Department of Chemical Engineering,Sichuan University,Chengdu 610065,China

Keywords:Rotor-stator reactor Liquid-liquid flow pattern Liquid holdup Droplet size distribution Average droplet diameter

ABSTRACT Rotor-stator reactor (RSR),an efficient mass transfer enhancer,has been applied in many fields.However,the hydrodynamic characteristics of liquid flow in RSR are still a mystery despite they are fundamental for the mass transfer performance and processing capacity.In view of the above,this paper studies the liquid-liquid flow and liquid holdup in RSR under various conditions with a high-speed camera.The paper firstly demonstrates two flow patterns and liquid holdup patterns that we obtained from our experiment and then presents in succession a flow pattern and a liquid holdup criterion for the transition of film flow to filament flow and complete filling to incomplete filling.It is found that experimental parameters,including rotor-stator distance,rotational speed and volume flow rate exert great influence on the average droplet diameter and size distribution.Besides,by comparison and contrast,we also find that the experimental values match well with our previous predicted calculations of the average diameter,and the relation between the average diameter and the mean energy dissipation rate.

1.Introduction

The demand for process intensification in the field of multiphase operations has led to the rapid development of diverse kinds of multiphase reactors.A most important one is the rotor-stator reactor(RSR)[1],which has been widely applied in liquid-liquid systems[2,3],gas-liquid systems[4,5],and solid-liquid systems[6,7].On the basis of the RSR,we proposed a novel rotor-stator reactor,consisting of a spiralgrooved rotor disc and a smooth stator disc[8].In RSR,when there is a co-current liquid-liquid flow through the rotor-stator cavity,the spiral-grooved rotor disc with high rotation speed creates a centrifugal force and facilitates the mixed phases to detach and re-attach repeatedly,resulting in high efficiency of mass transfer.As reported,studies on the hydrodynamic characteristics of liquid flow in devices are vital for industrial scale-up[9].However,scarce researches on the hydrodynamic characteristics in RSR have been launched,which impedes our profound comprehension of its mass transfer and processing capacity.

The hydrodynamic characteristics of fluid flow in rotating devices have attracted much attention in the past few years and scholars and experts have devoted a lot to the fluid flow in rotating devices.For instance,Visscher et al.[10]used a camera with stroboscope to observe the liquid-liquid flow in an impeller-stator spinning disc reactor and reported that the liquid-liquid flow is characterized by six different flow regimes.Burns and Ramshaw [11]observed that there were three types of liquid regimes:drop,pore flow,and film in a rotating packed bed by a 35 mm camera.Visscher et al.[6]used a camera to photograph liquid-liquid flow behaviour in a rotor-stator spinning disc reactor(RSSDR)and observed three flow patterns.Effects of the aqueous to organic flow ratio and the rotational speed on the liquid-liquid flow behaviour were investigated.Meeuwse et al.[12]utilized a camera with MATLAB to investigate the gas holdup in an RSSDR and demonstrated that the gas holdup depended on the radial velocity and the inward radial velocity of the gas bubbles.Guo[13]studied the liquid holdup in a rotating packed bed by measuring conductivity of the liquid flow and established a mathematical model of liquid holdup.Li et al.[14]showed the effects of various operating parameters on the average diameters in a RSR by using a high-speed camera and predicted the average diameter with a correlation.Sang et al.[15]investigated the droplet diameter and size distribution in the cavity of a rotating packed bed.

The aforementioned hydrodynamic characteristics of fluid flow studies mainly focus on the rotating packed bed and rotor-stator reactor.However,the study on the liquid-liquid flow,including flow pattern and liquid holdup in the rotor-stator zone,droplet diameter size and distribution in the cavity of a RSR has been less discussed.Therefore,this paper aims to study the effects of volume flow rate,rotational speed,and rotor-stator distance on liquid-liquid flow pattern and liquid holdup in the rotor-stator zone,with the help of images taken by a high-speed camera.On the basis of image analyzing,liquid-liquid flow and liquid holdup transition pattern are presented.An investigation on the effects of volume flow rate,rotational speed,and rotorstator distance on average droplet diameter and size distribution is performed by a high-speed camera with the Image-Pro Plus 6.0 software.Furthermore,we also explore the correlations of the average droplet diameter,and the relation between the average diameter and the mean energy dissipation rate.

