Formation dynamics and size prediction of bubbles for slurry system in T-shape microchannel

Zhen Chen, Chunying Zhu,*, Taotao Fu, Xiqun Gao, Youguang Ma,*

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

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

Keywords:Microfluidic T-shape microchannel Bubble Slurry Dynamics

ABSTRACT The bubble formation dynamics and size manipulation in the slurry of polystyrene microspheres in the microfluidic T-junction were visually investigated by a high-speed camera.Based on the evolution of the bubble neck with time,the formation process of bubbles is divided into three stages:filling,squeezing and pinch-off.The particle concentration has an obvious effect on the squeezing stage,while less impact on the filling and pinch-off stages.In the squeezing stage, the evolution of the dimensionless minimum neck width of bubbles with time could be described by a power-law relationship.The increase of the particle concentration or continuous phase flow rate could lead to the increase of body flow of the continuous phase and the enhancement of the squeezing force acted on the bubble neck, correspondingly,the power-law index α in the squeezing stage enlarges.Moreover, the bubble size increases with the increase of the gas phase flow rate and the decrease of the particle concentration and continuous phase flow rate.However,the effect of the particle concentration on the bubble size weakens with the increase of the continuous phase flow rate.In addition, a new prediction correlation of the bubble size for the slurry system in a T-shape microchannel was proposed with good prediction accuracy.

1.Introduction

The gas-liquid-solid system was usually encountered in the chemical synthesis, such as hydrogenation reaction [1,2], olefin polymerization[3,4],photooxidation reaction[5,6].In recent years,due to the advantages of process safety, high efficiency, high controllability,easy amplification and integration[7,8],the application of microfluidic technology in the gas-liquid-solid system has become increasingly widespread.In the chemical reactions, solid particles could be the reactant, catalyst or product in the microreactor.Kobayashiet al.[9]used a palladium catalyst in microreactor to conduct hydrogenation reactions that proceeded smoothly to afford the desired products within 2 min for a variety of substrates.Yunet al.[10]proposed a liquid flow-focusing and gas displacing method to produce continuously solid lipid nanoparticles (SLNs)in microchannel.The solid nanoparticles with small size and narrow particle size distribution were obtained.

In the absorption process in microreactor, solid particles were usually dispersed into liquid to enhance the mass transfer between gas and liquid.Hajiani and Larachi[11]explored the effect of magnetic nanoparticles colloidal suspension on the mass transfer process in the microchannel, it could be found that the magnetic nanoparticles created rotation around the Taylor bubbles under transverse rotating magnetic field, which remarkably intensified the mixing inside the liquid film around the bubble, thereby enhancing the mass transfer between gas and liquid phases.Caiet al.[12]studied the influence of different particles on the mass transfer of CO2absorbed into slurries under the condition of Taylor flow in the microchannel.The results showed that the adsorption capacity and size of particles were important to the enhancement of mass transfer.As the adsorption capacity of particles increases,the mass transfer enhancement factor increases.Additionally,Microfluidic technology is widely applied to the sieving of solid particles or cells.Yuet al.[13]achieved the separation of particles with different sizes in suspensions.The particle separation would occur once the thickness of the lubricating liquid film falls between the diameters of the two different particles.The large particles would aggregate at the bubble surface, while small particles were leaked out from a special thin film into the fluid region behind the bubble.Kuntaegowdanahalliet al.[14]designed an inertial microfluidic system for separating nerve cells with high vitality.In the spiral microchannel, the particles with different sizes were divided into single-size particles focused flow due to the difference of internal inertial force.

Most of these studies were aimed at the flow process of bubbles in the slurry system.Although the size of microbubbles has a significant impact on the enhancement of mass transfer [15,16],chemical reaction,the sieving of particles,and the internal circulation in liquid slugs [17,18], the research on bubble formation is extremely lacking.Therefore, the study of bubble formation dynamic and size manipulation in slurry system in the microchannel has important practical significance.

