The role of mixing in traveling-wave convection

Abstract

In binary fluid mixtures with negative separation ratio, the conduction state has a vertical concentration gradient, due to the Soret effect, which opposes the destabilizing effect of the vertical temperature gradient. The first convective states are traveling waves (TW) with a phase velocity which is much lower than that of the linear instability. Recent perturbation theory calculations and numerical simulations of this nonlinear, traveling-wave state predict that the linear concentration gradient in the conduction state is eliminated in the interior of the fluid by convective mixing, and the concentration gradient remains only in the boundary layers. It is the persistence of the concentration gradient in these boundary layers which leads to the small but nonzero wave speed. As the Rayleigh number R is increased, convective stirring of the mixture decreases the concentration boundary layers, and the TW phase speed goes continuously to zero. We report experimental studies of these nonlinear, traveling-wave states in ethanol/water mixtures in an annular geometry. The measured TW phase speed as a function of R is in excellent agreement with the theoretical predictions over the entire TW branch. The experiments also confirm that this transition to stationary convection is not hysteretic. The role of mixing and the transport of concentration in the dynamics of nonlinear fronts and pulses observed in this system will also be discussed. [Work supported by DARPA URI Contract No. N00014-86-K-0758.]