Baoqing Liu,Yijun Zheng,Ruijia Cheng,Zilong Xu,Manman Wang,Zhijiang Jin*

Institute of Process Equipment,College of Energy Engineering,Zhejiang University,Hangzhou 310027,China

Keywords:Non-Newtonian fluids Coaxial mixer Gas holdup Relative power demand Mass transfer

A B S T R A C T The effects of impeller type,stirring power,gas flow rate,and liquid concentration on the gas–liquid mixing in a shear-thinning system with a coaxial mixer were investigated by experiment, and the overall gas holdup,relative power demand,and volumetric mass transfer coefficient under different conditions were compared.The results show that, the increasing stirring power or gas flow rate is beneficial in promoting the overall gas holdup and volumetric mass transfer coefficient,while the increasing system viscosity weakens the mass transfer in a shearing–thinning system.Among the three turbines,the six curved-blade disc turbine(BDT-6)exhibits the best gas pumping capacity;the six 45°pitched-blade disc turbine(PBDT-6)has the highest volumetric mass transfer coefficient at the same unit volume power.

1.Introduction

Gas–liquid mixing equipment is applied widely in industries such as pharmaceutical,food,biochemical,and petrochemical engineering.The mixing operation will expand the contact area between phases,promote the gas–liquid dispersion,and enhance the heat transfer,mass transfer,and reaction between phases[1–7].

The survey results indicate that the influence factors and evaluation indexes for the gas–liquid mixing are numerous and complex.On the structure parameters,Vasconcelos et al.[8]researched the influence of the blade shape on the gas–liquid dispersion,and found that streamlined impellers had lower power consumption and stronger pumping capacity.On the operating parameters,Zhang et al.[9]investigated the influences of stirring speed and gas flow rate on the gas–liquid mixing.It was found that the mixing time would increase with the increasing gas flow rate when the stirring speed was higher than critical flooding point.Gao[10]investigated the influences of gas flow rate,stirring speed,and system temperature on the local bubble size,and found that the bubble size increased with increasing gas flow rate and system temperature and decreasing stirring speed.Some researchers focused on the power consumption of the gas–liquid mixing.Taghavi et al.[11]investigated the gas–liquid mixing of dual Rushton turbines and found that power consumption decreased as gas flow rate increased.Other researchers investigated the flow pattern in the mixing process.Morud and Hjertager[12]investigated the gas flow field with a Rushton turbine by Laser Doppler Anemometry technology.They found that gas was accelerated in radial direction at impeller level and reached a maximum at the impeller tip.Wang et al.[13]experimented and simulated the gas–liquid mixing with a single Rushton turbine,and found that a secondary circulation loop appeared with increasing stirring speed.However,most scholars adopted water as the liquid phase to investigate gas–liquid mixing by experiment[14–16].

In practical industrial process such as fermentation,most agitated materials are viscous system and even non-Newtonian fluid[17].The influence of the system viscosity is an essential factor on the gas dispersion and mass transfer.Gavrilescu and Roman[18]found that apparent viscosity had more effect on the mass transfer coefficient than that on the overall gas holdup.Gabelle et al.[19]studied the influences of impeller type,impeller diameter,and vessel diameter on the gas dispersion in xanthan gum solution,and established formulas on power consumption and volumetric mass transfer coefficient.Zhou[20]investigated the gas–liquid dispersion of air–xanthan gum system under three-layer impellers,and found that the lowest impeller affected the relative power demand a lot.

Single impeller or multiple impellers on a single shaft are mostly adopted in the traditional fermentation industry. To improve the mixing performance with better gas dispersion and mass transfer,larger blades or higher stirring speed is required to be achieved. However, large shear rate under high stirring speed will destroy the structure of the cell or molecule in the agitated material and affect the product quality.Hence,a coaxial mixer was adopted to study the gas–liquid mixing in a viscous system in these years.It is a kind of mixer with two independent systems of inner and outer shafts.The action of the outer impeller decreases the requirement of inner impeller speed and leads to a better dispersion in the vessel.Liu et al.[21,22]studied the influence of impeller combination on the gas holdup and bubble size in viscous malt syrup with a coaxial mixer.Hashemiet al.[23–25]investigated bubble behavior and mixing time in an aerated coaxial mixing vessel filled with viscous corn syrup,and established novel correlations for the gas flow number and gassed power.For a shear-thinning system,a single-axial mixer will lead to obvious viscosity gradient,which makes gas difficult to spread out of the blade area.The benefits of a coaxial mixer are more significant under this working condition. However, few researches were reported on this.Though Espinosa-Solares et al.[26,27]creatively studied the gas–liquid mixing with an outer ribbon impeller in a shear-thinning system,their investigations about the mixing time and flow pattern were qualitative and do not refer to the mass transfer behavior.

