumbbell bubble to grenade bubble;double dot-dash lines are transition lines from grenade bubble to slug bubble II.

Fig.5.Effect of bubble deformation on bubble velocity:(a)comparison of superficial velocity and bubble velocity under different viscosities in channel 1(uB was measured at x=59 mm).Solid symbols represent slug bubbles,hollow symbols represent dumbbell bubbles,semi-solid symbols represent grenade slug bubbles;(b)evolution of bubble velocity in channel 1.Defined as x=0 mm at upstream T-junction (μ=32.82 mPa·s).

Fig.6.The morphology of bubble at position x from T-junction in channel 1.Defined as x=0 mm at upstream T-junction, Qc= 1.8 ml·min-1, Qd= 1.8 ml·min-1.

Fig.7.The movement process of the tracer particles in channel 1,Qc=1.8 ml·min-1,Qd= 1.8 ml·min-1.

The flow state of the continuous phase around the bubbles is an important factor to appear the interesting phenomenon.To clearly understand the abnormal phenomenon,5 μm visible microspheres as tracer particles were added in the continuous phase,and the flow of the gas-liquid two-phase system in the microchannel was observed using a high-magnification lens.In the literature,it was found that the continuous phase velocity in the corner region is equal to or even greater than the bubble velocity in the microchannel [28,29].However,it could be found from Fig.7 that the particles originally located at the head of the bubble move along the edge of the bubble towards the tail,indicating that the velocity of the continuous phase in the corner is much smaller than that of the bubbles under the experimental condition.We perceive that the velocity difference causesa‘‘loss”of the continuous phase at the front of the bubble.The variation of the distance between the two bubbleslcat different positions in the channel is shown in Fig.8.It could be seen that the distance between the two bubbles gradually decreases with bubbles moving forward until the flow gets to an equilibrium state.This indicates that the continuous phase at the front of the bubble indeed exists a ‘‘loss” phenomenon during the flow process.It could also be seen from Fig.8 thatlcrelates markedly to bubble morphology.lcdecreases rapidly in the first half of the channel and hardly changes in the second half,as shown in Fig.6,the bubble deformation mainly occurs in the first half of the channel.

Fig.8.Variation of distance lc between two bubbles over x in channel 1(μ=32.82 mPa·s).

Accordingly,the mechanism of bubble deformation could be depicted as follows.As the viscosity of the continuous phase increases,the friction force between adjacent fluid layers increases,which causes a great velocity difference between the fluids near the wall and the bubble (Fig.7),and thereby resulting in the continuous phase gradually flowing towards the tail of the bubble(Fig.8).However,it is hard for this part of liquid to mix with the liquid behind the bubble under laminar flow regime,leading to that the bubble tail is squeezed,and accordingly the tail detaches from the wall.The force analysis of section A-A(Fig.9)shows that the pressurePSgenerated by the squeeze force and the Laplace pressurePLgenerated by the depression contribute jointly to the shrinkage of the tail.

From dumbbell-shaped to grenade-shaped,it is more like a backward shift of the I position,implying that the transformation of shape is related to the force in the flow direction.The component force in thex-axis direction at the I position was analyzed,as shown in Fig.9.The depression formed at the tail will provide a forward surface tensionFσ,and the backward friction forceFFis introduced when the bubble flows.Under the condition of lower flow rate,theFFis small,in this case,the I position of the bubble would move forward,and thereby appearing dumbbell bubble.However,at the higher flow rate,theFFis larger,and the I position of the bubble moves backward and consequently forms grenade bubble.

The above mechanism could explain the effect of deformation onuBin the channel (Fig.5).The competition ofFσ andFFmakes the front section of dumbbell bubble and the mid-section of grenade bubble closer to the wall.As the bubble flows,FFon the deformed bubble is greater than that of the undeformed bubble.More importantly,the resistance caused by friction force increases with the viscosity of the fluid.Hence,when the viscosity increases from 21.77 to 32.82 mPa·s,the resistance loss resulting in deformation would not cause an obvious increase inuB.In addition,since the continuous phase near the bubble head flows to the tail,the space vacated from this part fluid would be filled by the bubble,which facilitates the acceleration of the bubble.

Fig.9.Schematic diagram of force analysis of deformed bubble.

Moreover,it could also be observed from Fig.6 and Fig.8 that the deformation degree of bubble increases with the flow distance.Therefore,two microchannels with different lengths were used to compare the deformation of bubbles.Fig.10 displays the experimental results for the shape of bubbles under the same experimental conditions in the two channels.As can be observed,the length of channel does not play a marked role in the shape of bubbles.At the same time,the measured pressure drop per unit length of the two channels under the corresponding flow rate is almost the same.Before the analysis and discussion,considering the elbow channel could generate additional pressure loss,even in laminar flow,secondary vortices could also be generated,which might affect the deformation.Hence,it is necessary to analyze the effect of the elbow on the pressure drop in channel 2.It has been confirmed that when theDeis less than 27,the effect of the elbow on the pressure drop could be ignorable [30]:

wheredis the equivalent diameter of the elbow,Ris the radius of the elbow.In our experiment,the maximumDeis about 0.54 in channel 2,hence,the effect of the elbows of channel 2 on pressure loss should be negligible.The ΔP/Lin different channels only relies on theCa,when the flow rates of the gas and liquid phases are both fixed[22].These conclusions seem to indicate that the deformation is almost exclusively related to fluid conditions,and not to channel structure or residence time and so on (Fig.11).

