Breakage of drops and bubbles in a stirred tank:A review of experimental studies

Basim O.Hasan

Department of Chemical Engineering,Technical University of Berlin,Germany

Department of Chemical Engineering,Al-Nahrain University,Iraq

1.Introduction

Stirred gas-liquid or liquid-liquid dispersions are of a practical significance in many industrial processes.The phenomenon of drop or bubble breakage is encountered in a variety of processes such as mixing,extraction,absorption,biochemical reactions,food industry,water and waste water treatment,pharmaceutical synthesis,and various operations in the chemical process industry.An understanding of the parameters that affect the breakage of drops or bubbles( fluid particles)in dispersion systems is a very important issue in mixing processes.The fluid particle in a stirred system is a subject to different internal and external forces leading to break it into a number of daughter particles.The interactions between the agitation time and the level of turbulence close to the impeller will determine the drop breakage and coalescence rates for a given dispersion system[1].Over the years,there were numerous studies that have investigated the breakage of fluid particle(bubble or drop)in the stirred tank.These investigations used different techniques and methods to characterize the breakage phenomenon.Therefore,they arrived to different conclusions regarding the breakage mechanism and the effect of operating parameters.The objective of present text is to review the previous experimental works concerning the breakage of fluid particle in stirred tank systems.The review aims to present and discuss the major findings concerning the breakage mechanism and the effect of operating parameters.It is aimed also to identify the scientific gaps that still need further investigation and specify possible future developments in characterizing the breakage phenomenon.

2.Turbulence and Particle-Eddy Interaction

In a turbulent flow conditions,the breakage of fluid particles is caused mainly by the fluctuations of turbulent pressure on the fluid particle surface,or it is called particle-eddy collisions[1,2].The particle modifies its shape with the fluctuation of the surrounding fluid.When the amplitude of the oscillations approaches that required to cause the fluid particle surface being unstable,it starts to deform and break up into number daughter particles[3].Anders son and Anders son[4]stated that the turbulence is very structured eddies and the stresses which act on the particles because of the local velocity differences.They suggested that the interaction between particle and the turbulent eddies can take four ways as shown in Fig.1.The fluid particle can interact with several small turbulent eddies(Fig.1a),interact with a large turbulent eddy(Fig.1b),transported with a large eddy(Fig.1c),or it may be trapped by pair of eddies(Fig.1d).In case c,dispersed drops of lower density than the continuous phase are pushed toward the low pressure region in the eddy center.Higher density drop are pushed outward through the velocity gradient outside the eddy.Pairing of eddies(case d)is very probable and the trapping of fluid particles between two counter rotating eddies leads to transfer the energy from eddies.The contact time between fluid particle and the turbulent eddies is effective to cause a breakage which is dependent on the lifetime of the eddy[4].In general,larger eddies cause only transportation of the particles,while smaller eddies,only deform the fluid particles[5,6].

Fig.1.Interaction between turbulent eddies and fluid particles,a)interaction with several eddies,b)interaction with outer edge of eddy,c)transport with large eddy d)collision with paired eddies[4].

3.Breakage in the Stirred Tank

Understanding the mechanism of fluid particle breakage in the stirred tank and the factors influencing these phenomena is important for evaluating the transport phenomena in such systems and also for successful equipment design and process optimization.Different mechanisms have been proposed for the breakage of mother fluid particles.In general,the validation of such mechanisms against experimental results is still limited due to the complexity of the phenomenon and the experimental difficulties associated.

Many works have been carried out for particle size distribution while very limited experimental works have studied in details the mechanism of particle breakage in turbulent flow[7].It is well known that the hydrodynamics of stirred tanks are quite complicated with zones of high turbulence and others of low turbulence in which the viscous shear is more important.It was demonstrated that about60%of the energy transferred to the fluid by the impeller was dissipated in the impeller vicinity.The volume of this region is only about 10%of the total tank volume[8].Thus,most studies concerning the breakage showed that this region is characterized by high breakage rate.

Literature reveals that the breakage of fluid particles has been studied by two ways.First way,which is the early work,is the investigation of the breakage by determining the maximum stable particle diameter(dmax)or average particle diameter(d32)for the evolved population of particles.Then,the breakage rate was determined using inverse problemviaemploying the probability balance equation.Andersson and Andersson[4]stated that this method gives still images of the breakage at different locations in the flow.However,in this case the size distribution of the resulting daughters and the number of fragments formed upon breakage must be assumed.Hence,the breakage rates are not determined clearly and errors are possible.Determination of maximum or average diameter is useful to know the size distribution and its evolution.However,it does not provide knowledge about the surface phenomena of breaking fluid particle.The majority of data presented in literature for breakage are only the time dependency of drop size distribution which gives no direct in formation of how the breakage occurs[4].

The second way is by studying the surface phenomenon during the breakage stages of a single fluid particle using high speed imaging.This method is the best method which includes a direct experimental study of single breakage event.The use of high speed imaging,allowed the determination of breakage probability,breakage time,breakage type,and the breakage rate without the need of assumptions of the number and size of daughter particles.Despite that the high speed imaging has several limitations,it led to a deeper insight of the breakage phenomena.The data obtained using high speed imaging provide direct in formation on how the breakage occurs,the deformation and elongation,the number of fragments produced,the sizes and shapes of the daughter particles,the trajectory followed,and the relative location of breakage event.

4.Mechanism of Breakage in the Stirred Tank

Observing previous literature starting from the early work of Kolmogorov[9]and Hinze[2]and the subsequent analyses,reveals that the breakage mechanisms in stirred tanks are classified into four main categories:

(1)Turbulent fluctuations and collisions:Turbulence is characterized by the presence of high kinetic energy turbulent eddies which are highly rotating fluid elements.The highest values of turbulent intensity are observed at the blade tip and it decreases toward the tank's wall[10,8,11].Sanjuan-Galindoet al.[11]noticed that the deformed drops are pushed in the radial direction and then deformed and broken as a result of periodic collisions with the turbulent eddies.When the eddy interacts with fluid particle,it causes eddy-particle interaction.The response of fluid particle is not only dependent on the strength of interaction but also on the time scale of the interaction[4].This interaction continues for a time equals to the lifetime of eddy.Thus,the fluid particle tends to deform and stretch.If the lifetime and the energy of eddy are enough to overcome the coherence forces that hold the particle,the particle breaks up into number daughter particles.Small fluid particles or particles with high viscosity are more stable against the disruptive forces[12].Eddies containing less energy cause particle deformation only rather than breakage.One high energy eddy can result in the breakage or more low-energy eddies in succession can break the mother particle[5,6].

