Mass transfer intensification and mechanism analysis of gas-liquid two-phase flow in the microchannel embedding triangular obstacles

Xuanyu Nie,Chunying Zhu,Taotao Fu,Youguang Ma

State Key Laboratory of Chemical Engineering,School of Chemical Engineering and Technology,Tianjin University,Tianjin 300072,China

Keywords:Enhancement factor Microchannels Gas-liquid flow Mass transfer Triangular obstacle

ABSTRACT An effective mass transfer intensification method was proposed by embedding different triangular obstacles to improve the gas-liquid mass transfer efficiency in microchannel.The influences of triangle obstacles configuration,obstacle interval and flow rate on the volumetric mass transfer coefficient,pressure drop and energy consumption were investigated experimentally.The enhancement factor was used to quantify the mass transfer enhancement effect of triangle obstacles.It was found that the isosceles or equilateral triangle obstacles are superior to the rectangular obstacles.The maximum enhancement factor of equilateral triangle obstacles was 2.35.Considering comprehensively mass transfer enhancement and energy consumption,the isosceles triangle obstacle showed the best performance,its maximum enhancement factor was 2.1,while the maximum pressure drop increased only 0.41 kPa(22%)compared to the microchannel without obstacles.Furthermore,a micro-particle image velocimetry(micro-PIV)was utilized to observe the flow field distribution and evolution,in order to understand and analyze the enhancement mechanism.The micro-PIV measurement indicated that the obstacle structure could induce the formation of vortex,which promotes convective mass transfer and thins the flow boundary layer,accordingly,the gas-liquid mass transfer efficiency is remarkably improved.This study can provide theoretical guidance and support for the design and optimization of microchannel with triangular obstacles.

1.Introduction

Gas-liquid mass transfer is widely encountered in chemical processes,including gas absorption [1],distillation [2],gas dehumidification[3],and chemical reaction[4].Many traditional equipment such as the plate reactor,spray tower and bubble column are usually applied to these processes.In comparison with these traditional equipments,microchannel device has advantages of large phase contact area[5],short diffusion path[6]and low liquid consumption [7].Nevertheless,mass transfer in microreactor relies primarily on molecular diffusion [8] owing to the low Reynolds number in microchannel [9].As we know,the convective flow or turbulence is more effective for mass transfer than only molecular diffusion [10],hence,inducing turbulence in microchannel is an effective method to enhance mass transfer [11].

Generally,the enhancement methods in the microreactor include active and passive methods.The active method needs external driving device.Comparatively,the passive method is to change the channel configuration,which is more facile to manufacture [12],for example,embedding obstacles or designing the meandering microchannel.Besides,the passive method could avoid the instability of system induced by external field sources[13].

Wuet al.[14]designed an effective micromixer based on a converging-diverging meandering microchannel with semi-elliptical sidewalls.They perceived that the multi-directional vortices enhanced remarkably the mixing.The dean vortices caused by centrifugal force on the transverse cross-section and separation vortices caused by the constricted and expanded cross-section of the curved channel under the conditions of high flow rate and sufficiently small radius of curvature.Subsequently,Zhanget al.[15]proposed a passive spiral micromixer with rectangular baffles to enhance the mixing process.The baffles were arranged alternately on both sides of the spiral mixing channel wall.The centrifugal force significantly increased the lateral movement of the fluid.The local fluid motion around the baffle was accelerated and the advection effect was remarkably enhanced.Thus,the mixing was greatly intensified.Recently,Guanet al.[16] proposed an integrated passive (zigzag microstructure) and active (adding an acoustic field to generate oscillating microbubbles) mixing method,which was applied to low-viscosity and high-viscosity liquid mixing.It was found that the generation or movement of microbubbles could create stable cavitation and generate counter-rotating vortices,thereby resulting in turbulent fluid flow and enhancing the mixing effect.

Additionally,Seoet al.[17] designed and studied numerically electrodynamic hybrid microchannels with various obstacle configurations.It was found that the microchannel with triangular obstacles showed better uniformity and stability.Sarkaret al.[18] utilized computational fluid dynamics simulation method to investigate the mixing performance of inwardly projecting rectangular,triangular,and semicircular structures.The shrinkage of cross-section facilitates the contact of fluids,which leads to an increased molecular diffusion concentration gradient and better mixing performance.Santanaet al.[19] proposed a micromixer with triangular baffles and circular obstacles to enhance mass transfer by shortening molecular diffusion paths,splitting and reorganizing streams,and inducing vortices.It was observed that the mixing performance could be greatly improved by using this micromixer.

