Article

Abstract

A theoretical treatment of the double-diffusive convection instability is presented, with a focus on the isothermal case of two solutes in a common solvent, initially forming a distinct interface. Linear stability analysis is used to determine the wave number of the marginal mode and symmetry properties of the corresponding fluid flow for realistic values of two control parameters: (i) the ratio of the diffusion coefficient of the solute in the lower solution to that in the upper solution (τd), and (ii) the ratio of the excess densities (relative to the solvent) of the upper to the lower solutions (τp). It is shown that the instability has two regimes: (i) τd-3/2 < τρ < τd-1 in which diffusion precedes convection, and (ii) τd-1 < τρ < 1 in which convection is immediate. The two regimes are separated by a point (τρ = τd-1) through which the wavelength diverges and the fluid velocity undergoes a continuous symmetry change. Above this point, columns of alternating up-and-down flow fade continuously into the solutions above and below the original interface. Below it, the flow within a column undergoes at least one reversal. The horizontal nodal plane associated with such a reversal should be observable.Key words: double-diffusive convection, fluid instability, pattern formation, solutions.