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Chemical Engineering Journal
journal homepage:www.elsevier.com/locate/cej
Characteristics of gas-liquid Taylor fl ow with di ff erent liquid viscosities in a rectangular microchannel
Chaoqun Yao
a, Jia Zheng
b, Yuchao Zhao
c, Qi Zhang
a, Guangwen Chen
a,⁎aDalian National Laboratory for Clean Energy, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
bSchool of Science, Dalian Maritime University, No.1 Linghai Road, Dalian 116026, China
cShandong Collaborative Innovation Center of Light Hydrocarbon Transformation and Utilization, College of Chemistry & Chemical Engineering, Yantai University, Yantai 264005, China
H I G H L I G H T S
•
The effect of liquid viscosity (0.89–45.6 mPa·s) on Taylorflow is investigated.•
Higher viscosity leads to more stable instantaneousflow rate during formation stage.•
Thefilm thickness at short planes are much larger than predicted in literature.•
A distinct bubble shape with sharpened rear cap is observed.•
A correlation representing the effect of recirculation on pressure drop is proposed.A R T I C L E I N F O
Dedicated to the 70th anniversary of the Dalian Institute of Chemical Physics, Chinese Academy of Sciences
Keywords:
Multiphase Viscous effect Mircoreaction Microfluidic Microchannel
A B S T R A C T
Characteristics of gas-liquid Taylorflow with different liquid viscosities are investigated in a rectangular mi- crochannel, aiming at providing knowledge and aid in the design of processes involving viscousfluid, such as polymers and ionic liquids. The effect of liquid viscosity on the bubble formation dynamic,film thickness, bubble velocity, and pressure drop is investigated. The results reveal a specific viscous effect compared to those in square or circular channels. For the same capillary number, both the liquidfilm thickness at the corners and at the short planes are much larger than in square channels. New correlations are proposed for predicting thefilm thickness in the rectangular channel. The bubble shape sheared by the liquid phase is also distinct from literature observations that a smaller radius occurs at the rear cap. For the conditions studied (0.00065 <Ca< 0.0525), increasing the viscosity leads to an increase in the instantaneousflow rate, and also an later shift fromfilling stage to squeezing stage. As the bubble formation is driven by both squeezing pressure and shearing force, the bubble/slug length is affected by both capillary number andflow rate ratio. The recirculation inside liquid slugs is found to play an important role in the pressure drop, which can be well described by an empirical correlation including dimensionless liquid slug length and capillary number.
1. Introduction
Microreaction technology has been more and more frequently ap- plied in chemical synthesis and process intensification[1,2,3]. With miniaturized devices, this technology brings many advantages in- cluding substantially enhanced mass/heat transfer rate, easier manip- ulation offlow regimes and capability of handling harsh reaction con- ditions [3]. Also, the operation in continuous mode enables better control over parameters or processes, providing efficient synthesis paradigm such as side reaction suppression, anhydrous and air-free
synthesis, and in-situ separation/purification[4].
Gas-liquid Taylor flow is an important research subject for the multiphase systems in the microreaction technology, as it serves ideal reaction environment for gas-liquid reactions due to uniform bubble size, low back mixing and high radial mass transfer. Currently, plenty of studies have been conducted to understand the transport behavior, in- cluding bubble formation [5,6], liquid film distribution [7,8], re- circulation inside liquid slugs[9,10], pressure drop[11,12]and mass transfer[13–16], etc. These studies shed considerable light on the un- derstanding and can provide good guidance for reactor/process design.
https://doi.org/10.1016/j.cej.2019.05.051
Received 22 February 2019; Received in revised form 3 May 2019; Accepted 9 May 2019
⁎Corresponding author.
E-mail address:[email protected](G. Chen).
Available online 10 May 2019
1385-8947/ © 2019 Elsevier B.V. All rights reserved.
T
Whereas, most studies only involve less viscous liquids (i.e., < 10 mPa·s) and the available knowledge cannot fulfill the requirement for processes with highly viscousfluids, which are frequently encountered nowadays as more and more applications are developed, such as CO2
absorption [17–19], polymers and ionic liquids involved processes [20,21], and so on.
