We use molecular dynamics simulations to study phase separation of a 50:50 (by volume) fluid mixture in a confined and curved (Taylor-Couette) geometry, consisting of two concentric cylinders. The inner cylinder may be rotated to achieve a shear flow. In nonsheared systems we observe that, for all cases under consideration, the final equilibrium state has a stacked structure. Depending on the lowest free energy in the geometry the stack may be either flat, with its normal in the z direction, or curved, with its normal in the r or θ direction. In sheared systems we make several observations. First, when starting from a prearranged stacked structure, we find that sheared gradient and vorticity stacks retain their character for the durations of the simulation, even when another configuration is preferred (as found when starting from a randomly mixed configuration). This slow transition to another configuration is attributed to a large free energy barrier between the two states. In case of stacks with a normal in the gradient direction, we find interesting interfacial waves moving with a prescribed angular velocity in the flow direction. Because such a wave is not observed in simulations with a flat geometry at similar shear rates, the curvature of the wall is an essential ingredient of this phenomenon. Second, when starting from a randomly mixed configuration, stacks are also observed, with an orientation that depends on the applied shear rate. Such transitions to other orientations are similar to observations in microphase separated diblock copolymer melts. At higher shear rates complex patterns emerge, accompanied by deviations from a homogeneous flow profile. The transition from steady stacks to complex patterns takes place around a shear rate 1/ τdv, where τdv is the crossover time from diffusive to viscous dominated growth of phase-separated domains, as measured in equilibrium simulations.

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The spinodal decomposition of quenched polymer/solvent and liquid-crystal/solvent mixtures in a miniature Taylor-Couette cell has been simulated by molecular dynamics. Three stacking motifs, each reflecting the geometry and symmetry of the cell, are most abundant among the fully phase separated stationary states. At zero or low angular velocity of the inner cylindrical drum, the two segregated domains have a clear preference for the stacking with the lowest free energy and hence the smallest total interfacial tension. For high shear rates, the steady state appears to be determined by a minimum dissipation mechanism, i.e., the mixtures are likely to evolve into the stacking demanding the least mechanical power by the rotating wall. The partial slip at the polymer-solvent interfaces then gives rise to a new pattern: A stack of three concentric cylindrical shells with the viscous polymer layer sandwiched between two solvent layers. Neither of these mechanisms can explain all simulation results, as the separating mixture easily becomes kinetically trapped in a long-lived suboptimal configuration. The phase separation process is observed to proceed faster under shear than in a quiescent mixture.@en

We study the relaxation dynamics of capillary waves in the interface between two confined liquid layers by means of molecular dynamics simulations. We measure the autocorrelations of the interfacial Fourier modes and find that the finite thickness of the liquid layers leads to a marked increase of the relaxation times as compared to the case of fluid layers of infinite depth. The simulation results are in good agreement with a theoretical first-order perturbation derivation, which starts from the overdamped Stokes' equation. The theory also takes into account an interfacial friction, but the difference with no-slip interfacial conditions is small. When the walls are sheared, it is found that the relaxation times of modes perpendicular to the flow are unaffected. Modes along the flow direction are relatively unaffected as long as the equilibrium relaxation time is sufficiently short compared to the rate of deformation. We discuss the consequences for experiments on thin layers and on ultralow surface tension fluids, as well as computer simulations.@en