Although the microchannel with obstacles has attracted widespread attention,a few studies were focused on the gas-liquid mass transfer processes.Yinet al.[20] conducted an experimental investigation for enhancement of gas-liquid mass transfer by the rectangular baffles embedded in the microchannel.The influence of baffle size on mass transfer and pressure drop was studied.It was found that the proper baffle configuration could effectively improve the mass transfer performance,while the pressure drop was increased slightly.Successively,Zhanget al.[21] studied systematically the effect of flow velocity and the number of sudden expansion units on the pressure drop and the volumetric mass transfer coefficient.It was proven that the structure could significantly enhance gas-liquid mass transfer.The enhancement factor increased with the increase of the number of sudden expansion units and the gas-liquid flow rate ratio,while the pressure drop had only negligible increase.

From the previous experimental and numerical investigations in the literature,it could be found that embedding obstacles in microchannel is an effective passive method to enhance mass transfer.Therefore,in this work,different triangular obstacles were designed and embedded in the microchannel to achieve the enhancement of gas-liquid mass transfer.The influences of the width,interval,and shape of triangular obstacles on the mass transfer enhancement were studied systematically.Meanwhile,a micro-particle image velocimetry(micro-PIV)was used to observe the fluid velocity field distribution and evolution for revealing the enhancement mechanism.Furthermore,the mass transfer coefficient and enhancement factor were calculated,the pressure drop and energy consumption were also comprehensively evaluated.

2.Experimental

2.1.Materials

CO2(purity ＞99%,Tianjin Liufang Gas Workstation,China)was used as the gas phase in this experiment.Ionic liquid[BMIM][BF4](purity up to 99%,Henan Lihua Pharmaceutical Co.,Ltd.,China)aqueous solution with 15% (mass) was used as the liquid phase.To avoid droplet adhesion in the channel wall and keep fluid flow stability,the surfactant sodium dodecyl sulfate(SDS)(Tianjin Standard Chemical Reagent Co.,Ltd.,China) was added to the liquid phase.

The microchannel chips were made of polymethyl methacrylate(PMMA),which is easy to fabricate and has a light transmittance of up to 92%.The microchannel was milled on PMMA board with thickness of 8 mm and sealed with another PMMA board with thickness of 3 mm.The main channel length is 34.6 mm,the widthwis 0.8 mm,and the heighthis 0.4 mm.A length of 8 mm is reserved in front of the obstacle structure area for bubble generation.Fig.1 is the top view of the channel.The number of obstacles is 12,the height of the obstacle is 0.4 mm,and the variables are the shape,widthd,and distanceDof the obstacles.The detailed dimensions of four microchannel chips are listed in Table 1.

Table 1The geometry of the microchannel chips

2.2.Method

The micro-syringe pump(Harvard PHD2000,USA)was used for gas-liquid two phase delivery.The pictures were taken by a highspeed camera (Nikon 24-85mmf/2.8-4D IF,Japan).The shooting frequency was 1000 frames per second.A LED light (Yulangnuo LHP-40WP,China) was used as the light source.Inlet pressure was measured by a pressure sensor (Honeywell ST3000,USA).All experiments were conducted at ambient temperature and atmospheric pressure.The range of liquid phase flow rateQLwas 50-80 ml·h-1and the gas phase flow rateQGwas 40-220 ml·h-1.The experimental device is shown in Fig.2.

The micro-PIV is used to observe the velocity field distribution and evolution.The fluorescent polymer microspheres tracer with a diameter of 1.0 μm (Thermo,USA) was dispersed in the liquid phase by ultrasonic at a volume ratio of 1:30 and these microspheres moved with the fluid.The laser beam irradiated twice in a very short time,the camera captured two instantaneous images,and the recorded images were divided into multiple domains.Cross-correlation calculations were performed on each domain to obtain the velocity field of the entire domain.