Up to now, the knowledge about viscous effect on gas-liquid Taylor flow is mainly on the formation regime, bubble length andfilm dis- tribution in circular or square microchannels[20]. At the small scale, interactions between immiscible phases are mainly dominated by sur- face forces, hence the relative importance of viscous effect is usually represented by capillary number. It has been shown that at low capil- lary number (Ca< 0.0058) [6] the bubble formation is under squeezing regime in which the breakup of an emerging bubble is chiefly driven by the buildup of pressure upstream, and bubble length is solely determined by the two-phaseflow rate ratio and the inlet geometry[5].
In shearing regime (Ca> 0.01,LB/W < 1), the shear force dominates over the breakup and bubble length depends on capillary number only [6,22,23]. In mediumCarange (0.0058 <Ca< 0.01) or with long bubble length (LB/W > 1.5), the breakup process is driven by both shear force and squeezing regime[6,22]. Along with the variation of Ca, the liquidfilm between gas bubbles and channel wall is also in- fluenced[17,24–26]. For liquid-liquid systems, the viscous effect on film thickness also appears in the viscosity ratio between two phases [27]. Generally, thefilm thickness in circular channels, as a function of bubble capillary number (CaB=μUB/σ), can be well described by the correlations shown inTable 1. In square channels, thefilm thickness at the wall planes agrees reasonably well with these correlations [7,26,28], despite the influence of the corners. Kreutzer et al. [26]
developed an empirical correlation (Table 1) to scale thefilm thickness at the corners (δcorner) in square channels, based on both experimental and simulation results in literature [28–30]. Han and Shikazono[8]
proposed a more complex correlation to scaleδcornerin the visco-inertial regime for square channels. It is in good agreement with the correlation of Kreutzer et al.[26]when the inertial term is neglected. The above review suggests that a relatively thorough understanding on the effect
of viscosity on bubble formation and film distribution in circular or square microchannels has been built, which is the basis to analyze pressure drop, mass transfer, and so on.
Research on rectangular channels was motivated by the easy fab- rication with MEMS techniques (i.e., photolithography and etching techniques). The Taylorflow behaves differently in rectangular chan- nels compared to in square channels[11,31,32]due to different con- finement by the walls. Choi et al.[11]found that the bubble velocity decreased with the increase in aspect ratio. Yao et al.[33]found the film thickness at the corners in a rectangular channel was significantly larger than the predictions of Kreutzer et al.[26]and Han and Shika- zono[8]due to the effects of inertial force. Although there were a lot of studies conducted in rectangular channels, the viscous effects on gas- liquid systems was hardly studied. Only several studies with numerical simulation have been conducted, which all showed thatfilm thickness at vertical short planes decreased with the increase in aspect ratio [9,30,32]. Abadie et al.[22]showed a slight decrease in recirculation volume and a significant increase in recirculation time with the in- creasing of channel aspect ratio. However, these studies considering Taylorflow only involved the largeCarange (0.04–1.8) to identify the liquidfilm due to the limitation of computational cost. Therefore, it is necessary to make more efforts to understand the viscous effect in rectangular channels, especially in smallerCarange.
The present work aims at improving the fundamental understanding of gas-viscous liquid Taylor flow in a rectangular microchannel.
Different glycerol solutions are used to vary the liquid viscosity andCa in the range of 0.00065–0.0525. The bubble formation process (in- stantaneousflow rate evolution), bubble and slug lengths, liquidfilm thickness and pressure drop will be investigated in a rectangular mi- crochannel with T-junction.
2. Experimental section
2.1. Microfluidic device and experimental setup
The microchannel device used in the experiments was made of BF33 Nomenclature
A cross-sectional area, m2 DH hydrodynamic diameter, m
Ca capillary number of two-phaseflow,=μ jC TP/σ CaC capillary number of continuous phase,=μ jC C/σ CaB capillary number based on bubble velocity,=μ U σD B/ j superficial velocity, m/s
L length, m
P pressure
Q flow rate, m3/s U velocity, m/s
V volume, m3
W Channel width, m H Channel height, m
Greek symbols δ film thickness μ viscosity, mPa·s
σ interfacial tension, mN/m ρ density, kg/m3
Subscripts
B bubble
C continuous phase
CH channel
D dispersed phase F liquidfilm
G gas
L liquid
S slug
TP two phase
Table 1
Correlations of normalizedfilm thickness for gas-liquid Taylor in circular channels.