(2)Laminar shear stresses:A fluid particle in a flow is a subject to shear stresses as drag forces or/and lift forces.These shear stresses will establish a velocity difference around the interface which causes a deformation and breakage.Shear stresses also occur due to the wake effect.If the larger part of the particle is outside the wake region,the shear stress across the boundary of the wake can break the particle due to stretching,threading and necking.The particle firstly elongates into two lumps separated by a thread and breaks into two or more daughter particles[13-15].In case the thread is relatively thin,the high agitation speed can break it in to a relatively large number of fragments(daughter particles).Rueger and Calabrese[16]stated that the breakage resulting from simple shear is increased with increasing continuous phase viscosity.

Fig.2.Elongational flow field in front of blade[18].

(3)Shear of the impeller blade:According to this mechanism the breakage occurs due to the shear effect of the turbulent shear layer on the blade surface and due to the elongational flow field presentclose to the blade tip(Fig.2)[17-19].Due to no-slip condition close to the blade wall,the viscous layer in the wall vicinity provides a region for deforming and breaking the dispersed fluid particles even at low agitation speed.According to Kumaret al.[17],the flow pattern in the front of the blade can break the drops by stretching them.Because of the high gradient between mother particle and the shear layer in the blade vicinity,the mother particle can be broken into several daughters.Fig.3 shows the mechanism of breakage of fluid particle in the boundary layer of the blade as suggested by Shimizuet al.[20].The authors postulated that a strong shearing effect is presented in the boundary layer of the blades that leads to a breakage.Cristiniet al.[21]considered the mechanism is that the drops are broken by shear forces generated at the blade discharge.

Fig.3.Breakage of fluid particle in the boundary layer of the blade[20].

(4)Breakage due to the collision of particle with the blades:The impellers of sharp blades break the fluid particles without previous deformations or with low deformation time.Thus the energy required for breakage is low.Therefore,for such case,the inertia of fluid particle plays important role in the breakage[19].Sanjuan-Galindoet al.[11]stated that the mechanical impacts of impeller,baffles,and wall play a minorrole in the breakage of the drop.Martinet al.[19]found that,for Rushton turbine,the impeller rotation moves the bubble into the blade where it breaks up at the discharge.

5.Breakage Studies Through d32 and d max

Over the years,there were many works devoted to study the breakage of fluid particles by determining Sauter mean diameter(d32)and maximum particle diameter(dmax)when the dispersions process is breakage control,i.e.low dispersed phase fraction conditions.In this case,thed32is related todmax[19]which is a direct representative of breakage phenomenon.These studies showed that the breakage of the dispersed fluid particle is influenced by different operating parameters such as physical properties of the two phases,the hydrodynamics,the geometry size of the vessel,and the time of exposure of the mother particle to the flow field.Therefore,the major findings of previous works will be discussed here by the influence of these operating parameters.Table 1 lists a summary of previous works that investigated the breakage of fluid particles in stirred tanks through daughter particle size(d32anddmax).Table 1 includes the conditions investigated in each work,the two phase system,the dimensions of experimental apparatus,the breakage characterization parameters determined,and the measuring technique used.

5.1.Physical properties

The viscosity of both continuous and dispersed phases and the interfacial tension between them play a vitalrole in the occurrence of breakage.Stamatoudlset al.[22]found that the effect of continuous phase viscosity ond32is a function of the agitation speed.For kerosene,at low agitation speed,thed32increased with increasing viscosity of the continuous phase reaching a maximum and then decreased.For the case of mineral oil dispersion,thed32increased slightly and then decreased considerably when the viscosity of continuous phase increased to reach an asymptotic value.The authors reasoned the large decrease ind32to the high viscosity ratio between dispersed and continuous phases that increased the shearing effect of the continuous phase on the dispersed phase which enhanced the breakage.

Wang and Calabrese[23]found that increasing the dispersed phase viscosity(for the range shown in Table 1)led to an increase ind32,i.e.,the breakup decreases.The authors noticed that at low dispersed phase viscosity,drop sizes increase by more than a factor of six.While,for the high viscosity values,the drop sizes only vary by a factor of two because the influence of interfacial tension becomes less pronounced with the increase in the viscosity.In addition,increasing interfacial tension resulted in an increase ind32due to the decrease in breakage rate.Nishikawa,et al.[24]found thatd32increases linearly when decreasing the viscosity of the continuous phase.Sathyagal and Ramkrishna[25]investigated the breakage of 4 organic compounds(shown in Table 1)of different viscosities and inter facial tension.The authors found the breakage rate decreases with increasing both the viscosity and inter facial tension of the dispersed drops.The compound of highest inter facial tension gave the largest equilibrium drop sizes.This indicates that the higher the inter facial tension is the higher the daughter drop sizes regardless the viscosity value.

Shimizuet al.[20]noticed that the non-Newtonian properties of the continuous phase led to increase thedmaxparticularly at low agitation speed.Ruizet al.[26]noticed that the increase in temperature from 22 to 32°C decreases thedmaxfrom 0.43 to 0.37 mm due to the decreased viscosity of the dispersed phase.Kraumeet al.[27],for dispersion of different compounds in water,showed that the compound of lowest viscosity and highest interfacial tension(toluene)gave lowest particle size(d32),i.e.highest breakage rate.Additionally,the compound of highest viscosity(anisole)gave the highest value ofd32although its interfacial tension was low.That means that the viscosity is more effective than interfacial tension.This is in contrast to the finding of Sathyagal and Ramkrishna[1996]stated previously that the interfacial tension is the decisive.Maasset al.[28]and Solsvik and Jakobsen[7]for the breakage of different compounds in water in presence of surfactant PVA,found that the compounds of highest viscosity resulted in the highestd32.Patil and Kumar[29]noticed that thedmaxincreases approximately linearly with increasing interfacial tension and viscosity of the dispersed phase for low agitation speed.However,dmaxexhibited unstable trends with these two parameters for high agitation speed.Bak and Podgorska[30]noticed that the addition of PVA surfactant leads to a clear decrease ind32of the dispersed toluene droplets due the decreased interfacial tension which resulted in high breakage rate.

