Qianqing Liang,Xuehu Ma *,Kai WangJiang ChunZhong LanTingting HaoYaxiong Wang

1 Liaoning Key Laboratory of Clean Utilization of Chemical Resources,Institute of Chemical Engineering,Dalian University of Technology,Dalian 11624,China

2 School of Chemical Engineering,Inner Mongolia University of Science&Technology,Inner Mongolia,Baotou 014010,China

Keywords:Meandering rectangular micro-channel T-junction Fluid properties Bubble breakup mode Bubble/slug length

ABSTRACT In order to reduce or avoid the fluctuations from interface breakup,a meandering microchannel with curved multi-bends (44 turns)is fabricated,and investigations of scaling bubble/slug length in Taylor flow in a rectangular meandering microchannel are systematically conducted.Based on considerable experimental data,quantitative analyses for the influences of two important characteristic times,liquid phase physical properties and aspect ratio are made on the prediction criteria for the bubble/slug length of Taylor flow in a meandering microchannel.A simple principle is suggested to predict the bubble formation period by using the information of Rayleigh time and capillary time for six gas-liquid systems with average deviation of 10.96%.Considering physical properties of the liquid phase and cross-section configuration of the rectangular mcirochannel,revised scaling laws for bubble length are established by introducing Ca,We,Re and W/h whether for the squeezing-driven or shearing-driven of bubble break.In addition,a simple principle in terms of Garstecki-type model and bubble formation period is set-up to predict slug lengths.A total of 107 sets of experimental data are correlated with the meandering microchannel and operating range:0.001 ＜CaTP＜0.05,0.06 ＜WeTP＜9.0,18 ＜ReTP＜460 using the bubble/slug length prediction equation from current work.The average deviation between the correlated data and the experimental data for bubble length and slug length is about 9.42%and 9.95%,respectively.

1.Introduction

Microfluidic platforms provide an excellent capability in controlling fluid flow,heat and mass transport for chemical engineering,pharmaceutical industry,material science and biochemical application[1-5].There is a growing interest in precise controlling bubbles or droplets formation via microfluidic devices[6,7],where the liquid phase physical properties such as viscosity and surface tension profoundly affects fluid flow behavior[8].Recently,Taylor flow has received extensive attentions for wide operating range,little liquid back-mixing and high mono-dispersity[9,10].Bubbles are always encountered in Taylor flow in microchannel and manipulation of the bubble size is of great importance for microanalysis,on-chip separation,and micro-chemical reaction[11].T-junction is the most employed inlet geometry to produce bubble/droplet and passively tailor the bubble/droplet size.Therefore,the regulation and predication of the Taylor bubble/slug length in T-junction microchannel are crucial issue for the application of the microfluidic technique.The bubble breakup and formation process involve complex mechanism in microchannel,which is mainly relevant to drag force competition from interfacial tension,viscous shearing and possible force perturbations out of the system.These forces originate from three aspects[12,13]:properties of the fluids(viscosity and surface tension),configuration of the microchannel(cross-section geometry and gas/liquid inlet contact angle)and fluid flow conditions(gas/liquid flow rate or velocity).Numerous works,either the process of breakup or quantitative analysis of the bubble/droplet size,have been conducted recently[14-27].

Precise control over the process of bubble and slug formation is the basis of the microfluidic platform applications.Characterization or scaling of the bubble/slug length in the form of function of the physical properties and flow parameters offers a guideline to exactly control the mass transport and chemical reaction applied in the microfluidic device.Fu and Ma[14]summarized that bubble formation can be specifically classified into dripping regime,jetting regime,squeezing regime and squeezing-to-dripping regime,which is correspondingly dominated by one or two mechanism:squeezing mechanism[15]and shearing mechanism[16,17].Garstecki et al.[15]at first quantitatively have described the squeezing dominating process in a T-junction microchannel,and also set-up a simple scaling law to predict the bubble length.Simultaneously Garstecki et al.[15]and van Steijn et al.[18]indicate that the bubble size in the squeezing regime is controlled by the ratio of the gas and liquid velocity and channel width,without consideration of viscosity and surface tension.De Menech et al.[16]propose the crucial transition condition from squeezing to dripping in the microfluidic T-shaped junction.Specifically,squeezing regime is driven chiefly by the buildup of pressure upstream and influenced weakly of capillary number,the dripping regime is derived from the competition between interfacial and viscous stresses,and jetting regime highly depends on capillary number.Fu et al.[17]have demonstrated that long bubbles formed in the squeezing regime,while short or dispersed bubbles respectively in the transition and dripping regime.This transition from the squeezing regime to the dripping regime is only found at the highest jLof 1.0 m·s?1in the microchannel,where Ca ranged from 0.017 to 0.034.However,Yue et al.[19]have found that transition from the squeezing to the shearing regime is mainly affected by the liquid velocity,which is also observed by Yao[20].They also agree that the aspect ratio of the microchannel is an important parameter for the transition.The shearing mechanism is evidenced through the work from Thorsen [21]and Husny [22]that the main driving force is derived from the balance between the surface tension and viscous shear stress until the shearing stress is large enough to break through the gas-liquid interface.Most of the studies investigate not only the bubble formation mechanism,but also the quantification of the bubble/slug length in two ways.The first way for predicting bubble length has been firstly put forward from Garstecki[15],whose model only accounts for the influences of the gas and liquid flow rate and the width of the inlet channel.The following researches have focused on the modification of the scaling laws relating to several physical properties of the fluids and geometric parameters of the channel and the inlet.Van Steijn et al.[18]have considered the case of aspect ratio～1.0,and modified geometry parameter of Garstecki-model to be 1.5.Tan et al.[12]have added the influences of physical properties of liquid phase and the angle between entrance channels,and have derived the bubble length in the form of LB/W=1/2(QG/QLsin θ+2/5 cot θ)1/2Ca?1/5.Later research from Leclerc et al.[23]also has concerned the impact of the inlet geometry to modify the Garstecki-type scaling law for bubble length prediction.Xiong and Chung [24]have introduced the inertial force and aspect ratio of the channel to further broaden the model for the squeezing regime of the T-junction microchannel.Yao et al.[25]have found that inertial force is the main factor affecting bubble length and thus use We to improve the model application scope.However,the aforementioned works mainly focus on the bubbles in Taylor flow in the squeezing regime with a relative lower Ca number(＜0.01).

