Direct integration method applied to Soret‐driven instability

A direct integration approach coupled with Newton’s iteration scheme was devised to determine the linear stability of a hydrodynamic system with general boundary conditions. A fundamental set of linearly independent solutions was constructed whose coefficients are to be determined by the boundary conditions. In order to assure the existence of nontrivial solutions for the coefficients, a secular equation must be solved whose solution determines the stability criteria to an arbitrary degree of accuracy. This method was applied to a two‐component liquid system with rigid‐rigid boundaries and an imposed temperature gradient. No approximation was made of the Soret‐effect term and of the primary‐state configuration. A slope discontinuity was found in the critical Rayleigh number as the Soret coefficient increases in the positive region. The frequency of the oscillatory mode was found to be very sensitive to the variation of the negative Soret coefficient near the bifurcation point, and to the variation of the concentration near zero or unity. Comparison with existing experiments is also discussed.