Overall,the results of the effect of physical properties stated above indicate that the effect of physical properties is mainly represented by the influence of two factors:the viscosity of both phases and the interfacial tension of the dispersed phase.The increase in the viscosity of the dispersed phase,leads to an increase in the disruptive forces exerted on the dispersed phasethat overcome the coherence forces that hold the dispersed particle entity.Therefore,the breakage rate increases and new daughter particles of smaller sizes are produced.The increase in the viscosity of the dispersed phase and in the interfacial tension,leads to an increase in the coherence forces that resist the disruptive forces and,thus,hold the dispersed particle entity.Therefore,the higher the viscosity or interfacial tension is the higher the daughter particle sizes.The value of the increase in the particle size with the viscosity or interfacial tension is not linear but dependent on the ranges of these two properties.However,observing above findings regarding the effect of physical properties reveals that there is confusion in the results regarding the effects of the viscosity and the interfacial tension on the sizes of the daughter particles.Where some studies showed that the interfacial tension is more effective than the viscosity while others showed the opposite.The interpretation of this can be as follows:both viscosity and interfacial tension influence the sizes of the produced daughter particles due to their influence on the coherence forces that resist the disruptive forces.In general,the higher the interfacial tension and/orviscosity is the higher the sizes of the produced particles.If the viscosity values of two compounds are comparable,the compound with high interfacial tension will result in higher particle size.If the values of interfacial tensions of the two compounds are comparable,the compound of high viscosity will result in higher particle size.If the values of interfacial tension and viscosity are considerably different for both compounds,the size of daughter drops depends on how much is the difference.The compound of high viscosity will produce larger particle sizes if the difference between the interfacial tensions is relatively small,whereas,the compound of high interfacial tension will produce larger particle sizes if the difference between the viscosities is relatively small.

Table 1Review of experimental works that investigated the bubble/drop breakage in stirred tank systems

Table 1(continued)

5.2.Hydrodynamics

The hydrodynamic behavior between the continuous and dispersed phases in the stirred tank is very complicated and,thus,it is not yet well understood.The roles of turbulent eddies,circulation,and vortices induced by the impeller that finally dissipate the kinetic energy are not so clear[3,31].

The majority of previous works that considered the effect of agitation speed on the particle breakage in agitated vessels showed that increasing the agitation speeds or energy dissipation rate leads to an increase in the breakage frequency.The percent increase depends on the physical properties of the two phases.Leng and Quarderer[32]indicated a sharp decrease in particle size with the agitation speed due to the increased breakage even for high values of dispersed phase fraction of 50%because of the use of surfactant(PVA)that prevented the coalescence.Nishikawaet al.[24]noticed that increasing the energy dissipation rate by increasing the agitation speed leads to a decrease in the drop size(d32anddmax).Takahashi and Nienow[33]showed that the increase in the impellers peed decreases the daughter bubbles diameter for different gases.Shimizuet al.[20]for weakly non-Newtonian continuous phase found that thedmaxdecreases by about 40%when the agitation speed is increased from 400 to 700 r·min-1.Ruizet al.[26]found that increasing the agitation speed led to increase the breakage frequency of the organic drops leading to a decrease in the sizes of the daughter drops.Siset al.[34]noticed that the asymptotic value ofd32of oil in water increases by about 6 times when the agitation speed decreased from 2500 to 1000 r·min-1.Angle and Hamza[35]and Patil and Kumar[29,36]found that increasing the agitation speed leads to a decrease ind32depending on the agitation time.In addition,no reduction in the daughter sizes was noticed beyond 1000 r·min-1.The work of Duabet al.[37]demonstrated that the increase in the power input decreases thedmax.Samarset al.[38]revealed no effect of the speed on the size and number daughter bubbles diameter.

The discrepancy in the results of previous works regarding the effect of hydrodynamics can be ascribed to different reasons.Firstly the ranges of the power input investigated in each particular study,and secondly the physical properties of the investigated dispersed and continuous phases.In addition,the uncertainty in the measurement techniques used also plays a role.For instance,the incapability of capillary suction probes to catch range of particle size,the disturbance of flow patterns associated with the probe insertion,the difference in sampling location,the use of imaging method for high dispersed phase fractions that produce overlapping and blurring,and the presence of range of fluid particles lower than the minimum detectable size of the cameras.The injection position of mother particles and the sampling location is a very important issue in determining the results.This is ascribed to the fact that close to impeller the breakage rate is high and decreases away from the impeller as has been evidenced by various workers[7,19,33].

5.3.Geometry

From the practical point of view,the industry includes various mixing tank geometries for different liquid-liquid or gas-liquid systems and conditions.The optimum design of stirred tank and the successful selection of impeller type and dimensions are important for successful mixing process.Geometry of the mixing system affects the breakage process by affecting the local energy dissipation rate.The impeller geometry has a direct influence on the breakage of fluid particles because the breakage occurs mainly in the impeller region[8,39].

Table 1 indicates that different geometries and dimensions of agitated systems have been used to investigate the breakage phenomenon for various experimental conditions.Leng and Quarderer[32]found that the presence of baffles causes a reduction in the particle size up to 70%.The authors reasoned that to the increased shear at the impeller tip due to the presence of baffles.Observing the results of Nishikawaet al.[24]indicates that for a constant value of energy dissipation rate,increasing the impeller diameter leads to an increase ind32.This trend seems to be in contradiction with the findings of Konnoet al.[40]that showed that the higher the impeller diameter is the lower the daughter drop size.Zhou and Kresta[1]investigated the effect of the impeller geometry on the drop size(d32)using four impeller types(shown in Table 1)with varying diameters and relative positions from the tank's bottom,i.e.the clearance.The results indicated that there are noticeable differences in the size of drops evolved for each case due to the difference in breakage rates.The differences in thed32reached up to 300%.Giaposet al.[41]found that thed32decreases linearly with increasing number of blades.The decrease reached up to 50%when the number of blades increased from 2 to 8.Sechremeliet al.[42]observed that the open style impeller produces larger diameter daughter drops than that produced from disc impeller at the same speed.The reason was that the power number of disc style impeller was higher than that of open style impeller and therefore energy dissipation rate is higher.Martinet al.[19],for different impeller geometries,indicated the breakage rate in case of propeller impeller was relatively low due to the absence of sharp edges.