At present, in the gas-liquid system, bubble formation in microchannels had been deeply studied.Garsteckiet al.[19]investigated the formation process of bubbles in microfluidic T-junction,and the effects of gas and liquid flow rates and interfacial tension on the size of bubbles were studied systematically.They found that the bubble size increased with the gas phase flow rate but decreased with the liquid phase flow rate.Furthermore,van Steijnet al.[20]measured the flow field evolution during the formation process of bubbles in microfluidic T-junction by a micro-PIV, they found that when the bubble completely blocked the channel, at least 25% of the liquid leaked downstream through the corners of the channel.Korczyket al.[21]revealed the dependence of bubble size on the gas-liquid flow ratio, capillary number and channel structure based on squeezing mechanism,and a prediction correlation was proposed.In gas-liquid-solid system,Tanget al.[22]studied preliminarily the bubble formation size in the microfluidic Tjunction,the results showed that the bubble tended to evolve from the squeezing regime to the dripping regime, and the formation size of bubbles decreased with the increase of the particle concentration.However, the formation and regulatory mechanisms of bubbles in slurry in microchannel are still unclear and needs further study.In this work, the bubble formation dynamics and size manipulation in slurry were explored.The effects of particle concentration, dispersed phase flow rate and continuous phase flow rate on bubble formation were investigated.Furthermore, a new prediction model of bubble size was proposed for the gas-liquidsolid system in T-shape microchannel.

2.Experimental

Fig.1 illustrates the sketch of the microchannel and the experimental setup.The microchannel with 0.8 mm × 0.8 mm in depth and width was processed by a precision milling.The continuous phase slurry and the dispersed phase N2were separately injected to two inlets of microchannel by micro-pumps(PHD 22/2000,Harvard Apparatus, USA).Bubbles were formed at the T-junction and flowed past the straight channel into the collector.A high-speed camera (SA1.1, Photron, Japan) was used to record the formation process of bubbles in the T-junction.The frame rate of the camera was set to 6000-8000 frames per second in the experiment.When the flow rate of the gas or slurry was adjusted, the bubble formation process was recorded after the flow pattern remained stable at least 5 min.The polystyrene microspheres were added into the aqueous solution of sodium dodecyl sulfate (SDS, 0.35%(mass)), and then sonicated for 15 min to prepare the uniform slurry.The mean diameter of the polystyrene microspheres is 5 μm and the density is 1050 kg·m-3.The surface of the microspheres was hydrophilically modified to prevent particles adsorption on the channel wall.In order to avoid the deposition of particles and blockage of microchannel,the low particle mass concentration less than 2% is generally used [23-25].Therefore, slurries with 0%,0.5%,1%,2%particles were chosen in this experiment.

In this study,the Taylor bubbles are primarily focused considering its wide applicability in practical process.The experimental conditions are as follows: the continuous phase flow rateQCis from 20 to 100 ml·h-1, the gas phase flow rateQGis from 60 to 300 ml·h-1,and the mass fractions φ of spherical particle in slurry are 0%, 0.5%, 1%, 2%.The effective shear rate γ could be estimated by the following equation [26]:

whereQCis the flow rate of continuous phase,Wis the width of microchannel.In this experiment, the shear rate range is 0-150 s-1, thus the rheological properties of slurries in the range of shear rate 0-256 s-1were measured.The rheological properties of slurries with different particle concentrations were determined by a rheometer (Discovery HR-2, TA Instruments, USA) and shown in Fig.2.The rheological property of slurry could be described using the power-law model:

Fig.2. Rheological properties of slurry with different particle mass concentrations.

where μ is the viscosity,Kandnare the consistency coefficient and flow index.Values ofKandnfor slurries used in this experiment were listed in Table 1.Additionally, the surface tensiometer(OCAH200, Dataphysics, Germany) and pycnometer were used to measure the interfacial tension σ of N2-slurry and density ρ of slurry.Experiments were conducted at 293.15 K and atmospheric pressure.The physical properties of slurries are also listed in Table 1.

Table 1Physical properties of slurries used in the experiments

3.Results and Discussion

Fig.3 displays the formation process of N2bubble in the slurry at T-junction.The bubble formation process could be divided into filling stage, squeezing stage and pinch-off stage.This is the same to that in shear-thinning fluid[27].In the filling stage(0-10.5 ms),the bubble tip fills gradually T-junction due to the continuous supply of gas until the bubble neck width reaches its maximum.In the squeezing stage (10.5-33 ms), the bubble tip develops downstream along the main channel,meanwhile, the bubble neck thins under the squeezing action of the continuous phase, and the bubble neck interface is always convex.In the pinch-off stage (33-36 ms), the bubble neck transforms into the concave interface and quickly thins until breakup.Subsequently, the interface of bubble tail rapidly deforms to a circular arc shape.