The second way to scale the bubble/slug length depends on a series of dimensionless parameters(Ca,We,Bo,Re,etc.),which particularly pronounces the effect of the physical confinement of the fluids on the interfacial dynamic for the bubble formation process.Although the bubble formation mechanism is exhaustively investigated,there are few works on slug length scaling law of Taylor flow.Garstecki et al.[15]have proposed a similar prediction of the slug length as the bubble length.Qian and Lawal[26]also have posed an empirical correlation to predict bubble/slug length through numerical simulation considering the influence of dimensionless number (Re,Ca,εG,εL)in a T-junction microchannel.Notably,this type of correlation is always significantly associated with the influence of phase fraction ε.Accordingly,Yao et al.[20,25]put forward a similar correlation replacing Re and Ca with We.Recently,Haase[27]offer the correlations to predict bubble and slug length in the gas-liquid co-flowing microchannel using 6 dimensionless groups(jG/jL,ReL,WeL),(din/dh),(dout/dh),and θ on the basis of the Pitheorem.Table 1 summarizes the literature correlations on bubble/slug length in the T-junction inlet microchannel,except for a co-flowing nozzle-tube from Haase[27]and Y-junction inlet from Yao et al.[20].

According to aforementioned reports,a reasonable scaling law for bubble/slug length leads a guideline for cruise control for gas-liquid flow.Although numerous studies focus on modifying the bubble length scaling law for the squeezing regime[14-26](Ca ＜0.01),few works concerned the case of shearing regime[17](Ca ＞0.01).Additionally,Fu et al.[17]proposed three formulas to extensively predict the bubble length for the squeezing mode,transition mode and shear mode of bubble formation using different concentrations of sodium dodecyl sulfate(SDS,0.1 wt%,0.25 wt%,0.5 wt%)as surfactants.However,it cannot eliminate the effect of surfactant on the gas-liquid interface.Simultaneously,there are relatively few studies[20,25,26]on the slug length during the bubble formation only for CO2/N2/air-water and with Ca below 0.02.Consequently,our work will offer a more extensive and applicable scaling law for bubble/slug length for Taylor flow in a meandering microchannel within the operating range:0.001 ＜CaTP＜0.05,0.06 ＜WeTP＜9.0,18 ＜ReTP＜460.A comparable investigation on bubble/slug length for Taylor flow is experimentally conducted through six gas-liquid systems,i.e.,CO2/N2mixture-H2O(CO2-H2O),CO2/N2mixture-2% (mole fraction)N-propanol aqueous solution (CO2-2%NPA),CO2/N2mixture-5%NPA aqueous solution(CO2-5%NPA),CO2/N2mixture-Methanol(CO2-MT),CO2/N2mixture-Ethanol(CO2-EA)and CO2/N2mixture N-propanol(CO2-NPA),involved in two important characteristic times(τRand τT),main physical properties of liquid phase(viscosity and surface tension)related to three dimensionless numbers(Ca,We,Re)and geometry of the cross-section aspect ratio(W/h)for the meandering microchannel.Then a series measurements of the bubble formation period,bubble/slug length for different gas-liquid systems are methodically carried out through visualization results.

