Soret effect on the onset of viscous dissipation thermal instability for Poiseuille flows in binary mixtures

Abstract

We investigate numerically the Soret effect on the linear instability properties in convection due to viscous dissipation in a horizontal channel filled with a binary fluid mixture. Two sets of boundary conditions of experimental interest are considered. Both have no-slip boundaries for the velocity and no mass flux through them. The lower boundary is considered adiabatic, while the upper boundary is isothermal for case A and inversely for case B. As no external temperature or concentration difference is imposed on the layer, the cause of thermal instability is the flow rate through the volumetric heating induced by the viscous dissipation and the Soret effect inherent to binary mixtures. It is found that longitudinal rolls (LR) represent the preferred mode for the onset of convection. For case A, both oscillatory and steady-state LR may develop depending on the value of the separation ratio ψ, which represents the ratio between the mass contribution and the temperature contribution to buoyancy forces. The dependence of the instability thresholds on the separation ratio is discussed near and far from the codimension-two bifurcation point. For case B, the basic state remains stable for positive separation ratios, while it loses its stability via a stationary bifurcation with zero wave number for negative values of the separation ratio. The relevance of the theoretical results for the observability of such instability in real systems is discussed. Finally, we suggest a protocol to determine Soret coefficients by using the stability diagrams obtained in the current paper.