A summary of new predictive high frequency thermo-vibrational models in porous media
Résumé
In this chapter, we consider the effect of mechanical vibration on the onset of convection in porous media. The porous media is saturated either by a pure fluid or by a binary mixture. The importance of transport model on stability diagrams are presented and discussed. The stability threshold for the Darcy-Brinkman case in the RaTc-R and kc-R diagrams are presented (where RaTc, kc and R are the critical Rayleigh number, the critical wave number and the vibration parameters respectively). It is shown that there is a significant deviation from the Darcy model. In the thermo-solutal case with the Soret effect, the influence of vibration on the reduction of multi-cellular convection is emphasized. A new analytical relation for obtaining the threshold of mono-cellular convection is derived. This relation shows how the separation factor Ψ is related to controlling parameters of the problem, Ψ = f (R, ε*, Le) when the wave number k -> 0. The importance of vibrational parameter definition is highlighted and it is shown how, by using a proper definition for vibrational parameter, we may obtain compact relationship. It is also shown how this result may be used to increase components separation.
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