Effects of hydrophilic particles on bubbly flow in slurry bubble column

Accepted Manuscript Effects of hydrophilic particles on bubbly flow in slurry bubble column Shimpei Ojima, Kosuke Hayashi, Akio Tomiyama PII: DOI: Reference:

S0301-9322(13)00140-7 http://dx.doi.org/10.1016/j.ijmultiphaseflow.2013.09.005 IJMF 1945

To appear in:

International Journal of Multiphase Flow

Received Date: Revised Date: Accepted Date:

2 April 2013 10 September 2013 11 September 2013

Please cite this article as: Ojima, S., Hayashi, K., Tomiyama, A., Effects of hydrophilic particles on bubbly flow in slurry bubble column, International Journal of Multiphase Flow (2013), doi: http://dx.doi.org/10.1016/ j.ijmultiphaseflow.2013.09.005

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Effects of hydrophilic particles on bubbly flow in slurry bubble column Shimpei Ojima*, Kosuke Hayashi*, Akio Tomiyama** *Graduate School of Engineering, Kobe University 1-1, Rokkodai, Nada, Kobe, 657-8501, Japan **Corresponding author: [email protected]

Abstract To investigate the effects of hydrophilic particles on slurry bubble flows in a bubble column, distributions of the local gas holdup and the bubble frequency are measured using an electric conductivity probe. Particles are made of silica and their diameter is 100 m. The particle volumetric concentration CS is varied from 0 to 0.40. The measured data imply that the presence of particles promotes bubble coalescence. The film drainage time for two coalescing bubbles in a quasi two-dimensional bubble flow in a small vessel is also measured to quantitatively evaluate the particle effect on coalescence. A particle-effect multiplier is introduced into a coalescence efficiency model by taking into account the data of film drainage time and is implemented into a multi-fluid model. The main conclusions obtained are as follows: (1) the local gas holdup and bubble frequency in slurry bubble flows decrease with increasing the particle concentration, (2) the hydrophilic particles enhance bubble coalescence and the enhancement saturates at CS ~ 0.45, (3) the particle effect on coalescence is well accounted for by introducing the particle-effect multiplier to the film drainage time, and (4) the multi-fluid model can give good predictions for the distribution of the local gas holdup in the slurry bubble column. Keywords: Bubble column, Slurry, Bubble coalescence, Simulation, Multi-fluid model

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1 Introduction Slurry bubble column reactors using the Fischer-Tropsch synthesis reaction have been utilized in various chemical plants. Since the interaction between bubbles and particles would play an important role in flow structures of the slurry bubble flow, many studies on effects of hydrophilic particles on the total gas holdup in the slurry bubble column have been carried out, e.g. Koide et al. (1984), Yasunishi et al. (1986), Khare and Joshi (1990), Li and Prakash (1997), Krishna et al. (1997), Gandhi et al. (1999), Li and Prakash (2000), Vandu and Krishna (2004) and Mena et al. (2005). Most of them reported that the gas holdup decreases with increasing the particle concentration (Koide et al., 1984; Yasunishi et al., 1986; Krishna et al., 1997; Li and Prakash, 1997; Gandhi et al., 1999; Li and Prakash, 2000; Vandu and Krishna, 2004). Yasunishi et al. (1986) measured bubble frequencies in a slurry bubble column. They confirmed that as the particle concentration increases, the local gas holdup and bubble frequency decrease and the bubble size increases. They speculated that the interaction between bubbles and particles enhances the bubble growth at gas inlets, resulting in the reduction of gas holdup and bubble frequency. On the other hand, de Swart et al. (1996) observed slurry bubble flows in a pseudo two-dimensional column to investigate the effects of particles and found that the presence of particles promotes bubble coalescence. Most of the studies support the latter explanation on the effect of particles, that is, the hydrophilic particles enhance bubble coalescence, which makes bubble sizes larger and the bubble rising velocities larger, and therefore, the gas holdup decreases as the particle concentration increases (Hillmer et al., 1994; Krishna et al., 1997; Li and Prakash, 1997; Jianping and Shonglin, 1998; Gandhi et al., 1999; Li and Prakash, 2000; Vandu and Krishna, 2004). However the effects of particle

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concentration on the bubble frequency have not been made clear. Furthermore the particle effect on bubble coalescence has not been quantitatively investigated, so that it has not been taken into account in numerical simulations based on multi-fluid models (Chen et al., 2004; Troshko and Zdravistch, 2009). In this study, distributions of local gas holdup and bubble frequency in a slurry bubble column were measured by using an electric conductivity probe to make clear the effects of hydrophilic particles on bubbly flows in the slurry bubble column. The slurry consisted of water and hydrophilic particles of 100 m in diameter. A wide range of particle volumetric concentration, i.e. from 0 to 0.40 (0 to 40 %), was tested. A numerical method for predicting the slurry bubble flow was also proposed. A hybrid model consisting of a multi-fluid model and an interface tracking method is the basis of the numerical method (Tomiyama and Shimada, 2001; Tomiyama et al., 2006). The effect of particles on bubble coalescence was taken into account in a bubble coalescence model.

2 Bubbly Flows in Slurry Bubble Column Figure 1 (a) shows the experimental setup. The column was made of acrylic resin and its width, depth and height were 200, 200 and 1200 mm, respectively. The hydraulic diameter DH of the column was 200 mm. It has been pointed out that the effect of DH on the total gas holdup of air-water bubbly flows is not significant if DH > 150 mm (Vandu and Krishna, 2004; Su et al., 2006), and therefore, the present results might be applicable not only to this column but also to larger columns. Air was supplied from the oil-free compressor (Hitachi, Ltd., SRL-2) to the column through the air chamber. As shown in Fig. 1 (b), an air diffuser plate was placed at the column