Fig.10.Final morphology of bubbles in channels with different lengths(Qc=1.8 ml·min-1,μ=32.82 mPa·s,the length of channel 1 is 60 mm,and the length of channel 2 is284.25 mm).

Fig.11.Variation of pressure drop in different channels (μ=32.82 mPa·s).Solid symbols represent slug bubbles,hollow symbols represent dumbbell bubbles,semisolid symbols represent grenade slug bubbles.

3.2.Breakup dynamics of deformed bubble

Fig.12 shows a typical breakup process of deformed bubbles.After the head of the mother bubble touches the tip of the Yjunction,the bubble enters into the two branch channels driven by the continuous phase.The moment when the bubble completely enters the junction is defined as the momenttb=0,and the moment when the bubble completely breaks into two subbubbles is defined as the end of breakup process.Accordingly,the duration is a breakup periodTb.The breakup regime of bubbles could be divided into breakup with permanent obstruction,breakup with partial obstruction,and breakup with permanent tunnel according to whether the gap between the bubble and the wall appears and its appearing time [19,31].It could be seen from Fig.12 that the breakup regime of the deformed bubble follows into the breakup with partial obstruction.In the breakup process,the continuous phase entering the Y-junction could be divided into two parts.One part squeezes the bubble neck to make it thin,and the other part flows to the downstream sub-channels through the gap and corners,which is called leakage flow.The breakup of the bubble is controlled by the squeeze force on the neck and the shear force of the leakage flow on the bubble,where the force of the squeeze force is more important than the shear force [32].

Fig.12.The breakup process of deformed bubble at Y-junction,μ=32.82 mPa·s,Qc= 1.8 ml·min-1, Qd= 1.8 ml·min-1.

We firstly investigated the effect of bubble deformation on the breakup periodTb.It could be seen from Fig.13(a) that theTbandCaobey a power-law relationship when the continuous phase viscosity is less than 32.82 mPa·s,in this case,and no visible bubble deformation could be observed.However,when the viscosity is up to 32.82 mPa·s,the bubbles become deformed,and theTbandCaabide by a two-stage power-law relationship.Besides,it could be seen that the variation tendency ofTbof the grenade bubbles with the largest deformation degree creates obvious deviation from that of slug and dumbbell bubbles.Based on the variation curve of the dimensionless minimum neck width as shown in Fig.13,it could be found that the grenade bubble corresponding to the dispersed phase of 1.2 ml·min-1and the dumbbell bubble corresponding to 1.0 ml·min-1have almost the same changing regulation in the minimum neck width.However,their working conditions such as velocity,bubble length,and channel pressure drop are much different,as is well known,all these parameters are important to affect the evolution of the bubble neck (Table 2),in which the velocity has been proved to be positively correlated with the squeezing force acting on the neck[32].This indicates that the bubble deformation could notably affect the bubble rupture process,which might be attributed to that the liquid film around the axisymmetric cylindrical tail is very thick,after entering the Yjunction,the bubble starts to rebound in the radial direction under the action of surface tension.As the thickness remains still larger than that at the Y-junction tip,thus the flow rate of the leakage flow increases.Meanwhile,the accumulated pressure of the continuous phase at the bubble neck caused by the clogging of the branch channel is partially released through the leakage flow,and the squeezing effect on the bubble neck becomes weakened,leading to a longer rupture period of the grenade-like bubbles.

Table 2 Movement parameters of bubble in channel.

3.3.Asymmetric breakup of deformed bubble

The downstream bifurcation is usually used to further regulate the size of the bubble,in which the monodispersity of the subbubble is always expected.However,it could be found that the grenade bubbles are more inclined to asymmetric breakup.For facile description,the deformation index δ is defined in Eq.(2) and the asymmetry index β of breakup is defined in Eq.(3):

Fig.13.(a) The relationship between breakup period Tb and Ca;(b) evolution of dimensionless minimum neck width over time (μ=32.82 mPa·s).Solid symbols represent slug bubbles,hollow symbols represent dumbbell bubbles,semi-solid symbols represent grenade slug bubbles.

whereDminis the minimum diameter of the rear segment,Dmaxis the maximum diameter of the front segment,approximately equal to the channel width,l1is the longer bubble length in the two sub-branches,l2is the shorter bubble length in the two subbranches (Fig.14).

