Numerical and experimental investigations of liquid mixing in two-stage micro-impinging stream reactors☆

Tianyu Guo ,Bin Ruan ,Zhiwei Liu ,Muhammad Ali Jamal,Lixiong Wen ,2,*,Jianfeng Chen ,2

1 State Key Laboratory of Organic-Inorganic Composites,Beijing University of Chemical Technology,Beijing 100029,China

2 Research Center of the Ministry of Education for High Gravity Engineering and Technology,Beijing University of Chemical Technology,Beijing 100029,China

1.Introduction

Uniform and stable element distributions are essential for guaranteeing the product quality and stability for reacting systems with more than two reacting components.To achieve that,quick micromixing among the different reacting components is the key during continuous or repeated production processes,especially for fast reactions such as the precipitation of nanoparticles[1].However,it is difficult to achieve a rapid micromixing in traditional stirred reactors due to their poor mixing and mass transfer performance[2].Many novel reactors,such as T-type microchannel reactor[3],rotating packed bed reactor[4],microporous tube-in-tube microchannel reactor[5],and con fined impinging jets reactors(CIJR)[6],for intensifying the micromixing performance have then been designed.All these reactors can achieve rapid and homogeneous micromixing,but most of these intensifying equipments can only operate with two input flow streams.Therefore,a pre-mixing step for some components before entering the reactor will be required if the reacting systems are composed of more than two components.However,the pre-mixing step is often conducted in a stirred tank,which has the slow micromixing problemand may still lead to an uneven element distribution of the products.In addition,this separate pre-mixing step introduces extra labor-intensive and time consuming operations to the production processes.If the pre-mixing also utilizes a micromixing intensifying device and can be integrated with the reactor,both the poor micromixing problem and the breakage of continuous operation for multi-component reactions by the separate stirring pre-mixing step will be solved.Forthese purposes,the continuous microchannel reactors and capillary-reactors own distinct advantages due to their capabilities of constructing multi-stage structures,which integrate the mixing-intensifying step and reaction step together,and have drawn a lot of attention[7–9].Ishizakaet al.employed a multistage flow microchannel reactor to synthesize gold nanoparticles,in which the particle size and morphology could be successfully controlled by tuning the feed rate of NaOH solution[10].A single step gold nanoparticles synthesis and deposition on the graphene oxide carriersurface using chip-based micro fluidic reactor was reported for the first time by Wojnicki[11].Other researchers also used similar continuous microchannel reactors to prepare various inorganic nanoparticle materials[7,12,13].However,such multi-stage flow microchannel reactors are easy to have severe blocking problems during the precipitation process due to the tiny channels inside the reactors,which allows only a small working throughout(usually in the range of 0.01–10 ml·min−1[7,8,11,14–21])and limited production capacities as a consequence.

In this work,a continuous two-stage micro-impinging stream reactor(TS-MISR)was built to integrate the pre-mixing step and reaction step together for reactions involved three components,based on our previous studies on MISR[19].The first-stage of TS-MISR was consisted of one commercial T-junction and three steel micro-capillaries,which is the same as a traditional T-type microchannel reactor.For a three component precipitation reaction that needs a precipitant to initiate the reaction,the first-stage structure can act as an intensified micromixer for the two components other than the precipitant,which will not react with each other without the precipitant;hence no blocking at the outlet channel of the first-stage will happen.The outlet channel of the first-stage is then connected with another steel microcapillary by the second T-junction but without assembling the outlet tube(or assembling with a big-sized pipe at the outlet to lead the reacted mixture into a container for the subsequent treatment),forming the MISR reactor as the second-stage structure.Therefore,it eases pressure within the second T-junction to let the two input liquid streams impinge on each other directly to create a high energy dissipation region for intensified micromixing.Such structure design can not only achieve uniform element distributions for higher product quality in reacting systems with multiple components due to its intensified micromixing performance,but also significantly reduce the blocking problem in the outlet channel of the second-stage caused by the precipitated particles and hence increase the working throughout dramatically to ＞100 ml·min−1from the 0.01–10 ml·min−1range of other multistage microreactors with the same tube size.The integrated TS-MISR reactors also have the advantage of easy manufacture and can be readily operated in continuous mode for multiple-component reactions without other separate premixing steps.It can also be applied to reacting systems with more than three components by adding more-stage structure.