According to two film theory [22],the mass transfer resistance is embodied in two stagnant films.The gas phase used in the experiment is pure CO2,thus the mass transfer resistance in the gas film is negligible and the mass transfer resistance is mainly in the liquid film.The total liquid side volume mass transfer coefficientkLacould be obtained:

whereQLis the liquid phase flow rate,VMis the total volume of the microchannel,Ceis the equilibrium concentration of CO2in liquid phase under experimental conditions.Coutis the concentration of CO2in liquid phase at the outlet.

wherePis the average pressure of inlet and outlet,andHis the Henry coefficient.

where Δnis the molar amount of the substance transferring from gas phase to liquid phase in a mass transfer unit.Vsis the volume of liquid phase in a mass transfer unit.The inlet pressurePinis measured by pressure gauge.The outlet pressurePoutis calibrated by a contrast experiment to eliminate the deviation caused by outlet capillary.A microchannel without main channel is constructed,which only includes two phase inlet and outlet capillary.The pressure drop caused by the outlet capillary at the corresponding flow rates is measured and the experimental data is calibrated.Vinis the virtual volume of the generated bubble without mass transfer.Voutis the volume of the bubble near the outlet,which is obtained by the picture recorded by the camera.Ris the ideal gas constant,andTis the experimental temperature.The cross section of the microchannel is rectangular.For slug flow,the bubble head and tail could be considered as symmetrical ellipsoids,and the bubble body is an elliptic cylinder,whose long axis and short axis are the widthwand heighthof the microchannel respectively.Lbis the length of the bubble.We have:

Fig.1.Schematic diagram of the microchannel structure.

In addition,the sub-bubbles generated for broken-slug flow are considered as spheres.

The enhancement factorEwas used to quantify the mass transfer enhancement effect.Where the subscript ‘‘ob” represents the microchannels with obstacles,and‘‘c”represents the microchannel without obstacles.

Energy consumption ε is the product of pressure drop and flow rate.

3.Results and Discussion

Four microchannels were designed,including one microchannel with rectangular triangle obstacles (RT),two microchannels with equilateral triangle obstacles (ET1,ET2),and one microchannel with isosceles triangle obstacles(IT).The influences of microchannels with different obstacles on mass transfer were studied.

3.1.Flow pattern

As shown in Fig.3,two flow patterns were observed in this experiment: slug flow and broken-slug flow.Slug flow occurs under relatively low gas flow rate,in this regime,the bubbles remain unbroken.Broken-slug flow appears under higher gas flow rate.When the bubble flows through the obstacles area,the bubble would be subjected to the squeezing force of the wall and the shearing force of the liquid phase simultaneously,the speed of the bubble head becomes unequal to the tail owing to the pressure gradient,thus the bubble is stretched violently [23].It could be seen from Fig.3(b),the bubble tail forms a neck (marked by the red ellipse).Once the neck radius is less than the critical radius,the liquid pressure and shearing force would exceed the force that maintains the bubble stable [24],then the bubble would burst to produce smaller sub-bubbles.The rupture always occurs at the rear cap,which could be attribute to the velocity of bubble rear cap is larger than the velocity of bubble front cap [25].

Fig.2.Schematic diagram of experimental device.

Fig.3.(a)Slug flow in different obstacle microchannels(QL-QG:50-40 ml·h-1).(b)Broken-slug flow in ET2(QL:70 ml·h-1).The pictures were shot by the high-speed camera.

Dessimozet al.[26] observed the bubbly flow and slug flow using CO2/water-based fluids.Differently,the bubbly flow has not been observed in this experiment.In the experiment,the value of capillary numberCa(Ca=μLU/σ,0.0026-0.0087) is low,therefore the interfacial tension predominates over the viscous force.The interfacial tension is the dominating force during the formation process of bubbles [27].Thus,the gas phase tends to evolve into slug flow rather than bubbly flow.

3.2.Influence of obstacle structures on the mass transfer

Mass transfer in gas-liquid slug flow includes two parts:bubble body to liquid film and bubble caps to liquid slug.The thin liquid film could get saturated more easily (the order of 10-6m) [6].Hence,the mixing between liquid film and liquid slug is of key importance to improve the mass transfer in microchannel[28,29].The turbulence introduced by specific structure in channel has been proved to be an effective method to promote the mixing between liquid film and liquid slug[11].In this study,the influence of triangular obstacles embedded in microchannel on mass transfer was analyzed based on the velocity field.