Maasset al.[43]found that the drop breakage is influenced by different geometrical parameters such as impeller type,baffle dimensions,liquid height,and clearance between the impeller and the tank's bottom.Their results showed that the blade baffles give smaller particle diameter(d32)than the cylindrical ones for the investigated range of mixing time.The average difference ind32reached about 20%.Patil and Kumar[29,36]found that the larger the impeller diameter is the lower the value ofdmax.Thedmaxattained in the case of an impeller diameter of 60 mm is 2/3 of that attained by and impeller diameter of 40 mm.Duabet al.[37]found that a higher power input is necessary to achieve the samedmaxfor the larger ratio ofDi/DTthan for the smaller ratio.Furthermore,thedmaxdecreased with the increased power input.

It is to be noted from the above stated results that the tank dimensions,impeller geometry and baffle types and dimensions influence the produced drop sizes significantly by affecting the breakage phenomena.However,the influence depends on the properties of the continuous and dispersed phases and on the agitation speed.As a general trend,increasing the impeller diameter leads to a decrease in the daughter size due the increased energy dissipation rate.Nevertheless,Nishikawaet al.[24]found that increasing the impeller diameter caused an increase in daughter drop size.The reason behind that could be in that work the samples were taken at a point above the impeller at almost midpoint between the impeller and liquid surface.At this point the coalescence is probable[44,45].The size of the tank and its design such as baffle shape,dimensions,and impeller geometry influence the trajectory followed by the injected mother fluid particles.Therefore,the breakage rat will be influenced also by the design parameter because it is a direct function of the trajectory followed as has been observed by some studies[7,19].When the trajectory approaches the high energy dissipation rate region,the breakage probability increases and smaller daughter particles are produced.

5.4.Agitation time

The studies listed in Table 1 for various conditions and fluids,reveal several attempts to characterize the breakage by estimating the maximum particle diameter(dmax)or Sauter mean diameter(d32)that is attained with increasing agitation time.Konnoet al.[46]showed that increasing the agitation time from3 min to 300 min reduces the average drop diameter by up to 75%due to the increase in the drop breakup.Nishikawaet al.[8]found thatd32decreases rapidly with time when the agitation speed increases from 100 to 200 r·min-1reaching an asymptotic value after about 2.5 min.

The results of Wright and Ramkrishna[47]revealed that the reduction in the agitation speed from 1200 to 400 r·min-1increases thed32from 108 μm to 202 μm at 40 min after the reduction.This is due to the decreased breakup and increased coalescence.The results of Lamet al.[48]indicated that for low viscosity dispersed phase,the drops continue to break throughout 8 to 10 h,while for high viscosity dispersed phase,no breakup occurred after 8 h.It can be noted from the work of Lamet al.[48]that the high surface tension compound continues to break up longer than the lower surface tension ones.Sathyagal and Ramkrishna[25],for the dispersion of different organic compounds in water,observed that the breakup continues up to 30-75 min of agitation.The results of that study indicated also that the high surface tension compounds take longer agitation time(75 min)than other compounds to reach the equilibrium daughter drop size.The results of Sathyagal and Ramkrishna[25]also revealed that the lowest viscosity and surface tension compound give the lowest values of equilibrium drop diameters and take the shortest agitation time to reach these values.Fornon-Newtonian fluids investigated by Shimizuet al.[20],the time required to reach the equilibrium diameters was 1 h.The results of Kraumeet al.[27],for dispersion of anisole in water,indicated that the sizes of large daughter drop decrease by up to 50%after 1 h of agitation time.When the agitation time continues from1 to 65 h,the further decrease in the sizes is up to 50%too.Hence,the largest decrease in the daughter drop diameters is in the first hour due to the presence of large drops which are easily broken by hydrodynamic forces arising from viscosity and/or turbulent pressure fluctuations.Sechremeliet al.[42]for toluene dispersion in water found that the agitation time of15 h is required to reach the equilibrium state(constantdmax).The same trend was noticed by Siset al.[34]for agitation time up to 65 min for a wide range of agitation speed.

The data obtained by Patil and Kumar[36]indicated that thedmaxis attained after about 20 h of agitation forDi=40-70 mm.Maasset al.[43],for the dispersion ofn-butyl chloride in water,noticed a sharp decrease in thed32with time especially at the first 10 min of agitation.Then,the diameter reaches asymptotic value with no significant change ind32after about 1 h.The results of Maasset al.[28]indicated that for toluene dispersion in water,the required agitation time to reach the equilibrium value is independent of the dispersed phase fraction.In addition,the daughter drop sizes of toluene decrease significantly in the first few minutes of agitation reaching an asymptotic value after about 10 min.Furthermore,the time required to reach the asymptotic value is weakly dependent on agitation speed and dispersed phase fraction.Bak and Podgorska[30],for toluene dispersion in water,noted that the largest decrease ind32was in the first 30 min of agitation due to the easy breakage of big drops.In addition,the time required to reach the equilibrium size was clearly independent of the agitation speed.Duabet al.[37]noticed that after 90 min of agitation,the drop size reaches a stable value.Further agitation up to 9 h resulted in a decrease in drop size by up to 10%.Tokanai and Kuriyama[49]found that the mean drop size decreases slightly with agitation time up to 8 h.The trend of daughter drop size with agitation time indicated that the highest decrease was in the first 2 h.