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bottom on which 49 stainless tubes of 1.4 mm diameter and 300 mm long were flush mounted to make the flow rate from each hole the same by a large pressure drop in the tubes (Garnier et al., 2002). The air flow rate was measured using a flowmeter (Nippon flow cell, STO-4, full-scale accuracy + 3 %). Water purified by using a Millipore system (Merck, Elix 3) at room temperature (20 + 2 oC) and atmospheric pressure was used for the liquid phase. The temperature was measured by using the thermometer (Netsuken Ltd., SN3000, accuracy +0.5 oC). Spherical silica particles (Fuji Silysia Chemical Ltd., CARiACT , grade code Q, product name Q-10) were used for the solid phase. The average diameter, apparent and true densities were 100 m, 1.29x103 kg/m3 and 2.25x103 kg/m3, respectively, where the apparent density was evaluated by taking the volume-weighted average for the true density and density of water filling its pore volume. The particles were made of silica gel. It is known that pure silica particles are hydrophilic, e.g. the contact angle of pure silica particles measured by Galetl et al. (2010) is 15 + 3 deg, so that the contact angle of the present particles would be within this range. The column was initially filled with slurry consisting of water and particles up to 800 mm above the diffuser plate. Superficial gas velocities, JG, tested were 0.020 and 0.034 m/s. Maekawa et al. (2008) measured sphere-volume equivalent bubble diameter, dBin, at gas inlets using the same bubble column and at the same superficial gas velocities and confirmed that the Davidson-Schuler correlation (1960) agreed well with the measured dBin for gas-liquid two-phase bubbly flows. This correlation gives dBin = 11 and 13 mm at JG = 0.020 and 0.034 m/s, respectively. The particle volumetric concentration, CS, ranged from 0 to 0.40. Local gas holdups were measured by using an electric conductivity probe at the two elevations z/DH = 2 and 3, where z is the elevation from the diffuser plate. At each

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elevation, local gas holdups at 13 points in the x direction were measured as shown in Fig. 1 (a). A platinum wire of 100 m in diameter was used for the probe and a stainless tube of 2.1 mm in diameter supported the wire. The probe tip shown in Fig. 2 was sharpened to reduce its effects on bubble motion by electro polishing. The resultant tip diameter was less than 4 m. The sampling rate was 4 kHz and the sampling time was 900 s for each measurement point. Figure 3 shows an example of the measured voltage signals. The voltage steeply changes at time t = 0.011 s, at which the tip pierced a bubble. After the bubble passage, the voltage returned to the value of the liquid phase. These voltage signals were analyzed using a two-point multiple threshold discrimination (Žun et al., 1995) to obtain the time-averaged gas holdup,

B.

The

processed signal is also shown in the figure by a dashed-line. The number of bubbles detected during 15 minutes measurement was used for calculating the frequency, fB, of bubble passage at the probe tip, i.e. the bubble frequency. The flow was observed by using a digital camera (NIKON, D200) and a high-speed video camera (Redlake, Motion Pro X-3). Four reflex lamps were used for back illumination. The relative standard errors in

B

and fB were evaluated by repeating the

measurement 30 times under the conditions of CS = 0 and 0.40 and JG = 0.020 and 0.034 m/s. The errors in

B

and fB were within +2 % and +2 % in all the cases.

To check the visibility of flow fields from the outside of the column, a transparent sheet with a grid was inserted in the column and observed from the outside of the column. Figure 4 shows images of the sheet in the slurry of CS = 0.20 and 0.40. The sheet was placed at several distances away from the column wall. The visibility became lower as CS increased. Only the bubbles near the front wall were visible in slurry conditions. 5

Images of bubbly flows at JG = 0.034 m/s are shown in Fig. 5. Close-up views of these flows are also shown in Fig. 6. The number of bubbles is high and the sphere-volume equivalent bubble diameter, dB, is less than about 10 mm at CS = 0, whereas the bubble number density in the near wall region becomes lower and larger bubbles appear as CS increases. Distributions of

B

and fB for JG = 0.020 and 0.034 m/s are shown in Figs. 7 and 8,

respectively. The gas holdup decreases with increasing CS at both JG. The bubble frequency also decreases with increasing CS. As discussed in the literature (Hillmer et al., 1994; Li and Prakash, 1997; Jianping and Shonglin, 1998; Gandhi et al., 1999; Li and Prakash, 2000; Vandu and Krishna, 2004), the main cause of the reduction of

B

and fB can be understood as follows: the presence of hydrophilic particles enhances bubble coalescence, which reduces the number of bubbles, i.e. fB, and enhances the formation of larger bubbles rising faster than small bubbles, which in turn causes the reduction of B. The gas holdups and bubble frequencies at z/DH = 2 and 3 are compared in Fig. 9. In the case of the gas-liquid flow (CS = 0),

B

and fB at z/DH = 2 slightly differ from those

at z/DH = 3, i.e. the root mean square defined by

ε rms =

1 NM

NM

∑ [ε

Bi

( z / D H = 3) − ε Bi ( z / D H = 2)] 2

(1)

i =1

where i is the index of the measurement point, and NM the number of the measurement points (NM = 13) was 0.0061 at JG = 0.020 m/s. This means that the birth rate of each bubble class and the death rate of that class do not reach their equilibrium state at z/DH

6

= 2. On the other hand, in the slurry conditions (CS > 0.20), the differences in between z/DH = 2 and 3 are small, i.e.

rms

B

and fB

= 0.0016 at CS = 0.40 and JG = 0.020 m/s.

Therefore the increase in CS enhances the development of flow to an equilibrium state, in which all the bubble classes are in their birth-death equilibrium. Maekawa et al. (2008) pointed out that the increases in bubble coalescence and breakup rates promote the development of two-phase bubbly flows in a bubble column. In the present experiments, the presence of hydrophilic particles also promotes the bubble coalescence, resulting in the enhancement of the rapid flow development.

3 Quasi Two-Dimensional Bubble Flow Though the present experimental results show that hydrophilic particles enhance bubble coalescence, it is difficult to quantitatively evaluate the particle effect on coalescence because of the low visibility. The time elapsed from bubble contact to the rupture of the liquid film between the bubbles, i.e. the film drainage time tC, was therefore measured using a quasi two-dimensional bubble flow in a small vessel filled with the slurry to investigate the particle effect. The experimental setup is shown in Fig. 10. The vessel was made of acrylic resin, and its width D, height and depth were 100, 330 and 3 mm, respectively. Owing to the small depth, bubbles in the vessel were clearly observed even at the highest CS. The bottom corners of the vessel were slanted at 45 degree to prevent particle sedimentation. The gas, liquid and solid phases were the same as those in the bubble column experiment. The initial water level was 276 mm above the gas injection hole of 1.4 mm in diameter. The gas flow rate through the hole was 5.0x10 6 m3/s and was measured by using the mass flow controller (Kofloc Co. Ltd., CR-300, full-scale

