Xin Wei,Hong Wang,Zhen Yin,Saood Qaseem,Jianxin Li*

1State Key Laboratory of Separation Membranes and Membrane Processes,Tianjin Polytechnic University,Tianjin 300387,China

2School of Materials Science and Engineering,Tianjin Polytechnic University,Tianjin 300387,China

3School of Environmental and Chemical Engineering,Tianjin Polytechnic University,Tianjin 300387,China

1.Introduction

The electrochemical technique as one green and sustainable chemical process has attracted much attention in organic synthesis and water treatment during recent years[1].In the electrochemical process,the“clear”electron can be used as oxidizing or reducing reagents without necessary addition of any chemical reagents[2,3].However,a low current efficiency(faradic efficiency)and high energy consumption in the electrochemical process remain a great challenge as a result of slow mass transfer on the surface of the electrode and weak cell conductivity[3].Hence,how to improve current efficiency and lower down the energy consumption of electrochemical reaction become the critical issues during the practical applications of electrochemical technique.

Currently,the porous or membrane electrode with high surface area has been designed and used in the electrochemical water treatment and oxidation of organic compounds so as to improve cell conductivity and mass trans fer on the surface of the electrode[4–9].Specifically,the porous membrane electrode as a carrier to immobilize nanoscale particle catalysts could realize the catalyst recovery,regeneration,and reuse in successive catalytic runs.For instance,a novel strategy of an electrocatalytic membrane reactor(ECMR)with self-cleaning function has been designed for in dustrial waste water purification[4].Anano-TiO2loading porous conductive carbon membrane functioned both as filter and anod etotreatoily waste water in an ECMR.TheTiO2/car bonmem brane generated micro flows and reactive intermediates that alleviated concentration polarization and decomposed organic foul ants into CO2and H2O or small biodegradable products on the membrane surface or in pores.The results showed that the removal rates of oil and chemical oxygen demand(COD)were up to 86 and 94%,respectively[4].Furthermore,a functional ECMR assembled with a nano-MnOx(22–25 nm)loading tubular titanium(Ti)membrane electrode with the porosity of 23.7%and the average pore size of 7.0 μm as anode and stainless steel as a cathode was designed and employed to efficiently produce STFP from TFP.92%conversion of TFP and over 99%selectivity to STFP were obtained under the optimum conditions[6].Under this circumstance,the current efficiency of ECMR was13.7%.Meanwhile,a reaction mechanism was proposed briefly as follows[6].The initial deprotonation of TFP occurs in a basic solution to form an alkoxy intermediate and promote the oxidation.During the ECMR operation,the electron/hole pair was generated to produce absorbed hydroxyl radicals on the electrified MnOx/Ti electrode.Then the absorbed hydroxyl radicals interacted with the oxygen of the MnOxlattice in the MnOx/Ti anode to generate a higher valent oxo-manganese species(MnIV=O).As a strong chemical oxidant,the higher valent oxo-manganese species reacted with the absorbed deprotonated TFP molecule to produce TFPA by redox reaction or electron transfer.The former was consumed and reduced to MnIII=O,which interacts continuously with the absorbed hydroxyl radicals to form MnIV=O.Then,TFPA reacted with the sodium hydroxide to form STFP.Similarly,Binet al.[7]reported that such ECMR was employed to yield gluconic acid(GA)and glucaric acid(GLA)from glucose under mild condition.The results indicated that 99%conversion of glucose and 99%total selectivity to GA and GLA were obtained.The excellent performance of the controllable oxidation of glucose is mainly attributed to the electrochemical oxidation and convection-enhanced mass transfer as well as the timely removal of the desired products in the reactor.

However,the membrane reactor performance depends on not only catalyst or reaction conditions but also reactor parameters including the length and diameter of membrane electrode,which would influence the flow distribution and reaction efficiency in essential[10–14].For example,Liet al.[11]found that the local flux close to the suction source of the submerged hollow fiber membrane module was the highest,whereas the local flux became the lowest far from the open ends of hollow fiber membrane module.It is ascribed to non-uniform distribution of trans membrane pressure(TMP)and hydrodynamics along the hollow fiber membrane.Tale bizadehet al.[12]reported that the reaction efficiency would increase with the extension of mean residence time in non-thermal plasma reactor for the nitrogen oxide removal.Equally,the non-uniform distribution of reactant flow rates across the porous catalyst layer and the tubular membrane in ECMR would lead to the non-uniform distribution of reaction residence time and further affect the reaction conversion,selectivity and efficiency.Thus one of the challenges is how to design and optimize the reactor so as to control flow distribution along the tubular ECMR.

