hydrodynamic characteristcs of mixing of three phase

INTERNATIONAL JOURNAL OF CHEMICAL

REACTOR ENGINEERING

Volume 6 2008 Article A90

Hydrodynamic Characteristics of Mixing ina Non-Newtonian Liquid-Gas-Solid System

Thamer Mohammed Jassim∗ Abbas Hamid Sulaymon†

Asawer Abdul Raswel Al-Wasiti‡

∗University of Technology, Baghdad, thamer [email protected]†University of Baghdad, inas [email protected]‡University of Technology, Baghdad, [email protected]

ISSN 1542-6580Copyright c©2008 The Berkeley Electronic Press. All rights reserved.

Hydrodynamic Characteristics of Mixing in aNon-Newtonian Liquid-Gas-Solid System∗

Thamer Mohammed Jassim, Abbas Hamid Sulaymon, and Asawer AbdulRaswel Al-Wasiti

Abstract

This work presents the study of mixing a three phase non-Newtonian systemin a QVF gas sparged vessel. The three phase system consists of air-non New-tonian liquid (polyacrylamide solution)–solid (alumina catalyst). The critical gasvelocity for complete suspension of solid particles, mixing time, and bubble char-acteristics (bubble rise velocity, bubble diameter, bubble frequency, gas hold up,and number of bubbles) was studied with different polyacrylamid (PAA) concen-trations (0.01, 0.03,0.05, 0.07) wt%, different particle diameters of alumina (63-500)µm, and different solid loading of alumina (0.5, 1.0, 1.5, 2.0)Kg. The criticalgas velocity was found to increase with increasing apparent viscosity, solid load-ing, and particle diameter. Mixing time increases with increasing apparent vis-cosity, and decreases with increasing solid loading, and particle diameter. Bubblecharacteristics were measured axially and radially using a modified electrocon-ductivity probe consisting of four tips, an interface, a visual basic program, anda personal computer. The results showed that increasing apparent viscosity andparticle diameter caused an increase of bubble coalescence and hence, an increasein bubble diameter and bubble rise velocity and a decrease in gas hold up.

KEYWORDS: hydrodynamics, three phase, non-Newtonian liquid, mixing

∗I would like to thank the staff of the Chemical Engineering Department at the University ofTechnology and the University of Baghdad for supporting this research.

1-Introduction Gas- Liquid- solid three phase sparged reactor have been widely used in coal conversion processes (Fisher-Tropsch reaction, divert coal liquefaction), biochemical processes (production of single cell protein, production of variety of chemicals using fermentation), waste water treatment (aerobic, biological treatment, wet water oxidation), catalytic hydrogenation and oxidation. Also, it sometimes fulfills the real need in applications such as corrosive liquid and they are the preferred reactor type of synthesis gas conversion. They are flexible and may be tailored to produce high quality transportation fuel and a verity of products operation at high temperature and pressure. (Chen, et.al, 1995), (Wang, et.al, 2003)

Koid et.al (Koid et.al, 1983), studied the critical gas velocity for complete suspension by visual observation and hydrostatic pressure. Their experiments were carried within (air-water, glycerin solution, and ethylenglycol – glass sphere and bronze sphere) in (0.1-0.3)m column diameter with conical bottom, their results showed that critical gas velocity increases with increasing terminal velocity of single particle, column diameter, and density difference between solid and liquid, and decreases with increasing liquid viscosity and liquid surface tension. Also, critical gas velocity decreased when conical bottom is used instead of flat one.

Pandit and Joshi (Pandit and Joshi, 1987) studied the effect of physical properties of liquid phase and solid suspension on critical gas velocity in three phase sparged column 0.2m inside diameter using air-water, CMC solution –quartz with different particle size and solid loading. They found that critical gas velocity was proportional to solid hold up as ( VGC α εS

0.5-0.6 ) for εS < 0.1and ( VGC α εS

-0.2 ) for εS >0.1, where VGC and εS are the critical gas velocity and solid hold up respectively.