In this work,we investigate the gas–liquid mixing performance in a shear-thinning system with a coaxial mixer.Gate paddle with better shearing action than ribbon impeller is adopted as the outer impeller.The influences of inner impeller types,operating parameters,and material characteristics are investigated on the gas–liquid dispersion and mass transfer.

2.Experiment

2.1.Experimental setup

As shown in Fig.1,experiments were conducted in a system consisting of a PMMA stirred vessel with a standard elliptical head,a W-0.36/8 air compressor for gas suppling,a LZB-15 rotor flow meter for gas flow controlling,a DOG-3082 industrial dissolved oxygen instrument for oxygen concentration measurement,and a data acquisition&processing system.The stirred vessel of 380 mm inner diameter T and 428 mm liquid level height H was equipped with a gas distributor near the bottom.Coaxial mixers consisting of one inner impeller and one outer gate paddle(GT)were employed.Inner impellers of the three combinations were six flat-blade disc turbine(Rushton),six curved-blade disc turbine(BDT-6)and six 45°pitched-blade disc turbine(PBDT-6),respectively.Previous work[28]investigated the influence of rotation mode,and found that a coaxial mixer under counter-rotation mode exhibited better gas pumping capacity and gas dispersion than a coaxial mixer under co-rotation mode or single inner impeller at the same power consumption.Hence,counter-rotation mode was adopted in the following experiments.

The geometrical parameters of impellers and gas distributor are given in Fig.2.The center of inner impellers and gas distributor was 204mm and 120mm high from the vessel bottom respectively. The distance between the outer GT paddle and vessel bottom was 10 mm.

2.2.Experimental material

CG-T xanthan gum produced by CPKelco Company was selected as the liquid phase.The aqueous solution of xanthan gum is a kind of shear-thinning fluid,whose apparent viscosity meets Eq.(1)as follows.

The rheological characteristic parameters of xanthan gum solution under different mass fractions ω measured by a HAAKE RS6000 rheometer are tabulated in Table 1.Fig.3 provides the corresponding rheological curve for shear rates between 10 and 700 s-1.

2.3.Experimental method

Impeller type,stirring speed,gas flow rate,and system viscosity are important factors to influence the gas–liquid dispersion with a coaxial mixer.On account of the better comparability for the working conditions with different impeller types and experimental materials, unit volume stirring power PVwas used to replace stirring speed.In addition,considering xanthan gum solution as a kind of shear-thinning fluid,solutions under different mass fractions were used to investigate the influence of system viscosity on the gas–liquid mixing.

Overall gas holdup ag,relative power demand RPD,and volumetric mass transfer coefficient kLa were measured to describe the gas–liquid mixing performance.The RPD is the ratio of aerated shaft power Pgand unaerated shaft power P0under the same condition,which can characterize the gas pumping capacity of impeller.The kLa was measured by the linear part of the response curve for oxygen concentration varies with time reported in the literature of Arjunwadkar et al.[29].It can be calculated by Eq.((2))without the consumption of oxygen[30].

Fig.1.Experimental system:1.air compressor,2.rotor flow meter,3.valve,4.electromotor,5.torque sensor,6.outer impeller,7.inner impeller,8.gas distributor,9.dissolved oxygen electrode,10.stirred vessel,11.transmitter,12.control cabinet,13.host,14.screen.

Fig.2.Structures of impellers and gas distributor:(a)Rushton;(b)BDT-6;(c)PBDT-6;(d)outer GT paddle;(e)gas distributor.

Considering the large effect of temperature,the kLa was corrected by Eq.(3)[31,32].

The detailed experimental procedures are given below[33]:

(1)Preparation of xanthan gum solution

Xanthan gum powders were dissolved in 40°C water and stood 15h until completely expanded and dissolved.The mixture was poured intothe vessel to the specified height and mixed by a coaxial mixer,till the colorless and transparent steady liquid was obtained.

Table 1Physical parameters of xanthan gum solutions

Fig.3.Rheological curves for xanthan gum solution under different mass fractions.

(2)Measurement of overall gas holdup

Liquid level difference method was used to measure agunder different conditions.

(3)Measurement of volumetric mass transfer coefficient

a)Gas flow was blown into the vessel by an air compressor and regulated by a flow meter.Saturated oxygen concentration C*was obtained when the value of the dissolved oxygen instrument remains constant.

b)After starting the coaxial mixer,nitrogen was blown into the vessel to remove oxygen.

c)The valve of nitrogen was closed when the oxygen concentration CLapproaches 5%of C*.Gas flow was blown into the vessel and the initial oxygen concentration C0was recorded by a data acquisition system.

d)Air compressor was turned off when CLreaches a stable value in the interval of 80 to 90%of C*.The kLa was calculated by Eqs.(2)and(3).

