Stability of ternary mixtures mechanical equilibrium in a square cavity with vertical temperature gradient - Lyubimova, Tatiana Petrovna; Zubova, Nadezhda Alekseevna (Computational Continuum Mechanics, 2014)
The linear stability of mechanical equilibrium in ternary mixtures in a square cavity under the action of gravity and subject to vertical temperature and concentration gradients is studied numerically. Cavity boundaries are assumed to be solid and impermeable to the substance. Lateral boundaries are thermally insulated, and horizontal boundaries are permanently maintained at different temperatures. Ternary mixtures with a fixed positive separation ratio of the first component and various separation ratios of the second componentare considered. The plots of the critical Rayleigh number and the critical perturbation frequency versus the separation ratio of the second component of the mixture are constructed. For both binary and ternary mixtures heated from below, the monotonic instability is observed at positive and negative small absolute values ofand the oscillatory instability at negative valuesexceeding some small modulus value. In the case of the mixture heated from above at negative values ofthere takes place monotonic instability. The results obtained for binary and ternary mixtures are compared. It has been found that the addition of a third component of a binary mixture with a positive separation ratio causes destabilization of monotonic and oscillatory instabilities for heating from below and stabilization of the monotonic instability for heating from above.
Keywords: convection; multi-component mixture; diffusion; thermal diffusion; mechanical equilibrium; monotonic and oscillatory instability; closed cavity