2.Experimental

2.1.Materials

With the objectivity to study the liquid-liquid flow pattern and liquid holdup in RSR,de-ionized water made by Aquapro RM-220(Ever Young Enterprises Development Co.,Ltd.,China)was employed as the aqueous phase and kerosene (Sichuan Zhongcui Chemical Co.,Ltd.,China)was used as the organic phase.To identify flow characteristics,methylene blue (Beijing Chemical Co.,Ltd.,China)was dissolved in the aqueous phase and SUDANIII dye (Chendu Jinshan Chemical Co.,Ltd.,China)was dissolved in the organic phase.The density of the de-ionized water and kerosene were measured with a density bottle[16].The interfacial tension between the de-ionized water and kerosene was evaluated by an automatic surface tension-meter(BZY-201,Shanghai Fangrui Instrument Co.,Ltd.,China).The viscosity of the de-ionized water and kerosene were measured with an Ubbelohde viscometer[17,18].The value of density,viscosity and interfacial tension for the de-ionized water and kerosene are shown in Table 1.De-ionized water was employed as the liquid streams to obtain the data of droplet diameter and size distribution.

2.2.Structure of RSR

Fig.1(a)illustrates the structure diagram of a RSR which employed in this study.Its parameters are listed in Table 2.The spiral-grooved rotor disc made of stainless steel,is shown in Fig.1(b).A detailed description of the spiral-grooved rotor disc can be found in Wang et al.[8].The kerve of the reactor and the stator disc are made of transparent PMMA for visualization purpose.

2.3.Experimental setup and procedure

The experimental setup as shown in Fig.2(a)and(b)is composed by a RSR system and an image acquisition system.The experimental setup in Fig.2(a)was employed to survey the liquid-liquid flow pattern and liquid holdup.Fig.2(b)was used to gain values of the liquid droplet diameter and its size distribution.For the RSR system,a detailed description of the experimental procedure can be found in Wang et al[8].The experimental pressure was maintained at～0.1 MPa and the temperature of liquid was measured before and after the experiments at(25±1)°C.

The image acquisition system consists of a high-speed camera(Pco.dimax Cs,PCO,Germany),a lens(AF 60 mm,Canon Co.,Japan),a lamp(AIT-100P,Advanced Intelligence Technology Co.,Ltd.,China)and a computer(Lenovo-5000,Lenovo Co.,Ltd.,China).The lamp was employed as supplementary light and placed around the shooting area.And the lens was mounted on the high-speed camera,which connects a computer.The specifications of the lens and the camera are shown in Table 3.For the image acquisition system in Fig.2(a),the lens equipped high-speed camera with vertical installation abovethe cavity zone of the RSR in Fig.2(b),was placed directly beneath the stator disc.

Table 1 Physical properties of de-ionized water and kerosene at 0.1 MPa and 25°C

To obtain the value of average droplet diameter,100 droplets from the images recorded in different frames were measured under every experimental condition.The droplet diameters in the images were measured by the Image-Pro Plus 6.0 software[19].The droplet diameter d was defined as[20]:

As shown in Fig.3,the minor and major axis lengths of the oval droplet in pixels are represented by d3and d4,respectively.φ is the calibrated spatial resolution of the droplet image (0.6154 mm·pixel?1)in this study.

3.Results and Discussion

3.1.Liquid-liquid flow pattern in the rotor-stator cavity

3.1.1.Typical liquid-liquid flow patterns

When comprehending the mass transfer performance and flow characteristics in an RSR,it is crucially important to analyze the liquid-liquid flow pattern under various experimental parameters.As shown in Fig.4,two typical liquid-liquid flow patterns of film flow and filament flow are observed.For the filament flow,the width of the water and kerosene flows is very narrow and both of them are torn into filaments and dispersed.For the film flow,the widths of the water and kerosene flows are visibly wider than that of the filament flow and both of them are continuous flows.When there is a slow rotational speed,two different film flows are obtained.One of the film flows is a radial water and kerosene outward flow and both flows are observed as a continuous spiral,respectively(A in Fig.4).The water spiral is entwined with the kerosene spiral,which is similar to other spinning disc reactor [6].As the rotational speed increased to 150 r·min?1,another type of the film flow is formed(B in Fig.4).The widths of the water spiral and kerosene spiral are narrower than those of the film flow with a lower rotational speed(A in Fig.4).In addition,the number of the water spiral and the number of kerosene spiral rise from that of the film flow with a lower rotational speed(A in Fig.4).As the shear force increased,the film flow broke up into filament flows under the high rotational speeds(C in Fig.4).Both the regular water spiral and kerosene spiral stretched into irregular filament flows.Furthermore,due to the high centrifugal force and the limited volume flow rate,the filament flows are accelerated to go through the rotorstator zone quickly and they are hard to fill the rotor-stator zone completely [8],resulting in few filament flows in the rotor-stator zone.

