Tanny, J., Chen, C. C. and Chen, C. F. (1995)
Effects of interaction between Marangoni and double-diffusive instabilities, Journal of Fluid Mechanics, Vol. 303, pp. 1-21.

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ABSTRACT
The effect of surface tension on the onset of convection in a horizontal double-diffusive layer was studied both experimentally and by linear stability analysis. The experiments were conducted in a rectangular tank with base dimension of 25 x 13 cm and 5 cm in height. A stable solute (NaCl) stratification was first established in the tank, and then a vertical temperature gradient was imposed. Vertical temperature and concentration profiles were measured using a thermocouple and a conductivity probe and the flow patterns were visualized by a schlieren system. Two types of experiments were carried out which illustrate the effect of surface tension on the onset of convection. In the rigid-rigid experiments, when the critical thermal Rayleigh number, R^T, is reached, large double-diffusive plumes were seen simultaneously to rise from the heated bottom and descend from the cooled top. In the rigid-free experiments, owing to surface-tension effects, the first instability onset was of the Marangoni type. Well-organized small plumes were seen to emerge and persist close to the top free surface at a relatively small R_M^T (where subscript M denotes 'Marangoni'). At larger R_t^T > R_M^T (where subscript t denotes 'top') these plumes evolved into larger double-diffusive plumes. The onset of double-diffusive instability at the bottom region occurred at a still higher R_b^T > R_t^T (where subscript b denotes 'bottom'). A series of stability experiments was b conducted for a layer with an initial top concentration of 2 wt% and different concentration gradients. The stability map shows that in the rigid-free case the early Marangoni instability in the top region reduces significantly the critical RT for the onset of double-diffusive convection. Compared with the rigid-rigid case, the critical R^T in the top region is reduced by about 60% and in the bottom region by about 30%. The results of the linear stability analysis, which takes into account both surface tension and double-diffusive effects, are in general agreement with the experiments. The analysis is then applied to study the stability characteristics of such a layer as gravity is reduced to microgravity level. Results show that even at 10^-4g₀, where g₀, is the gravity at sea level, the double-diffusive effect is of equal importance to the Marangoni effect.

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