Although the flow behaviors and micromixing of the two stages,i.e.,the first-stage T-junction mixer and the second-stage MISR reactor,have been explored separately,the interactions between them are not clear and need further investigations.In this study,the micromixing efficiency of TS-MISR was then studied experimentally by the Villermaux-Dushman method based on the iodide–iodate reaction system[22–24],as well as by computational fluid dynamics(CFD)method focusing on the first-stage pre-mixing behavior for optimizing the operating conditions and physicalstructure ofthe reactor.The effects of both operating parameters and reactor configurations,such as jet Reynolds number(Rej),volumetric flow ratio(R),the first-stage junction angle(φ),the connecting capillary length(Lc)and connecting capillary diameter(dc)on micromixing efficiency were investigated and optimized.All the computational work was carried out by using the commercially available software ANSYS FLUENT 13.0.

2.Experimental

2.1.Materials

Materials used for the iodate–iodide reactions are listed in Table 1 and were prepared according to the provided initial concentrations.Injecting stream A(inlet 1)was deionized water and stream B(inlet 2)was diluted sulfuric acid solution.Injecting stream C(inlet 3)was the iodide,iodate and borate ion solution.To prepare injecting stream C,KI and KIO3powders were firstly dissolved in deionized water to form a KI/KIO3solution;H3BO3and NaOH solution was then prepared as a buffer solution;and finally the KI/KIO3solution was added into the buffer solution.This sequence of mixing operation must be carefully followed so that iodide and iodate ions can coexist in a basic solution,which prevents thermodynamic iodine formation[22].

2.2.Parallel competing reaction system

One of the widely used methods to characterize micromixing in chemical reactors is the Villermaux-Dushman parallel competing reaction system.However,there are still some doubts about the unclear kinetics of the Dushman reaction[25,26].Kölblet al.proposed that the choice of the acid or the dissociation constant of sulfuric acid has to be considered for a quantitative estimation from the experimental product distribution of measures such as mixing times[27].While Commenge and Falk claimed that the use of various acid would not cause big difference even in quantitative investigations[28].Nevertheless,the iodide–iodate reaction system with the following classic kinetics is still a popular reaction scheme to investigate the micromixing of different mixers or the effect of process conditions on micromixing qualitatively.

The Villermaux–Dushman parallel competing reaction system is given in the following scheme[24].

Table 1Reagents used in the experiments and their initial concentrations

In this reaction system,Reactions(1)and(2)are competing for H+.In a perfectly quick micromixing condition,H+will be instantaneously and completely consumed by H2BO3−according to Reaction(1)and thus no I2will be generated.In other cases,I2will be formed by I−with a local excess of acid resulted from imperfect micromixing,and further react with I−to form I3−according to Reactions(2)and(3).In order to quantify the micromixing performance,a segregation indexXSis defined as follows

The value ofXSis within the range of 0＜XS＜1 for partial segregation.XS=0 is for perfectly quick micromixing andXS=1 for total segregation[23].

2.3.Experimental procedures

The experimental setup of TS-MISR was shown in Fig.1.The two streams A and B were injected through inlets 1 and 2,respectively,by high precision piston pumps(Beijing Satellite Manufacture Factory,2PB8008)and collided into the first-stage T-junction (Beijing Xiongchuan Technology Co.Ltd.,SS-1UTF),which got further mixed with each other in the connecting capillary between the two T-junctions.The mixture then impinged severely and reacted with stream C,which was driven from inlet 3 by a high precision piston pump(Beijing Satellite Manufacture Factory,2 PB20005),in the second-stage MISR reactor.The product was collected at the T-junction outlet and analyzed by a spectrophotometer(Shimadzu,UV-2550)at 353 nm[31]for the calculation ofXS.Both the first-stage volumetric flow ratior(VA/VB)and second-stage volumetric flow ratioR(VC/(VA+VB))were mainly kept as 1,with varying volumetric flow rate ofVCwithin the range of 10–140 mL/min,which corresponded to a liquid flow velocityucin MISR(the second-stage)ranged from 0.59 to 8.25 m·s−1when the inner inlet diameter(di)of TS-MISR was 0.6 mm.