To facilitate discussion,several physical parameters are defined to characterize the formation of the bubble as shown in Fig.3.Wmis the minimum width of the bubble neck.Lis the bubble length,andlis the development length of the bubble tip.The length and neck width of bubble were obtained from images recorded by the high-speed camera with an error ± 2 pixels.For each experimental condition, 10 images were processed and their average value was used as the experimental result to eliminate the accidental error.The uncertainty for length and neck width of bubbles was estimated to be ± 4 μm including systematic and measured errors.

Fig.3. Bubble formation processes at the T-junction (QC = 60 ml·h-1, QG = 140-ml·h-1, φ = 1%).

3.1.Dynamics of neck for bubble formation

Comparatively, the gas-liquid-solid three-phase systems are more complex than the gas-liquid two-phase system, in which more interactions need to be considered in the bubble formation process: (1) the fluid-particle interaction, (2) the particle-particle interaction, (3) the particle-wall interaction, and (4) the interaction between the particles and the gas-liquid interface.The slurry would be shear thinning or shear thickening due to the interactions of the fluid-particle, particle-particle and particle-wall, and accordingly display typical rheology [28], which would also dramatically affect the formation of bubbles.

Fig.1. Schematic diagram of experimental device and microchannel structure: (a) the microfluidic channel, (b) the experiment setup.

The flow field of continuous phase in squeezing stage was measured by μ-PIV as shown in Fig.4.In T-junction,due to the obstruction of the bubble neck,the velocity of continuous phase decreases,and a part of continuous phase deflects and flows downstream along the corners of the channel.Accordingly, the flow of the continuous phase could be divided into two parts: (1) the body flow(QN), squeezing the neck of the bubble to create deformation and rupture; (2) the leakage flow (QB), flowing through the corners of the rectangular channel, without contribution to squeezing neck of bubble [21].

Fig.4. Flow field of continuous phase in squeezing stage(QC=20 ml·h-1,QG=100-ml·h-1, φ = 2%).

As shown in Fig.5, the neck width of bubble presents different tendencies with time in three stages.(I) Filling stage:Wmrapidly develops to the maximum value.This process starts when the gas and slurry contact and form an interface at the T-junction,and completes when the neck width of bubble reaches its maximum.It could be perceived from Fig.5 that the duration of filling stage is short andWCis almost independent of particle concentration.(II) Squeezing stage:Wmslowly decreases due to the squeezing of the slurry flow.(III) Pinch-off stage:Wmquickly decreases until the neck breaks up to form the tail of the previous bubbleand the tip of the next bubble.Compared to the squeezing stage,the duration of the pinch-off stage is quite short, only about 2.5 forQC= 60 ml·h-1and 13.5 ms forQC= 20 ml·h-1.Obviously, the squeezing stage is a vital period for bubble formation, here it would be primarily analyzed.

From Fig.5, the increase of the particle concentration would lead to the reduction of squeezing stage, and the declining rateof the dimensionless minimum neck width(Wm/W)of bubble with time would be speeded up.Additionally, the dimensionless minimum neck width (Wm/W) of bubble nonlinearly thins with time in the squeezing stage, and the relation betweenWm/Wand dimensionless time ((t-tf)/T) satisfies the scaling-law [29].

Fig.5. Evolution of dimensionless minimum width of bubble neck with time(QG=180 ml·h-1).□:φ=0%;○:φ=1%;Δ:φ=2%.Solid symbols for QC=20 ml·h-1,hollow symbols for QC = 60 ml·h-1.Thin lines are transition lines from filling stage to squeezing stage,thick lines are transition lines from squeezing stage to pinch-off stage: ——, transition lines for QC = 20 ml·h-1; -·-·-, transition lines for QC = 60 ml·h-1.