When the liquid flows through the narrowest part of the channel,the sudden shrinkage of the channel cross-section causes the liquid to accelerate.Based on the energy conservation,the pressure will decrease as the liquid is accelerated.After the liquid passes through the narrowest part,the channel gradually widens and the liquid flow slows down.A part of the kinetic energy of the fluid would be converted into pressure energy,thus the pressure would rise.Moreover,another part of the kinetic energy would serve to overcome the frictional resistance.At a certain point after the narrowest part,all the kinetic energy of the liquid in the boundary layer would be exhausted,and the flow velocity declines to zero,a stagnation point is formed.When the liquid flows over the stagnation point,the channel gradually widens,the liquid continues to decelerate and the pressure elevates.Eventually,the liquid near the wall is forced to flow backwards under the actions of pressure and inertial effect [30],then interacts and collides with the fluid behind.The liquid is disturbed intensively and the boundary layer would separate from the wall.Successively,the vortexes are formed,as shown in Fig.4.The strong collision and mixing of fluid in the vortex area are the primary reasons for the thinning of the flow boundary layer and the increases of energy consumption and pressure drop [31,32].

Fig.4 shows the velocity field in microchannels.The maximum velocity is observed at the separation zone when the liquid passes around the obstacle.The lowest velocities are shown around the obstacle.The obstacles can reduce the effective width of the microchannel and significantly increase the main flow velocity.In the meantime,the centrifugal force of the vortex is available to liquid mixing [33].

Fig.5 illustrates the variations of liquid side volumetric mass transfer coefficientkLaand enhancement factorEwith gas flow rate.Comparing ET1 (D=2.8 mm;d=0.4 mm) and IT(d=0.6 mm).Under same gas-liquid flow rate,thekLaof ET1 is greater than IT.In the vortex area,the fluid velocity is low and the flow direction is disordered.The liquid continues to collide wall,accordingly,the boundary layer becomes thinned because of the violent disturbances [34].Besides,the obstacles accelerate the fluid flow and accordingly facilitate the liquid surface renewal,which enhances the mixing between the liquid film and the liquid slug,and reduces saturation degree of the liquid at the gas-liquid interface[35].Hence,the mass transfer is enhanced.Besides,specific surface areaais increased due to the deformation of the bubble,which contributes to the mass transfer.Thus,both the enhancement effect of ET1 and IT are greater than straight microchannel.As the deformation degree of the bubble in IT is greater,the mass transfer enhancement performance in IT is more noticeable.This indicates that the appropriate increase of the obstacle width is conducive to the enhancement.The conclusion is consistent with Choet al[36].

The velocity fields in microchannels taken by micro-PIV are shown in Fig.4.It could be seen from Fig.4(a) and (d),the vortex area of ET1 is larger,thus the disturbance caused by ET1 is more dramatic,and thetransfer frequency between the interface and the bulk liquid is higher.Consequently,as shown in Fig.5,the enhancement effect of ET1 is greater than RT.

The obstacle interval in ET2 (D=2.0 mm) is shorter comparing with ET1,thus the bubble body in ET2 is further stretched,the gas-liquid specific area of ET2 is larger.Meanwhile,the average liquid flow velocity of ET2 is higher than ET1,as shown in Fig.4(a) and (b),which facilitates to liquid surface renewal.Therefore,thekLain ET2 is higher than ET1.This indicates that properly reducing the obstacles interval could improve the mass transfer enhancement effect,which is also proved by Yinet al[37].

Fig.4.Velocity field in microchannels with different triangular obstacles calculated by micro-PIV (QL-QG=50-40 ml·h-1): (a) ET1 (D=2.8 mm; d=0.4 mm),(b) ET2(D=2.0 mm),(c)IT(d=0.6 mm),(d)RT.Images of the bubble at similar location are selected.

To further evaluate the mass transfer enhancement effect of the microchannels with obstacles,the turbulence intensity,namely the ratio of root mean square of velocity fluctuation to average velocity,was calculated and plotted in Fig.6.

By comparing the turbulence intensity contour of the four microchannels with obstacles,it could be found that ET2 has the maximum turbulence intensity and the largest higher turbulence intensity zone,and RT has the largest flow dead zone.Thus,the enhancement performance of ET2 is the best and IT is the lowest.Moreover,the total turbulence intensity of IT is larger than ET1,thus IT has better mass transfer performance.

3.3.Influence of flow rate on mass transfer

Flow rate is an important operating parameter determining bubble size,flow pattern,and mass transfer efficiency in microchannel.Under high gas flow rate,the flow pattern would evolve into broken-slug regime.Effect of gas flow rate onkLaandEare shown in Fig.7.As gas flow increases,thekLacontinues to increase especially in broken-slug regime.The bubble is gradually lengthened with gas flow rate and the sub-bubbles in the brokenslug regime would not coalesce due to the addition of surfactant,soaincreases.Moreover,we could observe from Fig.3(b): when gas flow rate is 160 ml·h-1,the bubble tail bursts at the fourth obstacle.The rupture location will be in the front with the increase of gas flow rate.This could be attributed to that shear force and deformation degree of bubbles increase with gas flow rate,which facilitates bubble rupture.