Strictly speaking,the results of the effect of agitation time mentioned previously indicate that the agitation time affects the particle size distribution by increasing the probability of breakage due to the longer exposure to viscous and inertial stresses.The major reduction in the size of daughter particles is at the start of the agitation due to high breakage rate because most fluid particles are relatively large.As the agitation time proceeds,the particle sizes decrease in an asymptotic manner reaching an equilibrium value beyond which no further breakup is possible.At equilibrium,the disruptive forces are no longer able to overcome the coherence forces that stabilize the particle because more energy will be required to overcome the stabilizing forces.The agitation time required to reach the equilibrium size is weakly dependent on the agitation speed.However,it is strongly dependent on the interfacial tension and viscosity of the dispersed phase.The relatively high sizes of daughter particles evolved in the case of high interfacial tension and high viscosity fluids,need longer agitation time to reach the equilibrium.This is due to the fact that the energy required to break the large size particles is low compared to the energy required to break the small ones.As the daughter particles of the fluids of high interfacial tension and viscosity are relatively large,they survive longer and,thus,the time required to reach the equilibrium diameter becomes longer too.

6.Breakage Dynamics Studies of a Single Fluid Particle

In the last decade,important results regarding the breakage dynamics and mechanisms were obtained from a single fluid particle breakage using the high speed imaging technique.This type of study is very successful and informative to understand and characterize the surface behavior of breaking particle to estimate breakage rate.This is attained by following the mother particle motion using high speed cameras to observe the deformation,the number of mother fluid particles that break up,the breakage locations in the tank,and the instantaneous birth of daughter particles.In addition,it enables to estimate the sizes and number of daughter particles under highly non-uniform turbulent conditions.Following the particle behavior before breakage when approaching the breakage zone and after the breakage when it is pushed away,is very interesting to understand the breakage mechanism and surface phenomena.In addition,this way provides deep understanding of the deformation before the breakage,the shapes of daughter particles,trajectory followed,deformation time,and breakage time that is prerequisite to estimate the breakage rate.

The breakage models proposed over the years give different predictions of breakup rates as these models are based on different breakage mechanisms.Investigating the dynamic breakage mechanism in detail by single bubble/drop breakup experiments improved the prediction of breakage models[50,51].Studies concerning the breakage of fluid particle by following a single drop or bubble using high speed camera are listed in Table 2.The table includes the investigated two phase system,the dimensions of experimental apparatus,the operating conditions,and the measured breakage characterization parameters.

6.1.Deformation

The particle dynamics influence the behavior prior to breakage.In turbulent field,the mother drop/bubble undergoes continuous deformation and relaxation processes.Kolmogorov[9]and Hinze[2]proposed that the velocity fluctuations over a distance approximately equal to particle diameter are able to cause a large deformation.The extent of deformation is determined by the stabilizing interfacial tension,viscosity,and deforming forces of successive turbulent eddies[52].If the trajectory of mother bubble or drop approaches the impeller vicinity,the deformation will be larger than the case if the trajectory is far from the impeller vicinity.In addition,when the difference between the speed of flow currents discharged from the impeller and the mother fluid particle is high,a large deformation may occur.In this case the deformation may lead to a breakage or may not,depending on the surface tension of dispersed phase and viscosity of both phases.The mother fluid particle may break up or become highly deformed and relax without breakage.In the case of high energy dissipation,the flow currents that are discharged from impeller may push the mother particle away to break up relatively far from the impeller.In this case,the breakage occurs often with low breakage time.The deformation would cause a breakage if it is large enough[53].Previous works showed clearly that the drop elongation plays an important role in the breakage of mother drop[54].The elongation value and the time depend on the physical properties particularly on the viscosity of the dispersed fluid particle.A high viscosity drop often highly deforms before breaking up[4].

Figs.4 and 5 show the experimental results of elongation of different viscous particles in the blade region obtained by some previous workers[7,55,56,58].In Fig.4,the mother drop elongates to a long thread taking a certain interval of time and then it breaks up into several daughters.Taking thread shape makes it easier for the mother particles to break up into relatively large number of small daughters because the surface will no longer resist the disruptive forces.Observing literature indicates that the deformed mother particle can take different shapes depending on the level of turbulence,the physical properties,and the size of mother fluid particle.Fig.5 shows typically deformed shapes of fluid particle in a stirred tank obtained by different authors by using high speed camera.Kekesiet al.[78]showed that the deformation starts atWeof 1 where the drop turns into oblate spheroid and becomes more stretched.The deformation of a drop increases asWeincreases reaching a critical value of 12 at which the breakage occurs(Fig.6).

Konnoet al.[46]noticed that the multiple breakages often occur after gradual elongation of drops in different directions.Nachtigallet al.[6],in the investigation of drop deformation and breakage when crossing a single blade,noticed that the drop undergoes a microscopic deformation after forming a dumbbell-shaped geometry.The drops get elongated forming spherical ends connected through a thin filament.The authors noticed that the addition of surfactant(SDS)leads to an increase in the deformation of fluid particle producing a longer thinner filament.The building of spherical ends considerably became less pronounced when adding SDS.The high viscosity paraffin oil was noticed to form spherical ends and dumbbell shaped.Fig.7 shows the deformation of paraffin drop obtained by Nachtigallet al.[6].This figure indicates that the strong deformation is more likely to result in a breakage(cases a and b).In case c there is no breakage despite the large deformation of mother drop.

For viscous fluid particle,Sanjuan-Galindoet al.[11]observed that some of these filaments are stretched,elongated,and breakup.When the filaments are pushed into a non-turbulent flow,they simply recoil or remain stable.In the stirred tank,the two cases are possible due to non-uniform flow patterns that may exhibit turbulent or nonturbulent conditions.

Table 2Studies concerning single particle breakage in stirred tanks

Fig.4.Elongation of toluene drop when crossing the blade[55].

Fig.5.a-toluene-in-water[7],b-air bubble prior to breakage[58],c-air bubble flattened prior to breakage[56].

Fig.6.Increasing deformation with increasing We[78].

Fig.7.Paraffin oil drop crossing single blade,A-dumbbell shape deformation(significant deformation)resulting in a breakage,B-irregular deformation result in a breakage,C-deformation without breakage[6].