The variations of the asymmetry index β withCaand flow rate ratio of two phasesQd/Qcare shown in Fig.15.Under μc≤21.77 mPa·s,the asymmetric breakup could appear only under extremely largeCaandQd/Qc＞1,and β is about 1.06.When μcreaches 32.82 mPa·s,the asymmetric breakup could be observed more markedly in a larger two-phase flow rate range.With the increase ofQc,the critical capillaryCaCrfor the asymmetric breakup is larger,and the critical flow rate ratio of two phases(Qd/Qc)Cris smaller.Therefore,increasing μcandQccould facilitate asymmetric breakup.

Breakup asymmetry has a strong correlation with deformation.The transformation of the dispersed phase cross-section in the rectangular channel from non-axisymmetric to axisymmetric shape depends on the critical capillary numberCaCr[33,34].WhenCa＞CaCr,the bubbles become axisymmetric,and the diameter relies onCa.Although this theory is inapplicable for the gradual change process of the bubble in this experiment,it could well describe the bubble tail diameter variation.It could be seen from Fig.16 that δ linearly varies withCa,but there exists a turning point at 0.052.WhenCais greater than 0.052,the δ starts to decrease rapidly.Similarly,Ca=0.052 is also the turning point of the β variation withCa.WhenCais greater than 0.052,l1andl2would no longer be the same,and β increases significantly with increasingCa.It means that δ and β are intrinsically dependent.The asymmetric breakup is closely related to theCaand flow field asymmetry [35,36],it is also affected by the feedback effects of bubble collisions in the loop[20].In this experiment,the feedback effect could be ignored,because the cavity of the exit section is large enough,and the two sub-bubbles after rupture do not come into contact when they enter the cavity.For the grenade bubble,the contracting tail complicates the surrounding fluid flow,which is caused the asymmetric flow field,resulting in an asymmetric breakup.

Fig.14.Definition of the relevant parameters for the grenade bubble: (a)deformation index;(b) breakup asymmetry index.

Fig.15.Effect of different factors on asymmetry index: (a) β - Ca;(b) β - Qd/Qc.

Fig.16.Variation of deformation index and breakup asymmetry index with bubble velocity (μ=32.82 mPa·s, Qc=1.8 ml·min-1).

The relationship between deformation and asymmetry breakup could be confirmed according to the flow field evolution,as shown in Fig.17.When the thinner tail is about to enter the junction,the front of the bubble is closer to the wall than the tail,which could be observed in Fig.17(a).Fig.17(g) shows that the liquid in the main channel flows through the gap between the bubble tail and the wall into the two branch channels at different speeds.The fluid flows down the nether subchannel with a greater velocity,hence,resulting in the increase of friction force on the bubble surface.Meanwhile,the squeeze force that promotes the bubble forward is reduced.Although the friction force is conducive to the forward movement of the bubbles,it is far insufficient to compensate for the weakened squeezing force.Therefore,the volume of bubble in the lower side channel is smaller.Moreover,it could be found from 0 to 4.0 ms that the difference in bubble length still causes obvious velocity difference of fluid flowing downstream.When the bubble neck begins to shrink from 2-dimensional to 3-dimensional(tb=8 ms),it could be seen that the asymmetric flow field at both sides of the Y-shaped tip has less influence on the length ratio of bubbles in the two sub-channels,but which remarkably affects the position of the neck.Therefore,the effect of bubble deformation on the breakup asymmetry is mainly reflected in the stage of bubble entering the junction and the squeeze stage of breakup.

Fig.17.Flow field evolution for asymmetric breakup process of grenade bubble.

4.Conclusions

Declaration of Competing Interest

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

Acknowledgements

This article is specially published for commemorating my esteemed supervisor,Academician Yu Guocong (K.T.Yu) for his 100th birthday! I would like to deeply appreciate him for his outstanding contribution to the Journal ofChinese Journal of Chemical Engineeringas one of the founders and for his extraordinary achievements in promoting the development of chemical science and technology in China.

This work is supported by the National Natural Science Foundation of China(21978197),and thanks for the aid of Opening Project of State Key Laboratory of Chemical Engineering of China (SKLChE-21Z03).

Nomenclature

By-and-bye the fame of his riches reached the ears of the king, and, as he himself was always in need of money, he sent for Don Giovanni, as he wished to borrow a large sum

CaCapillary number

DeDean number

dequivalent diameter of the elbow in channel 2

Khcurvature of bubble head,m-1

Ktcurvature of bubble tail,m-1

lclength between two adjacent bubbles,m

ΔPinlet gauge pressure,kPa

Qccontinuous phase flow rate,m3·s-1

Qddispersed phase flow rate,m3·s-1

Rradius of elbow in channel 2,m

Tbbreakup period of the bubble at the Y-junction,s

tbtime for the bubble breakup at the Y-junction,s

uBinstantaneous velocity of the bubble flowing in the channel,m·s-1

uSsuperficial velocity of the fluid,m·s-1

Wwidth of cross-section of the square microchannel,m

Wmminimum width of bubble neck,m

xdistance from T-junction,m

β asymmetry index

δ deformation index

μ viscosity of continuous phase,Pa·s

ρ density of continuous phase,kg·m-3

σ surface tension,N·m-1