2.Experimental

A schematic of the test setup is shown in Fig.1.The microchannel is fabricated on a borosilicate glass(BOROFLOAT?33)made by Suzhou Genso Optoelectronic Technology Co.,Ltd.,China.The inlet,outlet and main channels have the same rectangular section of 600 μm(width)and 300 μm(depth).The most common oscillatory slug flow occurs in pulsating heat pipes,where flow transitions are induced by boiling and condensation sections.It is found that the number of turns of the oscillating heat pipe(OHP)will affect the numbers of bubble and liquid slug,the flow pattern of gas-liquid two-phase flow and the state of gas-liquid interface,which then would affect the heat transfer performance of OHP[28].The more turns,the more easier to form a stable circulating flow,and the better heat transfer performance of the OHP.Rittidech et al.[29]used 40 turns in a closed oscillating heat pipe to ensure that bubbles and liquid slug could easily form a stable and directional flow,thus promoting heat transfer performance of the OHP.In addition,according to the investigation of Van Steijn et al.[30],the bubble breakup and bubble fluctuations during the movement may be reduced or avoided if the total pressure drop is increased.The total pressure drop can be significantly improved by increasing the turns of the microchannel.Thus,according to the multi-turn structure of the oscillating heat pipe,a long(number of turns:44)meandering microchannel is designed in order to form a stable and uniform Taylor flow in this work.

A pseudo T-junction inlet configuration is used to inject the gas and liquid phases into the microchannel.Gas flow is offered by the differential pressure-based mass flow controller (D07-7B,Beijing Seven star Electronics Co.,Ltd.,China)with an accuracy of±0.5%.The high pressure pump (P230P II,Dalian Elite Analytical Instruments Co.,Ltd.,China)with an accuracy of ±0.3% is used to control the liquid flow rate.The gas mixture is provided in a cylinder connected to a pressure regulator.The pressure drop for the gas inlet and outlet is directly measured by the pressure transducers (CCY13-X-08-A1-01-B-G,Beijing Star Sensor Technology Co.,Ltd.,China)with an accuracy of±0.25%.A buffer tank is used to eliminate the pulsation of the inlet liquid flow.The two-phase mixture leaving the meandering microchannel enters a phase separator to separate the gas and liquid stream based on the gravity.All experiments are conducted under ambient conditions(0.1 MPa,25 °C).The gas mixture (95% CO2and 5% N2,volume fraction)issupplied by Dalian Special Gas Co.,Ltd.,China.And analytical reagents,i.e.,methanol,ethanol,n-propanol (NPA)have been provided by Tianjin Kemiou Chemical Reagent Co.,Ltd.Table 2 has summarized the properties of liquids[31]at 25°C used in this work.

Table 1 Previous correlations for bubble length in Taylor flow through T-junction microchannel

Fig.1.Schematic of the experimental setup.

Table 2 Physical properties of liquids used in this work

The system is run for at least 5 min to reach a steady state at a constant flow rate.In each case of operational condition,experiments are conducted at least thrice.After steady state is achieved,two-phase flow patterns are visualized using a high-speed camera (Photron,Fastcam Apx-Rs)at capture rates of 5000 frame·s?1and a resolution of 1280×1000 pixels,to obtain suitable movie time intervals and distinct images.The obtained images are analyzed by Image-Pro Plus software to determine the bubble length and slug length.At least 10 images are respectively analyzed to give the average value for the bubble length(LB)and slug length(Ls).For a pixel size of the CCD camera translating to a distance of 7.5 μm,at least 2 pixel are required to detect the interface of the bubble.For a 5 mm long bubble,the uncertainty in measuring LBis 0.3%.The bubble formation period is simply determined by recording the time interval between two Taylor bubbles in terms of work from Yao et al.[20].

3.Results and Discussion

The operating conditions are as follows:0.088 ＜jG＜0.378 m·s?1,0.023 ＜jL＜0.417 m·s?1,0.001 ＜CaTP＜0.05,0.06 ＜WeTP＜9.0,18 ＜ReTP＜460.Here,water is used as a reference fluid to find appropriate operating conditions for Taylor flow in the meandering microchannel.Thus,the investigations on bubble formation mode and transition condition,determination and scaling law both for bubble length and slug length could be progressively carried out in various gas-liquid systems.

3.1.Characteristics of bubble formation mode

It is generally accepted that the breakup in a microfluidic T-junction classified to be squeezing-driven and shearing-driven on the basis of bubble formation mechanism aforementioned.The visualization experimental results provide a unifying picture of the dynamic process of bubble formation in a meandering microchannel including both of the squeezing and shearing-driven type breakup.For the squeezingdriven mode,bubble formation process of Taylor flow in rectangular microchannel can be typically described by three steps,namely filling stage,squeezing stage and pinch-off stage as elaborated from van Steijn[18].