Interestingly,CFD is a powerful numerical tool for predicting the effects of design features on hydrodynamics on a fundamental aspect.Wuet al.[15]investigated the effect of upstream flow distribution on the light-off performance of a catalytic converter using CFD simulation.They found that a good uniformity of fluid flow resulted in a high conversion and efficiency.Abejónet al.[16]reported that a CFD model was used to simulate tubular enzymatic membrane reactors under three different con figurations:dead-end,tangential flow with a porous enzymatic membrane and nonpermeable enzymatic wall for attaining optimal designs.According to their results,the tangential con figuration was more favorable to obtain the best conversions in permeate streams.Consequently,to better understand the effect of flow distribution on the conversion and efficiency of ECMR through the numerical simulation so as to realize the design and optimization of the reactor is of important significance for the practical applications of ECMR.

The objective of the present study is to develop a method of CFD simulation based on the porous media model to predict the hydrodynamic behavior and its effects on the ECMR performance.The experimental investigation of the tubular ECMR with different lengths and diameters for electro catalytic oxidation of TFP into STFP was carried out to con firm the simulation results.In the reactor,the MnOx/Ti membrane electrode as the anode and the stainless steel wire mesh as the cathode were connected by a DC power to constitute the ECMR.The reactor parameter optimization of ECMR would be explored.

2.Simulation Approach

The fluid modeled in ECMR flowed from feed tank to permeate into a tubular membrane as a porous medium through a peristaltic pump shown in Fig.S1 in supporting information.The mass and momentum inside ECMR are described by the Navier–Stoke equation with a source term for porous media in the momentum equation,as given below.

2.1.Continuity equation

The flow field was obtained by solving the continuity equation and the momentum balance equations of the system.The continuity equation is expressed by:

where ρ is the density(kg·m-3),tis time(s),uandvare velocity vectors onxandyaxes(m·s-1),respectively.

2.2.Momentum equations

wherepis the pressure per unit volume(Pa),is the velocity vector(m·s-1),μ is the viscosity(Pa·s),SuandSvare the source terms of momentum conservation.

2.3.Porous media model

The porous media model has already been used in a wide field to determine the pressure drop including flow through packed beds,perforated plates, flow distributors,and tube banks[17,18].

The flow resistance of fluid through porous media is modeled by means of a source termSiadded in the momentum equation[19].The source termSiis composed of two parts:a viscous loss term and an inertial loss term,as follows[17,20]:

whereSiis the sour ceterm for theith(xory)momentumequation,andDijandCijare matrices called viscous resistance factor and inertial resistance factor,respectively.

In the case of simple uniform porous media including the tubular porous Ti electrode in the ECMR system,the coefficient matricesDandCcan bespecified as diagonal matrices with1/α andC2as follows[17,21]:

whereαis the permeability andC2is the inertia resist ancefactor.The first term in Eq.(5)indicates that the pressure loss across the porous media is proportional to the permeate velocity,which comes from Darcy's law.It is dominant only when the fluid velocity is very low.When the average fluid velocity increases,the inertial term becomes significant and prevails on the previous one[18,19].The inertial loss term exhibits a quadratic dependence on the fluid velocity[22].

The momentum source terms can be also expressed as follows,on account of representing the pressure drop per unit length[17]:

where Δnis the thickness of the porous medium,a1anda2are the coefficients andQis the permeate flow rate.Hence,the viscous and inertial resistance coefficients can be defined from the experimental data between the pressure drop Δp(Pa)and the permeate flow rateQ(ml·min-1)in ECMR.

2.4.Simulation

Fig.1.Reactor sectional view with the boundary conditions(a)and2 Dmesh generation of ECMR system obtained from CFD(b).

