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Mechanism of mass transfer between a bubble initially composed of oxygen and molten glass. (English) Zbl 1211.80024
Summary: The bubble removal from molten glass is an important problem in glass melting process. In this paper, the mass transfer undergone by a bubble rising in molten glass is studied, the multicomponent feature being taken into account. In order to identify the time scaling of the bubble shrinkage, a careful dimension analysis is performed.
A characteristic time to describe the mass transfer for each gaseous species in a bubble is introduced with an alternative expression of the permeability. This new permeability has the dimension of a diffusion coefficient, which is useful to compare to other transport phenomena. From the physical data known for soda-lime-silica glasses, a fast equilibrium state of water between a bubble and molten glass is determined. The opposite situation is observed for nitrogen.
Experimental results giving the bubble size versus time with a dimensionless form leads to a good match at short time whatever the glass nature and the temperature. Finally, a simple equation to determine bubble size as a function of time is given, based on the dimension analysis previously established.

##### MSC:
 80A20 Heat and mass transfer, heat flow (MSC2010) 76T10 Liquid-gas two-phase flows, bubbly flows 76V05 Reaction effects in flows 80-05 Experimental work for problems pertaining to classical thermodynamics
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##### References:
 [1] Beerkens, R. G. C.: Modeling of the melting process in industrial Glass furnaces, , 17-73 (2002) [2] Beerkens, R. G. C.: Analysis of advanced and fast fining processes for Glass melts, , 3-24 (2003) [3] Beerkens, R. G. C.; De Waal, H.: Mechanism of oxygen diffusion in glassmelts containing variable-valence ions, J. am. Ceram. soc. 73, 1857-1861 (1990) [4] Bejan, A.: Convection heat transfer, (1995) · Zbl 0599.76097 [5] Clift, R.; Grace, J. R.; Weber, M. E.: Bubbles, drops, and particles, (1978) [6] Doremus, R. H.: Diffusion of oxygen from contracting bubbles in molten Glass, J. amer. Ceram. soc. 43, 655-661 (1960) [7] Greene, C. H.; Gaffney, R. F.: Apparatus for measuring the rate of absorption of a bubble in Glass, J. amer. Ceram. soc. 42, 271-275 (1959) [8] Greene, C. H.; Kitano, I.: Rate of solution of oxygen bubbles in commercial glasses, Glastech. ber. 32K, No. 5, 44-48 (1959) [9] Greene, C. H.; Lee, H. A.: Effect of as2o3 and nano3 on the solution of O2 in soda – lime Glass, J. amer. Ceram. soc. 48, 528-533 (1965) [10] Greene, C. H.; Platts, D. R.: Behavior of bubbles of oxygen and sulfur dioxide in soda – lime Glass, J. amer. Ceram. soc. 52, 106-109 (1969) [11] Hirashima, H.; Yoshida, T.; Brückner, R.: Redox equilibria and constitution of polyvalent ions in oxide melts and glasses, Glastech. ber. 61, 283-292 (1988) [12] Kloužek, J.; Němec, L.: Modelling of Glass refining kinetics. Part 2: bubble distribution models and methods of measurement of refining properties, Ceramics 47, 155-161 (2003) [13] Levich, V. G.: Physicochemical hydrodynamics, (1962) [14] Mysen, B. O.; Richet, P.: Silicate glasses and melts: properties and structure, (2005) [15] Němec, L.: The behaviour of bubbles in Glass melts. Part 1: bubble size controlled by diffusion, Glass technol. 21, 134-138 (1980) [16] Němec, L.: The behaviour of bubbles in Glass melts. Part 2: bubble size controlled by diffusion and chemical reaction, Glass technol. 21, 139-144 (1980) [17] Němec, L.; Kloužek, J.: Modelling of Glass refining kinetics. Part 1: single bubbles, Ceramics 47, 81-87 (2003) [18] Onorato, P. I. K.; Weinberg, M. C.; Uhlmann, D. R.: Behavior of bulles in glassmelts: III, dissolution and growth of a rising bubble containing a single gas, J. am. Ceram. soc. 64, 676-682 (1981) [19] Paul, A.: Chemistry of glasses, (1990) [20] Pigeonneau, F.: Coupled modelling of redox reactions and Glass melt fining processes, Glass technol. Eur. J. Glass sci. Technol. A 48, No. 2, 66-72 (2007) [21] Pigeonneau, F.: Mass transfer of rising bubble in molten Glass with instantaneous oxidation – reduction reaction, Chem. eng. Sci. 64, 3120-3129 (2009) [22] Pigeonneau, F.; Martin, D.; Mario, O.: Shrinkage of oxygen bubble rising in a molten Glass, Chem. eng. Sci. 65, 3158-3168 (2010) [23] Pilon, L.; Fedorov, A. G.; Ramkrishna, D.; Viskanta, R.: Bubble transport in three-dimensional laminar gravity-driven flow-mathematical formulation, J. non-cryst. Solids 336, 71-83 (2004) [24] Ramos, J. I.: Behavior of multicomponent gas bubbles in Glass melts, J. am. Ceram. soc. 69, 149-154 (1986) [25] Readey, D. W.; Cooper, A. R.: Molecular diffusion with a moving boundary and spherical symmetry, Chem. eng. Sci. 21, 917-922 (1966) [26] Sadhal, S. S.; Ayyaswamy, P. S.; Chung, J. N.: Transport phenomena with drops and bubbles, (1997) · Zbl 0863.76001 [27] H. Scholze, Gases in glass. In Proceeding of the 8th International Congress on Glass, Londres, 1968. [28] Shelby, J. E.: Introduction to Glass science and technology, (1997) [29] Subramanian, R. S.; Chi, B.: Bubble dissolution with chemical reaction, Chem. eng. Sci. 35, 2185-2194 (1980) [30] Yoshikawa, H.; Kawase, Y.: Significance of redox reactions in Glass refining processes, Glass sci. Technol. 70, 31-39 (1997)
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