Fig.1.Photograph of TS-MISR:(1)the first-stage T-junction;(2)the second-stage T-junction;(3)precision piston pumps.

3.CFD Model

3.1.Momentum transport

For simplification,the compressibility of fluid is usually neglected and the liquid phase is considered to be incompressible by CFD studies,and fine agreement between numerical calculations and experimental data has been reported[32,33].Therefore,an incompressible model was applied in the study.The governing equation for continuity and momentum in the computational domain can be expressed as follows,

Continuity equation

z-Momentum equation

In the above equations,ρ is the fluid density,uis the velocity vector,μ is the dynamic viscosity,pis pressure;u,ν andware the velocity component in thex,yandzdirections,respectively;Su,SνandSware the generalized source terms of momentum conservation equation.The standardk-ε model has been widely used and validated for high Reynold number flow and showed better stability compared with the realizablek-ε model and RNGk-ε model.In addition,the model parameters in the standardk-ε model are a compromise to give the best performance for a wide range of different flows[34].Previous studies[32,33]of a con fined impinging jet reactor(CIJR)demonstrated that the standardk-ε model works satisfactorily whenRej≥ 200.The standardk-ε model was also applied in our previous work in simulating the liquid flow in MISR withinRejrange of 395–3161 and the simulations agreed well with experiments[19].Therefore,this model was applied in this work as well.The jet Reynolds number(Rej)was defined as follows:

whereujis the fluid velocity,ρ is the fluid density,μ is the dynamic viscosity,lis the length of the object that the flow is going through or around.

The standardk-ε model introduces two additional transport equations and two dependent variables,the turbulent kinetic energy(k)and the dissipation rate of turbulence energy(ε),which can be expressed as follows[35,36]

whereGkis the generated term of the turbulent kinetic energy due to the mean velocity gradient and the values ofC1ε,C2ε,are constants.σkand σεare the turbulent Prandtl numbers forkand ε,respectively[36].

The near wall region where the flow turns from turbulence to laminar needs a special treatment.Here the Enhanced Wall Treatment(EWT)model was used to solve the flow field down to the wall(with appropriate grid),by assuming linear velocity pro files in the laminar layer and solving one equation model of Wolfstein[37]for the transitional region[38].EWT is a near-wall modeling method combining a two-layer model with enhanced wall functions.Previous studies have con firmed that using the Standardk-ε model coupled with EWT is an appropriate approach to simulate the near wall effect[19,33].

3.2.Mass transport

The mass transport of the various species in Villermaux-Dushman reactions is governed by the convection-diffusion equation[36,39]

whereYiis the local mass fraction of speciesi,Jiis the diffusion flux of speciesi,which is generated due to concentration gradients,andRiis the net rate of production of speciesiby chemical reactions.

Compared with previous simulation on T-junction reactors[19],in which the Discrete Quadrature Method of Moments(DQNOM)with the interaction-by-exchange-with-the-mean(IEM)model was usually applied to simulate the liquid chemical reactions,the Finite-rate/Eddy dissipation model was chosen to calculate the reactions in this simulation on two-stage MISR with three inlets.The Finite-rate/Eddy-dissipation model is a turbulence-chemistry interaction model,which computes both the Arrhenius rate based on the Finite-rate model and the turbulent mixing rate based on the Eddy-dissipation model and takes the smaller as the net reaction rate.In the Finite-rate model,the net rate of creation/destruction of speciesiin reactionr,Ri,r,is given by[36,40]

The Eddy-dissipation model is proposed by Magnussen and Hjertager[41],in whichRi,ris given by the expression as below[36]

whereMw,i,YRandAdenote the molecular weight for speciesi,the mass fraction of a particular reactant and an empirical constant,respectively.Finally,the net rate of speciesi(Ri)is calculated as the sum over all the reactions the species participated in

3.3.Intensity of mixing,IM

whereNis the number of sampling points at the cross section;ciis the concentration fraction at sampling pointiandcmis the mean value of concentration fraction.The value ofIMis within the range of 0–1,with 0 for the case of a complete segregated system and 1 for perfect mixing state.