Fig.2 shows flow development and detailed bubble variation at each stage as time evolution for various gas-liquid systems at a constant gas and liquid velocity.Red solid line represents the boundary between filling stage and squeezing stage,while green solid line separates the squeezing stage and pinch-off stage.In the filling stage,a bubble starts to propagate into the main channel until the bubble fills up the T-junction.Once the bubble blocks the width of the channel,in the following stage of squeezing,the bubble begins extending down the length of the channel until the bubble neck is pinched by the continuous phase.Eventually the bubble divorces from the interface and forms a free bubble which is defined as pinch-off stage here.Surface tension displays different performances at different stages[15,18].Before the bubble blocks the width of the channel,surface tension is conductive to the growth of the bubble head and orients the upstream.The higher the surface tension,the earlier squeezing stage can be reached.For the squeezing stage,surface tension is still helpful to the bubble elongation.While for the pinch-off stage,the bubble breakup requires to overcome the constrain from the surface tension.It can been seen from Figs.2 and 3 that the pinch-off stage in the squeezing-driven mode takes more time(1.375 ms,1.006 ms and 0.835 ms)as the surface tension increases,and the pinch-off stage also spends more time (2.8 ms,1.9 ms and 2.167 ms)with the increase of the surface tension in the shearing-driven mode,indicating that the larger the surface tension,the more difficult for bubble breakup.However,for the shearingdriven mode,the pinch-off stage of CO2-2%NPA takes less time(1.9 ms)than that of CO2-5%NPA (2.167 ms)since 2%NPA aqueous solution has a larger viscosity than that of 5%NPA aqueous solution from Table 2.Specifically,Fig.2 also demonstrates that physical properties of the liquid phase,especially surface tension and viscosity played important role during the squeezing-driven bubble formation process.Specifically,horizontal and vertical axes respectively represent time evolution and liquid phase property variation direction.In the surface tension increasing direction,i.e.,CO2-H2O,CO2-2%NPA,CO2-5%NPA,each liquid phase presents nearly the same viscosity of approximately 1.0 mPa·s.It can be seen that the bubble formation period is gradually increased,from 8.016 ms to 11.375 ms,which indicates the bubble formation requiring to overcome surface tension.As the surface tension decreases,the filling stage requires more time to complete,in a sequence of 5.00 ms,5.80 ms and 6.012 ms,while the squeezing stage takes less time in an order of 10.00 ms,9.00 ms and 7.181 ms.

Fig.2.Squeezing mode of the bubble formation period evolution with liquid properties variation in(a)CO2-H2O,38.8 kPa(b)CO2-2%NPA,43.7 kPa(c)CO2-5%NPA,61.8 kPa(d)CO2-MT,14.6 kPa(e)CO2-EA,36.3 kPa(f)CO2-NPA,61.8 kPa.

Fig.3.Shearing mode of bubble formation period evolution with liquid properties variation in(a)CO2-H2O,80.5 kPa(b)CO2-2%NPA,79.1 kPa(c)CO2-5%NPA,107.7 kPa(d)CO2-MT,33.6 kPa(e)CO2-EA,76.8 kPa(f)CO2-NPA,133.2 kPa

In the viscosity increasing direction,i.e.,CO2-MT,CO2-EA and CO2-NPA,each liquid phase almost behaves the same surface tension of 22.2 mN·m?1and the bubble formation period is reduced from 8.800 ms to 6.333 ms,which is not considerably significant as the effect of surface tension variation and also exhibits exactly the opposite affect during the bubble formation.Thus it is concluded that liquid phase viscosity is a favorable motivation for the bubble breakup in the case of squeezing mode during the bubble formation.As the viscosity of the liquid phase increases,the filling stage occupies more time during the bubble formation period while the squeezing stage is remarkably shorten.Especially for the CO2/N2mixture-NPA system,it displays a sharp transition from the filling stage to pinch-off stage,even ignoring the squeezing stage.Although viscosity of liquid phase is beneficial for bubble breakup in the case of squeezing mode,and is not sufficient enough to collapse the gaseous thread in the squeezing-driven bubble formation.Actually,the squeezing pressure in the obstructed liquid phase from upstream is the dominant force to drive the bubble collapse process[16,17],however the inertial effects on the Taylor flow cannot be neglected in a rectangular microchannel [20].Additionally,the microchannel applied in our work has almost 44 bends,resulting in a non-negligible resistance.Consequently,it is indicated that inertial stress regarded as an important driving force to overcome the surface tension and then obtain a free bubble.Here,the bubble length scaling law is applicable to use the We number addressing the inertial effects for squeezing mode bubble break within the surface tension variation groups.