All computer drawings and meshes were developed using Gambit(Version 2.3.16).Fluid models were analyzed in Fluent(Version 6.3)using 2000 iterations or until convergence was achieved,and graphical representations were prepared in Tec plot.The reactor sectional view with the boundary conditions is shown in Fig.1a.Here,r0andr3represent the inside diameter(ID)of the outlet pipeline and the feed tank,respectively;r1andr2are theIDand outside diameter(OD)of the tubular membrane,respectively.Moreover,Lmeans the length of ECMR.The boundary conditions at outlet and inlet were driven as pressure with target mass flowratecorres ponding to there action condition.The pressures at inlet and outlet were set as the atmospheric pressure(Patm)and the subatmospheric pressure(Patm-constant)obtained by the peristaltic pump,respectively.The constant could be described as the pressure drop at the outlet.The membrane zone was set as the porous media and all other boundary conditions were set as wall.For there as on of symmetrical membranereactor,a 2Dmeshwas generated after simplification in Gambit to optimize computational demand,as shown in Fig.1b.As a critical issue for accurate and successful CFD modeling,the mesh qualities were checked before the simulation,i.e.for ECMR with 70 mm length(Fig.2e),the mesh contained 35350 triangle cells.At the same time,its maximum cell squish(0 for best,1 for worst)equaled 0.2895,maximum cell skewness(0 for best,1 for worst)equaled 0.4944,and the quality percent(from 0 to 0.1)was 98.02%,which indicated a high mesh quality in the simulations.The cross flow velocity pro files(m·s-1)along the membrane were obtained from the modeling results.All cross flow velocities mentioned below represent the permeate velocity of the fluid across the membrane.

Fig.2.Cross flow velocity distributions along the membrane tube with different lengths in ECMR:(a)22 mm;(b)29 mm;(c)42.5 mm;(d)50 mm and(e)70 mm.

The ECMR modeling in fluent contained the following assumptions:

(1)The system is at a steady-state and isothermal.Moreover,the intermittent disturbance from the peristaltic pump is ignored in the actual experiment.

(2)The velocity profile along the tubular membrane is fully developed under the condition of a slow fluid flow and without turbulence.

(3)The fluid in ECMR is a viscous incompressible Newtonian fluid with constant fluid viscosity and density.

(4)The liquid level in feed tank is constant,due to the permeate flow rates are very low.

(5)The motion is considered rotational and symmetrical.Hence,only a two-dimensional plane through the rotation axes of symmetry is considered.

(6)There is no slip condition at the membrane surface.

(7)The membrane medium is assumed to be simple,uniform porous material.

(8)The tubular membrane(x,y)has radiusrand lengthLin the case of laminar cross- flow.

3.Experimental Section

Commercially available tubular porous Ti membrane with an average pore size of 7.0 μm and a porosity of 23.8%was purchased from Shanghai Yiming Filtration Technology Co.,Ltd.China.The nano-MnOxloading tubular porous Ti membrane electrode(MnOx/Ti electrode)was preparedviaa sol–gel approach,i.e.thermal decomposition of manganese(II)nitrate on the original tubular porous Ti electrode.The procedure was described briefly as follows[6]:(1)the porous electrode was first pretreated in 10 wt.%boiled oxalic acid solution for 1 h,then cleaned with deionized water and dried at room temperature;(2)the pretreated electrode was dipped into 50 wt.%Mn(NO3)2solution for 0.5 h,and dried at room temperature after removing the solution;(3)the treated electrode was placed in a muffle furnace to sinter at a designed temperature for 2 h,then cooled to room temperature naturally.

