Comparative Studies of Silicon Dissolution in Molten Aluminum Under Different Flow Conditions Part II: Two-Phase Flow

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Following on a study of Si dissolution in molten Al, the effect of gas agitation is examined. The effects of gas flow rate, liquid bulk velocity, the position of a top injection lance, and bath temperature on the dissolution rate are quantified. A higher gas flow rate produced larger bubbles while bubble frequency remained relatively unchanged. This resulted in larger bubble-induced fluctuating velocities which in turn increased the dissolution rate. At lower bulk velocities, the effect of gas agitation is localized around the lance. By increasing the velocity, the effect of gas agitation is transported further into the bath. The dissolution rate enhancement varies with increasing bulk velocity, and explanations are provided. When combined with a bulk flow, gas agitation increases the dissolution rate regardless of lance position. Also, the enhancement of dissolution rate due to gas injection decreases at higher superheats, as the higher bath temperature increases the mass boundary thickness. In addition, the dissolution rate without gas agitation (single-phase flow) and with gas agitation (two-phase flow) is compared in terms of mean mass transfer coefficients. It was found that for the same liquid bulk velocities, the mean mass transfer coefficients are higher in two-phase flow than in single-phase flow. Finally, an increment to the single-phase flow bulk velocity that would be required to gain parity with the two-phase flow dissolution rate rise is demonstrated.

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A c S :

Sphere cross-sectional area, m2

C D :

Sphere drag coefficient

C Si Sat :

Saturation concentration of Si in molten Al

D :

Diffusion coefficient, m2 s−1

d :

Diameter of cylindrical Si specimen, m

d b :

Bubble diameter, m

(d b)max :

Maximum stable bubble diameter, m

d lance,OD :

Outer diameter of a lance or nozzle, m

F B :

Buoyancy force, N

\( F_{\text{D}}^{\text{L}} \) :

Lateral drag force, N

f :

Frequency of bubble formation, s−1

g :

Gravitational acceleration, m s−2

H :

Liquid height inside a tank, m

\( \bar{k}_{\text{m}} \) :

Mean mass transfer coefficient, m s−1

L :

Distance from the lance/nozzle tip to the bath surface, m

m d :

Dissolved mass of cylindrical Si specimen, kg

m i :

Initial immersed mass of cylindrical Si specimen, kg

P :

Static pressure of liquid at the lance/nozzle tip, Pa

P 0 :

Standard pressure, Pa

Q :

Gas flow rate at the lance exit, m3 s−1

Q S :

Gas flow rate at standard temperature and pressure [273.15 K (0 °C) and 100 kPa], m3 s−1

Re :

Reynolds number

Re T :

Reynolds number based on rms velocity fluctuations


Radius of cylindrical Si specimen, m

r0 :

Initial radius of cylindrical Si specimen, m

Sc :

Schmidt number [=ν/D]

\( \overline{\text{Sh}} \) :

Mean Sherwood number

T :

Temperature, K


Turbulence intensity

U b :

Bulk velocity of liquid normal to the centerline of a vertical cylinder or an injection lance, m s−1

x, y, z :

Cartesian coordinates

α :

Thermal diffusivity, m2 s−1

δ :

Momentum boundary layer thickness, m

δ m :

Mass boundary layer thickness, m

θ :

Relative angular position with respect to cylindrical Si specimen, deg

θ c :

Contact angle, deg

ν :

Kinematic viscosity, m2 s−1

ρ :

Density, kg m−3

σ :

Surface tension, N m−1


Initial condition


Liquid Al






Solid silicon


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The authors wish to acknowledge the generosity of the Natural Sciences and Engineering Research Council of Canada for the support provided for this project through a Strategic Grant.

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Correspondence to Stavros A. Argyropoulos.

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Manuscript submitted April 23, 2014.

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Seyed Ahmadi, M., Argyropoulos, S.A., Bussmann, M. et al. Comparative Studies of Silicon Dissolution in Molten Aluminum Under Different Flow Conditions Part II: Two-Phase Flow. Metall and Materi Trans B 46, 1290–1301 (2015) doi:10.1007/s11663-015-0300-7

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  • Dissolution Rate
  • Mass Transfer Coefficient
  • Mass Transfer Rate
  • Bulk Velocity
  • Mass Boundary Layer