Lumped models of gas bubbles in thermal gradients

Applied Mathematical Modelling

Volumn 21, Issue 6, 1997, Pages 371-386

  Ramos, J I ^a  

^a UNIVERSITY OF MÁLAGA   (Spain)

Author keywords

Buoyancy; Gas bubbles; Mass transfer; Thermal gradients; Thermocapillary

Indexed keywords

BUOYANCY; CAPILLARITY; MASS TRANSFER; NUMERICAL METHODS; SURFACE TENSION; THERMAL GRADIENTS; VISCOSITY; VISCOUS FLOW;

LUMPED MODELS; THERMOCAPILLARITY;

BUBBLES (IN FLUIDS);

EID: 0031165451     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0307-904X(97)00034-6     Document Type: Article

References (16)

1. Mattox, D. M., Smith, H. D., Wilcox, W. R., and Subramaniam, R. S. Thermal-gradient-induced migration of bubbles in molten glass. J. Amer. Ceramic Soc. 1982, 65, 437-442
2. Young, N. O., Goldstein, J. S., and Block, M. J. The motion of bubbles in a vertical temperature gradient. J. Fluid Mech. 1959, 6, 350-356
3. Němec, L. The refining of glass melts. Glass Technol. 1974, 15, 153-156
4. Ramos, J. I. Multicomponent gas bubbles: II. Bubble dynamics. J. Non-Equilib. Thermodyn. 1988, 13, 107-131
5. Němec, L. and Mühlbauer, M. Mathematical model of bubble behaviour during refining of glass melts. J. Non-Cryst. Solids 1980, 38/39, 593-598
6. Subramaniam, R. S. Slow migration of a gas bubble in a thermal gradient. AIChE J. 1981, 27, 646-654
7. Subramaniam, R. S. Thermocapillary migration of bubbles and droplets. Adv. Space Res. 1983, 3, 145-153
8. Clift, R., Grace, J. R., and Weber, M. E. Bubbles, Drops, and Particles. Academic Press, New York, 1978.
9. Harper, J. F. The motion of bubbles and drops through liquids. Adv. Appl. Mech. 1972, 12, 59-129
10. Shankar, N., Cole, R., and Subramaniam, R. S. Thermocapillary migration of a fluid droplet inside a drop in a space laboratory. Int. J. Multiphase Flow 1981, 7, 581-594
11. Abramowitz, M. and Stegun, I. A. Handbook of Mathematical Functions. Dover, New York, 1972
12. Gradshteyn, I. S. and Ryzhik, I. M. Table of Integrals, Series, and Products. Academic Press, New York, 1980
13. Kim, H. S. and Subramaniam, R. S. The thermocapillary migration of a droplet with insoluble surfactant: II. General case. J. Colloid Interface Sci. 1989, 27, 112-129
14. Cable, M. Study of refining: II. Glass Technol. 1961, 2, 60-70
15. Weinberg, M. C., Onorato, P. I. K., and Uhlmann, D. R. Behavior of bubbles in glassmelts: II, Dissolution of a stationary bubble containing a diffusing and a nondiffusing gas. J. Amer. Ceramic Soc. 1980, 63, 435-438
16. Cable, M. A study of refining. Part 3: The function of arsenious oxide during melting and refining. Glass Technol. 1961, 2, 151-158