Sanjuan-Galindo[11]proposed that the fluid particle breakage in a stirred tank follows a four step mechanism.The first step is the approach of mother particle to the turbulent field.The second step is the deformation of mother.The third step is the fragmentation.Fourth step is the dispersion of daughter particles away from the impeller.

The breakage probability is the ratio between the number of broken lfuid particles and the total number of injected fluid particles of a given size[55,57].Konnoet al.[46]investigated the breakage in a stirred tank by determining the transient drop diameter and by following the drop motion using high speed camera.The authors noticed that the ternary breakup is predominant for the whole investigated range ofdpand agitation speed.For single drop breakage in a stirred tank,Hancil and Rod[59]found that increasing the volume of the mother drop from 3 mm3to 39 mm3leads to an increase in the average number of daughter drops from 2.5 to 6.Kuriyamaet al.[60]for a single drop breakage of different viscosities noticed that the increase in the viscosity of mother drop leads to an increase in the number of daughter drops.For the range of mother drop diameter of 1 to 3 mm,Kuriyamaet al.[60]noticed that the number of daughter drops is from 4 to 20 depending on the viscosity and agitation speed.They noticed that increasing Reynolds number from

6.2.Breakage events

15000 to 42000 leads to an increase in the number of produced daughter drops from 5 to 26.Sathyagal and Ramkrishna[25]concluded that increasing the mother drop size results in an increase in the breakage rate.

Maasset al.[61]found that the majority of breakage events were binary.For the smallest mother drop(dp=0.56 mm),the probability of binary breakage was 60%.Fordp=1,the probability of binary breakage was 35%and fordp=2,it was about 12%.The mother drop diameter ofdp=2 mm,produced highest probability of multiple breakage.The authors found that increasing the mother drop size increases the probability of multiple breakages.Up to 20 daughter drops were produced from 2 mm mother drop.The lowest flow velocity gave highest probability of binary breakage.Maasset al.[62]noticed that the mother drop of toluene of 2 mm diameter breaks up into 27 daughters at velocity of 1.5 m·s-1.Maass and Kraume[55]found that the multiple breakage probability increases with increasing the mother drop diameter.Solsvik and Jakobsen[7,58]noticed that the number of fragments is dependent on the mother drop diameter(dp).Fordp=0.6-4 mm,the probability of multiple breakage increases with the increase indp.The mother drops of diameter from 2 to 4 mm produced more than 9 fragments.For binary breakups,the daughter drops were often of equal sizes.Galinatet al.[57]stated that the fraction of broken drops increases with the increase mother drop diameter and flow velocity.Solsvik and Jakobsen[58]found that the binary and multiple breakages often result in a non-equal-sized fragments.For the whole investigated range of agitation speed,the probability of equal size breakage was less than 10%.Fig.8 compares the values and ranges of breakage probability obtained by various authors for the stirred tank.The figure gives the ranges of binary and multiple probabilities.The ranges presented in Fig.8 are for different operating conditions and mother particle sizes in the stirred tank shown in Table 2.

The above stated studies reveal that,in general,the breakage probability increases with increasing agitation speed and mother particle size.In addition,it can be deduced from above previous works and from Fig.8 for single bubble/drop breakage that there is a clear discrepancy in the number of daughter bubbles(fragments)obtained.The fragments number can be 2 to up to several tenths depending on mother particle size and energy dissipation rate.The number of produced daughter particles is depending mainly on the agitation speed(or energy dissipation rate)and on the mother particle size.The higher the energy dissipation rate and mother particle size the higher the number of fragments.The discrepancy is also ascribed to the difference in the physical properties of fluids and to the precision of the measuring devices.Previous works indicate that the number of daughters in a stirred tank is relatively high compared to other systems such as pipe flow.The breakage is multiple often and therefore the assumption of binary breakage in the modeling of the stirred tank is certainly a rough assumption.The trend to multiple breakage increases with increasing energy dissipation rate in a manner depending on the mother particle size and physical properties of both phases.

6.3.Breakage time

Breakage time(tb)is the time scale of the fragmentation process taken from the start of deformation of a spherical mother particle to the occurrence of breakage that has produced the final population of daughter particles[7,58,63].Another definition oftbis the time needed to break the undeformed mother particle,i.e.the time taken from the beginning of deformation to the first breakage event[55,64].It is always more efficient to determine the breakage probability by experimentally determining the breakage time.Breakage time is a key parameter for calculating the breakage ratevia:

Literature reveals different ways for determining the breakage time and,thus,it shows a clear discrepancy of the values obtained experimentally.Hermannet al.[65],Maass and Kraume[55],and Nachtigallet al.[6]considered the breakage time to start from the instant when the drop crossed the stirrer blade until the breakage occurs.Heskethet al.[53]considered the time instant at which the breakage time starts the initiation of the large scale deformation that leads to a breakage.Solsvik and Jakobsen[6]considered the breakage time as the time that starts from the beginning of the deformation of a spherical drop to the last breakage event.Following Heskethet al.[53],Solsvik and Jakobsen[58]considered the breakage time starting from the relatively large deformation(extra deformation)that led to a breakage to the last breakage event.

Fig.8.Breakage probability by various authors,binary breakage multiple breakage.