3.4.Physical model and calculation procedure

Fig.2.The physical model and geometric parameters of TS-MISR:(a)the overall model of TS-MISR;(b)the internal structure of the first-stage pre-mixer on the symmetrical plane of z direction;(c)the internal structure of the second-stage MISRon the symmetrical plane of y direction.(d i=0.6 mm;d c=0.6 mm;d o=3.6 mm;D=1.2 mm;D o=1.6 mm;H=2.2 mm).

The size of the physical model and the material compositions in the simulations were the same as the experimental ones.Fig.2a illustrated the overall structure of TS-MISR,which contained three inlet capillaries,one connecting capillary and two T-junctions.The detailed configurations of the first-stage pre-mixer and the second-stage MISR were shown in Fig.2b and c,respectively.

The CFD simulations assumed the single-phase flow of an incompressible fluid in TS-MISR having constant physical properties and negligible gravity effects.Streams A,B and C were mainly composed of water;therefore,these streams were simply assumed to have the physical properties of water with a viscosity of 1.0 mPa·s.The inlets of the three solutions were set to velocity-inlet,and the fluid outlet was set to out flow.The Standardk-ε equations coupled with EWT were applied to simulate the complex turbulent flow in the three-dimensional model,and the turbulence–chemistry interaction equations with the Finite-rate/Eddy-dissipation model were employed for the volumetric reactions,which were given in details as above.Pressure–velocity coupling was solved by SIMPLE(Semi Implicit Pressure Linked Equation)viaa relationship between velocity and pressure corrections to enforce mass conservation and to obtain the pressure field.The PRESTO!scheme was used for pressure discretization,and the Second Order Upwind discretization scheme was applied for the other equations.The under-relaxation factors of the solution controls were kept as the default values of the parameter settings.The 10−6absolute convergence criterion was chosen for all the equations.In addition,a monitoring surface at the outlet was set to observe the changes of the triiodide concentration.The numerical simulations would not terminate until the triiodide concentration reached steady.Mesh independence explorations were conducted by applying different number of cells(0.60,0.81,1.03 and 1.25 millions),and the simulation results of various species concentration within the reactor andXSwere compared in each case.Results showed that a mixture of hexahedron and quadrilateral mesh consisting 1.03 million computational cells was precise enough to resolve the flow field and micromixing process,and was eventually applied in this study.Mesh refining was used in the near wall areas by using the in flation method.All simulations were carried on a computer with Intel Core i5 760 CPU(2.80 GHz and 2.79 GHz)and 8 GB of RAM.

4.Results and Discussion

4.1.Flow patterns inside TS-MISR

The flow patterns within TS-MISR were firstly investigated by CFD simulation,which are very difficult to be obtained by conventional experimental method.Fig.3 shows the contours of molar concentration of H+atRej3=3520(the jet Reynolds number of capillary inlet 3).The concentrations of H+in streams A and B were 0 and 0.10 mol·L−1,respectively,and the compositions of stream C were described in the section of“Materials”and Table 1.Fig.3 also shows the concentration distributions of H+at three cross-sections of the connecting capillary,i.e.,at the outlet of the first-stage T-junction,the middle of the connecting capillary and the inlet of the second-stage T-junction.It demonstrated that the mixing between streams A and B was getting enhanced along with the path of connecting capillary and reached uniformity before arriving at the inlet of the second-stage T-junction.The uniformly mixed stream A and B then impinged with stream C in the second-stage T-junction and initiated the reaction as well.The pre-mixing efficiency within the connecting capillary can be characterized byIMat the cross-sections and can be applied to optimize the structure of the first-stage pre-mixer.As displayed in Fig.3,H+distribution became uniform when reaching the second-stage MISR,indicating the first-stage pre-mixer can satisfy the continuous pre-mixing requirement for multi-components reacting systems.

