Mixing in open flows
Un article de Surface du verre et interfaces.
Emmanuelle Gouillart, Franck Pigeonneau
Many throughflow industrial processes involve stirring inhomogeneous fluid as it flows through a fixed mixing region. For viscous flows, efficient stirring protocols promote chaotic advection (see the page about chaotic mixing), which means that Lagrangian trajectories are chaotic while in the mixing region.
However, particles can have very different lifetimes in the chaotic region. The pictures below were obtained by releasing a single small spot of dye that is caught and stretched into many filaments by two stirring rods. Some filaments escape downstream very quickly, while others stay inside the mixing region where they are tremendously stretched (the main flow goes upwards in the pictures, so that filaments in the upper part of the pictures have escaped downstream of the rods). Characterizing the whole mixing process is therefore a difficult issue: particles experience only transient mixing, hence it is not possible to evaluate mixing with asymptotic indices such as Lyapunov exponents; furthermore the lifetime of chaos varies greatly from particle to particle...
As in our study of mixing in closed flows (see Mixing dynamics in closed flows and Topological mixing), we work on both
- describing mechanisms at play during the mixing process, which account for the mixing dynamics of impurities
- and proposing relevant mixing indices that estimate the efficiency of mixing.
Back to Chaotic mixing of viscous fluids
Collaborations
- Olivier Dauchot, Service de Physique de l'Etat Condensé, CEA Saclay
- Jean-Luc Thiffeault, University of Madison, WI USA.