wheretfis the duration of filling stage,Tis capillary time (= (ρW3/σ)0.5),α is the fitting parameter and changes from 0.687 to 0.910 in this experiment.Fuet al.[30]also found the minimum neck width of bubble presents a power law relationship with the remaining time for the squeezing stage of formation process in shear thinning fluid in microfluidic flow-focusing devices, and the exponent α = 0.16 ± 0.07, which is different from the values obtained in this work.It could be attributed to the differences of channel structure and rheology of continuous phase.Duet al.[31]found that the change of the neck width of Newtonian droplet formation with the remaining time conformed to the power law for squeezing stage in a flow focusing device, and the exponent α increased with the flow rate and viscosity of continuous phase.Additionally,the squeezing stage of bubble breakup in a T-junction microchannel,the dimensionless minimum neck width also exhibits a power-law relationship with dimensionless time, and the exponent α varies with flow rate and rheological property of continuous phase [32,33].These results indicate that the influence of rheological property of continuous phase on the power-law exponent of squeezing stage is noteworthy for formation and breakup of bubble or droplet in microchannel.

It can be seen from Fig.6 that the exponent α increases with the rise of continuous phase flow rate.In squeezing stage, the bubble head completely fills the main channel,the flow of the continuous phase is hindered due to the restriction of the microchannel,which would lead to the large liquid volume pressure and squeezing force in the upstream microchannel in a short time.Although the interfacial tension inhibits the reduction of the neck, the squeezing force of the continuous phase is much greater than interfacial tension.Simultaneously, the viscous shear force is also much smaller than squeezing force [19].Therefore, the squeezing force is the main force to drive the deformation of bubble neck.With the increase of the continuous phase flow rate, the squeezing force increases rapidly to speed up the thinning of the bubble neck,resulting in the increase of α.

Fig.6. Effects of flow rate and particle concentration on the squeezing stage.

Fig.6 also shows the effect of particle concentration on the coefficient α.It can be seen that α increases with increasing particle concentration due to the increscent squeeze of continuous phase on bubble neck, indicating that the breakup process of bubbles is accelerated.Tanget al.[22]simulated the bubble formation in the slurry system, and found that the pressure accumulation from the upstream on the neck in the slurry system was greater than that in pure solution, leading to a quicker rupture of bubbles.Our experimental results are consistent with their research results.

Under the restriction of the microchannel wall, a part of the fluid flows into the downstream channel through the corners between the bubble and the square channel, that is the leakage flow (QB).The leakage flow could be calculated according to the method of Yaoet al.[34].Thus the body flow of continuous phase(QN=QC-QB) could be obtained through the leakage flow.In order to analyze the influence of particle concentration on bubble formation dynamics,the body flowQNand leakage flowQBof slurry were calculated and compared with that of the water in microchannel(Fig.7).

It could be seen from Fig.7 that for a given slurry flow rate,the leakage flow rate decreases with the increase of particle concentration,accordingly,the body flow increases with the particle concentration.Based on the pressure balance proposed by Korczyket al.[21],the body flow and leakage flow could be regarded as a parallel pipeline, thus their pressure drops are equal [21]:

whereKtandKmare curvature of the quasi-static interfaces for bubble tip and neck, respectively.RB=aμlB/A2B,RG=bμGlB/A2N,aandbare constants depending on the channel structure,μ and μGare the viscosities of the continuous phase and the gas phase,lBis the flow distance of the leakage flow,ABis the cross-sectional area of the leakage flow, andANis the bubble cross section [21].Since the viscosity of gas phase is much smaller than that of the continuous phase, and the cross-sectional area of the bubble is much larger than the cross-sectional area of the leakage flow.Consequently,theRG(QG+QN) is much smaller than the viscous pressure drop of the leakage flowRBQB/4.Therefore, Eq.(4) could be simplified as:

The evolution of the bubble tip depends mainly on the gas phase flow rate [19], thuslBonly relates to development time and gas phase flow rate.In addition, the difference of bubble cross-sectional areas between the water and slurry is negligible,and the viscosity of continuous phase increases with the rise of particle concentration(Fig.2).Therefore,RBincreases with the rise of particle concentration,and then the leakage flow rate decreases and the body flow of continuous phase(QN=QC-QB)enlarges with the increase of particle concentration.Accordingly, the squeezing force of body flow on bubble neck strengthens,resulting in the larger thinning rate of the bubble neck width and the shorter duration of squeezing stage.Consequently, the α increases with particle concentration in slurry.Through the above analysis, we have clarified that the addition of solid particles could cause the decrease in leakage flow and the increase of body flow.Accordingly, the driving force of continuous phase on neck deformation increases with the particle concentration, which ultimately leads to the increase of the bubble neck thinning rate.In addition, the gas-liquid interface can be regarded as an elastic interface.In the slurry,the large number of solid particles could continuously collide with the bubble neck, which would accelerate the deformation of the bubble neck, accordingly shorten the formation period of bubble with the increase of particle concentration in slurry.

