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

Abstract

The stability of a long cylindrical domain in a phase-separating binary fluid in an external shear flow is investigated by linear stability analysis. Using the coupled Cahn-Hilliard and Stokes equations, the stability eigenvalues are derived analytically for long-wavelength perturbations, for arbitrary viscosity contrast between the two phases. The shear flow is found to suppress and sometimes completely stabilize 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 observations of a ''string phase'' in phase-separating fluids in shear. ͓S1063-651X͑98͒15909-3͔

Does shear flow stabilize an immersed thread?

“…Using Hurwitz's criterion, we find a range for the ratio of viscosities for which the shear stabilizes the thread. Although we make some corrections with respect to the boundary conditions as derived by Frischknecht [12] and follow a completely different approach, we find qualitatively comparable results. Due to these corrections, somewhat modified results for the range of the ratio of the viscosities in which no instability will occur are obtained.…”

“…Note that the jump in (36c) and the second term in the right-hand side of (36e) were incorrectly not included by Frischknecht [12]. This correction gives noticeable results for the range of ratios of viscosities above which the thread is stable, as we will discuss in the next section.…”

“…The thread is perturbed by a random perturbation. The perturbation and the quantities such as pressure and velocity fields are expressed as a complex Fourier series in the azimuthal coordinate and they are taken periodic in the axial coordinate with real wave number k. At the interfaces, we correct the boundary conditions derived by Frischknecht [12]. Here, we show that the velocity in the axial coordinate has a discontinuity due to the presence of the shear flow.…”

“…For instance, Frischknecht [12] considered the stability of a thread in a phase-separating binary fluid under influence of shear flow. Frischknecht explored the competition between the shear flow and the coarsening process.…”

Computation of multiphase systems with phase field models

“…Here the structures are much more complex with plates and strings forming. Stringlike structures have been observed in polymer blends which are thermodynamically near a phase transition point [37,38] and in immiscible viscoelastic systems in complex flow fields [39] and in dispersed droplets [39]. There is great current interest in micro and nano lengthscale technologies in which polymer blends could play an important role.…”