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accuracy +1.5 %). The particle concentration ranged from 0 to 0.50. Two consecutive bubbles coalescing were observed by using the high-speed video camera. The temporal and spatial resolutions were 0.96 ms (1040 frame/s) and 0.25 mm/pixel, respectively. The film drainage time was measured as follows. The minimum distance between the interfaces of two coalescing bubbles was measured (Fig. 11). The distance was approximately constant after bubble contact, and then, the liquid film between the two bubbles suddenly ruptured, at which the minimum distance was regarded as zero. The time duration of the constant distance corresponds to tC. The uncertainty in the measured tC at 95 % confidence was 2.3 ms. Since tC is a stochastic variable, tC was measured for one hundred pairs of coalescing bubbles at each CS to obtain a mean value. Bubbles in the small vessel at various CS are shown in Fig. 12. The frequency of bubble generation was about 28 Hz and bubble breakup was negligible. As CS increased, the number of bubbles in the vessel decreased and the bubble size increased, that is, bubble coalescence was promoted with increasing CS. Measured bubble size, rising velocity and some relevant dimensionless groups are given in Appendix A.1. The enhancement of bubble coalescence is shown more clearly in Fig. 13. The bubbles keep contacting without coalescence for a long time duration at CS = 0 as shown in Fig. 13 (a), whereas the bubbles coalesce immediately after contact at CS = 0.40 as shown in Fig. 13 (b). There are several studies on the particle effect on bubble coalescence. Most of the literature mainly deals with hydrophobic particles, e.g. van der Zon et al., (2002) and Gallegos-Acevedo et al. (2010), and enhancement of bubble coalescence was also confirmed for hydrophobic particles. van der Zon et al. (2002) pointed out that the

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contact lines between a hydrophobic particle, bubbles and the liquid film between the bubbles move so that the liquid film becomes thinner and thinner due to the hydrophobicity. According to this, bubble coalescence is promoted as the degree of hydrophobicity increases. Ata et al. (2003) however pointed out that the enhancement decreases over a certain degree of hydrophobicity. Joshi et al. (2009) investigated the mechanism of bubble coalescence induced by surfactant covered antifoam particles. They found that a surfactant laden hydrophobic particle moves toward the region of contact of two bubbles due to a surface tension gradient and the particle bridges the bubbles by crossing the air-water interface on both sides of the liquid film, which drains until it becomes thin enough to rupture. Omota (2005) investigated the particle effect on bubble coalescence using both hydrophilic and hydrophobic particles. He confirmed that both particles do not destabilize the film if the particles are static, whereas the particles promote the film rupture under the dynamic condition. He speculated that the motion of particles induce turbulence in the film, resulting the promotion of film rupture. The above-mentioned studies used quasi-stationary flotation froth or bubbles in their growth stage at bubble injection nozzles. The interaction between particles and rising bubbles has not been measured and has still been an open question. The physical understanding of particle-enhanced coalescence can be one of the challenging issues. Some discussion on the mechanism of particle-enhanced coalescence is given in Appendix A.2. Measured probability distribution functions (PDF) of tC are shown in Fig. 14. The number of coalescing bubble pairs at small tC increases with CS, e.g., over 80 and 90 % of the data are in the bin of 0 < tC < 0.020 s at CS = 0.30 and 0.40, respectively. The

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mean film drainage time tC is plotted against CS in Fig. 15. t C monotonously decreases with increasing CS, and the reduction rate d t C / dC S in 0.40 < CS < 0.50 is lower than that in 0.10 < CS < 0.40. This implies that the coalescence enhancement due to hydrophilic particles saturates at a certain value of CS, i.e. in this case about 0.45. The particle effect on bubble coalescence in the slurry bubble column might be reflected in the fB data. The mean bubble frequency, f B , which is the arithmetic mean of fB for the 13 measurement points at z/DH = 3, is shown in Fig. 16. f B shows a trend similar to t C , i.e., the monotonic decrease with increasing CS and a low rate of decrease at high CS. It should be noted that this trend was the same between z/DH = 2 and 3, since the flow was already fully developed at z/DH = 2. Hence the coalescence enhancement observed in the two-dimensional vessel is similar to that in the slurry bubble column. This might be because the interactions between particles and bubble interfaces of two coalescing bubbles during the film drainage in these flows are qualitatively similar due to the locality of coalescence phenomenon.

4 Implementation of Particle Effect into Bubble Coalescence Model Then, let us implement the particle effect into a bubble coalescence model. Tanaka et al. (2009) confirmed that a combination of bubble coalescence models proposed by Prince and Blanch (1990) and Wang et al. (2005) and a bubble breakup model proposed by Luo and Svendsen (1996) gives good predictions for gas-liquid two-phase bubbly flows in an air-water bubble column. The coalescence rate,

C( m, n),

between

bubbles in bubble classes m and n is given as the linear superposition of the contributions of the Prince's,

P C ,

and Wang’s,

10

C

W

, models:

C( m,

n)

=

C

P

( m,

n)

+

C

W

( m, n), where

Since

C

W

m

and

n

are the bubble volumes of the classes m and n, respectively.

accounts for the coalescence due to bubble entrainment into a wake of a large

bubble and

P C

is for the coalescence due to bubble contact, the particle effect is

considered only for

P C .

The

P C

is given by

s CP Ω CP (θ m , θ n ) = ( ωtmn + ω vmn + ω mn ) Pmn

where t,

v

and

s

(2)

are the collision rates due to turbulence fluctuation, velocity

difference between bubbles, and shear in the liquid phase, respectively, and PCP is the coalescence efficiency given by

⎡ t ⎤ CP Pmn = exp ⎢− Cmn ⎥ ⎣ τ mn ⎦

(3)

where tCmn is the film drainage time for bubbles in classes m and n and

mn

is the bubble

contact time. The tC for bubbles in a gas-liquid system is given by (Prince and Blanch, 1990).

t Cmn

3 ρ L h0 1 d Bmn = ln hf 8 2σ

where dBmn is (1/dBm + 1/dBn) 1,

(4)

L

the liquid density, the surface tension, h0 the initial

thickness of the film between the contacting bubbles, and hf the critical film thickness.

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The thicknesses, h0 and hf, are given as 1x10 4 m (Kirkpatrick and Locket, 1974) and 1x10 8 m (Kim and Lee, 1987). The contact time is given by (Levich, 1962).