(4)Calculation of stirring power

Inner and outer shaft torques Miand Mowere measured under the inner and outer shaft rotating speeds Niand Nowith corresponding working condition.No-load inner and outer shaft torques Mi,0and Mo,0at the same rotating speed were measured after empting the vessel and cleaning the impellers.The PVwas calculated by Eq.(4).

3.Results and Discussion

3.1.Influence of stirring power

Stirring speed exerts a tremendous influence on gas–liquid mixing.However,stirring power has a better comparability for different impeller types and experimental materials.Hence,PVdefined by Eq.(4)is adopted to investigate the influence of stirring speed on ag,RPD,and kLa in Figs.4 to 6.Coaxial mixers under counter-rotation mode with outer GT paddle and three kinds of inner impellers at Qgof 2.22 × 10-4m3·s-1were taken in these experiments.

Fig.4.Influence of unit volume power PVon overall gas holdup ag.

Fig.5.Influence of unit volume power PVon relative power demand RPD.

Fig.4 shows the influence of PVon ag.It can be seen that,(1)agincreases with increasing PV.Larger stirring power leads to stronger turbulence intensity in the vessel.Higher shear rate at higher stirring speed broke bubbles into small size,which leads to gas staying longer in the liquid phase.The increasing shear rate has more influence than the variation of viscosity.(2)The vessel with an inner BDT-6 turbine has the largest agat the same PV.It is because the most discharged liquid of the BDT-6 turbine results in the strongest turbulence and best gas dispersion..(3)The aggrows with increasing viscosity.It is because that bubbles stay in the liquid phase longer for the influence of viscosity force.

Fig.6.Influence of unit volume power PVon volumetric mass transfer coefficient kLa.

Fig.5 demonstrates the influence of PVon RPD,which shows that,(1)RPD decreases and then increases with increasing PV.Due to direct gas load at low stirring speed,gas goes into the blade area directly and easily forms stable cavitation in the negative pressure zone at the back of impeller blades,which leads to a decrease in pumping capacity and RPD.Gas load mode turns to indirect load when stirring speed continued to increase.Gas goes into the blade area through circulation and does not easily form cavitation,which leads to stronger pumping capacity.The indirect gas load becomes more obvious with increasing stirring speed.(2)The vessel with an inner BDT-6 turbine has the highest RPD among the three working conditions with 0.20%xanthan gum due to its best pumping capacity.The vessel with an inner PBDT-6 turbine has the lowest RPD at low PV,because down-pumping characteristic weakened the gas pumping capacity at direct gas load mode.(3)RPD decreases with increasing viscosity.It is because as the turbulence becomes weaker,bubbles easily adhere to the back of the blades to form cavitation and are hard to be destroyed due to the influence of viscosity force.The Pgis smaller with cavitation adhered on the blades at higher viscosity,which leads to a lower RPD(RPD=Pg/P0).(4)The turning point of PVfrom direct gas load to indirect gas load becomes larger with increasing system viscosity.It is because the weaker turbulence under higher viscosity leads to stable cavitation.Higher PVis required to change the gas load mode.

The influence of PVon kLa with different inner turbines and liquid concentrations is illustrated in Fig.6.(1)kLa increases with increasing PV.It is because the increase of stirring speed leads to lower system viscosity,stronger turbulence intensity,and smaller bubbles with larger contact areas,which are beneficial to the mass transfer between two phases.(2)The kLa in the vessel with an inner Rushton turbine or inner BDT-6 turbine is smaller than that in the vessel with an inner PBDT-6 turbine under the same PV.Though the Rushton turbine has the advantage of shearing action,and BDT-6 turbine has the advantage of liquid-discharged ability,both of these advantages can only be obtained by consuming power.These advantages will disappear under the same PV.(3)The kLa decreases with increasing viscosity.Because of the weaker turbulence,the lower cycling speed and broken probability under higher viscosity,contact area between phases decreases.Hence,the oxygen diffusion between two phases is impeded.These phenomena agree with the research results of Puthli et al.[34]with a single-axial mixer.

3.2.Influence of gas flow rate

The dimensionless gas flow number Flg(Flg=Qg/NiDi3)was used to replace gas flow rate Qgas the abscissa.Coaxial mixers under counterrotation mode with outer GT paddle and three kinds of inner impeller operating at inner and outer shaft rotating speeds of 342 r·min-1/19 r·min-1were taken to investigate the influence of Qgon ag,RPD,and kLa.

Fig.7.Influence of gas flow number Flgon overall gas holdup ag.