Correlation Channel Ca Reference
=
δ R/ C 0.5CaB0.5 Circular CaB< 0.01 Fairbrother and Stubbs[25]
=
δ R/ C 1.34CaB2/3 Circular CaB< 0.003 Bretherton[34]
= + δ RC
CaB CaB 1.34 2/3 1 3.35 2/3
Circular CaB< 1.4 Aussillous and Quéré[24]
= − −
δ R/ C 0.36[1 exp( 3.08CaB0.54)] Circular CaB< 2.0 Irandoust and Andersson[35]
=0.35−0.25 exp( 2.25− Ca )) δcorner
DH B0.445 Square CaB< 4.0 Kreutzer et al.[26]
glass with meandering channel, as shown inFig. 1. All the channels had the same rectangular cross section with 600μm × 300μm. The liquid was injected through Inlet 1 by a syringe pump (LSP02-1B, Long- erPump, China). Nitrogen was delivered from a gas bottle with pre- calibrated massflow controller (SC10, Sevenstar, China) through Inlet 3 (Inlet 2 blocked). Hence, Taylor bubbles were generated at the second T-junction. The channel length for two phaseflow was 440 mm. A tee joint was connected to the port of Inlet 3 to measure the pressure drop.
The reactor design involved a few half-circle bends (0.7 mm in central radius) to increase the channel length, which might produce additional pressure loss due to the secondary vortices even in laminarflow.Ładosz and Rudolf von Rohr[12]ascertained that negligible effect of bends on pressure drop could be achieved with Dean number smaller than 27. To minimize this effect, the range of flow rates was selected as that the values of two-phase Dean numbers varied from 0.16 to 100 and < 7%
of the Dean numbers were larger than 30. Hence, it was ensured the effects of the channel bends could be neglected.
In the present work, different glycerol solutions were used to study the effects of viscosity on gas-liquid two-phase flow. The physical properties of thefluids at 25 °C are provided inTable 2. The density and viscosity data were taken from literature[36]. The interfacial tension data were measured with an optical measuring device (OCA15, Data- physics, Germany), which agreed well with the reference[36]. All the experiments were conducted under 25 °C and atmospheric pressure.
2.2. Methodology for gasflow rate quantification
The pressure drop (ΔP) over the entire microchannel was in the range of 8–133 kPa depending onflow rates and liquid viscosity. Since the massflow controller only controlled gasflow rate in terms of mass flow, the actual volumetricflow rate was influenced by the pressure drop and needed to be quantified:
= +
Q 101.325Q 101.325 ΔP
G G set
1 ,
(1) whereQG,setwas the set volumetricflow rate under atmospheric pres- sure.
Another method to calibrate the gasflow rate was an online method based on the Taylor bubble volume, which was a convenient and widely used method with relatively high precision[37–39]. The gasflow rate QG,2was calculated by summing up the volumes of all the bubbles passing a specific location in afixed time duration (mostly 5 s in this work).
∑
= V QG2 tB
(2) This method required calculation of bubble volume, hence a model of bubble cross-section needed to be provided, as shown inFig. 2. The model assumed the gas-liquid interface at the corner was a quadrant.
The radius of the quadrant was the width (I) of the black zone at the bubble body, which was caused by the light reflection of the curved gas- liquid interface.
As the Weber number (We) in the experiments was far smaller than 1.0, the liquid film thickness at the horizontal wall planes could be described by the correlation of Aussillous and Quéré[24]:
= +
δ D1/ H 0.67Ca2/3/(1 3.35Ca2/3) (3) where Ca (=μ(jG+jL)/σ) was the two-phase capillary number. Ac- cording to this model, thefilm thickness at the channel corner could be calculated:
= + −
δcorner 2 (I δ2) I (4)
It needs to be noted that only for largeCa(> 0.02)δ2at the short planes was directly measured from captured images as the bubbles were detached from the side planes (Fig. 2b), with an measurement error smaller than 25% (one pixel in 4–7 pixels). For lowCa(< 0.02),δ2was
too small to be identified and measured directly from the images, and it was treated to be the same asδ1, though for rectangular channels it had been observed thatδ2tended to be larger thanδ1[30,33]. Hence, the measurement error of δcorner only originated from the measurement error ofI(< 8%, one pixel in 13–17 pixels) for lowCa(< 0.02) and from the error of (δ2+I) (< 7%, one pixel in 17–24 pixels) for largeCa (> 0.02). To be more conservative, 13% was chosen to represent the measurement error ofδcornerand 25% forδ2.