Another bubble formation mode in a microfluidic T-junction is shearing-driven breakup.A simple two-step was firstly proposed by van der Graaf et al.[32]Specifically,Steegmas et al.[33]and Fu et al.[17]both successfully use the two-step model to describe the droplet/bubble formation in a T-junction.Fig.3 schematically demonstrates the two-step model consisting of expansion stage and pinch-off stage for various gas-liquid systems.Green solid line represents the boundary between expansion stage and pinch-off stage while the pink solid line stands for the gas that just entered into the main channel.Whether surface tension of the liquid phase decreases or liquid phase viscosity increases,it takes a long time for bubble growing to the main channel for the expansion stage,especially for the case of liquid phase viscosity-increasing(～0 ms,0.667 ms,2.00 ms).Then the initially formed bubble(less than the radius of the main channel)gradually spreads in the main channel.Finally,the detached Taylor bubble would move downstream to restore the deformation and reoccupy nearly the entire cross section of the microchannel.In the surface tension increasing direction,bubble formation period shows less apparent regular pattern,varying from 4.667 ms to 5.90 ms,which behavesless significant differences than the viscosity variation groups.In the viscosity increasing direction,bubble formation period shows significant growth trend from 2.900 ms to 5.333 ms.Therefore,it is speculated that the shearing-driven breakup mode emphasizes the influences of liquid phase viscosity especially for the viscosity variation groups,i.e.,CO2-MT,CO2-EA,and CO2-NPA.Fu and Ma[17]have accounted that the viscous stress performances dominating driving force to overcome the surface tension and to form a bubble in the shearing-driven breakup process.Accordingly,the bubble formation period should be shorter in the viscosity increasing direction for the CO2-MT,CO2-EA,and CO2-NPA.However,it actually takes longer time to complete the bubble formation period for the viscosity variation groups,showing inconsistency with the conclusion from Fu and Ma[17].Firstly,the work from Fu et al.[17]cannot eliminate the effect of surfactant on the gasliquid interface.Secondly,Fu et al.[17]conducted the work applied in microchannel with a different aspect ratio of 3.0(aspect ratio of 2.0 in current work).Thirdly,the microchannel configuration is absolutely different,here the multi-bends produce significant increase of total pressure drop of the microchannel,which makes bubbles more difficult to break in the case of shearing mode.In other words,the pressure drop for the gas inlet and outlet greatly influences the bubble break,while the microchannel from Fu and Ma[17]is straight channel with negligible pressure drop.These differences would induce extra influence on the bubble formation mechanism,resulting in a different criteria for scaling bubble/slug length.Simultaneously,the gas-liquid Taylor flow pressure drop for the entire microchannel is increased as the liquid phase viscosity increased.Thus,bubble detachment depends on larger inertia force from the upstream liquid phase.Consequently,bubble length scaling law is appropriate to be modified using Re number in the case of shearing mode for the bubble formation.Based on the aforementioned analysis,it is interesting that action of viscous forces is different for two bubble formation mode.Liquid phase viscosity is a favorable motivation for the bubble breakup in the case of squeezing mode for the bubble formation.However,when the surface tension drops to around 22.0 mN·m?1,the liquid phase viscosity exhibits exactly the opposite effects in the case of shearing mode for the bubble formation in Taylor flow for a rectangular meandering microchannel.

Table 3 Parameter,a,b,τR,τTand δ for various gas-liquid systems

3.2.Determination and prediction of bubble formation period

Having compared characteristics of bubble formation mode in various gas-liquid systems,we now turn our attention to the bubble formation period.The bubble formation period is basically associated with the viscosity and the surface tension of the liquid phase.Rayleigh time(τR)and capillary time(τT)are the most frequent parameters to characterize time in the micro-system[34].τRis a time scale of the perturbation of an interface under the action of inertia and surface tension and τTis the time taken by a perturbed interface to regain its shape against the action of viscosity.The interaction between τRand τTaffects the growth cycle of the bubbles actually involved in three forces,i.e.,inertial force,viscous force and interfacial tension.Here,tcyclerepresents bubble formation period while τ particularly represents the gas as a single-phase flowing through the entire micro channel.The total length of the fabricated microchannel is 0.665 m,and the average gas velocity within the scope of the experiment is 0.233 m·s?1,so that the residence time of the gas phase through the meandering channel is 2.85 s.The dimensionless bubble formation period τcycle/τ,dimensionless Rayleigh time τR/τ and dimensionless capillary time τT/τ is respectively obtained through normalized treatment.The period of bubble generation is appropriately fitted by a double exponential function in term of the dimensionless Rayleigh time and dimensionless capillary time.The following equation can quantitatively described the bubble formation period.

where τRand τTare the Rayleigh time and capillary time.Parameters a and b are fitted and showed in Table 3 for different gas-liquid systems.δ represents the relative mean deviation between determined data and predicted result,which is totally less than 13.0% for the various gas-liquid systems involved in this work.

According to Table 3,Rayleigh time τRis in the order of 10?3s,and capillary time τTis the order of 10?5s,which differs by two orders of magnitude.It is generally accepted that capillary number exerts great influence on the transition mode during the bubble formation process,which is used as a referenced parameter to estimate the bubble formation period for various gas-liquid systems.The values of parameters a and b are almost equal,but a is positive and b is negative,which implies that τRand τTmutually acted in a synergistic and antagonistic way during the bubble formation process.And the equation raised here can yield good predictions for the bubble formation period,indicating that we can use the information of τRand τTfor various gas-liquid systems to predict the bubble formation period.The calculated bubble formation period would be utilized for scaling the slug lengths in the later section.

Fig.4.Comparison of dimensionless bubble length between experimental data and literature data with variations in jG/jLfor CO2-H2O.

Fig.5.Dimensionless bubble length variation with different jG/jLunder various gas-liquid system(a)CO2-H2O,(b)CO2-2%NPA,(c)CO2-5%NPA,(d)CO2-MT,(e)CO2-EA,(f)CO2-NPA.