3.2.Formation size of bubble

Fig.8 shows the variation of bubble size with slurry particle concentration φ for the continuous phase flow rate of 20, 40, 60,80, 100 ml·h-1.For constant gas and continuous phase flow rates,the bubble size decreases as the particle concentration increases.The similar results were also found by Tanget al.[22].The increase in particle concentration would lead to the reduction of the squeezing stage, thus, the formation time of bubbles is shortened and the bubble size decreases.For the slurry with a given particle concentration,the bubble size increases linearly with gas flow rate.

Fig.9 shows the evolution of bubble tip lengthlwith time atQC=60 ml·h-1.It could be seen that the gas flow rate has a significant influence on the variation tendency of bubble tiplwith time,while the particle concentration has a little influence on the development of the bubble tip.As the particle concentration increases,the bubble formation time decreases.Moreover, it could also be found that the growing rate of the bubble tip relies mainly on the gas phase flow rate.The bubble length could be obtained by integrating the bubble tip development rate over time.The increase of gas flow rate could accelerate the expansion of bubble tip and accordingly increase bubble formation size, although the bubble formation time has slight decline in this case.

Fig.7. Variations of leakage flow QB and body flow QN with continuous flow rate and particle concentration: (a) leakage flow, (b) body flow.

Fig.8. Variations of bubble dimensionless length with gas flow rate and particle concentration:(a)QC=20 ml·h-1,(b)QC=40 ml·h-1,(c)QC=60 ml·h-1,(d)QC=80 ml·h-1,(e)QC = 100 ml·h-1.

Fig.10 shows the effect of continuous phase flow rate on bubble size.It can be seen that with the increase of the continuous phase flow rate, the bubble size in slurry with different particle concentrations reduces, which is similar to bubble generation in the gas-liquid two-phase flow [19].

Moreover,the effect of the particle concentration on the bubble formation size declines with the increase of the continuous phase flow rate (Fig.10), which could be explained through the body flow.The difference of body flow rate between the slurry and aqueous solution could be expressed by:

where the subscript 0 represents the water system, the subscript S represents the slurry system.Fig.7 shows thatQB0/QC-QBS/QCdecreases while 1-QB0/QCincreases with rising theQC.Consequently, it could be obtained thatQNS/QN0decreases with the increase of the continuous phase flow rate until near 1.This means that when theQCincreases, theQNSof slurry would gradually tend to theQN0of aqueous solution.Therefore, the difference of the squeezing stage in the slurries with different particle concentrations reduces with increasing the flow rate of the continuous phase, and the effect of particle concentration on bubble size weakens.

Fig.9. Evolution of bubble tip with time(QC=60 ml·h-1).□:φ=0%;○:φ=1%;Δ:φ = 2%.+ center symbols for QG = 140 ml·h-1, hollow symbols for QG = 180 ml·h-1,solid symbols for QG = 260 ml·h-1.

Fig.10. Effect of continuous phase flow rate on dimensionless length of the bubble(QG = 180 ml·h-1).

3.3.Prediction of bubble size

The bubble size could be considered to be composed of two parts:

whereLfillis the developed length of bubble in the filling stage,andLneckis the developed length of bubble in the squeezing and pinchoff stage.Based on this assumption,Garsteckiet al.[19]investigated the relationship between the size of the generated bubble and the two-phase flow rate ratio in microfluidic T-junction, and proposed a prediction correlation:

where α is a constant relying on the channel structure.