The results of Konnoet al.[46]indicated that the larger the mother drop diameter the larger the breakage time and the longer the length of drop movement during the breakage.The values of breakage time attained were dependent on the geometry,agitation velocity,and the position in the tank.The average breakage time was in the range of 1.4-6.9 ms.Hancil and Rod[59]used lifetime(residence time)of mother drop to characterize the time required for breakage for different sizes of mother drop.They considered the lifetime to start from the instant of injection to the breakup.The authors noticed that the lifetime increases from 2.7 s to 26.7 s when the volume of mother drop decreases from 39 to 3 mm3.Maasset al.[61]found that the average breakage time is 10 ms for breakage of drop in the stirred tank.Maass and Kraume[55]found that the breakage time decreases in a non-linear manner with increasing the drop size for both toluene and kerosene drops.The trend showed a slight increase intbwhen the mother size became relatively large,i.e.there was a minimum.In addition,the breakage time for petroleum drop(higher viscosity and surface tension)was larger than that of toluene.Walter and Blanch[66]found that the breakup time increases with an increase in the viscosity of continuous phase.Values of breakage time of Maass and Kraume[55]showed a relatively high standard deviation around the average.The authors reasoned that to the fact that the trajectory of the bubbles determines the breakage time.Some drops take long trajectory before breaking while others break up when hitting the blade.In addition,the small drop exhibited long breakage time because its small size allows it to circulate for a relatively long time before breakage.The range of average breakage time for the chemicals used was 12.4-34.0 ms depending on mother drop size.Solsvik and Jakopsen[7]noticed that the breakage time increases with increasing diameter of the mother drop.This is in contradiction with Mass and Kraume[55]who found that the breakage time,generally,decreases with increasing mother size.The breakage time was in the range of 10-100 ms.The authors ascribed this to the increased breakage events when increasing the diameter of mother drop which led to uncertainty to determine the final breakage time.The 1-octanol exhibited highest breakage time amongst four chemicals used.The reason behind this was that the 1-octanol was of high viscosity and thus it showed higher degree of deformation.The higher the interfacial tension drop was the higher the breakage time.

Observing the results of Solsvik and Jakopsen[58]indicates that the breakage time is independent of the mother bubble diameter.In addition,for the range of agitation speed of 500 to 700 r·min-1,no clear effect of the agitation speeds on the breakage time.The authors reasoned the absence of expected trend of breakage time with speed and mother bubble size to the difficulty in determining exactly the beginning of a breakage process.Cliftet al.[67]and Nachtigallet al.[6]considered the drop to be still spherical if it undergoes deformation less than 10%.The results of Nachtigallet al.[6]indicated that the oscillation and deformation times were often below 25 ms for most mother drops crossing the blade.The average oscillation time was 34.7 ms.In addition the increase in the viscosity of the mother drop causes a higher deformation prior to the breakage.Therefore,the deformation time increases with increasing viscosity of the dispersed phase.

The wide discrepancy in breakage time and breakage probability values obtained by the previous studies can be reasoned as follows:

(1)The difference in the definition of the concept of breakage time adopted by various authors as stated above;

(2)The difference in the geometry and experimental conditions investigated;

(3)The difference in specifying the start of deformation that leads to a breakage;Because in stirred tank the turbulence is highly non-uniform,the beginning deformation that leads to a breakage cannot be specified accurately.This is because the mother particle is in continuous small-scale deformation and relaxation when approaching the impeller zone[53,58]due to the interaction with highly turbulent eddies.This issue is strongly dependent on the physical properties(viscosity and surface tension)and the size of mother particle.The largest deformation that causes breakup should be considered to determine the breakage time.In fact,the literature does not specify how much exactly the value of deformation from which one can start estimating the breakage time as this issue is a matter of argument.However,under certain conditions the mother breaks up with out clear deformation as in case of collision with the blade or when meeting turbulent eddies of high kinetic energy.In this case,the start of breakage time is more complicated because the beginning deformation is not so clear.

(4)The differences in the trajectories of mother particles because the trajectory is influenced by several parameters such as the level of turbulence,position of injection of mother particle relative to the impeller,and the size of mother particle;The length of the trajectory is influenced by fluid mother particle size as the small particle may resist the disruptive eddies more than the large ones and thus takes longer trajectory.

(5)Uncertainty in identifying exactly the instant of the first breakage event due to the resolution limitation of the cameras that causes missing of very fine daughters that may fragment at first moments of breakage process;In addition,the overlapping of daughters,especially in the case of high number of fragments,can also lead to uncertainty in identifying the last breakage event.Besides,the two dimensional image may also avoid seeing the instant of the beginning deformation that may occur in the third dimension.Failure in performing enough number of observations of breakage events(or experimental tests)also leads to uncertainty in the breakage time value and,thus dependency.In most studies,this issue has not been well considered,which can explain some of the disagreement in literature values[12,56].Accordingly,it is very important to perform enough number of experimental tests to obtain statistically significant and reproducible results.

All the works stated above investigated the breakage time which was considered as the interval from the start of deformation to the initial breakage or to the final breakage event.However,no attention is paid in literature to the interval between the initial breakage event(i.e.first breakage)and the final breakage event(i.e.last breakage).In fact,this interval is important because it can be including a number of breakage events depending on the size of mother particle and on the energy dissipation rate.If the size of mother particle is relatively large and the energy dissipation rate is relatively high,the mother particle will undergo successive breakages for a time interval producing more small daughters.This interval may also include coalescence depending on the number of daughter particles produced and the probability of collision between them.The trend of this interval with mother size and energy dissipation rate has not been characterized in the open literature.

6.4.Breakage zone relative to the impeller

In stirred vessels the breakage zones are quite unpredictable because of the complexity of hydrodynamics that produce anisotropic turbulence.Several investigators[11,54,68]have analyzed the hydrodynamics of stirred vessel and showed that the energy dissipation rate in the impeller region is larger than its average value in the whole vessel.Sanjuan-Galindoet al.[11]postulated that the maximum fluid speed is at the blade discharge which is about half the speed of blade tip.Therefore,the breakage rate is higher in the impeller region.

The reported literature indicates various spatial dependence of the breakage in stirred tanks.Takahashi and Nienow[33]noticed that the breakage in the tank is distributed over a wide area.The results of Laakkonenet al.[44,45]reveal a clear local difference in the bubble sizes(d32)around the impeller and also in the tank wall region due to the local dependence of breakage.There is also a tangential and axial variation ind32.The authors ascribed the tangential variation ind32to the effect of baffles that disturb the similarity of the flow patterns.

The use of high speed cameras helped a lot to understand the local dependence of breakage.Konnoet al.[46]observed that the breakage positions outside of the impeller-disc are different and distributed around the impeller and also far from it.Solsvik and Jakopsen[7]investigated the breakage locations in a relatively small stirred tank(dimensions are shown in Table 2)by injecting a single drop.They found that the active breakup zone was only close to the blade tip,while,it seldom occurred in the top,bottom,or wall region which is the same observation of Bak and Podgorska[30].The authors noticed that the breakage rate away from the impeller is very low or is completely not probable due to the very low dispersed phase fraction and small particle sizes.Solsvik and Jakopsen[58]found that the final breakage events occurred often close to the wall in front of the blade.They stated that the position of injecting the mother bubble influences the breakage zone because it influences the trajectory of the mother bubble.