τ mn

⎛d2 = ⎜⎜ Bmn ⎝ 4e

⎞ ⎟⎟ ⎠

1/ 3

(5)

where e is the dissipation rate of the turbulent kinetic energy and in this study it was assumed that e = JGg (Baird and Rice, 1975; Lakota et al., 2001; Sanchez Perez et al., 2006), where g is the magnitude of gravity acceleration. The particle effect shown in Fig. 15 can be accounted for in the Prince's bubble coalescence model by modifying PCP as

⎡ βt ⎤ CP = exp ⎢− Cmn ⎥ Pmn ⎣ τ mn ⎦

(6)

where is a particle-effect multiplier. According to the present observation, bubbles in the dense slurry (CS = 0.45) coalesce immediately after the contact. This can be accounted for by setting = 0 for CS > 0.45. The above equation should reduce to the original equation, Eq. (3), for gas-liquid flows (CS = 0). Hence must be unity at CS = 0. Based on these constraints and the data of t C (C S ) shown in Fig. 15, the values of were obtained as shown Fig. 17.

5 Numerical method

The numerical method used in this study is based on the NP2 (N plus 2 fields) model, 12

which is a combination of a multi-fluid model and an interface tracking method (Tomiyama and Shimada, 2001; Tomiyama et al., 2006). The following is the outline of the method. Details can be found in the literature. The slurry bubble flow consists of the continuous liquid phase (water), the continuous gas phase (air above the free surface), M bubble classes and N particle classes as shown in Fig. 18. The volume fractions, k, of these phases satisfy

M

N

p =1

q =1

ε CL + ε CG + ∑ ε Bp + ∑ ε Sq = 1

(7)

where the subscripts CL, CG, Bp and Sq denote the continuous liquid phase, the continuous gas phase, the pth bubble class and the qth particle class, respectively. The continuous liquid and gas phases are calculated based on the one-fluid formulation (Tryggvason et al., 2011). The velocities of the continuous liquid and gas phases are, therefore, represented by the single quantity, VC. The transport equations of

CL

and

CG

are given by

∂ε CL + ∇ ⋅ ε CLVC = 0 ∂t

(8)

M ∂ε CG + ∇ ⋅ ε CGVC = ∑ Γ GBp ∂t p =1

(9)

where

GBp

is the mass transfer at the free surface between CG and the bubble class Bp.

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For the dispersed phases, the following transport equations of the bubble and particle number densities, nB and nS, are solved to calculate the time evolution of the phase distributions:

∂n Bp ∂t

∂n Sq ∂t

+ ∇ ⋅ n BpV Bp = − γ GBp + R p

(10)

+ ∇ ⋅ n SqV Sq = 0

(11)

where VBp is the velocity of the pth bubble class, Rp the mass transfer rate between the pth bubble class and the other bubble classes,

GBp

the mass transfer rate between the

pth bubble class and the continuous gas phase, and VSq the velocity of the qth particle

class. The momentum equation for the mixture of the two continuous phases is given by

∂VC ∇ ⋅ ε C τC + σκnδ 1 +g + VC ⋅ ∇VC = − ∇P + ∂t ρC ρC εC

(12)

N ⎤ 1 ⎡M + + + ( M M ) M LSq ⎥ ⎢∑ LBp ∑ Γp ρ C ε C ⎣ p =1 q =1 ⎦

where G

C

is the mixture density of the continuous phases,

the gas density, P the pressure,

C

= ( CG G +

CL L)/( CG

+

CL),

the mean curvature, n the unit normal to the

interface between CG and CL, the delta function, g the acceleration of gravity,

C

the

VC + ( VC)T],

C

the

sum of

CG

and

CL, C

the viscous stress tensor given by

C

=

C[

mixture viscosity, the superscript T denotes the transpose and MLBp, M p and MLSq are

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the momentum transfer rates between CL and Bp, CG and Bp, and CL and Sq, respectively. The momentum equations of the pth bubble class and the qth particle class are given by

∂V Bp

+ V Bp ⋅ ∇V Bp = −

∂t ∂V Sq

+ V Sq ⋅ ∇V Sq = −

∂t

where

S

1 1 ∇P + g − ( M LBp + M Γp + M Rp ) ρG ρ G ε Bp

(13)

1 1 ∇P + g − M LSq ρS ρ S ε Sq

(14)

is the solid density. Models for MLBp, MLSq,

GBp

and

GBp

are given in

Appendix A.3. Bubble coalescence and breakup models are the same as those used in Tanaka et al. (2009), i.e. the Prince’s and Wang’s coalescence models and the Luo’s breakup model. It is assumed that bubble coalescence takes place between two bubbles and a bubble breaks into two bubbles. The transfer rate, Rp, is evaluated as (Kumar and Ramkrishna, 1996)

R p = ∑ ζ pk nBp − p≤k

nBp θp

∫

θ Bp 0

θΩ B (θ, θ p )dθ +

∑

k ,l θ Bp ≤ θ k + θl ≤ θ Bp+1

1 ηkl nBk nBl Ω C (θ k , θl ) 2

(15)

− nBp ∑ Ω C (θ p , θ k ) k

where

B

is the breakup rate of pth bubble class and

coefficients,

pk

and kl, are given by

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B p

=(p+

p 1)/2

(see Fig. 19). The

ζ pk = ∫

θ Bp+1

θ p +1 − θ θ p +1 − θ p

θ Bp

Ω B (θ, θ k )dθ + ∫

⎧ θ p +1 − (θ k + θl ) ⎪ ⎪ θ p +1 − θ p ηkl = ⎨ (θ + θl ) − θ p −1 ⎪ k ⎪⎩ θ p − θ p −1

θ Bp+1 θ Bp

θ − θ p −1 θ p − θ p −1

Ω B (θ, θ k )dθ

(16)

for θ p ≤ θ k + θl ≤ θ Bp +1

(17) for θ ≤ θ k + θl ≤ θ p B p

Equation (16) is computed using a numerical integration, in which each bubble class is divided into five subgroups as shown in Fig. 19. The modified Prince model, Eq. (6), for slurry bubble flows is adopted for the coalescence due to turbulence fluctuation, velocity difference between bubbles, and shear in the liquid phase. The coalescence rate of Wang’s wake entrainment model is given by

CW Ω WC (θ m , θ n ) = Aωwmn Pmn

where

w

(18)

is the collision rate due to the wake effect and PCW the coalescence efficiency

given by:

CW mn

P

5 ⎡ ⎛ ρ 3L e 2 d Bmn ⎜ ⎢ = exp − 0.46⎜ σ3 ⎢⎣ ⎝

⎞ ⎟ ⎟ ⎠

1/ 6

⎤ ⎥ ⎥⎦

(19)

The subscript m and n denote the leading and trailing bubble classes. A is a parameter for turning

C

W

off for small leading bubbles:

16

⎧ dc (d Bm − B ) 6 ⎪ 2 ⎪ c A=⎨ dB 6 d Bc 6 ( − ) + ( ) d ⎪ Bm 2 2 ⎪ ⎩0

for d Bm ≥

d Bc 2

(20)

otherwise

where the critical diameter, dBc, is originally given by

d Bc = 4

σ (ρ L − ρ G ) g

(21)

This equation gives dBc = 11 mm for the air-water system. In the present experiments, the bubble coalescence due to the wake entrainment was not observed for dB 11 mm but for much larger bubbles. Therefore the simulations of gas-liquid two-phase bubbly flows (CS = 0) were carried out at various dBc and confirmed that the optimum value was 27 mm. This value was used in the following simulations.