The cross-sectional area of the bubble was determined as
= − − − −
AB (W 2 )(δ2 H 2 )δ1 4(I2 πI2/4) (5) For simplicity, the bubble caps were treated as spherical caps of which the height h was directly determined from the captured 2-D images to be 0.21W. The radius of the base circle of the spherical caps was assumed as 0.5DH. Thus, the volume of the caps was expressed as the following:
= +
V 1πh D h
6 (0.75 )
cap H2 2
(6) It should be noted that the shape of the bubble caps was largely influenced by the capillary number, whereas the deviation was negli- gible as it only took a very small fraction of the total bubble volume.
With all these parameters defined, the bubble volume could be calcu- lated as the following:
= − +
VB (LB 2 )h AB 2Vcap (7)
The deviation of the calibrated gas flow rate between the two methods were rather small, suggesting the validity of the both methods.
Hence, the actual gasflow rate was calibrated using Eq.(1)while the film thickness at the channel corner was estimated with Eq.(4)using the proposed cross-sectional model.
3. Results and discussion 3.1. Bubble formation dynamics
It has been well proved that the periodic variation of pressure [23,40]and velocity profile[40,41–43]at the T-junction is induced by
quid
Liquid Gas
Fig. 1.Structure of the meandering microchannel.
the periodic formation of Taylor gas bubbles. Thefluctuation can also transfer to the regular flow in the downstream, where only smaller magnitude of fluctuation remains [44]. In our previous studies, we found that the instantaneous flow rates of both phases also varied periodically for the slugflow regime[41,42]. The periodicfluctuation characteristics gives novel view into the detailedflow behaviors. In this work, such analysis was performed to study the effect of liquid viscosity on the gas-liquid interaction mechanism during the formation stage.
The instantaneous flow rates of each phase were estimated by tracking the interface of the gas thread with an assumption that the interface curvature in depth-wise direction was constant. The detailed information about the method can be found in our previous study[42].
Fig. 3shows a typical evolution of both gas and liquidflow rates. The evolution of liquid phase was the same with previous observation [41,42]. The instantaneousQLwas the smallest at the start of squeezing stage due to the bubble blockage, and then kept almost constant until the collapsing of the bubble thread. In this stage,QL/Qsetwas much smaller than 1.0, which was induced by the leakageflow in the channel corners[42,45–47]. After pinch-off, the instantaneousQLreached the highest peak due to the sudden release of the accumulated pressure, and then decreased gradually. Considering the evolution of in- stantaneous QG, it did not always go in the opposite direction of the continuous phase due to the compressible effect of gas phase [42].
Fig. 3 shows there was several points where the thread contracted, which led to more complexfluctuation, and similar phenomena were observed in our previous study[41].
Fig. 4displays the effect of viscosity (different glycerol concentra- tion) on the evolution for different gasflow rates. Firstly increasing the viscosity lead to more stable flow, in consistent with the pressure evolution. Secondly, the calculated instantaneousflow rate increased
with the increasing viscosity. All these could be attributed to that in- creasing viscosity was not beneficial for the leakageflow[46]. Finally, it can also be seen that the collapsing stage moved towards left side (i.e, smaller t/T) for larger liquid viscosity, which means decreased squeezing stage and increasedfilling stage. For low gas phaseflow rate, as the glycerol concentration exceeded 60%, the bubble tip was too short to produce an effective blockage and the formation of the Taylor gas bubble was dominated by the shearing force, which made the evolution similar to thefilling stage. For large gas phaseflow rate, the long bubble tips was formed and the blockage was effective, thus ob- vious peak always existed in all solutions, as shown inFig. 4(b). The shifting of the collapsing stage was more clearly observed.
