Longwave Marangoni instability in a binary-liquid layer with deformable interface in the presence of Soret effect. The case of a finite Biot number

We investigate the long-wave Marangoni instability in a binary-liquid layer with a deformable interface in the limit of a finite Biot number $B$ and a specified heat flux at the solid substrate and in the presence of the Soret effect. In the fundamental case (a) of both finite Galileo and Lewis numbers, $G$ and $L$, respectively, and a large inverse capillary number $S$, both monotonic and oscillatory instabilities are present. The monotonic instability takes place with the critical Marangoni number $M_{mon}=48\,L\,\chi^{-1}$, where $\chi$ is the Soret (separation) number when $-1<\chi<0$. When $(1+\chi)/\chi >0$, this instability emerges if $L