Their observations are consisted with those reported by Pandit and Joshi (Pandit and Joshi, 1983) and Koid et.al (Koid et.al, 1983). They also found that critical gas velocity for non- Newtonian liquid 0.125% gurm gum concentration increased by about 15% compared to that with water. They proposed that the suspension of large particles mainly depends upon liquid turbulent intensity. The non-Newtonian behavior of gurm gum solution can substantially decrease the liquid turbulent intensity and hence increase critical gas velocity.

On the other hand, Muthukumar et.al (Muthukumar et.al, 2004), showed that the adding of organic additives (propanol, benzoic acid and iso-amylalcohol) in airlift loop reactor with low density particle of (Nylon-6 and polystyrene) reduced the critical gas velocity, while it increased with increasing solid loading and density of the particles used.

1Jassim et al.: Hydrodynamics of Three Phase Mixing

Published by The Berkeley Electronic Press, 2008

The effect of non Newtonian behavior of CMC solution on mixing time was studied by Guy et.al, (Guy et.al, 1986) using three phase bubble column of air-water, glycerin, CMC, and PAA solution-glass beads in 0.2m diameter of bubble column. Their results showed that mixing time increases as the viscosity or shear thinning properties of liquid increase, mixing time was strongly affected by sparger type design.

Ravinath et.al, (Ravinath et.al, 1987), studied the effect of various parameters such as superficial gas velocity, liquid height to diameter ratio (L/D), sparger type, sparger location, and physicochemical properties of liquid on mixing time in short bubble column with inside diameter 0.2m and ratio of (L/D < 0.5). They found that sparger design and location are very important parameters for getting minimum value of mixing time, using multipoint sparger gave lower mixing time value than single point sparger.

Pandit and Joshi (Pandit and Joshi, 1986) discussed the effect of particle size and loading on fractional gas hold up in 0.2m and 0.38m diameter of column. They showed that when the solid loading is higher than 0.6% the average bubble diameter increases with particle size up to (1000 micron) because of bubble coalescence, as a result the gas hold up decreases. While using particle size more than (1000 micron), the bubble diameter decreased because of particle penetration into the bubble and hence the average bubble size decreases with an increase in particle size, therefore gas hold up increases with an increase in particle size.

Similar results were obtained by Dharwadkar et.al, (Dharwadkar et.al, 1987), who studied the effect of solid loading on gas hold up in three phase sparged reactor 0.2m diameter using air-non-Newtonian liquid of CMC solution and glass bead of two sizes (250 and 500 micron). They showed that gas hold up decreased with increasing solid loading.

Miura and Kawase (Miura and Kawase, 1997), studied the hydrodynamics and mass transfer in three phase fluidized bed with non Newtonian liquid in 0.068m diameter of bubble column, using air-water, CMC and gurm gum solution- glass beads. They concluded that the values of gas hold up for Newtonian liquid are slightly higher than that for non-Newtonian liquid in which gas hold up decreased as a non-Newtonian behavior increased. This might be attributed to the behavior rheological properties of non-Newtonian that enhanced the bubble coalescence.

The objectives of this work are showing the conditions which affect the critical gas velocity for complete suspension of three phase system and studying the hydrodynamic parameters (bubble rise velocity, bubble diameter, bubble frequency and gas hold-up) as well as mixing time of three phase mixing of non-Newtonian liquid with different concentrations, different solid loading and solid diameter.

2 International Journal of Chemical Reactor Engineering Vol. 6 [2008], Article A90

http://www.bepress.com/ijcre/vol6/A90

2- Experimental Work

The experiments were carried out in a quick visible flow (QVF) glass vessel 0.46m inside diameter and 1.0m height with static liquid height to vessel diameter 1.1 and hemispherical bottom using single ring sparger with a ration of diameter to vessel diameter 0.5, 136 holes with and size equal to 1mm, as shown in figure(1).

Compressed air was distributed to the vessel through a single ring sparger made of copper with free area of holes to cross sectional of the vessel 0.064.