Fig.4a–d displays the contours of molar concentrations of various species in the second-stage T-junction for the symmetrical plane in z direction.If the micromixing was perfect,H+(Fig.4a)would be completely neutralized by H2BO−3(Fig.4b)to form H3BO3according to Reaction(1).In imperfect micromixing condition,local excess of H+would be achieved after complete consumption of the local H2BO−3,which would be turned into I2(Fig.4d)by Reaction(2)and further reacted with I−(Fig.4c)to form I3−by Reaction(3).Therefore,the concentration contours can reveal important information on the micromixing behaviors within the second-stage MISR of TS-MISR.As shown in Fig.4,H+was consumed completely in a very short time and concentrations of H2BO3−,I−and I2became almost uniform when reaching the outlet.In addition,the tiny amount of the produced I2and the almost undetectable I3−suggested that H+was mostly consumed by Reaction(1),indicating a quick micromixing was achieved within the second-stage MISR.

Fig.3.Contours of molar concentration of H+(kmol·m−3)([H+]A0=0 mol·L−1,[H+]B0=0.10 mol·L−1,r=1,R=1,Re j3=3520).

Fig.4.Contours of molar concentration of various species in the second-stage T-junction of the symmetrical plane in z direction(kmol·m−3)([H+]A0=0 mol·L−1,[H+]B0=0.10 mol·L−1,r=1,R=1,Re j3=3520):(a)H+,(b)H2BO3−,(c)I−,(d)I2.

4.2.Effects of inlet jet Reynolds number on micromixing

Fig.5 displays the effects of inlet jet Reynolds number onXSof the second-stage MISR of TS-MISR.Both experimental and numerical methods indicates thatXSdecreased quickly asRej3increased at low level,but approached constant whenRej3was above 2000,indicating that the micromixing efficiency got intensified with rising liquid flow velocity.The enhanced micromixing efficiency was due to the intensified dissipation rate of the turbulent kinetic energy within the MISR chamber with increasingRej3,which provided the driving force for micromixing.Fig.5 also shows that the match between CFD simulations and experimental results was very well at the highRej3range but the divergence became noticeable at the lowRej3range,probably due to the deviation introduced in both experiments and simulations.When the flow rate was very small,the fluctuation of the fluid streams coming out the pumps became remarkable and the micromixing performance might be affected by the sampling process.On the other hand,the usage of turbulence model in simulation within the wholeRej3range might also lead to bigger errors because the turbulent intensity could only be roughly predicted by the standardk-ε model at low jet Reynolds numbers[43].However,the overall tendency of CFD predictions agreed well with the experimental results for the whole range ofRej3,demonstrating the applicability of the CFD models used in this work.

Fig.5.Effects of Re j3 on X S([H+]A0=0 mol·L−1,[H+]B0=0.10 mol·L−1,r=1,R=1).

4.3.Effects of the second-stage volumetric fl ow ratio R on micromixing

The effects of second-stage volumetric flow ratioR(R=1,2,3 and 4,respectively)on micromixing were investigated by both experiments and simulations,on the premise that the first-stage volumetric flow ratiorwas 1,as shown in Figs.5 and 6.The volumetric flow rate of stream C(VC)was changed from 40 to 140 ml·min−1,corresponding toRej3ranged from 1408 to 4928.The values ofVAandVBwere then adjusted according to the studyingR.In order to eliminate the influence of possible non-uniform concentration distribution of the liquid mixture coming from the first-stagemixer at differentR,which was actually very unlikely to occur as shown in Fig.3,streams A and B were both composed of diluted sulfuric acid solution with the same H+concentration,e.g.,both H+concentrations were set to 0.05 mol·L−1atR=1.In addition,the concentration of H+was adjusted to keepNC/(NA+NB)=VCCC0/(VACA0+VBCB0)=constant according to the selectedR,for ensuring the same component content at the impinging plane in the chamber of second-stage T-junction.

As illustrated in Figs.5 and 6,Xsincreased with increasingRwhenR≥1,and the numerical prediction agreed well with the experimental results.This trend was similar with that of single-stage MISR,which was reported previously[19].WhenRwas greater than 1,the mixture stream of A and B coming from the first-stage mixer with less volume but higher H+concentration would be more difficult to be dispersed uniformly into stream C;therefore,a longer time to achieve homogeneous micromixing between them would be needed.In addition,lagerRintroduced bigger momentum imbalance between the two impinging streams and the macromixing might then play a bigger role at that time.