Fig.5.Variations of volumetric mass transfer coefficient and enhancement factor with gas flow rate in different microchannels (QL=50 ml·h-1).Solid symbols: slug flow;Half-solid symbols: broken-slug flow.

Fig.6.Turbulence intensity contour in microchannels with different triangular obstacles (QL-QG=50-40 ml·h-1): (a) ET1 (D=2.8 mm; d=0.4 mm),(b) ET2(D=2.0 mm),(c) IT (d=0.6 mm),(d) RT.Fifty consecutive images are selected to calculate the turbulence intensity.

Fig.8(a) shows the velocity field in ET2.Comparing Fig.4(b)with Fig.8(b),as gas flow rate increases,both the vortex area and intensity would increase under fixed liquid flow rate,thereby the liquid phase mixing and the mass transfer between liquid slug and bubble caps would be improved[21].Meanwhile,the augment of gas flow rate could elongate bubble and shorten liquid slug,which is not conducive to the mixing between liquid film and liquid slug[38].Therefore,liquid film is easier to be saturated and the mass transfer between liquid film and bubble body is weakened.In addition,aincreases with gas flow rate.As a competitive result of above different factors,thekLaandEincrease with gas flow rate.Besides,it could be observed that the flow pattern has unobvious influence onE.The mother bubble would break up under high gas flow rate for broken-slug flow.The rupture of bubble would induce local turbulence in continuous phase,which is conductive to mass transfer.However,the velocity of mother bubble would decrease [39],the leakage flow in the liquid film would become weakened and the residence time of mother bubble would be lengthened,which leads to the decrease of the average mass transfer coefficient[40].The combined influences result in that the variation tendency ofEwithQGunder the broken-slug flow is similar to that under the slug flow.

As shown in Fig.7(a) and (b),kLaincreases with the rise of liquid flow rate.The dominant resistance of mass transfer is on the liquid side.The mixing between liquid film and liquid slug could be increased by increasing liquid flow rate,which delays saturation of the liquid film near gas-liquid interface.It also could be seen from Fig.8 that the turbulence is more intensive under higher liquid flow rate.However,the specific areaadecreases with increasing liquid flow rate,as a compromising result,kLaincreases with liquid flow rate,implying that the enhancement of mixing plays a dominated role onE.The similar situation was also observed by Ganapathyet al[41].Fig.7(c) and (d) indicate thatEdecreases with the rise of liquid flow rate.The trend was similar as the result of Zhanget al[21].This should be due to that at high liquid velocity,liquid phase has already relatively high degree of mixing.Thus,the influence of obstacles on the fluid mixing is insignificant,resulting in the decrease ofEwith the liquid phase flow rate.

3.4.Analysis of pressure drop and energy consumption

The fluid would be speeded up in microchannel with obstacles[42],which would increase the fluid frictional pressure loss with wall.Meanwhile,local pressure loss could be caused by obstacles.Moreover,vortices would create extra energy consumption [43].The bubbles would experience extrusion,deformationand rupture,which could increase pressure drop [44].

Fig.9(a)shows the variation of pressure drop with gas flow rate.It could be observed that for given liquid flow rate,pressure drop elevates as gas flow rate increases and the slope of the pressure drop curve is larger for broken-slug flow than slug flow.Fig.9(b)illustrates that pressure drop rises with the increase of liquid flow rate,which was also observed by other researchers [45,46].If the slug flow is considered as a quasi-steady process,the two-phase total pressure drop in a unit cell (one bubble plus and one liquid slug)is generally regarded to consist of the frictional loss in liquid slug,and the Laplace pressure drop at the bubble caps[47].Due to the existence of obstacles,the pressure drop at bubble body is non-ignorable.Under constant gas flow rate,with the increase of the liquid flow rate,the length and velocity of liquid slug and the number of bubbles increase,which leads to the increase of pressure drop at liquid slug and bubble caps.Conversely,the pressure drop at bubble body decreases with the decrease of the bubble length.As an integrated result,the two-phase total pressure drop elevates with liquid flow rate.

Fig.7.The effects of gas flow rate on volumetric mass transfer coefficient and enhancement factor.Solid symbols: slug flow;Half-solid symbols: broken-slug flow.