3.3.Determination and prediction of bubble length

The influences of the surface tension and viscosity of the liquid phase acting on the bubble formation process is respectively manifested in bubble breakup mode and bubble formation period.We now turn our attention to bubble length determination and scaling law.Taking CO2-H2O system as an example,Fig.4 shows the variation of dimensionless bubble length with the changing gas-liquid velocity and also comparison with the literature data.More specifically,red solid data points denote the experimental data in the current work,and the hollow data points are the literature data[20,23,25,35].Dimensionless bubble length presents a linear increase trend as the ratio of the gas and liquid velocity increases whether for the experimental or for the literature data,and the differences between data from this work and the literature are also showed for different microchannel configuration and experimental operation condition.Considering the diversity operating condition,Abadie et al.[35]show the worst prediction results.When the gas velocity jGwas 0.186 m·s?1and 0.378 m·s?1,the experimental data showed a certain consistency with the data from Yao et al.[20,25](jG:0.155 m·s?1and jG:0.480 m·s?1),which possibly resulted from the closer aspect ratio of rectangular cross section.Although Leclerc et al.[23]do use the multi-bends microchannel as current work,there is also a discrepancy,which is mainly due to different aspect ratio and operating range.Fig.5 explains the determined dimensionless bubble lengths displaying a linear increase with the increasing jG/jLfor various gas-liquid systems.As the gas velocity increased,the slope of the line progressively reduces,which implies that the growth rate of the bubble length decreases.This phenomenon is more strongly pronounced in the lower surface tension system (CO2-5%NPA),as illustrated in Fig.5.Simultaneously,Fig.5 also shows that the longer the bubbles appear in the lower gas velocity (jG＜0.283 m·s?1),the shorter the bubbles occur in the higher gas velocity(jG＞0.283 m·s?1).The above-mentioned is also applicable for the viscosity dominated system,i.e.,CO2-MT,CO2-EA,and CO2-NPA.As the liquid phase viscosity increases,the growth rate of the bubble length is dropped in a sequence of CO2-MT,CO2-EA,and CO2-NPA,also showed in Fig.5.

As aforementioned in the Introduction section,for a T-junction microchannel,there is no disagreement that dimensionless bubble length LB/W is a function of the gas and liquid phase velocity,which could be correlated as Eq.(1)[15].This model is exclusively applicable to predict bubble size in the squeezing-driven bubble formation,but neglects the influence of the viscosity and surface tension of the liquid phase.However,Section 3.1 mentioned above already proved that surface tension and viscosity crucially influence the bubble formation including breakup and bubble formation period.The squeezing mode and shearing mode simultaneously appear in CO2-H2O,CO2-2%NPA and CO2-5%NPA for the surface tension variation groups,while the shearing mode almost governs bubble break for all the viscosity variation groups.Capillary number is a crucial parameter for the bubble break mode transition whether in the surface tension variation or viscosity variation groups.Accordingly,capillary number is an important parameter for scaling of the bubble length in various gas-liquid systems.Simultaneously,for addressing the inertia effect on gas-liquid Taylor flow,the bubble length scaling law should be revised using We number and Re number respectively for the surface tension variation groups and viscosity variation groups,owing to characteristics analysis of bubble break driven mode in Section 3.1.In the case of surface tension variation groups,i.e.,CO2-H2O,CO2-2%NPA and CO2-5%NPA,a novel scaling law for the bubble length isestablished by collaboration of Ca and We,while for the viscosity variation groups,i.e.,CO2-MT,CO2-EA,and CO2-NPA,the novel scaling law is set-up using Ca and Re.Based on the Garstecki-type model,introducing the aspect ratio of cross-sectional shape,two equations for predicting bubble length with variations in gas-liquid systems are proposed in Table 4 respectively for surface tension variation groups and viscosity variation groups in the meandering microchannel.

Table 4 Proposed equations for predicting bubble length in current work within variations for gas-liquid systems in a meandering microchannel

CO2-H2O system and CO2-EA are used as the important referenced systems to verify the reliability of the proposed equations mentioned above.Fig.6 shows the comparison results from experimental data and predicted data,black round solid points are the predicted data based on the correlation from current work,and other data are the prediction results from literatures.The predicted bubble length from Xiong et al.[24]presents the largest deviation for tremendous aspect ratio of 7.425.The smallest deviations appears in the prediction results from Tan et al.[12]for the thorough consideration of the physical properties of the liquid phase and the angle between entrance channels.And the deviation may be caused by the different cross section geometries.The model from Yao et al.(aspect ratio of 2.678)[20,25]and Fu et al.(aspect ratio of 3.0)[17]also showed a poor prediction performance compared with the current work(aspect ratio of 2.0)for different aspect ratios.Garstecki et al.[15],van Steijn et al.[18]and Leclerc et al.[23]also obtain a poor prediction results for only considering the width of gas inlet channel.Haase[27]acquires an even poor prediction results for using a gas-liquid co-flowing microchannel different from the T-junction inlet in our work.Current work firstly predicts the bubble length through LB/W=1+jG?tcycle/W using the information of bubble formation period tcycle,which provided poor prediction results(gray data points)from Fig.6.The main reason for the poor prediction is that LB/W=1+jG?tcycle/W is applicable only for the squeezing mode bubble break.However,for surface tension variation groups,i.e.,CO2-H2O,CO2-2%NPA and CO2-5%NPA,squeezing-driven mode and shearing-driven mode will exist within the experimental scope;for viscosity variation systems (CO2-MT,CO2-EA,and CO2-NPA),the shearing-driven mode mainly governs the bubble formation.Consequently,based on the literature work,the recommended equations proposed in Table 4 demonstrate the superior predictive performance compared with the literature model[12,15,17,18,20,23-25,27].