Fig.6.Effects of the second-stage volumetric flow ratio R on X S([H+]A0=0.10 mol·L−1,[H+]B0=0.10 mol·L−1,r=1,R=2;[H+]A0=0.15 mol·L−1,[H+]B0=0.15 mol·L−1,r=1,R=3;[H+]A0=0.20 mol·L−1,[H+]B0=0.20 mol·L−1,r=1,R=4).

4.4.Effects of fi rst-stage junction angle on micromixing

Fig.7.Contour of molar concentration(kmol·m−3)of H+at different first-stage junction angles([H+]A0=0.00 mol·L−1,[H+]B0=0.10 mol·L−1,r=1,R=1,Re j1=2464):(a)90°,(b)120°,(c)150°,(d)180°,(e)210°,(f)240°.

The pre-mixing performance of TS-MISR for different first-stage junction angles φ from 90°to 240°was numerically investigated to find out the optimum junction angle for micromixing,by calculatingIMat the middle position of the connecting capillary.Fig.7 illustrates the contour of molar concentration of H+at different first-stage junction angles and it demonstrated clearly that it took the shortest path for the mixture of streams A and B to achieve homogeneous mixing when φ =180°.The effect of first-stage junction angle onIMat the middle cross-section of the connecting capillary between the two junctions is displayed in Fig.8.It also shows thatIMwas affected noticeably by φ andIMreached the maximum at φ =180°,which corresponded to the best pre-mixing performance.Therefore,the first-stage junction angle of TS-MISR would be fixed at 180°in the following work.

Fig.8.Effects of first-stage junction angle on I M at the middle cross-section of the connecting capillary([H+]A0=0.00 mol·L−1,[H+]B0=0.10 mol·L−1,r=1,R=1).

4.5.Effects of connecting capillary length Lc on micromixing

In order to investigate the effects of connecting capillary lengthLcbetween the two junctions onIM,a TS-MISR withLc=55.6 mm was simulated and theIMvalues of cross-sections at different positions within the connecting capillary were calculated,as shown in Fig.9.In addition,the effects of liquid viscosity onIMwere also investigated within 1.0–3.0 mPa·s.It was found thatIMincreased with increasingLcand/or decreasing viscosity.At higher viscosity,both the Reynolds number and the turbulence kinetic energy in the chamber of the first stage pre-mixer would be lowered,which required longer connecting capillary for achieving sufficient mixing between the two streams.However,further increasingLcwould increase the pressure drop within the connecting capillary as shown in Fig.10,indicating that more and unnecessary energy would be consumed;therefore,it is essential to optimize the connecting capillary length for achieving the desired mixing performance and energy saving.On the assumption ofIM=0.99 as desired complete mixing,optimum connecting capillary lengths of 32.5 mm,38.0 mm and 47.5 mm corresponding to different viscosities of 1.0 mPa·s,2.0 mPa·s and 3.0 mPa·s,respectively,were obtained forVA=70 mol·L−1andR=1.

Fig.9.Effects of connecting capillary length L c on I M at different viscosities([H+]A0=0.00 mol·L−1,[H+]B0=0.10 mol·L−1,r=1,R=1,V A=70 ml·min−1).

Fig.10.Pressure drop along connecting capillary L c at different viscosities([H+]A0=0.00 mol·L−1,[H+]B0=0.10 mol·L−1,r=1,R=1,V A=70 ml·min−1).

4.6.Effects of connecting capillary diameter dc on micromixing

Effects of connecting capillary diameter on the mixing performance between the two streams were numerically studied at four differentdcin the range of 0.6–1.2 mm.The contours of molar concentration of H+at a fixedRej1of 2464 are illustrated in Fig.11.The enhanced concentration maldistribution at biggerdcsuggested that the mixing efficiency was declining with increasingdc,which was also verified by the decreasingIMat the middle position of the connecting capillary,as shown in Fig.12.At the same inlet Reynolds number,largerdcwould significantly decrease the Reynolds number in the connecting capillary and hence decline the turbulent intensity,leading to weakened mixing performance of the first-stage pre-mixer.In addition,largerdcmight also increase the diffusion distance in the radial direction to reduce the mixing efficiency.

