Incollection,
Turbulence and Coarsening in Active and Passive Binary Mixtures
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
When a binary fluid mixture at the critical concentration is cooled
from a high temperature to a sufficiently low temperature (below a
critical one), the original homogeneous phase becomes unstable and
spontaneously evolves into two phases separated by an interface. As
time advances an out-of-equilibrium process of phase ordering takes
place through the formation of domains of a single phase that grow
algebraically in time. In fluids, the presence of a
hydrodynamic velocity field makes this process more complicated than
the corresponding one in solid alloys.\\
Phase ordering dynamics becomes
even more complex and less understood when the fluid mixture is
externally driven; beyond their theoretical
interest, phase separating binary fluids under flow embody a great
technological interest for their distinctive rheological
properties. This problem has been extensively investigated in shear
flows where coarsening becomes highly
anisotropic.
Less clear is the case in which the mixture is stirred by a turbulent
flow. Here, phase separation may be completely suppressed, or a dynamical steady
state with domains of finite length and well defined phases may
develop.
In this work we investigate phase separation between two fluids in
two-dimensions by means of Direct Numerical Simulations of coupled
Navier-Stokes and Cahn-Hilliard equations. We study the phase
ordering process in the presence of an external stirring acting on the
velocity field.\\
For both active and passive mixtures we find that,
for a sufficiently strong stirring, coarsening is arrested in a
stationary dynamical state characterized by a continuous rupture and
formation of finite domains. Coarsening arrest is shown to be
independent of the chaotic or regular nature of the flow; indeed, this phenomenon is a
consequence of the competition between thermodynamic forces and stretching
induced by local shears.\\
Moreover we find numerical evidence that the dependence
of the arrest scale on the shear rate follows a power law behavior with an exponent
close to the one measured in experiments and numerical simulations in pure shear flows.
Our results might suggest the existence of a mechanism independent of the nature of the
flow in the coarsening arrest. Further numerical and experimental investigations, with
the aim of clarifying the dependence of the arrest scale on the flow properties, would
be extremely interesting.