In the equations from Table 4,the exponents of W/h,jG/jL,Ca,We and Re are quantitatively specified.Whether for the surface tension variation groups or the viscosity variation groups,the value of exponents for W/h is constant.The power of We is negative,implying the non-negligible influence of the inertia on the bubble formation process,while the evident discrepancy between the two equations is the value of exponent respectively for jG/jL,Ca,We and Re.The absolute exponent 0.075 of Ca number for the surface tension variation groups is smaller than that of 0.659 for the viscosity variation groups,indicating that surface tension and viscous force played different roles in different gas-liquid systems.The term of Ca0.08is between 0.6 and 0.8 mainly for the surface tension significant systems.However,the term of Ca?0.659is on the order of 10.0 predominantly for shearing-driven mode in the viscosity variation groups.Additionally,inertia force exhibits a significant action whether in the surface tension variation groups or in the viscosity variation groups.The exponent of We number and Re can give more explanations about this point.Accordingly,a total of 107 sets of experimental data are correlated with a 600 × 300 μm rectangular meandering microchannel and operating range:0.001 ＜CaTP＜0.05,0.06 ＜WeTP＜9.0,18 ＜ReTP＜460.The average deviation between the correlated data and the experimental data is almost less than 10%for each gas-liquid system.Thus,the two simple equations(Table 4)can yield good predictions for dimensionless bubble length,indicating that it is an easy way to scaling of the bubble lengths either for squeezing-driven mode or shearing-driven mode bubble formation process.Fig.7 shows in detail the comparison of predicted dimensionless bubble lengths with experimental data for various gas-liquid systems in this work.

Fig.6.Experimental vs.predicted values of dimensionless bubble length respectively in(a)CO2-H2O and(b)CO2-EA.

3.4.Determination and prediction of Slug length

Fig.7.Experimental vs.predicted values of dimensionless bubble length in various gas-liquid systems(a)CO2-H2O,(b)CO2-2%NPA,(c)CO2-5%NPA,(d)CO2-MT,(e)CO2-EA,(f)CO2-NPA.

Fig.8.Comparison of dimensionless slug length between experimental data and literature data with variations in jG/jLfor CO2-H2O.

The dimensionless slug lengths for CO2-H2O system are determined and compared with the literature data[20,23,25,32,36].It can be seen from Fig.8 that dimensionless bubble lengths from the current work presents a decline trend and then tended to a fixed value with the increasing ratio of the gas and liquid velocity jG/jL.Higher jG/jLproduces shorter liquid slug,and the data growth trend of this work are in agreement with literature data from Abadie et al.[35]and Zaloha et al.[36].Leclerc et al.[23]have found that slug length almost remains constant with the increasing of jG/jL.However,the experimental data shows exactly the opposite characteristics compared with the data from Yao et al.[20,25].It is probably because of the different configuration of the microchannel,the multi-bends microchannel can reduce or avoid fluctuations during the bubble break[28],which may not cause a significant net leakage flow at the T-junction entrance like the straight channel [37],and thus will not produce a continuous growth of the liquid slug.

Fig.9.Dimensionless slug length variation with different jG/jLunder various gas-liquid systems(a)CO2-H2O,(b)CO2-2%NPA,(c)CO2-5%NPA,(d)CO2-MT,(e)CO2-EA,(f)CO2-NPA.

Fig.9 shows that the measured dimensionless slug length is getting shorter with the increasing jG/jL,either for the surface tension governing system or for the viscosity variation groups.For the surface tension variation groups,i.e.,CO2-H2O,CO2-2%NPA and CO2-5%NPA,the measured dimensionless slug length shows an apparent downward trend as the jG/jLincreases.In the lower gas velocity range (jG:0.088-0.186 m·s?1),the measured dimensionless liquid slug displays a drastic reduction as jG/jLincreases,while it shows a more moderate decline and then remains constant in the higher gas velocity range(jG:0.283-0.378 m·s?1).Meanwhile,for the viscosity variation groups,i.e.,CO2-MT,CO2-EA,and CO2-NPA,it shows a decline trend and intentionally remains constant.Similarly,for the lower gas velocity range(jG:0.088-0.186 m·s?1),the measured dimensionless liquid slug displays a more drastic reduction than that for the higher gas velocity range(jG:0.283-0.378 m·s?1).