3.1.2.Flow pattern transition

Fig.5 shows the effect of different structures and operation parameters on the liquid-liquid flow pattern transition and transition curves.The regions with error bars are considered as the liquidliquid flow pattern transition region,where two flow patterns coexist.Fig.5(a)investigates the dependence of flow pattern transition on volume flow rate and rotational speed.It is evident that the rotational speed has influence on the flow pattern transition for the volume flow rate(ranging from 5 to 80 ml·min?1).As indicated in Fig.5(a),the flow transition from film to filament flow is promoted by decreasing the volume flow rate or by increasing the rotational speed.The descent of volume flow rate or ascent of rotational speed means the addition in centrifugal force or contact time of the liquidliquid flow and stronger performance of the liquid-liquid disturbance,leading to flow shifts from film one to filament one.In addition,the regression equation for the transition from film flow to filament flow is also exhibited in Fig.5(a).Liquid-liquid flow patterns show the formation tendency of filament flow and film flow in the area above and below the transition region,respectively.Fig.5(b)indicates the dependence of flow pattern transition on rotational speed and rotor-stator distance.We can see the flow transition from film one to the filament one is strengthened by the increasing rotational speed or rotor-stator distance.The increment of rotor-stator distance and rotational speed may improve the liquid-liquid disturbance and reduces the chance to form the film flow,contributing to the transition of film flow into filament flow.

Fig.1.(a)Schematic of RSSDE and(b)image of Spiral-grooved rotor disc surface(1)motor;(2)rotor disc;(3)kerve;(4)stator disc;(5)inlet;(6)outlet;(7)spindle.

3.1.3.Flow pattern transition criteria

So as to acquire a criterion for liquid-liquid flow transition from film to filament flow,dimensionless groups were employed to research the flow pattern transition[21].The influence of seven parameters,including liquid initial velocity u0(corresponding to volume flow rate,u0=Q/60πr2),angular velocity ω(corresponding to rotational speed,ω=2πN/60),rotor-stator distance H,rotor disc radius R,immiscible fluids density ρm,immiscible fluids viscosity μmand liquid interfacial tension σ on the flow pattern transition,are remarkable and can bepresented by:

Table 2 Size of the RSSDR and operating conditions

To generalize the corresponding and model results,the fundamental dimension groups are defined as:

Re is the Reynolds number and We is the Weber number.They are defined as the ratios of inertial force and viscous force or liquid interfacial tension,respectively[22].Q represents the dimensionless liquid initial velocity[15].G is the ratio of rotor-stator distance and rotor disc radius[23].ρmand μmare defined the average immiscible fluids density and viscosity,respectively[24,25].Our assumption is that the transition characteristics are pertinent to the four dimensionless parameters and the transition standard can be expressed as follows:

Fig.2.Schematic of(a)experimental setup for liquid-liquid flow and liquid holdup studies and schematic of(b)experimental setup for droplet diameter size and distribution(1)motor;(2)rotor disc;(3)kerve;(4)stator disc;(5)inlet;(6)collection bottle;(7)spindle;(8)constant flow pump;(9)aqueous phase;(10)high-speed camera;(11)lamp;(12)computer;(13)organic phase.

The Eq.(10)applicable conditions are as follows:

The exponent of Re is 1.17±0.18,G 2.49±0.43 and We 1.93±0.37.These certify how small confidence intervals for Eq.(10)they are.Eq.(10)is shown in Fig.6,with ±20% relative errors.According to Fig.6,it is clear that the transition from film to filament flow is promoted by increasing G2.49We1.93and by decreasing qRe1.17under the experimental conditions.The regions above and below the curve represent the formation of film and filament flow,respectively.