A non-Newtonian liquid of polyacryamide solution with different concentration (0.01, 0.03, 0.05, and 0.07) wt% were used as a liquid phase. Polyacrylamide solution is considered as a time independent fluid of pseudoplastic type that is characterized by power law model. Its rhelogical properties of flow index (n) and consisting index (m) were calculated using Fann Viscometer (model 35A) (Chung, 1986). Other physical properties such as density and surface tension were measured by means of pycnometer and two capillary tubes having diameters of (1 and 2) mm respectively. These properties are tabulated in table (1)

Figure (1): The schematic diagram

Compressor

Mercury-tube manomet Electro conductivity probe

Gas flow

Stabilizer

Valve

Rotameters

QVF glass vessel

To drain Sparger

Inclined manometer

Interface PC



Table (1) : The Physical Properties of Liquids

Liquid Concentration

of PAA wt%

Flow Behaviorindex,

n

Consistency

Index,

M , Pa.sn

Density

at 303K

ρL, Kg/m3

Surface Tension,

σ, N/m

0.01 0.8 0.0062 1000.2 0.0208

0.03 0.72 0.0139 1000.5 0.0214

0.05 0.651 0.0289 1000.7 0.0232

0.07 0.594 0.0589 1001.01 0.0245

The flow behavior of psudoplastic PPA solution was characterized by the power law model of Ostwld-de-Waele as

τyx = m ( γyx )n (1 )

μeff = m ( γyx )n-1 (2 ) where τ is the shear stress, m is the consistency index, γ is the share rate, n is the

power low index In order to calculate the effective viscosity prevailing in the sparger

vessel, the effective shear rate was calculated using a relation proposed by Nishikawa, et.al (Nishikawa, et.al, 1977) as:

γ =5000 VGC ( 3 )

The solid used is alumina oxide (Al2O3) with different particle sizes (63-125, 125-212, 212-300, 300-500) µm with density of 4000 kg/m3. These sizes were selected to suit the sizes of catalyst that is used in industrial three phase reactors. Different solid loading of (0.5, 1.0, 1.5, and 2.0) Kg was used.

The critical gas velocity for complete suspension of particles was calculated using hydrostatic pressure measurement (Pandit and Joshi, 1986, Smith, et.al, 1986).

A pulse technique was used to measure the mixing time (Haque et.al, 1986 and Haque et.al, 1987). A pulse of electrolyte solution of HCL of 20ml volume and 20 wt% was added to the dispersed phase at the inside wall of the



vessel near the top. A pH cell (platinum) was placed near the bottom of the vessel at the opposite side of the injection of the solution. The response of pH was recorded by means of a digital pH meter.

The bubble monitoring and analyzing system were used to measure the local gas hold up, bubble frequency, bubble rise velocity, number of bubbles, and size of bubbles. This system consists of electoresistivity probe, interface, computer and software program (Visual Basic).

A modified electoresistivity probe was employed in this work. The present probe consists of four channels (tips) in order to sense more bubbles local interface that gives more accurate reading. 3- Results and Discussion 3-1 Critical Gas Velocity Effect of PAA Concentration Four different concentrations of PAA were used (0.01, 0.03, 0.05, 0.07) wt% with power index of (0.8, 0.72, 0.65, 0.59), respectively. The effect of effective viscosity on critical gas velocity and total applied power per unit volume at different particle sizes and loading is shown in figure (2)

It can be noticed from these figures, for all solid loading and particle size that critical gas velocity increases with increasing liquid effective viscosity (PAA concentration). This can be attributed to increasing PAA concentration means an increase in effective viscosity, i.e. increase in liquid viscous force, which gives a resistance force for particles movement. Hence, a high gas velocity will be required to make particles in suspension state.

The increase in critical gas velocity with increasing liquid effective viscosity may also be explained due to the increase in bubble size, the large bubbles don’t generate sufficient liquid circulation or turbulent flow to lift the particles, as will be discussed. Similar results obtained by Pandit and Joshi (Pandit and Joshi, 1987), while this result differs from that achieved by Kassim (Kassim, 2002) and Hadi (Hadi, 2004). This difference can be attributed to the difference in rhelogical properties of liquid used.