6. Comparison

Numerical conditions were the same as the experimental conditions for the bubble column. The number of bubble classes was seven. The bubble diameters of these classes ranged from 3.6 to 57 mm, which covered dB observed in the experiments. The computational domain was the rectangular parallelepiped, whose height, width and depth were 1.0, 0.20 and 0.20 m, respectively. The side, top and bottom boundaries were slip, continuous outflow and inflow, respectively. Cubic computational cells were used. The cells of 8, 10 and 13.3 mm in width were used to investigate the effects of the spatial resolution, i.e. 25, 20 and 15 cells for these cell sizes, respectively. The cells

17

of 8 and 10 mm gave the same results in time-averaged gas holdups, whereas the predicted gas holdups with the 13.3 mm cell differed from those of the finer cells. The 10 mm cells were therefore used in the following simulations. The time step size was 1 ms. The initial water level was 0.80 m. Initially, there were the liquid and solid phases in the column and the particle concentration was uniform. The inlet bubble size, dBin, was estimated using a correlation proposed by Davidson and Schuler (1960), which gave dBin = 11 and 13 mm at JG = 0.020 and 0.034 m/s, respectively. For comparisons with the measured data, the predicted physical quantities were averaged over the time duration of 200 seconds after the flow reached a quasi-steady state. Predicted distributions of local gas holdup,

B

(=

Bp),

at CS = 0, 0.20 and 0.40 on the

center plane (y = 0) are shown in Fig. 20 (a). The instantaneous image shows that the gas holdup locally takes high values (~ 0.20). The solid holdup, S, is shown in Fig. 20 (b). Particles distribute in the whole domain. Due to the vortical structure of the liquid flow,

S

also shows weak non-uniformity.

To compare the predicted flow structure with the observed one, the distribution of

Bp

of the largest bubble size dBp (= 57 mm) on the plane 5 mm apart from the front wall is drawn in Fig. 21. The amount of large bubbles increases with CS, which qualitatively agrees with the observation. Distributions of the local gas holdup for the air-water bubbly flows (CS = 0) are compared with the measured data in Figs. 22 (a) and 23 (a) for JG = 0.020 and 0.034 m/s, respectively. Accurate predictions are obtained for the air-water bubbly flows. Distributions of the gas holdup at CS = 0.20 and 0.40 are shown in Figs. 22 (b), (c) and 23 (b), (c). The predictions with Eq. (3) largely differ from the experimental data especially at high CS, whereas the coalescence efficiency model with the particle-effect

18

multiplier, Eq. (6), gives good predictions for CS = 0.20 and 0.40. Figure 24 shows the bubble size distributions. The numbers of large bubbles at both JG increase with CS. This increase in the population of large bubbles causes increase in the bubble velocity and the bubble relative velocity, VB VC, as shown in Figs. 25 and 26.

7. Conclusion

Experiments on bubbly flows in a slurry air-water bubble column were carried out to investigate effects of hydrophilic particles on the bubbly flows. The local gas holdup and the bubble frequency were measured using an electric conductivity probe. Particles made of silica were used and their mean diameter was 100 m. The particle volumetric concentration ranged from 0 to 0.40. The superficial gas velocities were 0.020 and 0.034 m/s. The increase in the particle concentration decreases the gas holdup and bubble frequency. It was speculated from the measured data that the reduction in the bubble frequency is caused by the enhancement of bubble coalescence due to the presence of particles. Since the visibility of the slurry bubble flows in the column became lower with increasing the particle concentration, it was difficult to evaluate the particle effect on bubble coalescence. The particle effect was therefore quantitatively investigated by measuring the film drainage time in a quasi two-dimensional slurry bubble flow in a small vessel. A particle-effect multiplier, which is based on the experimental data of the film drainage time, was introduced into the bubble coalescence efficiency model for gas-liquid two-phase bubbly-flows proposed by Prince and Blanch. Numerical simulations of the slurry bubbly flows were carried out using a multi-fluid model and the particle-effect multiplier. The conclusions obtained are as follows:

19

(1) The local gas holdup and bubble frequency in the slurry bubble flow decrease as the particle concentration increases.

(2) The hydrophilic particles enhance bubble coalescence and the enhancement saturates at a certain particle concentration.

(3) The particle effect on bubble coalescence is well accounted for by introducing a particle-effect multiplier to the film drainage time in the Prince’s model.

(4) The multi-fluid model can give good predictions for the gas holdup distribution in the slurry bubble column.

Acknowledgement

This work has been supported by the Japan Society for the Promotion of Science (JSPS) (grants-in-aid for scientific research (B), No. 24360070)

Appendix A. 1 Measured Bubble Size and Velocity

The circle-area equivalent diameters, dT, and the rising velocities, VT, of bubbles in the quasi two-dimensional bubble flow in sec. 3 were measured from randomly-selected video images. The numbers of sampled bubbles were 40 at each CS to obtain mean values. The bubble Reynolds number, ReT, Eötvös number, EoT, and Weber number, WeT, of the bubbles were then calculated from dT and VT as shown in Table A1. These dimensionless numbers are defined by 20

ReT =

ρ SLVT d T μ SL

(A1)

EoT =

(ρ SL − ρ G ) gd T2 σ

(A2)

WeT =

ρ SLVT2 d T σ

(A3)

where

SL

is the apparent density defined by

viscosity of slurry.

