Stability of domains in phase-separating binary fluids in shear flow.

摘要

Phase-separating binary fluids form complex patterns of domains at late times after a quench below the coexistence curve. This domain morphology is significantly modified in the presence of an external shear flow. The shear flow deforms the domains and competes with the phase separation so that the fluid tends toward a dynamic steady state far from equilibrium. The domains can become highly elongated along the flow direction, and in some cases form a “string phase” consisting of macroscopically long cylindrical domains. This is surprising since in the absence of the shear flow, elongated domains are unstable to varicose instabilities.; To elucidate these effects of a shear flow on a phase-separating binary fluid, I perform linear stability analyses of extended domains aligned along the flow direction. The system is modeled with simple phenomenological equations of motion, the coupled Cahn-Hilliard and Stokes equations. I consider two different geometries, first that of a single two-dimensional, lamellar domain and second that of an isolated cylindrical domain, both immersed in an unbounded region of the other phase. The stability eigenvalues can be derived analytically for long wavelength perturbations by writing the eigenvalue equation as an effective matrix equation in the basis set of the various perturbation modes of the domains.; I find that in the presence of an external shear flow, the lamellar domain is stabilized for all wavelengths above a critical shear rate that depends on the viscosity and size of the domains. The shear flow stabilizes the original unstable varicose mode by mixing it with other, stable perturbation modes. I find similar results for the stability of a cylindrical domain in shear. The shear flow suppresses and for some parameter values stabilizes both the hydrodynamic Rayleigh instability and the thermodynamic instability of the cylinder against varicose perturbations, by mixing with nonaxisymmetric perturbations. The results are consistent with recent experiments and provide an explanation for the stability of the observed dynamic steady state, at least for bicontinuous domain morphologies.