Table 3 Specifications of the lens and the high-speed camera

3.2.Liquid holdup in the rotor-stator cavity

3.2.1.Liquid holdup transition

The comprehension of liquid holdup pattern transition with various experimental parameters is vital for the in-depth understanding of processing capacity in RSR.As shown in Fig.7,two typical liquid holdup patterns of complete filling and incomplete filling are observed.For the liquid holdup pattern of complete filling,it means that the processing capacity fulfills or exceeds the processing capacity of the RSR under the experimental conditions.For the liquid holdup pattern of incomplete filling,it means that the processing capacity of the RSR fails to be achieved under the experimental conditions.When the rotational speed is slow,the liquid-liquid flow fills the rotorstator zone,as shown in Fig.7(A).The rotor-stator zone is not filled by the liquid-liquid flow at high rotational speed,as shown in Fig.7(B and C).Besides,the liquid holdup pattern transition and transition curves under different structure and operation parameters are demonstrated in Fig.8.Fig.8(a)shows the dependence of liquid holdup pattern transition on volume flow rate and rotational speed.It is clear that the liquid holdup transition from complete to incomplete filling is boosted by decreasing volume flow rate and increasing rotational speed.The increase of rotational speed and decrease of volume flow rate promotes the speed of liquid flow and reduces the liquid flux,leading to the transition from complete to incomplete filling[8].The results also indicate that the rotational speed and volume flow rate pose a significant impact on the liquid holdup pattern transition.The regression equation for the transition from complete to incomplete filling is displayed in Fig.8(a).Liquid holdup patterns represent the respective formation of incomplete filling to complete filling in the area above and below the transition region.Fig.8(b)shows the dependence of liquid holdup pattern transition on rotor-stator distance and rotational speed.As shown in Fig.8(b),the liquid holdup transition from complete to incomplete is strengthened by the growing rotorstator distance and the rotational speed.The increase of the rotational speed and rotor-stator distance results in a decrease in the residence time of the liquid-liquid flow in the rotor-stator cavity and an increase in the space of the rotor-stator cavity for the liquid-liquid flow to go through.At last,the complete filling may transform into incomplete filling.

Fig.3.Typical photograph of droplets.

3.2.2.Liquid holdup pattern transition criteria

To obtain the criterion for filling transition from complete one to incomplete one,the method proposed in Section 3.1.3 is employed to study the liquid holdup pattern transition.The transition criterion is showed as follows:

The applicable conditions for Eq.(11)are as follows:

The exponent of Re is 0.43±0.07,G 1.93±0.37,and We 0.89±0.15.These number illustrate how small confidence intervals for Eq.(11)they are.The transition curve,according to Eq.(11)with±20%relative errors,is shown in Fig.9.And the Fig.9 sheds light on that the transition from complete to incomplete filling is promoted by an increase of G1.93We0.89and a decrease of qRe0.43under the experimental conditions.The regions above and below the curve indicate the formation of complete filling to incomplete filling,respectively.

3.3.Average droplet diameter size in the cavity zone

3.3.1.Effect of rotational speed

Fig.10 illustrates the influence of rotational speed on the average droplet diameter size.Obviously we can find from Fig.10 that the average droplet diameter size diminishes with the increase of rotational speed.One of the explanations for this phenomenon may be that that more energy is available for generating dispersion with growing rotational speed,which further shortens the average droplet diameter.Another explanation is that the relative movement of the liquid and rotor and the hydrodynamic instabilities between air and liquid varies proportionately with the increase of the rotational speed in the cavity zone,resulting in a larger shear effect and consequently smaller average droplet diameter[15].

Fig.4.Photograph of flow pattern in the rotor-stator zone.Conditions:O/A=1:1,Q=80 ml·min?1,H=1 mm,μm=1.07 mPa·s,σ=44.10 mN·m?1.

Fig.5.Dependence of flow pattern transition on(a)rotational speed and volume flow rate,(b)rotational speed and rotor-stator distance.

Fig.6.Liquid flow pattern transition curve.

3.3.2.Effect of volume flow rate

Fig.11 depicts the influence of volume flow rate on the average droplet diameter size,from which it is not difficult to figure out that the average droplet diameter size grows with the increase of volume flow rate.This probably is brought about by the shortening residence time,since the volume flow rate increases with a consistent rotational speed.Consequently,the longer the liquid flow stays in the rotorstator cavity with a consistent rotational speed,the greater probability that droplets can avoid being over-dispersed and finally bring a bigger average droplet diameter.In addition,the droplets might have more chance to collide and coalesce with a growing volume flow rate,leading to an increase of average droplet diameter.

