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A summary of new predictive high frequency thermo-vibrational models in porous media

Abstract : 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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Yazdan Pedram Razi, Abdelkader Mojtabi, Marie-Catherine Charrier-Mojtabi. A summary of new predictive high frequency thermo-vibrational models in porous media. Transport in Porous Media, Springer Verlag, 2009, vol. 77, pp.207-228. ⟨10.1007/s11242-008-9332-7⟩. ⟨hal-00967258⟩

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