Dialogue of the deaf : « Hydrodynamics » with dissipation. Towards mixing or demixing ?
En français: Dialogue de sourds : « Hydrodynamique” avec dissipation. Vers un mélange, ou une ségrégation ?
P. Evesque , Lab MSSMat, UMR 8579 CNRS, Ecole Centrale Paris, 92295 CHATENAY-MALABRY, France, firstname.lastname@example.org
In recent articles on granular gas in a box subjected to vibrations (see P&G17,577 (2009) and P&G18, 1,(2010)), the existence of a new force │P+│-│P-│ , due to the fact that he “pressure” P on the two sides of a fixed plane is different, was observed in the reference frame of the mean flow (<v>=0). So, the system looks as two jets coming in opposite direction, which mix, defining two local “phases”. Can one treat correctly this problem with hydrodynamics modelling? Moreover, one may wish to study cases that generate discontinuities such as mixing or demixing; it is not obvious that in those cases continuity of pressure does exist; does they require introduction of capillary forces? Or what else should the model include in addition to classic hydrodynamics? In fact, when a hydrodynamic system is ready to demix, the Euler equation based on continuity of pressure cannot be valid anymore. This shall introduce a new force term that acts on particles. This paper is an attempt to settle the granular problem theoretically, introducing new effect of dissipation. This might be also useful in treating some problems of turbulence.
Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn ; 45.35i ; 45.70.Mg; 83.80.fg ; 46.80.Ff ; 05.20.-y
poudres & grains 20 (1), 1-28 (Juin 2012)