3.2. Bubble and slug lengths
In the experiments, the gas-liquid two-phase Ca ranged from 0.00065 to 0.0525, covering the squeezing regime, transition regime and shearing regime. Hence, the influences offluid properties andflow rates were significant [6,22,23,48]. The effect of liquid viscosity on bubble length is shown inFig. 5. As expected, the bubble length sig- nificantly decreased with the increase in glycerol concentration. Inter- estingly, the bubble length still obeyed the linear law for each glycerol concentration atfixed liquidflow rate, irrespective of formation re- gimes. This was different to the previous predictions (i.e.,LB∼(jG/jL)a Cab) for the transition regime[6,22]. Another effect can be seen in Fig. 5is that the slope of the linear line decreased with increasing liquid viscosity. Since the bubble lengths were all larger than the channel width in the experiments, the blockage effect still played an important role. According to Garstecki et al. [5], the bubble growth during blockage is determined by the shrinking timedneck/ushrink. The slopeλ2
stems from the scaling relation (dneck/ushrink)/
× ∼ × ∼
W ugrowth dneck/ W (Q QG/ L) λ j
2jG
L. When the shrinking is only caused by the squeezing of pressure,λ2is constant for differentfluid systems. When shrinking is caused by both the squeezing and shearing as in the present study, the smallerλ2is then explained by that the shear stress resulted in largerushrink.
Based on the above analysis, it can be concluded that for bubbles with length larger than channel width, their lengths were influenced either by sole squeezing or by both squeezing and shearing. As the squeezing was affected by leakageflow, which was also a function of capillary number[42,45], a modification of the model in Eq.(8)with Cawas proposed to interpret the effects of the squeezing and shearing:
= + −
L
W Ca j
1.197 0.763 j
B G
L 0.154
(8) As the bubbles and slugs were generated alternatively, the ratio of Table 2
Physical properties offluids at 25 °C.
Fluid (wt%)
Densityρ(kg·m−3) Viscosityμ(mPa·s) IFTσ(mN·m−1)
Water 997.05 0.89 72
20% glycerol 1044.7 1.52 71
40% glycerol 1096.1 3.14 69.3
60% glycerol 1150.6 8.84 67
70% glycerol 1177.8 18.2 67
80% glycerol 1205.1 45.6 66.9
Fig. 2.(a) Schematic of the cross-sectional model of a Taylor gas bubble (b) Captured image of plane view of a Taylor gas bubble.
0.1 1 10
0.0 0.5 1.0 1.5 2.0 2.5 3.0
t/T
Q/Qset
Liquid phase Gas phase
Fig. 3.Evolution of the estimated instantaneousflow rates of gas and liquid phases with water-nitrogen system.QL= 0.30 mL/min,QG= 0.39 mL/min.
bubble to slug lengths should be a function of the gas to liquidflow rate ratio (LB/LS= 1.49 jG/jL). It can be seen in Fig. 6 that excellent
performance of predictions were achieved with the empirical correla- tions.
3.3. Film thickness and bubble velocity
The thickness offilm around bubbles is a function of the capillary number[24,28]. In square channels, the liquidfilm distribution and cross-sectional shape of bubble are not cylindrically symmetric due to the corners. However, plenty of researches have shown that gas bubble shape will shift from non-axisymmetric to axisymmetric above a tran- sitional value of Ca about 0.04–0.1 [26,28,30,32]. For rectangular channel, an extra control parameter of the aspect ratio enters the pro- blem, which strongly influences the bubble shape. Simulation results [30,32]] showed that forCarange of 0.04–1.8 increasing the aspect ratio can lead to the reduction infilm thickness in the plane of shorter semi-axis (δ2).
In this work, thefilm thickness at both channel corners and planes will be discussed and compared to literature predictions in a medium Ca range of 0.0005–0.0525. Results of film thickness were plotted againstCaBbased on bubble velocity (=μUB/σ), and also compared to literature studies. Since there are no studies dedicated to in rectangular channels in the presentCarange,film thickness at the cornerδcornerand at the wallδ2are compared to literature studies in square channels and circular channels, respectively[8,24,26,30,32,35]. It can be seen from Fig. 7thatδcornerwas significantly larger than both the predictions of Kreutzer et al.[26]and Han and Shikazono[8]forCaB> 0.005. The smallerδcornerforCaB< 0.005 is because the prediction of Aussillous and Quéré [24]used in the present model (Eq.3) gave smallerfilm thickness at wall planes than fact. The measurement done by Fries et al.
[7]suggested that thefilm thickness at wall planes varies very little CaB< 0.006 and was about 0.02DH, which was much larger than the prediction of Aussillous and Quéré[24]. In fact, ifδcornerwas calculated based on 0.02DH, the values (not presented here) were then comparable to the prediction of Kreutzer et al.[26].