Effective Viscosity , (Pa.s)

Cri

tical

Gas

Vel

ocity

, (m

/s)

0.022

0.023

0.024

0.025

0.026

0.027

0.028

0.002 0.003 0.004 0.006 0.008 0.009

WS = 0.5KgWS = 1.0KgWS = 1.5KgWS = 2.0Kg


Cri

tical

Gas

Vel

ocity

, (m

/s)

0.023

0.024

0.025

0.026

0.027

0.028

0.029

0.002 0.003 0.004 0.006 0.008 0.009


(a)

(b)




Cri

tical

Gas

Vel

ocity

, (m

/s)

0.023

0.024

0.025

0.026

0.027

0.028

0.029

0.002 0.003 0.004 0.006 0.008 0.009



Cri

tical

Gas

Vel

ocity

, (m

/s)

0.025

0.026

0.027

0.028

0.029

0.030

0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009


(c)

(d)

Figure (2): The effect of effective viscosity on critical gas velocity for air-PAA solution-alumina of different solid loading at: (a)dp=(36-125)µm, (b) dp=(120-

212) µm, (c) dp=(212-300) µm, (d) dP = (300-500)µm.



Effect of Particle Size Different particle sizes (63-500)μm have been used to find their effect on the critical gas velocity and total applied power per unit volume.

It was found that critical gas velocity increases with increasing particle diameter, this can be explained if consideration is taken that increasing the particle size means an increase in its settling velocity due to increase in its weight . Hence, a higher gas velocity as well as higher power consumption will be required to give higher liquid circulation and turbulence to suspend the particles. The present results are in agreement with other workers ((Kassim, 2002, Hadi, 2004).

Effect of Solid Loading The effect of different solid loading (0.5, 1.0, 1.5, and 2.0) Kg on critical gas velocity is shown in figure (2).

All these figures show that increasing solid loading caused an increase in critical gas velocity for all PAA concentrations used. Since the presence of particles damps the liquid circulation and turbulence intensity, therefore, higher gas velocity is required to obtain a certain liquid circulation and turbulence to suspend the solid particles of higher loading. Similar behavior has been shown by other workers (Muthukumar, et.al 2004, Abdul-Kareem, 1999). Power Law Model The critical gas velocity for complete suspension was correlated to the above variables using Buckingham π- theorem, the following equation was derived:

( ) ( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ= −−

LLSS

GC CwFrWeVV

ρρρ942.0426.0045.0Re12.0 (4)

Where VGC is the critical gas velocity, VSS is the settling velocity of the solid, Re is Reynolds number (=ρVd/μ), We is Webber number (=VGC

2 dp ρL/σL), Fr is Froud number (=VGC

2/gdP), Δρ is density difference between liquid and solid phase, ρL is liquid density and Cw is weight concentration of solid per unit volume of slurry.

The correlation coefficient of the above equation was 0.998 and the absolute error was 3%. A comparison of between the experimental results and the predicted values is shown in figure (3).



Figure (3): The observed and predicted values of equation (4) of critical gas velocity.

3-2 Hydrodynamic Parameters Gas Hold Up Gas hold up profiles, as a function of probe position in the vessel for different particle size (63-500)μm, different PAA concentrations (0.01-0.07) wt%, and different solid loading (0.5-2.0)Kg, are shown in figure (4).

Examining these figures it can show that gas hold up has its maximum value in the center of the vessel while its minimum value is on the wall of the vessel, which means a higher presence of bubbles in the center. This may be attributed to the high gas velocity in the center of the vessel compared to that on the wall.