Fig.7 shows the influence of Flgon ag.It can be seen that,(1)agincreases with increasing Flg,and the growth rate becomes smaller and smaller.It is because the increasing Qgleads to more amounts of bubbles and larger probability of bubble coalescence.The resistance time of larger bubbles in the liquid phase is shorter due to the influence of buoyancy force,which causes lower growth rate.(2)Atlow Flg,the vessel with an inner BDT-6 turbine has the largest ag.When Flgis larger than 0.03,the vessel with an inner Rushton turbine has the largest ag.The BDT-6 turbine has more discharged liquid to improve the circulation in the whole vessel and leads to better gas dispersion.With the increasing Flg,more gas is pumped into the vessel and the advantage of the BDT-6 turbine becomes fading.The better shearing action of the Rushton turbine makes bubbles smaller and stay longer in the liquid phase.Compared with the effect of liquid-discharged ability of the BDT-6 turbine,the shearing action advantage of the Rushton turbine has more influence on agat high Flg.

Fig.8 demonstrates the influence of Flgon RPD,which shows that,(1)RPD decreases with increasing Flg,and the reduction rate becomes smaller and smaller.It is because gas load mode changes from indirect load to direct load with increasing Flg.After leaving the gas distributor,gas goes into the blade area directly to form cavitation on the back of the impeller blades.Cavitation grows and tends to be stabilized,which leads to the smaller reduction rate.These experimental phenomena agree with the research results of Albaek et al.[35]with a single-axial mixer.(2)The coaxial mixer with an inner BDT-6 turbine has the highest RPD and strongest pumping capacity among the three impeller combinations at the same stirring speed.The BDT-6turbine has the best liquid-discharged ability.It is hard to form cavitation at the tips of backward curved-blades,which leads to fast liquid circulation and well bubble dispersion[36].

Fig.8.Influence of gas flow number Flgon relative power demand RPD.

The influence of PVon kLa with different inner turbines and liquid concentration are illustrated in Fig.9.(1)kLa increases with increasing Flg,and the growth rate becomes smaller.It is because the contact area between phases grows with the increasing bubble amount,which leads to the increase of kLa.The increasing bubble amount leads to larger probability of bubble coalescence,which results in the decrease of growth rate.(2)At the same stirring speed,the vessel with an inner PBDT-6 turbine has the lowest kLa,the vessel with an inner Rushton turbine has higher kLa than that of the vessel with an inner BDT-6 turbine at high Flg.Because the better shearing action of the Rushton turbine leads to lower viscosity of xanthan gum solution and smaller bubbles,both of which intensify the mass transfer between two phases.The better liquid-discharged ability of the BDT-6 turbine leads to more gas in overall circulation at low Flg,but this advantage is not obvious at high Flg.

Fig.9.Influence of gas flow number Flgon volumetric mass transfer coefficient kLa.

Ranges of the effective Reynolds numbers in Figs.4–9 are listed in Table 2.The modified Reynolds numbers for non-Newtonian fluids[19]are calculated by Eq.(5).

Table 2Ranges of the effective Reynolds numbers

4.Conclusions

The influences of PV,Flgon ag,RPD,and kLa with different impeller types and system viscosities were investigated under the advantageous counter-rotation mode.

(1)agand kLa increase with increasing PV,while RPD increases at first and then decreases.

(2)agand kLa increase and RPD decreases with increasing Flg.The curves tend to be flat.

(3)The vessel with an inner BDT-6 turbine and outer GT paddle has the highest agand RPD,the vessel with an inner PBDT-6 and outer GT paddle has the highest kLa at the same PV.

(4)agincreases and RPD andkLa decrease with increasing mass fraction of xanthan gum solution.

Nomenclature

A vessel cross sectional area,m2

a specific area,m-1

agoverall gas holdup,%(volume)

C* saturated oxygen concentration in the liquid phase,mg·L-1

CLoxygen concentration in the liquid phase,mg·L-1

C0initial oxygen concentration in the liquid phase,mg·L-1

Diinner impeller diameter,mm

FlgGas flow number

g gravitational acceleration,m·s-2

H liquid level height,mm

K consistency index,Pa·sm

kLliquid side mass transfer,m·s-1

kLa volumetric mass transfer coefficient,s-1

kSMetzner-Otto constant,kS=11.5

Miinner shaft torque,N·m

Mi,0no-load inner shaft torque,N·m

Moouter shaft torque,N·m

Mo,0no-load outer shaft torque,N·m

m flow behavior index

N rotating speed,s-1

Niinner shaft rotating speed,s-1

Noouter shaft rotating speed,s-1

Pgaerated shaft power,W

Piinner shaft power,W

Poouter shaft power,W

PVunit volume power,W·m-3

P0unaerated shaft power,W

Qggas flow rate,m3·s-1

R2correlation coefficient

RNrotating ratio,RN=Ni/No

Remmodified Reynolds number

RPD relative power demand,RPD=Pg/P0

T vessel diameter,mm

t time,s

V volume,m3

γ shear rate,s-1

θ temperature,°

μaapparent viscosity,Pa·s

ρldensity,kg·m-3

ω mass fraction,%(mass)