For δ2, the experimental values were directly determined from captured images when the bubble was clearly detached from the channel wall.Fig. 7shows that the increase inδ2with increasingCaB
was also much more obvious than the widely used correlations of Aussillous and Quéré[24]and Irandoust and Andersson[20,35]. For rectangular channels, there is a tendency to drive the liquid from the horizontal planes towards the vertical planes[33]. This tendency be- came more obvious with the increasingCaBdue to the smaller viscous resistance in the corners, which explains the rapid increase in both δcorner andδ2. Under experimental conditions,δcornercould be well 0.1
1 10
0 0.5 1 1.5 2
t/T Q/QL
80% 70%
60% 40%
20% 0%
a
glycerol concentration
0.1 1 10
0 0.5 1 1.5 2
t/T Q/QL
80% 70%
60% 40%
20% 0%
b
glycerol concentration
Fig. 4.The effect of liquid viscosity (different glycerol concentration) on the evolution of instantaneous liquid flow rate. (a) QL= 0.30 mL/min, QG= 0.39 mL/min; (b)QL= 0.30 mL/min,QG= 0.69 mL/min.
0 1 2 3 4 5 6 7
0 0.5 1 1.5 2 2.5 3
jG/jL
LB/W
0% 20%
40% 60%
70% 80%
Fig. 5.Bubble length as a function of gas to liquidflow rate ratio for different fluid systems atQL= 0.3 mL/min.
0 2 4 6 8
0 2 4 6 8
Experimental lengths
Predicted lengths
bubble length slug length
Fig. 6.Comparison between predicted and experimental bubble and slug lengths (dimensionless).
correlated with the following equation (standard deviation of 0.3% and determination coefficient of 0.988).
= − −
δcorner/W 0.217 0.154 exp( 8.428CaB0.628) (9) With respect toδ2, it was also largely affected by the droplet length and could be correlated with an empirical correlation (standard de- viation of 0.44% and determination coefficient of 0.875).
= − −
δ W2/ 0.15[1 exp( 8.221CaB0.972)]
(10) Along with the increase in thefilm thickness, the plane-view bubble shape became slender by increasingCa. Due to the viscous shearing, the bubble front cap is usually smaller than the back cap, leading to a bullet-like shape[10,49–52]. This was also the condition for the bub- bles right after their formation in the present study. However, such bullet-like shape rapidly (about 6 mm downstream the T-junction) turned into a different shape in the rectangular channel, as shown in Fig. 8. The plane-view images of the bubbles under differentCasuggest that there was no significantflattening at the rear bubble cap. Instead, there was an abrupt change in the curvature at the front cap, which was represented by a protruding tip. It was caused by the rectangular cross section that provided stronger shear from the corners with thicker li- quidfilm. In order to explore the effect of viscous shear on the bubble shape, three simple parameters (radius of the leading, front and trailing menisci shown inFig. 8a) were defined and plotted as a function ofCaB
inFig. 8b. As can be expected, all the radii decreased with increasing CaB. At very lowCaB(< 0.002), the trailing radiusr1equaled the front r2. At highCaB(> 0.04), a protruding tip also existed at the rear cap, suggesting that the un-equal distribution of liquidfilm between hor- izontal planes and vertical planes was also serious there. The most in- teresting phenomenon was that for all the experimental conditions the trailing radiusr1was always smaller than the frontr2and the decrease rate ofr1withCaBwas larger than the other two radii, as shown in Fig. 8b. This was not only different from observations in square/circular channels with viscous shear [10,49–51], but also from observations from rectangular channels with shear by inertia [11,33]. The exact reason is unknown yet and needs further investigation.
The bubble velocity was also determined and compared to a simple drift model[11]:
=
UB C j1TP (11)
C1is a distribution factor which can be regarded as the ratio be- tween the areas of channel cross section and bubble cross section by assuming negligible film velocity [20,53]. The results are plotted in
Fig. 9as a function of capillary number. As can be seen, the actual bubble velocity was always smaller than the ratio ofACH/AB, suggesting that thefilm velocity could not be completely neglected. Similar phe- nomenon has been observed by Choi et al.[11]and Yao et al.[33]. In addition, Choi et al. [11] found that the bubble velocity was sig- nificantly reduced by increasing the aspect ratio. The reason can be explained by that due to the thinnerfilm the horizontal planes provided larger shear/resistance to the bubbles in rectangular channels, which was beneficial forfilm moving in the corners. The dimensionless bubble velocity increased with the increase in glycerol concentration orCaB
due to the increasedfilm thickness. Overall, the dimensionless bubble velocity ranged from 0.95 to 1.23 under experimental conditions. The range was small that it roughly presented a linear relationship between bubble velocity and the total superficial velocity, as widely reported in literature.