A schematic diagram of the ECMR system was shown in Fig.S1.The MnO2/Ti electrode was arranged in the center of the feed tank.The distance between the anode and cathode was 30 mm.In the reactor,the MnOx/Ti membrane electrode served as the anode and the stainless steel wire mesh surrounding the electrode as the cathode,which was connected by a DC power(Maynuo Electronics M8811)to constitute the ECMR.The reaction temperature of the ECMR system was controlled by thermostatic water bath(Jinghong XMTE-8112).The bottom of the tubular MnOx/Ti electrode was closed with a disk.A peristaltic pump(Longer Pump BT100-2J)was used to suck the filtrate through the electrode from the feed tank to the permeate tank in a dead-end manner.Thus,the permeate flow rate was able to control the residence time(RT)of the reactor.Electrocatalytic oxidation of TFP was carried out with the ECMR under atmospheric pressure.The reactor operating conditions were the TFP concentration of 40 mmol·L-1,reaction temperature of 60 °C and current density of 2.4 mA·cm-2.It was noted that the above parameters were derived from the prior work[6].Further,the current density was calculated on the basis of the nominal geometric surface areas of electrode according to Eq.(7)[6].

wherejis the current density(mA·cm-2),Iis the total current(mA),andAis the nominal geometric surface area of anode material(cm2).

TheRTis de fined as the ratio of the volume of the electrode to the permeate flow rate.RTwas described as Eq.(8)[23]:

whereRTis the residence time(min),V0is the volume of the tubular electrode(cm3),φ is the porosity of electrode,Qis the volumetric flow rate of solution(ml·min-1),Lis the electrode length(mm),andr1andr2are inside and outside radii(mm),respectively.

During the ECMR operation,the conversion of reactant TFP(CTFP)was calculated according to Eq.(9)[24].

The selectivity of product STFP(SSTFP)was calculated according to Eq.(10)[25].

whereCF-TFPandCP-TFPare the TFP concentrations in the feed and permeate(mmol·L-1),respectively,CP-STFPis the STFP concentration in the permeate(mmol·L-1).

During the ECMR operation,the energy consumption(EC)was calculated according to Eq.(11)[26]:

whereUis the voltage(V),Iis the current(A),tis the operating time(h),Vis the amount of feed liquid(m3).

The current efficiency(CE)is the ratio between the charge used to produce STFP and the total charge.It was calculated by Eq.(12)[27,28]:

whereCEis the current efficiency(%),mis the quality of product(g),Mis the molecular weight of product(g·mol-1),zis the number of transferred electrons,Fis the Faraday constant,Iis the total current(A),andtis the electrolysis time(s).

Product analysis in permeate was carried out by high performance liquid chromatography(HPLC)(Agilent 1100)equipped with a diodearray detector(DAD)(Agilent G1314A).The HPLC utilized a Partisil 10 SAX column(Whatman)using MeOH/0.02 mol·L-1KH2PO4=5/95(v/v)as eluent(1.0 ml·min-1).Moreover,reactant analysis in feed and permeate was conducted using a Waters e2695 HPLC equipped with a refractive index detector(RID)(Agilent G1362A).The HPLC applied a C18 column using 50%methanol aqueous as eluent(1.0 ml·min-1).All reactants and products were identified by comparison with authentic samples.

4.Results and Discussion

4.1.Coefficient of determination

Porous media setting demands for the definition of the inertial resistance factor(C2)and the viscous resistance factor(1/α)in order to consider the source termSiof the momentum balance equation.In order to obtain the resistance coefficients,a series of experiments between permeate flow rate(ml·min-1)and pressure drop(Pa)at the outlet was conducted with reactant solution under the operating temperature 60°C as shown in Fig.3.The experimental data were analyzed and plotted following the quadratic polynomial relationship of pressure dropversuspermeate flow rate with a correlation coefficientR2＞0.99,as follows:

The resistance coefficients(C2and 1/α)were obtained by substituting Eq.(13)into Eq.(6)and comparing with Eq.(5),as follows:

These resistance factors contribute to de fine the source term in the momentum balance equation.It could be calculated by Eq.(12)that the pressure drop at the outlet(the constant described in Section 2.4)was almost stable at 311 Pa under the corresponding reactionRTof 15 min(permeate flow rates from 0.09 to 0.30 ml·min-1).Hence,the outlet boundary condition was conducted at subatmospheric pressure ofPatm-311(Pa)with the corresponding target permeate flow rates in subsequent simulations(Sections 4.2–4.4).Remarkably,the target permeates were calculated by the reactionRTand Eq.(8).