Fig.8.Velocity fields in ET2 taken by micro-PIV:(a)QL-QG:50-160 ml·h-1,(b)QLQG: 70-160 ml·h-1.Images of the bubble at similar location are selected.

Fig.9.(a) Variations of pressure drop with gas flow rate at QL=80 ml·h-1;(b)Variations of pressure drop with gas flow rate in ET2 and straight channel.Solid symbols: slug flow;Half-solid symbols: broken-slug flow.

Fig.10.Variations of liquid side volumetric mass transfer coefficient with energy consumption.

Moreover,it could be found from Fig.9(a) that the decrease of obstacle interval would lead to the increase of pressure drop,especially under high gas flow rate.This could be attributed to bubbles would be compressed more frequently and easier to rupture when obstacle interval is shortened.Under experimental condition,the maximum pressure drop incrementof ET2 (relative to ET1) is 0.68 kPa (24.11%).Comparing the pressure drop variations of ET1 with IT,when the obstacle width is increased,the pressure drop value of IT is visibly lower than ET1 at high gas flow rate,the maximum pressure drop decrement (relative to ET1) is 0.32 kPa(9.70%).Furthermore,RT has minimum pressure drop under same flow rate.

Variations ofkLawith energy consumption ε are illustrated in Fig.10.Under same energy consumption,all microchannels with obstacles have higherkLathan straight microchannel.Under lower gas flow rate,the efficiencies of ET1,ET2,and IT are comparable,but the efficiency of RT is relatively lower.As gas flow rate increases,the energy consumption increases correspondingly,and the enhancement effect of IT onkLais more remarkable than ET2 at same energy consumption.However,as liquid flow rate increases,kLain the microchannels with obstacles inclines under same energy consumption,which is opposite to the microchannels without obstacles.It could be explained that the obstacles induce disturbance in liquid phase.When the liquid flow rate increases,the pressure drop would sharply rise in microchannel with obstacles.Differently,the pressure drop elevates slowly with liquid flow rate in microchannel without obstacles.Hence,the trend of energy consumption with liquid flow rate is converse in microchannels with and without obstacles.It could be concluded from above analysis that under lower liquid flow rate and higher gas flow rate,the enhancement effect of triangular obstacles on mass transfer in microchannels is more noticeable,and the symmetrical configuration is conducive to mass transfer intensification.

4.Conclusions

Four microchannels with different triangular obstacles were constructed to enhance gas-liquid mass transfer.Two flow patterns were observed: slug flow and broken-slug flow.For broken-slug flow regime,the bubble rupture could lead to the increases of specific surface area and thereby promoting mass transfer,but energy consumption would also be increased.It was found that embedding triangular obstacles in microchannel is an effective method to improve mass transfer efficiency.The symmetrical shape of triangular obstacles and appropriate obstacle interval are conducive to mass transfer intensification.Comparatively,the comprehensive performance of IT is the best under jointly considering the mass transfer enhancement and the energy consumption.This study of configuration on the enhancement of gas-liquid mass transfer process shows potential in the optimization and application of microchannel with triangular obstacles.

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 work was supported by the financial supports from the National Natural Science Foundation of China (21776200,92034303,and 21978197),and thanks the Program of Introducing Talents of Discipline to Universities (BP0618007).

Nomenclatures

aspecific surface area,m-1

Cconcentration,mol·m-3

Ceequilibrium concentration of CO2in liquid phase,mol·m-3

Eenhance factor

HHenry’s law constant,Pa·m3·mol-1

hheight of microchannel,m

kLliquid side mass transfer coefficient,m·s-1

kLaliquid side volumetric mass transfer coefficient,s-1

Lblength of the bubble,m

llength of obstacle area,m

nmolar mass,mol

Ppressure,Pa

ΔPpressure drop,Pa

Qvolume flow rate,m3·s-1

Rgas constant,J·mol-1·K-1

Ttemperature,K

Usuperficial flow velocity of gas-liquid two phases,m·s-1

Vvolume,m3

VMthe total volume of microchannel,m3

wwidth of microchannel,m

ε energy consumption,W·kg-1

μ viscosity,Pa·s

ρ density,kg·m-3

σ interfacial tension,N·m-1

ω mass fraction,%

Subscripts

b bubble

c straight channel

G gas phase

in inlet of microchannel

L liquid phase

out outlet of microchannel

ob obstacle

s slug