SL

SL

= (1 CS) L + CS S and

M=

L

the apparent

was evaluated by (Tsuchiya et al., 1997)

⎡ 1.8CS ⎤ μ SL = μ L exp⎢ ⎥ ⎣ 0.72 − CS ⎦

where

SL

(A4)

is the liquid viscosity. The Morton number M is defined by

μ 4SL (ρ SL − ρ G ) g

(A5)

ρ 2SL σ 3

Since the bubble size increases with CS due to the enhancement of bubble coalescence, EoT and WeT increase with CS. On the other hand, ReT decreases as CS increases due to the increase in

SL.

21

It was difficult to measure the bubble size and velocity in the three-dimensional bubble column mainly due to the high gas holdup and low visibility of the slurry. Since the predictions of the slurry bubble flows in the column agreed well with the measured data as shown in sec. 6, the predicted bubble diameter, velocity and some relevant dimensionless groups are given below for reference. Tables A2 and A3 show the mean bubble diameter and velocity obtained by averaging predicted values for all the bubble classes (7 classes) at z/DH = 3. The bubble Reynolds number, ReB, Eötvös number, EoB, and Weber number, WeB, were also summarized in the tables. These dimensionless numbers are defined by

Re B =

ρ SL | V B − V L | d B μ SL

(A6)

Eo B =

(ρ SL − ρ G ) gd B2 σ

(A7)

We B =

ρ SL | V B − V L | 2 d B σ

(A8)

dB and EoB increase with CS because of the increase in the population of large bubbles due to the enhancement of bubble coalescence. WeB also increases with CS, whereas ReB decreases with increasing CS due to the increase in

SL.

A.2 Some observation of the rupture of liquid film between coalescing bubbles

Bubble coalescence between two rising bubbles in the quasi two-dimensional bubble flow were measured. The experimental apparatus was the same as that used in sec. 3, whereas a high-speed video camera (Photron, SA5) mounted on a stereo microscope

22

(Nikon, SMZ800, objective lends: P-ED Plan 2x) were used to observe thin liquid films between bubbles. The gas flow rate was 5.0x10 6 m3/s and CS = 0 or 0.40. The measurement position is 220 mm above the gas inlet. Since the bubble coalescence is stochastic and the recorded region was small (5.1 x 5.1 mm2), about 10,000 bubbles were recorded to capture a film rupture within the visualized region. The spatial resolution of recorded images was 5 m/pixel and the frame rate was 7000 fps. An example of the measured coalescing bubbles in the absence of particles is shown in Fig. A1 (a). The bubble interfaces on both sides of the liquid film between two coalescing bubbles are smooth and gradually drains until it becomes thin enough to rupture. The final film thickness just before the film rupture is smaller than the spatial resolution of 5 m/pixel of this image. Figure A1 (b) shows images of coalescing bubbles in the presence of hydrophilic particles of 100 m in diameter. There is a three-particle layer in the liquid film (t = 0 s). Therefore the film thickness is about 300 m. Then the film suddenly ruptures in an extremely short duration of 3/7000 s (t = 0 ~ 3/7000 s). The ruptured region expands from the ruptured point due to surface tension force and particles are pushed out from the film. According to this observation, one of the possible scenarios to enhance bubble coalescence may be as follows: because of the presence of many hydrophilic particles, the liquid film between the bubbles takes a porous-like structure consisting of very thin liquid elements. Its spatial structure is very complicated and the thin element might be very fragile due to the particle motion. Therefore the liquid film densely packed with small particles may easily rupture after bubble contact.

23

A. 3 Models for Interfacial Momentum Transfer

Models for interfacial momentum transfer are described in this appendix. Since the solid phase in the present experiments is mono-dispersed, the number of particle class is one and

Sq

is simply written as

S

in the following. The momentum transfer rate,

MLBp, in Eq. (12) is given by

M LBp =

⎡ DV Bp DVC ⎤ 3 ε Bp − C DBp ρ C V Bp − VC (V Bp − VC ) + ε Bp CVMBp ρ C ⎢ ⎥ 4 d Bp Dt ⎦ ⎣ Dt

(A9)

+ ε Bp C LFBp ρ C (V Bp − VC ) × ∇ × VC + CTDBp ρ C k CL ∇ε Bp

where CD is the drag coefficient, CVM the virtual mass coefficient, CLF the lift coefficient, CTD the turbulent dispersion coefficient, and kCL the turbulent kinetic energy of the phase CL. MLS is given by

M LS =

3 εS ⎡ DV S DVC ⎤ C DS ρ C V S − VC (V S − VC ) + ε S CVMS ρ C ⎢ − + CTDS ρ C k CL ∇ε S 4 dS Dt ⎥⎦ ⎣ Dt (A10)

where dS is the particle diameter. Since the magnitude of the lift force is proportional to the particle volume, the lift force acting on particles is very small compared with the drag force due to the small particle size. The lift force acting on particles is therefore neglected. The drag coefficient, CDBp, is given by

S C DBp = C DBp (ε CL + ε S ) −0.5

(A11)

24

where ( CL + S) 0.5 accounts for the bubble swarm effect (Tomiyama et al., 1995) and CDBpS is the drag coefficient of a single bubble in a clean system (Tomiyama et al., 1998):

⎡ ⎡ 16 48 ⎤ 8 Eo Bp ⎤ S 0.687 = max ⎢min ⎢ (1 + 0.15 Re Bp ), C DBp ⎥ ⎥, Re Bp ⎥⎦ 3 Eo Bp + 4 ⎥⎦ ⎢⎣ Re Bp ⎢⎣

(A12)

Here the bubble Reynolds number, ReBp, and the Eötvös number, EoBp, are defined by

Re Bp =

Eo Bp =

where

ρ SL V Bp − VC d Bp

(A13)

μ SL 2 (ρ SL − ρ G ) gd Bp

(A14)

σ

SL

is ( CL L+ S S)/( CL + S) and

SL

the apparent viscosity of the slurry given by

(Tsuchiya et al., 1997).

⎡ 1.8ε *S ⎤ μ SL = μ L exp⎢ * ⎥ ⎣ 0.72 − ε S ⎦

where

S

*

(A15)

= S/( CL + S).