4.2.Effect of membrane length on ECMR performance

In order to explore the intrinsic flux distribution in the ECMR system, a series of 2D-CFD simulations were carried out with different membrane lengths from22mm to 70mm corresponding to experimental devices. The reference conditions were presented in Table S1 in supporting information.

The cross flow velocity distribution(m·s-1)along the membrane tube obtained from the simulation was plotted in Fig.2.It is noted that the outlet was marked as 0 mm.As shown in Fig.2a,the permeate velocity distribution along the membrane tube with a length of 22 mm presented a peak of inverted parabolic portion near the outlet with the maximum width of 24 mm and highest velocity of 0.20 m·s-1.The similar phenomena could be observed from the membrane tube with the length of29–70mm(Fig.2b–e).Interestingly,after that,the permeate velocity along the tube reached down to a very low value until to the dead-end of membrane.Evidently,the permeate velocity distribution along the membrane tube became more non-uniform with the increase of membrane length.The reason was that the flow near the outlet(or sucking pump)suffered from a lower flow resistance under the same sucking pressure or average operating flux,whereas the flow near the dead end had to overcome a higher flow resistance and gravitational potential energy through the longer pipeline[10,11].

Obviously,the permeate velocity distribution along the membrane tube with the different lengths could be divided two regions:one with detectable velocity and another with the velocity close to 0 m·s-1.The first region is de fined here as the enhanced mass transfer region,in where the fluid could flow effectively through the membrane from the outside in.In this case,the operation of ECMR for electrochemical oxidation is effective and controllable as the electrochemical reaction and product separation would happen in this region at the same time.Another region defined as the non-enhanced mass transfer regions,would play a role as a normal electrochemical reactor with low efficiency,which performs only diffusion instead of mass transfer enhancement.Hence,the growth of enhanced mass transfer region and the restriction of non-enhanced mass transfer region along the membrane tube could further improve the ECMR performance.In other words,an increase in the enhanced mass transfer region in the membrane tube length would be in favor with the improvement of ECMR performance.

In order to verify the simulation results,the TFP oxidation was carried out in ECMR with different membrane lengths from 22 mm to 70 mm under the operating conditions:RTof 15 min,reaction temperature of 60 °C,pH of 13.0,TFP concentration of 40 mmol·L-1,and current density of 2.4 mA·cm-2.Changes on TFP conversion and STFP selectivity with the membrane lengths were illustrated in Fig.4a.It is found from Fig.4a that TFP conversion gradually decreased from 44.6%to 30.6%with the increase of membrane length from 22 to 70 mm,whereas STFP selectivity was consistently higher than 99.9%.The reason was that the longer membrane suffered from more nonuniform permeate velocity distribution along ECMR,thus leading to a lower TFP conversion and efficiency[15].

Fig.4.Effect of membrane length on TFP conversion and STFP selectivity(a)and energy consumption and current efficiency(b).

In addition,the effect of membrane length on energy consumption and current efficiency was demonstrated in Fig.4b.Equally,the current efficiency decayed from 26.0%to 17.8%as the membrane length increased from 22 to 70 mm.On the contrary,energy consumption increased from16.5to22.9kWh·m-3with the increase of the membrane length[Fig.4(b)].The reason was that the relatively slow reactant moleculardiffusion to the electrode surface could not realize kinetically the effective electron transfer due to the mass transfer limitations in the reactor with a membrane length[29].Thereby,the Faradic losses in electrolysis(such as the oxidation of water to oxygen)could occur at nonenhanced mass transfer region seriously[30].It implies that a longer tube with a larger region of non-enhanced mass transfer would lead lower current efficiency and higher energy consumption.In summary,the experimental observations con firmed the simulation results.

4.3.Effect of membrane diameter on ECMR performance

For the tubular membrane reactor,the diameter of membrane is one of the most important geometrical parameters.In order to study the effect of membrane diameter on hydrodynamic distribution in ECMR,a series of models were carried out with different membrane diameters(ID=10,20,30,40,50,60,or 70 mm)as shown in Fig.5.The more reactor parameters were listed in Table S2.The thickness of membrane was5mm.Similar to the results obtained in Fig.2,the permeate velocity distribution along the membrane tube with anIDof 10 mm also presented a peak of inverted parabolic portion with the maximum width of 10 mm and highest velocity of 0.30 m·s-1as shown in Fig.5a.An interesting phenomenon can be seen from Fig.5 that the highest velocity gradually decreased and shifted toward the dead end with the increase ofIDfrom 10 mm to 70 mm.Besides,the enhanced mass transfer region became broader and broader.It suggested that the permeate velocity distribution along the membrane tube became more uniform with the increase of the membrane diameter.The reason was that the membrane with large diameter suffered from less filtration resistance and fluid resistance.Thereby the pressure drop along the membrane tube decreased with the increase of membrane diameter[31,32].

