Bidispersive thermal convection

We obtain the linear instability and nonlinear stability thresholds for a problem of thermal convection in a bidispersive porous medium with a single temperature. It is important to note that we show that the linear instability threshold is the same as the nonlinear stability one. This means that the linear theory is capturing completely the physics of the onset of thermal convection. This result contrasts with the general theory of thermal convection in a bidispersive porous material where the temperatures in the macropores and micropores are allowed be different. In that case the coincidence of the stability boundaries has not been proved.