**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,** pierre.evesque@ecp.fr

**Abstract :**

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)