It is well known that Garstecki-type model is a simple estimation approach to predict the linear evolution of the bubble and slug length with the gas-liquid velocity.Although Pohorecki and Kula[38]have proposed a ‘switching’ mechanism to set-up the scaling law for the bubble length in a Y-junction microchannel introducing an important parameter phase fraction ε.This is almost the same to the Garsteckitype model,expressed asNote that,the bubble/slug length is inversely proportional to the liquid/gas phase fraction,and this type correlation does not involve the bubble generation mode and channel structure.Although Qian and Lawal[26]considering the impact of surface tension and wall surface adhesion,they still obtain poor results,with a mean deviation of 20.15%and 43.71%respectively for CO2-H2O and CO2-EA in Fig.10.Compared with literature models for slug length scaling,current work obtains the most accurate predictions with a mean accuracy of 7.67% and 9.88% respectively for CO2-H2O and CO2-EA in Fig.10.The reason for the more accurate prediction results from current work is strongly addressing the influences of fluid viscosity.Simultaneously,due to the different inlet configuration,current work(T-junction inlet)prediction results exhibit excellent prediction performance than Haase's(co-flowing inlet)prediction results[27].Therefore,current work presents a more convenient and applicable predicting method using jL/jG,jLand tcyclebased on Garstecki-type model.tcycleis obtained through Eq.(17),mainly depending on Rayleigh time and capillary time,actually involving fluid properties,i.e.,density,surface tension and viscosity.The scaling law of the slug length can be expressed as

C1can be regarded as the contribution of effective distance of the liquid phase when the bubble neck moves a channel width distance at the same time.C2can be perceived as the time contribution to the slug length how long it takes the bubble accomplishing the squeezingstage and pinching off.C1and C2are fitted using nonlinear least squares method for different gas-liquid systems,and the obtained equations were showed in Table 5.C1and C2are different for the surface tension governing system and viscosity variation groups.Especially,the value of C1,0.403 for the surface tension governing system is larger than that of 0.00012 for the viscosity variation groups,indicating that the filling stage process for the surface tension system took a longer time for the viscosity system,which can be referred in Section 3.1.

The measured dimensionless slug length and predicted data are also used to test the applicability of the established equation in our current work as schematically described in Fig.11 both for CO2-H2O and CO2-EA.Also,Fig.11 provides the comparison results between predicted dimensionless slug length and experimental data for various gas-liquid systems,implying a good consistency.For the six gas-liquid systems,a larger deviation has been found in the CO2-MT system,which could be attributed to the relatively lower viscosity and surface tension of the fluid.More specifically,focusing on the impact from the density,surface tension and viscosity of the liquid phase and aspect ratio of the rectangular channel,a total of 107 sets of experimental data are correlated with a 600 × 300 μm rectangular meandering microchannel and operating range:0.001 ＜CaTP＜0.05,0.06 ＜WeTP＜9.5,18 ＜ReTP＜460.The average difference between the correlated data and the experimental data is less than 10%.Thus,the correlation results from Fig.11 imply that the simple principle has an extensive application to predict slug length for various gas-liquid systems either for squeezing-driven mode or shearing-driven mode bubble formation in a meandering rectangular T-junction microchannel.

4.Conclusions

The influences of surface tension and viscosity on bubble breakup mode,bubble formation period and bubble/slug length are experimentally and analytically investigated in a meandering rectangular T-junction micro-channel.The following conclusions can be drawn:

(1)In order to reduce or avoid fluctuations from interface breakup,a meandering microchannel with curved multi-bends(44 turns)is fabricated,resulting in a non-negligible resistance in gas-liquid Taylor flow.Bubble breakup requires the contribution of inertia to overcome the non-negligible resistance.Therefore,the bubble scaling law is suggested to be revised using We number and Re number respectively for surface tension variation groups and viscosity variation groups.

(2)In the analysis of bubble formation mode,it is interesting that in the meandering microchannel,the viscosity of liquid phase is a favorable motivation for the bubble breakup in the case of squeezing mode for the bubble formation,while it performances as a resistance in the case of shearing mode for the bubble formation with surface tension around 22.0 mN·m?1for Taylor flow for in a meandering microchannel.

(3)A simple equation is firstly present for predicting the bubble formation period by using the information of Rayleigh time and capillary time for various gas-liquid systems with an average deviation of 10.96%.

(4)The novel equations modified by Ca,We,Re and aspect ratio (W/h)for bubble lengths is proposed in a rectangular meandering microchannel with a mean relative deviation of 9.42%,which display good applicability whether for squeezingdriven or shearing-driven during bubble break process.

(5)In the absence of slug length prediction studies,the revised equations are set-up to broaden prediction scope for slug length based on Garstecki-type model and bubble formation period with a mean relative deviation of 9.95%.The new scaling equations is applicable either for squeezing-driven mode or shearing-driven mode bubble formation in a meandering microchannel.Such fundamental understanding and universal scaling laws of bubble/slug length involving various gas-liquid systems associated with fluid properties(surface tension and viscosity)of the meandering microchannel would offer a more universal principle for bubble/droplet manipulation.