Predicted Values

Obs

erve

d Va

lues

0.00

0.04

0.08

0.12

0.16

0.00 0.04 0.08 0.12 0.16

+3%

no. of points 8

-3%



X- Position , cm

Gas

Hol

d U

p

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

-5 5 15 25 35 45 55

SurfaceY=10cmY=20cmY=30cm

X- Position , cm

Gas

Hol

d U

p

0.08

0.10

0.12

0.14

0.16

0.18

0.20

-5 5 15 25 35 45 55


(a)

(b)



X- Position , cm

Gas

Hol

d U

p

0.07

0.09

0.11

0.13

0.15

0.17

-5 5 15 25 35 45 55


X- Position , cm

Gas

Hol

d U

p

0.065

0.075

0.085

0.095

0.105

0.115

0.125

0.135

-5 5 15 25 35 45 55


(c)

(d)

Figure (4) : Gas hold up verses probe position of air-PAA solution-alumina with WS=1.0kg and dP=63-125µm at different PAA concentration

: ( a ) 0.01%wt, ( b ) 0.03%wt, ( c ) 0.05%wt, ( d ) 0.07 wt% .



Also, these figures show slight increase in gas hold up with decreasing distance from the surface. This can be explained by considering that bubbles will break-up during its way to the surface which results in increasing their presence and increase in hold up. Same behavior has been shown by Shah et.al (Shah et.al, 1982) and Jackson et.al (Jackson et.al, 1996).

The effect of PAA concentration on gas hold up has been shown in figure (4). These figures show that gas hold up decreases with increasing PAA concentration. This can be explained on the basis of hindered gas bubble motion in viscous fluid, in which at high viscosities drag forces will be high enough to cause bubble coalescence this means increasing PAA concentration causes an increase in its viscous force that will depress bubble break-up (Fall, 2000). Moderate forces contribute to more uniform distribution of bubbles and hence higher hold up. Similar results are shown by Kelekar and Shah (Kelekar and Shah, 1985), Haque et.al (Haque et.al, 1986), Dharwadker et.al (Dharwadker et.al, 1987) and Abdul Kareem (Abdul Kareem,1999)

Increasing solid diameter causes a decrease in gas hold up as shown in figure (4). The same results have been achieved Dharwadker et.al (Dharwadker et.al, 1987). This behavior is mainly due to the higher tendency of bubbles to coalesce which leads to higher bubble diameter and hence lower gas hold up.

Knowing that gas hold up decreases with increasing solid loading, this behavior could be due to an increase in the apparent viscosity of the slurry (Kara,et.al, 1982). The reduction of gas hold up with increasing solid content is in agreement with the majority of workers while it differs from results obtained by Kassim (Kassim, 2002) and Hadi (Hadi, 2004). This difference may be attributed to the difference in the rheological properties of the liquid used. Bubble Rise Velocity The effect of different variables studied in this work on the bubble rise velocity is shown in figure (5).

The bubble rise velocity distribution shown in these figures indicates that bubble rise velocity has its maximum value in the center of the vessel and minimum value at the wall, since the superficial gas velocity as well as liquid circulation is at maximum in the center of the vessel. These observations were noticed by Kumar (Kumar, 1994) and Wang et.al (Wang et.al, 2003).

It could be also noticed from these figures that bubble rise velocity increases with increasing PAA concentration, since increasing the later will be coupled with increasing critical gas velocity as discussed in previous section. Also, this result indicates that coalescence tendency in the solution is enhanced by increase in effective viscosity. Same results have been coinciding with other



X- Position , cm

Bubb

le R

ise

Velo

city

, cm

/s

0

10

20

30

40

50

60

70

-5 5 15 25 35 45 55


workers (Dharwadkar et.al, 1987, Kelkar, and Shah, 1985), while it differs from those obtained by Hadi (Hadi, 2004).

The effect of particle size on bubble rise velocity is shown in figure (5). These figures show that bubble rise velocity increases with increasing particle size due to the proportional relation between gas velocity and bubble rise velocity, as mentioned by Wang, et.al (Wang, et.al, 2003).

Also, these figures indicate that bubble rise velocity increases with increasing solid loading. This increase in bubble velocity is due to the proportional relation between gas velocity and bubble rise velocity.