4.7.The micromixing time of TS-MISR

By using the incorporation model[23],the micromixing time of TS-MISR could be calculated with the obtainedXSdata,which is more straightforward in representing of reactor micromixing efficiency.In incorporation model,the mixing between the two fluids was simplified based on the following assumptions:stream A is dispersed into many separated parts and permeated by stream B;all mixing and reaction processes take place in numerous separated parts A.Therefore,the characteristics time of the surrounding between the two streams is regarded as the micromixing time.The calculation process can refer to previous reports[44].

Table 2 showed that the micromixing time of TS-MISR was in the range of 0.04–1 ms,which is similar as other microchannel reactors,but significantly lower than that of bigger-sized impinging stream reactors and stirred tank reactors,further con firmed the intensified micromixing of TS-MISR.

Fig.11.Contour of molar concentration(kmol·m−3)of H+with different connecting capillary diameter d c([H+]A0=0.00 mol·L−1,[H+]B0=0.10 mol·L−1,r=1,R=1,Re j1=2464).

5.Conclusions

An easily assembled two-stage micro-impinging stream reactor(TS-MISR)with the diameter of～1 mm was built with commercial parts.Both experiments and CFD simulations showed that the micromixing performance of the first-stage pre-mixer and the secondstage MISR reactorofTS-MISR were significantly affected by the operating conditions and structural configurations.The micromixing efficiency of the first-stage pre-mixer was greatly enhanced by increasing Reynolds number,which could be achieved by raising liquid flow velocity,and/or by reducing liquid viscosity and the diameter of the connecting capillary between the two junctions.The first-stage micromixing was also affected by the first-stage junction angle and 180°was found to be the optimal angle.Increasing the length of connecting capillary could not only enhance the micromixing performance in the first-stage pre-mixer but also raise the pressure drop;therefore,optimallength of connecting capillary should be applied to achieve both desired micromixing efficiency and energy saving.The micromixing performance in the second-stage MISR of TS-MISR was similar to our previously reported single-stage MISR reactor.It would be greatly strengthened by increasing jet Reynolds number and it was also affected dramatically by the volumetric flow ratio(R)and the most efficient micromixing was obtained atR=1.Compared with other devices,TS-MISR can achieve intensified micromixing among at least three reacting components in a continuous mode by adopting a first micro pre-mixing stage and a second micro-impinging stream reacting stage;therefore,uniform products and stable element distribution could be produced with the application of TS-MISR,especially for multi-component reacting systems.

Fig.12.Effects of connecting capillary diameter d c on I M at the middle cross-section([H+]A0=0.00 mol·L−1,[H+]B0=0.10 mol·L−1,r=1,R=1).

Table 2The micromixing time of different equipments

Nomenclature

Dinner chamber diameter of T-junction,mm

Doinner outlet diameter of T-junction,mm

dcinner diameter of connecting capillary between two T-junctions,mm

diinner inlet diameter of TS-MISR,mm

doinner outlet diameter of TS-MISR,mm

Hlength of T-junction,mm

IMthe intensity of mixing

Jidiffusion flux of speciesi

kturbulent kinetic energy

Lclength of connecting capillary between two T-junctions,mm

Liinlet length of TS-MISR,mm

Looutlet length of TS-MISR,mm

Mw,imolecular weight of speciesi

Nnumber of sampling points at the cross section

Rthe second volumetric flow ratio

RejReynolds number of inlet jet

Riamount of speciesiconsumed or produced by reactions

rthe first volumetric flow ratio

VAvolume flow rate of mixture A,ml·min−1

VBvolume flow rate of mixture B,ml·min−1

VCvolume flow rate of mixture C,ml·min−1

XSsegregation index

Yproduct yield in the iodide-iodate reaction

Yilocal mass fraction of speciesi

YSTthe value of Y in total segregation case

ΔPthe pressure drop along connecting capillaryLc

ε turbulent dissipation rate

μ dynamic viscosity,mPa·s

μtturbulent dynamic viscosity,mPa·s

ρ fluid density,kg·m−3

φ first-stage junction angle

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