The drag coefficient, CDS, is given by

25

25ε *S4 / 3 ⎤ S ⎡ C DS = C DS ⎢1 + ⎥ 3ε *CL3 ⎦ ⎣

(A16)

where the second term in the parentheses represents the particle swarm effect (Gmachowski, 1996),

* CL

=

CL/( CL

+ S), and CDSS is the drag coefficient for a solid

sphere (Clift and Gauvin, 1971)

S C DS =

24 0.42 (1 + 0.15 Re S0.687 ) + Re S 1 + 4.25 × 10 4 Re S−1.16

(A17)

where ReS is the particle Reynolds number defined by

ReS =

ρ L | V S − VC | d S μL

(A18)

The lift coefficient of a bubble is evaluated by using the following empirical correlation (Tomiyama et al., 2002):

C LFBp

⎧min[0.288tanh(0.121ReBp ), f ( EoHBp )] ⎪ = ⎨ f ( EoHBp ) ⎪ ⎩ − 0.29

for EoHBp ≤ 4 for 4 < EoHBp ≤ 10.7 for 10.7 < EoHBp

3 2 f ( EoHBp ) = 0.00105 EoHBp − 0.0159 EoHBp − 0.0204 EoHBp + 0.474

(A19)

(A20)

where EoHBp is the Eötvös number using the bubble major axis, dHBp, for the characteristic length scale.

26

CVM = 0.5 and CTD = 2.0 are used for both bubbles and particles. The turbulent kinetic energy, kCL, is evaluated by (Lopez de Bertodano et al., 1994)

M

k CL = ∑ ε Bp | V Bp − VC | 2

(A21)

p =1

The mixture viscosity

C

is given by

⎡ ε CG ε CL + ε S ⎤ 1 1 = + ⎢ ⎥ μC εC + ε S ⎣ μG μ SL ⎦

where

G

(A22)

is the gas viscosity. The surface tension force, n , in Eq. (12) is evaluated

using the continuum surface force (CSF) model (Brackbill et al., 1992). To deal with bubbles larger than the computational cell size, a shape factor, f, which is a scalar function representing the fraction of the bubble volume included in each computational cell as shown in Fig. A2, is introduced (Tomiyama et al., 2006). The volume fraction,

Bp,

is calculated by summing up the contributions from surrounding

cells:

ε Bp = ∑ n Bp f Bp Θ

(A23)

where is the volume of a computational cell. For Eo < 40, the aspect ratio, EBp, of a bubble is given by (Vakhrushev and Efremov, 1970)

27

E Bp

⎧1 for Ta Bp ≤ 1 ⎪ 3 = ⎨[0.81 + 0.206tanh(1.6 − 2log10Ta Bp )] for 1 < Ta Bp ≤ 39.8 ⎪0.24 for 39.8 < Ta Bp ⎩

(A24)

where TaBp is the Tadaki number defined by (Tadaki and Maeda, 1961).

Ta Bp = Re Bp M 0.23

(A25)

The bubble diameters of Eo = 40 are 17 and 14 mm at CS = 0 and 0.40, respectively. Since bubbles for Eo > 40 are highly distorted as shown in Fig. 6 and there are no models applicable to them, the aspect ratio is set at unity for Eo > 40. Bubbles arriving at the free surface are assumed to merge into the continuous gas phase during one time step. This assumption gives the following mass transfer rates for GBp

and

ΓGBp =

γ GBp =

GBp

(Tomiyama and Shimada, 2001):

ε Bp ε CG

(A26)

Δtε C n Bp ε CG

(A27)

Δtε C

where t is the time step.

28

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35

Figure captions

Fig. 1 Experimental setup

Fig. 2 Probe tip

Fig. 3 Measured voltage (solid line) and processed binary signals (dashed line)

Fig. 4 Visibility of slurry (L is the distance from the column wall to the sheet)

Fig. 5 Slurry bubble flows at JG = 0.034 m/s

Fig. 6 Close-up views of slurry bubble flows at JG = 0.034 m/s

Fig. 7 Distributions of (a)

B

and (b) fB at JG = 0.020 m/s and z/DH = 3

Fig. 8 Distributions of (a)

B

and (b) fB at JG = 0.034 m/s and z/DH = 3

Fig. 9 Comparisons of

B

and fB between z/DH = 2 and 3

36

Fig. 10 Experimental setup for two-dimensional bubble flow

Fig. 11 Measurement of tC

Fig. 12 Two-dimensional bubble flows in small vessel

Fig. 13 Bubble collision and coalescence

Fig. 14 Effect of CS on tC

Fig. 15 Mean tC

Fig. 16 Effects of CS on averaged fB

Fig. 17 Particle-effect multiplier

Fig. 18 Bubble and particle classes and continuous phases in NP2 model

Fig. 19 Bubble number densities of bubble classes (Each bubble class is divided into five subgroups when calculating Eq. (16))

Fig. 20 Distributions of

B

(=

Bp)

and

S

on the center plane of column at JG = 0.034

m/s

37

Fig. 21 Comparisons between predicted

Bp

(dBp = 57 mm) in the near wall region and

video image at JG = 0.034 m/s

Fig. 22 Comparisons between measured and predicted gas holdups at JG = 0.020 m/s and z/DH = 3

Fig. 23 Comparisons between measured and predicted gas holdups at JG = 0.034 m/s and z/DH = 3

Fig. 24 Predicted bubble size distributions at z/DH = 3

Fig. 25 Predicted bubble velocity at z/DH = 3 and JG = 0.034 m/s

Fig. 26 Predicted bubble relative velocity at z/DH = 3 and JG = 0.034 m/s

Fig. A1 High-speed video images of the rupture of liquid film between two rising bubbles

Fig. A2 Shape factor

38

Figure 1

DH = 200 mm 200 mm Measurement point y 15 mm x

1200 mm

z/DH = 3

Compressor

z/DH = 2 z/DH = 1

Air tank

z

Pressure P gauge

y x

Air Control valve

Flow meter

43 mm

(a) Experimental setup

Acrylic plate

300 mm

200 mm

25 mm

Hole (diameter = 1.4 mm) y 25 mm

x

200 mm Top view

Stainless tube Side view

(b) Diffuser plate with 49 holes

Figure 2

2.1 mm

20 m

Figure 3

Voltage

Gas

Liquid 0

0.01

0.02 t [s]

0.03

5 mm

Figure 4

CS = 0.20

L = 1 mm

3 mm

5 mm

7 mm

3 mm

5 mm

7 mm

0.40

1 mm

Figure 5

z/DH

DH = 200 mm

4

3

2

1

0

CS = 0

0.10

0.20

0.30

0.40

Figure 6

10 mm CS = 0

0.10

0.20

0.30

0.40

Figure 7

30

0.10

20

B

fB [Hz]

0.15

0.05

0.00 -100

CS 0 0.10 0.20 -50

0 x [mm]

(a)

10 0.30 0.40 50

100

0 -100

-50

0 x [mm]