3.3.3.Effect of rotor-stator distance

Fig.12 shows the effect of rotor-stator distance on the average droplet diameter size.It is clear that the average droplet diameter size increases with the growing rotor-stator distance.The boundary layers are divided by a region with a constant tangential rotating velocity,due to the extending rotor-stator distance[5].Two separate boundary layers are formed at both the rotor and the stator discs[5].The shear force weakens,when the rotor-stator distance grows,thus leading to a larger average droplet diameter.

3.3.4.Correlation for average droplet diameter

Correlation has been established to expound the effect of independent parameters on the average droplet diameter,like the rotational speed,rotor-stator distance,volumetric flow rate and liquid viscosity.The average droplet diameter is estimated with the various experimental values in advance.Levenberg-Marquardt algorithm is often used to obtain the correlation [26].The optimum value of average droplet diameter is judged by minimizing the following equation:

where K,a,b,c,and d are the regression coefficients,subscript cal and exp.are taken to calculate experimental values.Superscript x is the average droplet diameter of the x time.

The model equation established is shown as follows:

The applicable conditions for Eq.(13)are as follows:

As shown in Fig.13,the experimental data is in line with the value predicted by Eq.(13)with a deviation within±20%.Hence,the comparison of the experimental average droplet diameters with that of the calculated one reveals a good agreement with Eq.(13).Obviously,the average droplet diameter grows with the increase of rotor-stator distance and volumetric flow rate,and the decrease of the rotational speed.In addition,the average droplet diameter size is enormously influenced by the rotating speed under the experimental conditions.But the volumetric flow rate and rotor-stator distance appear to exert only a limited impact on the average droplet diameter.

Fig.7.Photograph of liquid holdup in the rotor-stator zone.Conditions:Conditions:O/A=1:1,Q=80 ml·min?1,H=1 mm,μm=1.07 mPa·s,σ=44.10 mN·m?1.

3.3.5.Relation between the average droplet diameter and the mean energy dissipation rate

The mean energy dissipation rate can be expressed as follows[27]:

Fig.8.Dependence of liquid holdup transition(a)rotational speed and volume flow rate,(b)rotational speed and rotor-stator distance.

The mean energy dissipation rate has been used to correlate the experimental data of average droplet diameter.For details,please see the following equation:

The voltage of the motor U is 220 V and the electric current of the motor I is detected by a digital display ammeter (DM4T-3A,CW Electronic Instrument CO.LTD).The standard deviation of exponent and coefficient in the correlation respectively are 0.24 and 0.09.As demonstrated in Fig.14,the experimental data is in good consistency with the correlation of Eq.(15).The average droplet diameter decreases,while by contrast the mean energy dissipation rate grows.

3.4.Droplet diameter size distribution in the cavity zone

Generally speaking,the average diameter size alone cannot provide abundant information to comprehend the separation of liquid-liquid flow process in the cavity of such RSR.Therefore,to accurately understand RSR,not only the average droplet diameter size,but also the droplet size distribution is of remarkable significance.As shown in Eq.(16),the Rosin-Rammler(R-R)distribution is proved to be a suitable droplet size distribution for the rotating equipment[20].

Fig.9.Liquid holdup transition curve.

Fig.10.Effect of rotational speed on the average droplet diameter.

where V is the cumulative volume fraction of droplets with diameters below d.The exponent m represents the value of the distribution width and a large m value stands for a narrow distribution and vice versa.c is the characteristic droplet diameter,defined as the diameter,of which the cumulative volume fraction is 63.2%.A comparison of experimental data and calculated value with the R-R distribution is presented in Fig.15.As a result,the droplet cumulative volume distribution turns to be well described by the R-R distribution.

3.4.1.Effect of rotational speed

Fig.16 illustrates the effect of rotational speed on c and m of the R-R distribution.The Fig.16 tells that m becomes larger with the increase of rotational speed from 400 r·min?1to 600 r·min?1,yet it becomes smaller with the increase of rotational speed from 600 r·min?1to 1000 r·min?1,and then it remains almost unchanged with the increase of rotational speed from 1000 r·min?1to 1200 r·min?1.Meanwhile,c witnesses a striking reduction with the increase of rotational speed from 400 r·min?1to 600 r·min?1,and then a subtle drop with the increase of rotational speed from 600 r·min?1to 1200 r·min?1.The above result proves that the droplets get smaller,as the rotating speed grows and the distribution becomes narrower,with the increase of rotational speed from 400 r·min?1to 600 r·min?1.As the droplets might collide and coalesce and the droplet coalescence might reach a balance with the increase of rotational speed from 600 r·min?1to 1200 r·min?1,the distribution becomes wider and then keeps nearly stable and unchanged[15].