Fig.5.Cross flow velocity distributions along the membrane tube with different IDs:(a)10 mm;(b)20 mm;(c)30 mm;(d)40 mm;(e)50 mm;(f)60 mm and(g)70 mm.

In effort to further understand the flow characteristics of fluid in the reactor,a series of velocity pro files along the vertical direction were extracted from the simulation results at different positions as illustrated in Fig.6.As shown in Fig.6,a contour of velocity magnitude in ECMR model is observed.The white dotted lines(curves a–e)represent the positions of velocity curves along the vertical direction.It can be found in Fig.6 also that the horizontal plane was divided into three regions marked in red,yellow and blue.The red region including line a and line b represents the membrane tube inside.Line c in the yellow region is the position of the membrane wall,and the blue region with line d and line e is the outside of membrane(the region between feed tank and membrane).

Fig.6.3D schematic of velocity distribution curves in the reactor.

For easy observation,a 3D-axis of the velocity distribution in the membranes withID20mm and70mm was shown in Fig.7,respectively.Among of them,thex-,y-andz-axes represent the distance from the outlet,the distance from symmetrical axis and the velocity value,respectively.For the reactor with a membraneIDof 20 mm,the positions of curves a–e were at 0,7,14,21,and 28 mm,respectively.As shown in Fig.7a,the velocity curves at five positions were divided into two parts.One with high velocity is the enhanced mass transfer region from the outlet to the membrane length of 19 mm,where the fluid could flow effectively from the feed tank through membrane porous media into membrane tube.Another part with a velocity close to 0 is the non-enhanced mass transfer region with the membrane length from 19 mm to 100 mm.The similar velocity distribution for the reactor with a membraneIDof 70 mm was shown in Fig.7b.The positions of curves a–e were0,17,37,50,and60mm,respectively.Obviously,the enhanced mass transfer region was the region from the outlet to the membrane length of89mm.Thus,it suggests that the tubular membrane with a larger diameter could form a wider enhanced mass transfer region and the relatively uniform cross flow velocity distribution along the tube,which are benefit for the improvement of the reactor performance.

Fig.7.Velocity distribution pro files in the reactor with ID:(a)20 mm and(b)70 mm.

To further confirm the above simulations, the following experiments were performed to investigate the effect of membrane diameter on the ECMR performance.A series of electrocatalytic TFP oxidations in the ECMR with differentIDs(15 mm,25 mm and 53 mm)were carried out under the following conditions:RTof 15 min,reaction temperature of 60 °C,pH 13.0,TFP concentration of 40 mmol·L-1,and current density of 2.4 mA·cm-2.Here,the tubular Ti membranes have the same thickness(2.5 mm)and length(40 mm),and the distance between the membrane tube and the feed tank was fixed at 30 mm.

Fig.8a showed that 45.0%improvement of TFP conversion(from 52.7%to 97.7%)was achieved with the increase of membraneIDfrom 15 to 53 mm.The high TFP conversion was attributed to the large membrane diameter with more uniform permeate velocity distribution along the membrane tube in ECMR[30].Simultaneously,all the STFP selectivities obtained reached up to 99.9%[Fig.8(a)].Further,it can be seen from Fig.8b that the current efficiency and energy consumption increased from 22.3%to 40.1%and from 16.4 to 24.8 kWh·m-3with the in crease of membraneIDfrom15to53mm,respectively.The results implied that the larger membrane diameter with a broader mass transfer region along the tubular ECMR was in favor with the increase of the current efficiency.The reason was that the large region of enhanced mass transfer would refrain from the Faradic losses along the membrane tube near the electrode surface as a result of the relatively slow reactant molecular diffusion[6,29].In summary,the reactor with large membrane diameter is beneficial to the excellent ECMR performance(high conversion and high current efficiency).