3.4. Pressure drop
Fig. 10shows the effect offlow rates and glycerol concentration on two-phase pressure drop. It can be seen that both liquidflow rate and glycerol concentration played more important roles than gasflow rate.
Forfixed liquidflow rate and glycerol concentration, the pressure only slightly increasefirstly and then kept almost constant when increasing gasflow rate. This is different from previous studies on liquid-liquid systems that either afirst increase followed with a decrease[54,55]or a first decrease followed with an increase[12]in pressure drop was ob- served, depending on the viscosity ratio between the immisciblefluids.
The reason was explained by the different contributions from the fric- tional pressure drops of each phase segments and interfacial pressure drop. In order to understand such mechanism as well as the influence of viscous effect on pressure drop, several models were compared to our 0.00
0.05 0.10 0.15 0.20 0.25
0.0001 0.001 CaB 0.01 0.1
į/W
present study Kreutzer et al.,2005 Han and Shikanozo,2009 Kuzmin et al.,2011 Hazel and Heil,2002
present study
Irandoust and Andersson,1989 Aussilous and quere,2002 Kuzmin et al.,2011 Hazel and Heil, 2002
įcorner/W į2/W
Fig. 7.Film thickness against capillary number based on bubble velocity (=μUB/σ).
0 0.1 0.2 0.3 0.4
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
CaB
r/W
r1 r2 r3
b
Fig. 8.(a) Plane-view images of bubbles under different capillary number (b) dimensionless radius of the leading, front and trailing menisci against capillary number. The liquidflow rate was 0.3 mL/min.
experimental results and to analyze the individual parts of pressure drop.
For Taylorflow, generally three terms are considered to contribute to the total pressure drop: frictional pressure drop of the continuous
phase slug (ΔPS) and dispersed bubble (ΔPB) and the Laplace pressure drop (ΔPI) over the bubble.
= + + +
P L P P P L L
ΔTP/ (ΔB ΔS Δ )/(I S B) (12)
The Laplace pressure drop can be obtained with the Young-Laplace equation, which needs to know the dynamic contact angle. Usually, a simplified correlation with the analytical solution of Bretherton[34]is taken into account to yield
=
P c Ca σ
Δ D2
I B
H
1 2/3
(13) wherec1accounts for the influence of the interface curvature, which was found to be 7.45 for ideal semispherical caps by Bretherton[34].
Wong et al.[45]found that pressure drop was smaller in rectangular channel and gave a value of 3.56 for square channel.
The pressure drop termΔPSis usually estimated by assuming a fully developed Hagen-Poiseuilleflow. Whereas the existing models in lit- erature are mainly focused on the dispersed phase term (ΔPB) [11,12,55,56]. Jovanovic et al.[55]developed two models by assuming stagnantfilm or moving annularfilm (i.e., annularflow) surrounding droplets respectively for circular channels. The prediction of moving film model is always smaller than the stagnantfilm model since the wall can be regarded as with infinite viscosity. In a recent study,Ładosz and Rudolf von Rohr[12]proposed a similar model for rectangular chan- nels by treating non-circular cross section as virtually circular. Two correlations are achieved for moving film model and no-film model respectively as following:
⎜ ⎟
= ⎛
⎝
− ⎞
⎠ +
− +
+ +
( )
P L
αμ j A
A A
j U αA
A j U
j σW H
A f
U c Ca Δ
1
TP
L TP CH
CH B
G B
CH B
G B
TP
μ μ
A A
A μ
CH
B B
B
1 1
1 2/3
G L
B CH
CH L 2
(14)
⎜ ⎟
= ⎛
⎝
+ + + ⎞
⎠ P −
L αμ j A
j j
μ μ
W H
α f jc Ca ΔTP L L 1
CH G L
G L
B L
1 B1/3
(15) whereαis the geometrical correction factor defined by
= +
−
α W H
WH 22
7
(2 2 ) 65
3
2
(16) Yue et al.[56]proposed a model just based on theflow character- istic features by neglecting thefilm, which then gave a simple 2-para- meter correlation as
⎜ ⎟
= +
⎛
⎝
+ −
+ ⎞
⎠ P
L L L
c μ L j c μ L D U
A c Ca σ
D
ΔTP 1 ( ) 2
B S
L S TP G B H B
CH B
H
2 2
1 2/3
(17) c2is a empirical parameter and should be equal to the geometrical correction factorα.