(a)



X- Position , cm

Bubb

le R

ise

Velo

city

, cm

/s

5

15

25

35

45

55

65

75

-5 5 15 25 35 45 55


X- Position , cm

Bubb

le R

ise

Velo

city

, cm

/s

0

10

20

30

40

50

60

70

80

-5 5 15 25 35 45 55


(b)

(c)



X- Position , cm

Bubb

le R

ise

Velo

city

, cm

/s

10

20

30

40

50

60

70

80

90

100

-5 5 15 25 35 45 55


(d)

Bubble Diameter The relation between bubble diameter and probe position at different particle sizes, solid loading, and PAA concentration for air sparger are shown in figure (6). These figures show that bubble diameter is larger in the center of the vessel than that on the wall due to the damping of bubble coalescence near the wall. This behavior was observed by Kumar (Kumar, 1994).

In addition, these figures show that bubble diameter increases with increasing PAA concentration, as discussed in previous section, that increasing effective viscosity enhances bubble coalescence which leads to increase in bubble diameter. This phenomenon is the same as that mentioned by Haque et.al (Haque et.al, 1987).

The relation between bubble diameter and particle diameter is shown in figure (6). These figures indicate that bubble diameter increases with increasing particle diameter because the relation between particle size and gas velocity

Figure(5) : Bubble rise velocity verses probe position of air-PAA solution-alumina with WS=1.0kg and dP=63-125µm at different PAA

concentration : ( a ) 0.01%wt, ( b ) 0.03%wt, ( c ) 0.05%wt, ( d ) 0.07 wt%



X- Position , cm

Bubb

le D

iam

eter

, cm

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-5 5 15 25 35 45 55


should consequently lead to an increase in bubble diameter as was observed by Miyahrd and Yamanakn (Miyahrd and Yamanakn, 1993).

Also, bubble diameter would increase by increasing solid loading as, shown in the figures, due to the proportional relation between gas velocity and bubble diameter.

(a)



X- Position , cm

Bubb

le D

iam

eter

, cm

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-5 5 15 25 35 45 55


X- Position , cm

Bubb

le D

iam

eter

, cm

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-5 5 15 25 35 45 55


(b)

(c)



X- Position , cm

Bubb

le D

iam

eter

, cm

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

-5 5 15 25 35 45 55


(d)

Figure(6) : Bubble diameter verses probe position of air-PAA solution-alumina with WS=1.0kg and dP=63-125µm at different PAA concentration : ( a )

0.01%wt, ( b ) 0.03%wt, ( c ) 0.05%wt, ( d ) 0.07 wt% .

Bubble Frequency The effect of different variables on bubble frequency is shown in figure (7). It is noticed from these figures that bubble frequency near the wall is lower than that in the center of the vessel. This might be due to downward movement of the bubble that leads to less frequent strike of the probe.

The bubble frequency values for different PAA concentrations showed a decreases with increasing concentration, since increasing PAA concentration enhances bubble coalescence which leads to increase in bubble diameter and decrease in bubble strike of the probe.

These figures also show that bubble frequency increases with increasing particle size The effect of solid loading on bubble frequency is shown in figure (7). It could be seen that the behavior obtained is similar to that of bubble rise velocity and bubble diameter.



X- Position , cm

Bubb

le F

requ

ancy

, 1/

s

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

-5 5 15 25 35 45 55


X- Position , cm

Bubb

le F

requ

ancy

, 1/

s

0.4

1.0

1.6

2.2

2.8

3.4

-5 5 15 25 35 45 55


(a)

(b)



X- Position , cm

Bubb

le F

requ

ancy

, 1/

s

0.5

1.5

2.5

3.5

4.5

5.5

6.5

-5 5 15 25 35 45 55


X- Position , cm

Bubb

le F

requ

ancy

, 1/

s

0.5

0.7

0.9

1.1

1.3

1.5

-5 5 15 25 35 45 55


(c)

Figure (7) : Bubble frequency verses probe position of air-PAA solution-alumina with WS=1.0kg and dP=63-125µm at different PAA concentration

: ( a ) 0.01%wt, ( b ) 0.03%wt, ( c ) 0.05%wt, ( d ) 0.07 wt% .

