Foaming behavior of slags
- PDF / 104,772 Bytes
- 4 Pages / 612 x 792 pts (letter) Page_size
- 93 Downloads / 252 Views
where h is the height of the foam at steady state when gas with superficial velocity us is passed through it. Based on dimensional analysis, Zhang and Fruhen[3] found that the experimental results for different slags obtained by their group could be adequately represented by the equation 兺 ⫽ 115 1.2 /( 0.2 ⭈ db0.9)
[2]
where , , and are, respectively, the viscosity, surface tension, and density of slag and db is the bubble diameter in Syste´me International (SI) units. Recently, Kim et al.[5] found that their experimental results for CaO-SiO2-FeOAl2O3 and CaO-SiO2-FeO-MgO-X, where X ⫽ Al2O3, MnO, P2O5, and CaF2, follow the relationship 兺 ⫽ C /( )1/2
[3]
The value of the constant C depends on the nature of a slag. It is 214 for a CaO-based slag and 999 for a MgOsaturated slag. The same relationship was proposed earlier by Ito and Fruehen[1] for CaO-SiO2-FeO slags containing 30 pct FeO, where C was found to be 570. Later, Jiang and Fruhen[2] studied the CaO-FeO-Al2O3-SiO2 system containing less than 15 pct FeO and modified the value of C to 115. All these studies, however, show that the foaming index defined by Eq. [1] is independent of the superficial velocity of a gas. On the other hand, Wu et al.[6] found that the foaming index depends on us . This shows that the factors that determine the foaming index and their relative importance are not clearly known. In the present article, an expression of the foaming index has been derived from the mechanism of bubble rupture and its applicability is discussed. The foam volume is determined by the following balance equation Rate of change of foam volume ⫽ (rate of gas generation or injection)
[4]
⫺ (rate of volume change due to bubble rupture) The bubble rupture on the top layer of foam causes a decrease in foam volume because of gas escape. Bubble rupture inside
A.K. LAHIRI, Professor, is with the Department of Metallurgy, Indian Institute of Science, Bangalore 560 012, India S. SEETHARAMAN, Professor, is with the Division of Metallurgy, Royal Institute of Technology, SE-100 44 Stockholm, Sweden. Contact e-mail: [email protected] Manuscript submitted November 15, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS B
the foam leads to bubble coalescence and, consequently, a change in the liquid film thickness between the bubbles and their packing. Coalescence of bubbles also leads to a decrease in foam volume. Besides, nonuniform bubbles, which are produced by coalescence, make the foam unstable.[7] Hence, the bubble rupture rate can be assumed to be proportional to the number of bubbles. Assuming that kinetics of bubble rupture follows first-order rate law, we can write Rate of volume change due to bubble rupture ⫽ kNvb [5] where vb is the average volume of a bubble, N is the total number of bubbles, and k is the rate constant for bubble decay. The total volume of foam and the bubble volumes are related by ⫽ Nvb /v
[6]
where is the average void fraction and v is the volume of foam. Using Eqs. [5] and [6], Eq. [4] can be written as dv/dt ⫽ Q ⫺ kv
[
Data Loading...