Fig.8.Effect of membrane ID on TFP conversion and STFP selectivity(a)and energy consumption and current efficiency(b).

4.4.Optimization of ECMR geometry

To fully evaluate the effect of reactor parameters on ECMR performance and establish a guide for the further application of ECMRs,the effects of membrane length and diameter on the percentage of enhanced mass transfer region were predicted and presented in Fig.9.It can be seen from Fig.9 that the percentage of enhanced mass transfer region for the membrane length of160mm increased gradually from 16.8%to 56.8%as the membraneIDgrew from 10 to 90 mm.Specifically,the percentage of enhanced mass transfer region for the membrane length of 20 mm rapidly increased from 87.5%to 100%with the increase of membraneIDfrom 10 to 30 mm and then reached a plateau(100%)as the membraneIDwas more than 30 mm.

It can also be found from Fig.9that the percentage of enhanced mass transfer region for the membraneIDof 10 mm quickly increased from 16.8%to 85.7%with the decrease of membrane length from 160 to 20 mm.Similarly,the percentage of enhanced mass transfer region for the membraneIDof 90 mm rapidly increased from 56.8%to 100%with the decrease of the membrane length from 160 to 40 mm and then reached a plateau(100%)with the decrease of the membrane length from 40 to 20 mm.That is to say,the percentage of enhanced mass transfer region can achieve above 90%for the membrane with the length of 20–40 mm and theIDof 50–90 mm.

Fig.9.Relationship between reactor parameters and percentage of enhanced mass transfer region.

5.Conclusions

A CFD technique was successfully applied to simulate the hydrodynamic distributions along a tubular ECMR for the electrocatalytic oxidation of TFP into STFP.A uniform distribution of permeate velocity along the tubular reactor and a high percentage of enhanced mass transfer region can be derived from the reactor with a short length and large diameter.Furthermore,the excellent performance of ECMR with the TFP conversion of 97.7%,the selectivity to STFP of 99.9%and current efficiency of40.1%were achieved from the reactor with a length of 40 mm andIDof 53 mm.The experimental results coincide well with the simulation analysis.Meanwhile,the comprehensive analysis shows that the percentage of enhanced mass transfer region could reach above 90%for the membrane with the length of 20–40 mm and theIDof 50–90 mm.

Nomenclature

Anominal geometric surface area of anode material,cm2

Ccoefficient matrix

CEcurrent efficiency,%

CF-TFPTFP concentrations in the feed,mmol·L-1

CP-STFPSTFP concentrations in the permeate,mmol·L-1

CP-TFPTFP concentrations in the permeate,mmol·L-1

CTFPconversion of reactant TFP,%

C2inertia resistance factor

D coefficient matrix

ePorosity,%

FFaraday constant,9.65×104C·mol-1

Itotal current,A

IDmembrane inside diameter,mm

jcurrent density,mA·cm-2

Llength of electrode,mm

Mmolecular weight of product,g·mol-1

mquality of product,g

Δnithicknesses of medium inx,y,andzdirections

ODmembrane outside diameter,mm

ppressure per unit volume,Pa

Qvolumetric flow rate of solution,ml·min-1

RTresidence time,min

r0IDof outlet tube,mm

r1IDof membrane,mm

r2OD of membrane,mm

r3IDof reactor,mm

Sisource term forith,x,orymomentum equation

SSTFPselectivity of product STFP,%

Su,Svsource terms of momentum conservation.

toperating time,h

Uvoltage,V

u,vvelocity vectors onxandyaxes,m·s-1

velocity vector,m·s-1

Vamount of feed liquid,m3

V0volume of electrode,cm3

vjvelocity components inx,y,andzdirections

znumber of transferred electrons

α permeability

1/αijentries in matrix D

μ viscosity,Pa·s

ρ density,kg·m-3

φ porosity of electrode

Supplementary material

Supplementary material to this article can be found online at http://dx.doi.org/10.1016/j.cjche.2016.05.020.

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