( d )



3-3Mixing Time The effect of different variables on mixing time is tabulated in tables (2-5)

Table (2): Mixing time for air-PAA solution-alumina with particle size of (63-125)μm Mixing time (sec) Solid Loading, kg

PAA concentration

0.5 1.0 1.5 2.0 0.01 0.03 0.05 0.07

13.64 14.8 15.9 18.5

12.49 12.93 14.9 17.1

11.85 12.1 13.9 16.8

10.39 11.84 12.8 15.8

Table (3): Mixing time for air-PAA solution-alumina with particle size of (125-

212)μm Mixing time (sec) Solid Loading, kg

CCCC

0.5 1.0 1.5 2.0 0.01 0.03 0.05 0.07

12.6 13.4 14.5 16.4

11.1 12.4 13.1 15.8

10.3 11.7 12.6 15

9.8 10.4 11.8 13.8

Table (4): Mixing time for air-PAA solution-alumina with particle size of (212- 300)μm

Mixing time (sec) Solid Loading, kg

PAA concentration

0.5 1.0 1.5 2.0 0.01 0.03 0.05 0.07

10.9 11.1 11.85

16

10.5 10.8 11.15 15.8

9.98 10.16 10.37 14.32

9.43 10

10.25 13.41



Table (5): Mixing time for air-PAA solution-alumina with particle size of (300-500)μm Mixing time (sec) Solid Loading, kg

PAA concentration

0.5 1.0 1.5 2.0 0.01 0.03 0.05 0.07

9.4 11.1 11.65 13.6

9.32 10.4 11.07 12.15

9.05 10.1 10.28 11.84

8.7 9.84 10.14 11.18

These tables show that mixing time increases with particle diameter

and decreasing with solid loading decrease. This result can be explained on the fact that increasing solid loading and particle diameter leads to increase in critical gas velocity as mentioned previously. As the critical gas velocity increases the bubble size and bubble oscillations increase too resulting in an increase in liquid circulation and inter cell exchange velocity which leads finally to decrease in the mixing time

Effective viscosity are drawn against mixing time figure (8).These figures show that increasing effective viscosity leads to an increase in mixing time, similar behavior was shown by Haqu et.al (Haqu et.al, 1987) . This result can be attributed to higher liquid viscosity promotes bubble coalescence, i.e., large bubbles are formed in high liquid viscosity that leads to decrease in gas hold up and decrease in the inter cell change velocity resulting in an increase in mixing time.




Mix

ing

Tim

e , s

9

11

13

15

17

19

21

0.002 0.003 0.004 0.006 0.008 0.009



Mix

ing

Tim

e , s

9

10

11

12

13

14

15

16

17

0.002 0.003 0.004 0.006 0.008 0.009


(a)

(b)




Mix

ing

Tim

e , s

8

9

10

11

12

13

14

15

16

17

0.002 0.003 0.004 0.006 0.008 0.009



Mix

ing

Tim

e , s

8

9

10

11

12

13

14

0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009


(c)

(d)

Figure (8): The effect of effective viscosity on mixing time for air-PAA solution-alumina of different solid loading at: (a)dp=(36-125)µm, (b)

dp=(120-212) µm, (c) dp=(212-300) µm, (d) dP = (300-500)µm.



4-Conclusions 1- The critical gas velocity for complete suspension of particles is

found to increase with increasing PAA concentration due to increasing of effective viscosity. It also increased with particle diameter, and solid loading.

2- Increasing effective viscosity, solid loading, and solid diameter, causes an increase in the values of bubble rise velocity as well as bubble diameter. Also, these values in the center of the vessel are more than those at the wall.

3- Increasing the apparent viscosity causes a decrease in the values of bubble frequency and gas hold-up, while increasing solid loading, particle diameter causes an increase in their values.

4- Mixing time is found to increase with increasing apparent viscosity, and decreases with increasing solid loading and particle diameter.

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hydrodynamic characteristcs of mixing of three phase

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