Evolution of convective patterns in a binary-mixture layer subjected to a periodical change of the gravity field

Abstract

A theoretical study has been made of the convective stability and developed heat transfer regimes in a horizontal, binary-mixture layer with negative Soret coupling. The system is under temperature gradient and finite-frequency vibration. Both analytical and numerical examinations are presented. The limiting case of long-wave disturbances is studied using the perturbation method. To find instability thresholds in the linear approximation the Floquet theory is applied. The stability borders and characteristics of critical disturbances are determined depending on the vibration frequency for typical gaseous, liquid, and colloidal mixtures. The phase mapping and the Fourier spectra are used to describe the nonlinear evolution of the convective system. It is shown that supercritical flows within the first and second resonance domains develop via soft-mode transitions at critical parameter values which are consistent with the predictions of the linear stability theory. The nonlinear convection patterns demonstrate the synchronous, subharmonic, or quasiperiodic dynamics. The hysteretic transitions between nonlinear regimes are also investigated. The influence of the vibrational Grashof number on the concentration field is discussed for standing wave and traveling wave modes.