Fig.11.Effect of volume flow rate on the average droplet diameter.

Fig.12.Effect of rotor-stator distance on the average droplet diameter.

3.4.2.Effect of volume flow rate

Fig.17 depicts the influence of volume flow rate on c and m of the R-R distribution.We can observe that m rises with the increase of volume flow rate from 20 ml·min?1to 80 ml·min?1firstly,and then drops with the increase of volume flow rate from 80 ml·min?1to 100 ml·min?1.Accordingly,the distribution firstly presents two relatively narrow curves and then the distance between the curves becomes rather broader,with the increase of volume flow rate.The aforementioned result persuades us that a lower volume flow rate improves the uniformity of liquid dispersion within a certain range and then the droplets might collide and coalesce with a growing volume flow rate.In addition,it is perceivable from Fig.17 that c elevates with the increase of volume flow rate.The result also indicates that the small droplets become larger with a rising volume flow rate and as expected,a larger volume flow rate with a shorter residence time might undermine the effect of breakup droplets,thus c increases.

3.4.3.Effect of rotor-stator distance

Fig.13.Comparison of experimental and calculated values of the average droplet diameter.

Fig.14.Average droplet diameter as a function of the mean energy dissipation rate.

Fig.18 delineates the impact of rotor-stator distance on c and m of the R-R distribution.The Fig.18 maps out that m decreases initially and then remain almost unchanged with the increase of rotor-stator distance.Possible explanation may be that the shear force is weakened by the extending rotor-stator distance,which contributes to a wider distribution of the droplets.As the rotor-stator distance continues to widen,the mixed boundary layers are divided by a region with a constant rotational tangential velocity,resulting in an almost unchanged distribution of the droplets size[5].At the same time,it can be seen from Fig.18 that c increases with the widening rotor-stator distance.In accordance with the experimental result,the size of the droplets shifts tends to approximately proportionate with the rotor-stator distance.The wider the rotor-stator distance,the larger the droplets.

The value of m ranges from 1.5 to 4 for most spray devices and can be as high as 9.43 for rotating packed bed[15].In this work,the value of m ranges from 7.0 to 16.62 and it is proved that the liquid has a better uniformity and plays an important role in the control of droplet size and distribution,which turns out to be beneficial for the separation of mixed phases in RSR.

4.Conclusions

Fig.15.Comparison of experimental and calculated values by using the R-R distribution.

Fig.16.Effect of rotational speed on the exponent m and characteristic droplet diameter c of the R-R distribution.

In this work,water and kerosene are employed to investigate the liquid-liquid flow and liquid holdup in RSR with a high-speed camera.We carried out a preliminary research on the influence of different parameters,including volume flow rate,rotational speed and rotorstator distance,on the liquid-liquid flow pattern and liquid holdup pattern.We observed the liquid-liquid flow pattern of film flow and filament flow,as well as liquid holdup pattern of complete filling to incomplete filling.In consequence,two curves are obtained:the liquidliquid flow pattern transition curve qRe1.17=221.81G2.49We1.93and the liquid holdup pattern transition curve qRe0.43=162.01G1.93We0.89.These two curves visualizes the mass transfer performance and processing capacity in RSR,providing a new perspective to completely comprehend the liquid-liquid flow pattern and the liquid holdup pattern.We also correlate the average droplet diameter and size distribution so as to better describe the effect of independent parameters,including rotational speed,rotor-stator distance and volumetric flow rate.The 20%deviation between the calculated values and experimental results declares that the correlation is an ideal variable to predict the average droplet diameter size.Furthermore,the average droplet diameter and the mean energy dissipation rate are correlated to describe the influence of the input energy on the average droplet diameter.And according to our experiment,the R-R distribution fits well with the distribution of droplet cumulative volume.Compared with other spray and rotating devices,the liquid enjoys a better uniformity in RSR.Additionally,the average droplet diameter size and distribution on the basis of our experiment are also helpful to understand the mass transfer performance in RSR.It is predictable that factors affecting residence time distribution and velocity fields of immiscible liquid-liquid phase flow are essential to be studied exhaustively,thereby providing an insightful comprehension of RSR.

Fig.17.Effect of volume flow rate the exponent m and characteristic droplet diameter c of the R-R distribution.

Fig.18.Effect of rotor-stator distance the exponent m and characteristic droplet diameter c of the R-R distribution.