van Steijnet al.[20]studied the formation size of bubble and found that contribution of filling stage to bubble size is larger than 1, and accordingly proposed a prediction equation:

where α1and α2are constants depending on the channel structure.α1represents the bubble developed length in the filling stage, and α2QG/QCis the bubble developed length in the squeezing and pinch-off stages.The deviations between experimental data in this work and calculated values by Eqs.(9)and(10)are±47%and±30%.The large deviation may be attributed to that the influence of particle on bubble formation is not considered.Although the filling stage is insensitive to the variation of particle mass concentration (φ) of slurry, the squeezing stage becomes shortened with the increase of particle concentration.Therefore, the second term in the right of Eq.(10) should be modified for slurry system.Based on the results of bubble formation in non-Newtonian fluid [30], the influence of particle concentration on bubble size could be considered by body flow of continuous phase.As theQNis the main contribution to the deformation of the neck in squeezing stage and could be remarkably affected by the particle concentration, thus the introduction of a correction factor to reflect the influence of particle concentration onQNin squeezing stage is necessary.Considering the linear relation of φ toQB/QC(Fig.7),QNS/QN0∝(A+Bφ) could be obtained from Eq.(7), and then the developed length of bubble in squeezing and pinch-off stages could be rewritten into α2QG/[(1 + α3φ)QC]for the bubble formation process in slurry.Consequently, the formation size of bubble in slurry for T-shape microchannel could be calculated by following equation:

where α1,α2and α3are fitting parameters.The prediction correlation of bubble formation size in slurry was attained by fitting experimental data:

The meanings of α1and α2in Eq.(11) are the same to those in Eq.(10).The influence of the rheological properties of the slurry onQNis taken into consideration by introducing the parameter α3.The comparison between the predicted values of the bubble size by Eq.(12) and the experimental values is shown in Fig.11.The maximum deviation is 12.6% and the average deviation is 3.7%, indicating that the present correlation has good predicting performance.

Fig.11. Comparison of predicted value of bubble formation size with experimental data.

Generally, the slurry has shear-thinning and shear-thickening characteristic [35].In this experiment, the shear rate is low,accordingly,the slurry shows only shear-thinning property.Hence,Eq.(12) is applicable to predict bubble size in T-shape microchannel for the shear-thinning slurry.

4.Conclusions

The bubble formation process for slurry system in microfluidic T-junction was investigated.The bubble formation process could be divided into three stages: filling, squeezing and pinch-off.Experimental results showed that slurry concentration has a obvious effect on the formation process of bubbles and the influence was mainly reflected in the squeezing stage.When the particle concentration increases,the body flow rate increases,the duration of the squeezing stage decreases and accordingly the formation size of the bubble decreases.As the flow rate of the continuous phase increases,the influence of the particle concentration on bubble size tends to become weakened.The bubble formation size in slurry increases with the increase of the gas flow rate and decrease of the continuous phase flow rate.For the slurry system, a parameter was introduced to characterize the influence of particle concentration on the body flow, and a new prediction correlation of bubble formation size in T-shape microchannel was proposed.Nevertheless,this study is primarily focused on the bubble formation in slurry system with different particle concentration.In the future, more slurry system with different particle diameter and surface properties should be considered.

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 National Natural Science Foundation of China (21978197 and 21776200).

Nomenclature

ABcross-sectional area of the leakage flow, m2

ANcross-sectional area of the body flow, m2

Kconsistency coefficient, Pa·sn

Kmcurvature of bubble neck, m-1

Ktcurvature of bubble tip, m-1

Lbubble length, m

Lfilldeveloped length of bubble in the filling stage, m

Lneckdeveloped length of bubble in the squeezing and pinch-off stage, m

lbubble tip development length, m

lBlength of leakage flow, m

nflow index

QBleakage flow rate, m3·s-1

QCcontinuous phase flow rate, m3·s-1

QGgas phase flow rate, m3·s-1

QNmain flow rate of continuous phase, m3·s-1

RBhydrodynamic resistance of leakage flow

RGhydrodynamic resistance of inside bubble

Tcapillary time,T=(ρW3/σ)0.5

ttime, s

tfduring time of the filling stage, s

Wwidth of the microchannel, m

Wmminimum width of bubble neck, m

α power-law index

γ effective shear rate, s-1

σ interfacial tension, N·m-1

μ viscosity, Pa·s

φ mass concentration of particle in slurry

Subscripts

0 water

S slurry