(b)

50

100

Figure 8

30

0.10

20

B

fB [Hz]

0.15

0.05

0.00 -100

CS 0 0.10 0.20 -50

0 x [mm]

(a)

10 0.30 0.40 50

100

0 -100

-50

0 x [mm]

(b)

50

100

Figure 9

0.15

0.15

CS = 0

0.10

0.10

0.05 0.00

0.05

z/DH 2 3

0.00

CS = 0.20

CS = 0.20

B

0.10

B

0.10 0.05 0.00

CS = 0

0.05 0.00

CS = 0.40

0.10

0.10

0.05

0.05

0.00 -100 -50

0 50 x [mm]

100

(a) JG = 0.020 m/s

CS = 0.40

0.00 -100 -50

0 50 x [mm]

100

(b) JG = 0.034 m/s

Figure 10

330 mm

D = 100 mm

Compressor

Air tank Pressure gauge P Mass flow controller

MFC

Air

Figure 11

Distance between bubble interfaces　

Distance between interfaces [mm]

t = 0.025 s

Rupture of liquid film

t = 0.096 s

5 4

Film rupture

3

Contact

2 1 0 0

tC

0.025

0.05 Time [s]

0.075

0.1

Figure 12

D = 100 mm

z/D 2

1

0

CS = 0

0.10

0.20

0.30

0.40

Figure 13

Contact

Approaching

(a) CS = 0 Approaching

0.00 s

0.01 s

0.02 s

(b) CS = 0.40

Coalescence

0.03 s

0.04 s

Figure 14

1.0 0.8

CS 0 0.10 0.20 0.25 0.30 0.40 0.45

PDF

0.6 0.4 0.2 0.0 0.00

0.04

0.08

0.12 tC [s]

0.16

0.20

0.24

Figure 15

0.08

tC [s]

0.06

0.04

0.02

0.00 0.0

0.1

0.2

0.3 CS

0.4

0.5

Figure 16

fB(C S) / fB(C S=0)

1.50 JG [m/s] 0.020 0.034

1.00

0.50

0.00 0.0

0.1

0.2 CS

0.3

0.4

Figure 17

1.0 0.8



0.6 0.4 0.2 0.0 0.0

0.1

0.2

0.3 CS

0.4

0.5

Figure 18

Computational cell

GBp

Continuous gas phase, CG

MLBp MLSq Rp

Particle class 1, S1 Particle class 2, S2 Bubble class 1, B1 Bubble class 2, B2 Bubble class 3, B3 Continuous liquid phase, CL

Figure 19

nB

Bubble class Bubble class Bubble class p-1 p p+1

Bp-1

p-1

Bp

p

Bp+1

p+1

 Bp+2

Figure 20

z/DH 4

B 0.2

3

S 0.45

2

1

0

CS = 0

0.20

(a) B

0.40

0

0.20

0.40

(b) S

0

Figure 21

z/DH 4

3

Bp 0.2

2

1

0

CS = 0

0.20

0.40

0

Figure 22

0.15 (a) CS = 0 0.10

0.05

0.00 (b) CS = 0.20

B

0.10

0.05

0.00 (c) CS = 0.40 0.10

0.05

0.00 -100

Measured Predicted with Eq. (6) with Eq. (3) -50

0 x [mm]

50

100

Figure 23

0.15 (a) CS = 0 0.10

0.05

0.00 (b) CS = 0.20

B

0.10

0.05

0.00 (c) CS = 0.40 0.10

0.05

0.00 -100

Measured Predicted with Eq. (6) with Eq. (3) -50

0 x [mm]

50

100

Figure 24

0.50 (a) JG = 0.020 m/s

PDF (Volume ratio: Bp/B)

0.25

CS 0 0.10 0.20

0.30 0.40

0.00 (b) JG = 0.034 m/s

0.25

0.00 0

20 40 Bubble diameter [mm]

60

Figure 25

Bubble velocity [m/s]

1.0

0.5

CS 0 0.10 0.20

0.0

-0.5 -100

-50

0 x [mm]

0.30 0.40 50

100

Figure 26

Bubble relative velocity [m/s]

0.5 0.4 0.3 0.2

CS 0 0.10 0.20

0.1 0.0 -100

-50

0 x [mm]

0.30 0.40 50

100

Figure A1

Liquid film thickness < 5 m

500 m

10 mm

t=0s

Film rupture

Wall

Ruptured film

Liquid Air

3/7000 s

6/7000 s (a) CS = 0 %

Liquid film thickness ~ 300 m

500 m

10 mm

t=0s

Wall

Film rupture

Liquid Air

3/7000 s (b) CS = 40 % with 100 m particles

6/7000 s

Figure A2

Bubble f = 0.05

0.20

0.05

0.65

1.00

0.65

0.05

0.20

0.05

Center of gravity

Figure 20 for black and white printed version

(a) B

(b) S

Figure 21 for black and white printed version

z/DH 4

3

Bp 0.2

2

1

0

CS = 0

0.20

0.40

0

Table A1 Measured bubble size and rising velocity in 2D vessel

dT [mm] VT [m/s] M

CS 0

17

0.20 0.40

19 24

0.42 0.42 0.39

2.5x10

EoT

ReT

WeT

11

39

7140

41

10

52 87

4250 1110

49 57

3.8x10 1.8x10 7

Table A2 Predicted bubble size and rising velocity in bubble column at JG = 0.020 m/s

CS 0 0.20 0.40

dB [mm] 8.7 11 21

|VB VC| [m/s] 0.23 0.25 0.30

M 2.5x10

EoB

ReB

WeB

11

10

2020

6.4

10

17 67

1460 740

9.9 29

3.8x10 1.8x10 7

Table A3 Predicted bubble size and rising velocity in bubble column at JG = 0.034 m/s

CS 0 0.20 0.40

dB [mm] 9.0 12 23

|VB VC| [m/s] 0.24 0.25 0.30

M 2.5x10

EoB

ReB

WeB

11

11

2140

7.0

10

20 80

1610 830

11 33

3.8x10 1.8x10 7

39

Highlights

(1) Local gas holdups in bubbly flows in a slurry bubble column are measured. (2) Effects of hydrophilic particles on bubble coalescence are investigated. (3) A wide range of particle concentration, up to 0.40, is examined. (4) A particle-effect multiplier is introduced into a bubble coalescence efficiency model. (5) Numerical simulations give good predictions for slurry bubble flows.

40