Longwave instability of a binary mixture flow in a vertical channel in the presence of vibration

The longwave instability of a hybrid (thermogravitational and thermovibrational) flow of a binary incompressible liquid mixture occurring in a plane vertical channel, whose boundaries are maintained at constant but different temperatures, is studied. The investigation is carried out with account for the Soret thermal-diffusion effect on the ranges of normal and anomalous values of the mixture separation coefficient. It is shown that, owing to the properties of the system, the subharmonic response to an external action is absent. The ranges on which secondary flows arise are analytically determined using the asymptotic expansion method, both under weightlessness conditions and in the presence of the gravity effect. The parameter ranges on which longwave disturbances present the greatest danger for the main flow stability are determined.