Applying the above models suggest very close predictions as shown inFig. 11, which is reasonable as the viscosity of gas phase is much smaller than the liquid phases and the contribution ofΔPBwere smaller than 3% of the total pressure drop. In addition, all the three models show a significant under-estimation of the experimental results for low CaB, whereas reasonably well prediction was obtained at large CaB. That largerΔP-pre/ΔP-expat higherCaBwas also observed in the study of Ładosz and Rudolf von Rohr[12], whereas no explanation was given.
Since the above models assume laminorflow in the liquid phase, a possible reason for under-prediction at lowCaBmay be that theflow deviated much from Hagen-Poiseuilleflow. The deviation originating from the recirculating vortices and vortices near bubble caps [10,49–51], may cause additional pressure drop in the liquid phase.
There are a lot of studies showing that the vortices decrease with the increase in slug length[9,16,57]orCaB[51]. Hence, an empirical term containing slug length andCaBwere used to modify the model of Yue 0.8
0.9 1.0 1.1 1.2 1.3 1.4
0.0001 0.001 0.01 0.1
CaB
UB/jTP
0 20%
40% 60%
70% 80%
ACH/AB
Glycerol concentration
Fig. 9.Ratio of bubble velocity to two-phase superficial velocity versus capil- lary number.
Fig. 10.Pressure drop as a function offlow rate ratio.
et al.[56]to illustrate this effect:
= + + + +
P L P P ξ P L L
Δ TP/ [Δ B Δ S(1 ) Δ ]/(I S B) (18)
= − −
ξ 0.0362(L DS/ H) 2.339CaB1.152 (19)
The parameters were obtained by a least square regression. The power indexes ofLSandCaBare negative, indicating the rationality of the speculation. The performance of the modified model is shown in Fig. 12. As can be seen, excellent prediction was achieved.
4. Conclusion
This study focuses on the gas-liquid Taylor flow characteristics under different liquid viscosities in a rectangular channel with a T- junction. Visualization experiments using a high speed camera has been performed to study the bubble formation dynamics, bubble and slug lengths, liquidfilm thickness, bubble velocities, gas hold-up and pres- sure drop. As many technological fluids in microfluidic studies are highly viscous, thefindings in this paper may serve as a useful guidance for the design of gas-liquid microreactors.
The studyfirstly investigates the effect of liquid viscosity on the instantaneous liquid flow rates. It is shown that increasing glycerol
concentration leads to more stable flow, as well as a shortened squeezing stage in a formation cycle. As the two-phaseCaranged from 0.00065 to 0.0525 in the study, the bubble formation is mainly under transition regime in which both squeezing pressure and shear force play important roles. Accordingly, bothCaandflow rate ratio are used to scale the bubble length, which presents excellent prediction. The vis- cous effect in the rectangular channel is shown to be different than in square channels. Due to the different lengths of the planes,film thick- ness at the short planes is much larger than in square channels when capillary number is higher than 0.02. This also leads to a much larger film thickness at the corners. Finally, the pressure drop is compared to several models in literature. It is shown that the models assuming Hagen-Poiseuille flow significantly under predicts the experimental values at low capillary number, which is explained by the unaccounted effect of recirculation in these models. A revised model is proposed to describe this effect and achieves good prediction performance. These findings will help to optimize the design parameters to improve mixing and mass transfer for viscousfluids.
Acknowledgements
We acknowledge gratefully thefinancial supports for this project from National Natural Science Foundation of China (Nos. U1662124, 21676263 and 91634204), the CAS supports of the Youth Innovation Promotion Association CAS (No. 2017229), DICP (ZZBS201706) and Dalian Science & Technology Innovation Fund (No. 2018J11CY019).
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