Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-11-18
Phys. Rev. E 63, 051503 (2001)
Physics
Condensed Matter
Statistical Mechanics
Version accepted for publication - Physical Review E
Scientific paper
10.1103/PhysRevE.63.051503
We investigate numerically the influence of an homogeneous shear flow on the spinodal decomposition of a binary mixture by solving the Cahn-Hilliard equation in a two-dimensional geometry. Several aspects of this much studied problem are clarified. Our numerical data show unambiguously that, in the shear flow, the domains have on average an elliptic shape. The time evolution of the three parameters describing this ellipse are obtained for a wide range of shear rates. For the lowest shear rates investigated, we find the growth laws for the two principal axis $R_\perp (t) \sim constant$, $R_\parallel(t) \sim t$, while the mean orientation of the domains with respect to the flow is inversely proportional to the strain. This implies that when hydrodynamics is neglected a shear flow does not stop the domain growth process. We investigate also the possibility of dynamic scaling, and show that only a non trivial form of scaling holds, as predicted by a recent analytical approach to the case of a non-conserved order parameter. We show that a simple physical argument may account for these results.
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