The probability of breakage in a certain position in the vessel depends on the turbulence intensity in that particular zone.The high turbulence zone provides a large probability of interaction between eddy and drop due to the high velocity fluctuations.Close to the blade tip,the breakage is mainly due to the shear effect while at a distance away from the blade tip,the breakage is due to the turbulent eddies or velocity fluctuation.The distinction between the two is difficult and thus it is difficult to know whether the particle breakage is caused by either mechanism.In general,for low stirring speed,the mother fluid particle tends to go close to the blade tip and breaks up there mainly by shear effect or by collision with blade.For high stirring speed,the flow currents that were discharged from the impeller tip push the mother particle away toward the wall to break up there by turbulent eddies mainly.The velocity gradient between the mother surface and the continuous phase is also effective in the case of high stirring speed.This is a general trend,but because the turbulence in the stirred tank is highly anisotropic,one can see some mother particles break up far from impeller even at low stirring speed.However,at high turbulence level,the mother particles can be driven by the flow currents and vortices to a location very close to the blade tip and break up into relatively high number of fragments.

The use of high speed imaging is a successful and promising method to study and characterize the breakage of fluid particle at various locations in the agitated vessels.This technique led to important specific information related to breakage mechanism particularly at high turbulence levels.Using high speed cameras,the motion of the fluid particle can be monitored clearly at different zones of the tank even at high agitation speed.However,disadvantages and difficulties are still associated with use of imaging method.These are[7,69,70]:the particle volume is not directly obtained only in two dimensional image,sometimes the very small particles cannot be captured by the camera,the particles present in the middle of flow or in the backside are notclear,and overlapping of daughter particles that avoids seeing some breakage events.

7.Conclusions

From this review,it is clear that in the last four decades,there were considerable efforts paid by researchers for understanding and characterizing the breakage of drops and bubbles in agitated tank systems.However,several issues regarding the phenomenon have not been well characterized yet.The investigations concerning the breakage of fluid particle are related to two major aspects.The first one concerns the surface and interfacial phenomena related to the mechanism of the breakage.The second one is the effect of various operating parameters on breakage phenomenon.The majority of breakage studies attempted to characterize the phenomenon through determining the size of daughter particles represented by maximum daughter particle diameter(dmax)or Sauter mean diameter(d32).Although such investigations provided important in formation,they were unable to accurately characterize the breakage rate and surface phenomena of breaking particle.In recent ten years,the use of high speed cameras of high capturing features led to a deeper insight of the breakage phenomenon especially for the concepts related to the mechanism and surface behavior.However,a comprehensive characterization of breakage phenomenon is still in the early stages and there are many challenges lying ahead.The review reveals a clear discrepancy and contrast in the experimental results concerning the surface behavior and the effect of operating parameters.The reasons behind this are the complexity of breakage phenomenon,the difference in the range of operating parameters investigated,the difference in physical and chemical properties of the used compounds,and the precision of the measuring techniques.The mechanism of the breakage in the stirred tank is related to four categories:turbulence fluctuation,shear effect of boundary layer in the blade vicinity,velocity gradient between mother particle and bulk fluid,and collision of mother fluid particle with the blade.As a general trend,the breakage frequency is increased with increasing energy dissipation rate,increasing continuous phase viscosity,and increasing agitation time.The probability of multiple breakage increases with increasing agitation speed and size of mother particle.There is no complete agreement in the literature about the trends of breakage time with agitation speed and mother particle size.The location of breakage event is dependent mainly on the trajectory followed by mother particle which in turn is a function of the prevailing conditions such as power input,mother particle size,and the dimensions and design of the stirring system.The highest breakage probability is close to the impeller region often.Further efforts are still required to investigate the breakage phenomenon using high speed cameras of high technical abilities to gain deeper insight of the parameters related to the mechanism of the breakage(such as deformation,breakage time,size and shape of daughter particles,the relative location of the breakage)and the effect of operating conditions.The effect of mother particle size on the breakage rate and on the size and number of daughter fluid particles is still not well characterized especially at high energy dissipation rate.Experimental works that considered the breakage under severe mixing conditions(high temperature,high pressure,high viscosity or high density fluids,etc.)are currently scarce in literature.

Nomenclature

Cclearance from vessel's bottom,m

Ddiameter,m

dparticle diameter,m

d32Sauter mean diameter,m

Gbreakage probability

Hliquid height,m

Nagitation speed,r·min-1

nbnumber of particles broken

nTnumber of particles injected

Ppower input per unit mass,cm2·s-3

Qvolumetric supply,m3·s-1

Rradius,mm

ReReynolds number

Ttemperature,K

ttime,s

Vvolume,m3

WeWeber number

μ kinetic viscosity,kg·m-1·s-1

σ inter facial tension,N·m-1

Φ dispersed phase volume fraction

Subscripts

b breakage

c continuous phase

d dispersed phase

i impeller

max maximum

p mother particle

T tank or total

Abbreviations

BCT benzene-carbon tetrachloride

BSD bubble size distribution

DEPSCT dirnethylpolysiloxane-carbon tetrachloride

DMPSCT 20 dimethylpolysiloxane(20 mPa·s)-carbon tetrachloride

DMPSCT 200 dimethyl polysiloxane (200 mPa·s) - carbon tetrachloride

DSD drop size distribution

HCT heptane-carbon tetrachloride

PVA polyvinyl alcohol

SDS sodium dodecyle sulfate

Acknowledgments

The author appreciates Alexander von Humboldt Foundation for supporting a research fellowship in the Technical University of Berlin.The author also wishes to thank Prof.Mathias Kraume/Chair of Chemical and Process Engineering/Technical University of Berlin,for hosting the research fellowship.Sincere thanks to Mr.Frederic Krakau/Technical University of Berlin,for his assistance during the research stay.

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