Decomposition driven interface evolution for layers of binary mixtures: {II}. Influence of convective transport on linear stability

We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in Part I [U. Thiele, S. Madruga and L. Frastia, Phys. Fluids 19, 122106 (2007)]. To this aim, the linearized bulk equations and boundary equations are solved using continuation techniques for several different cases of energetic bias at the surfaces, corresponding to linear and quadratic solutal Marangoni effects. For purely diffusive transport, an increase in film thickness either exponentially decreases the lateral instability or entirely stabilizes the film. Including convective transport leads to a further destabilization as compared to the purely diffusive case. In some cases the inclusion of convective transport and the related widening of the range of available film configurations (it is then able to change its surface profile) change the stability behavior qualitatively. We furthermore present results regarding the dependence of the instability on several other parameters, namely, the Reynolds number, the Surface tension number and the ratio of the typical velocities of convective and diffusive transport.Comment: Published in Physics of Fluic

Polymer drift in a solvent by force acting on one polymer end

We investigate the effect of hydrodynamic interactions on the non-equilibrium drift dynamics of an ideal flexible polymer pulled by a constant force applied at one end of the polymer using the perturbation theory and the renormalization group method. For moderate force, if the polymer elongation is small, the hydrodynamic interactions are not screened and the velocity and the longitudinal elongation of the polymer are computed using the renormalization group method. Both the velocity and elongation are nonlinear functions of the driving force in this regime. For large elongation we found two regimes. For large force but finite chain length $L$ the hydrodynamic interactions are screened. For large chain lengths and a finite force the hydrodynamic interactions are only partially screened, which in three dimensions results in unusual logarithmic corrections to the velocity and the longitudinal elongation.Comment: 6 page

Dynamical Model for Chemically Driven Running Droplets

We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the droplets that induces a wettability gradient on the substrate and provides the driving force for droplet motion. Two different regimes for moving droplets -- reaction-limited and saturated regime -- are described. They correspond to increasing and decreasing velocities with increasing reaction rates and droplet sizes, respectively. The existence of the two regimes offers a natural explanation of prior experimental observations.Comment: 4 pages, 5 figure

Interfacial layering in a three-component polymer system

We study theoretically the temporal evolution and the spatial structure of the interface between two polymer melts involving three different species (A, A* and B). The first melt is composed of two different polymer species A and A* which are fairly indifferent to one another (Flory parameter chi_AA* ~ 0). The second melt is made of a pure polymer B which is strongly attracted to species A (chi_AB 0). We then show that, due to these contradictory tendencies, interesting properties arise during the evolution of the interface after the melts are put into contact: as diffusion proceeds, the interface structures into several adjacent "compartments", or layers, of differing chemical compositions, and in addition, the central mixing layer grows in a very asymmetric fashion. Such unusual behaviour might lead to interesting mechanical properties, and demonstrates on a specific case the potential richness of multi-component polymer interfaces (as compared to conventional two-component interfaces) for various applications.Comment: Revised version, to appear in Macromolecule

Dynamics of Strongly Deformed Polymers in Solution

Bead spring models for polymers in solution are nonlinear if either the finite extensibility of the polymer, excluded volume effects or hydrodynamic interactions between polymer segments are taken into account. For such models we use a powerful method for the determination of the complete relaxation spectrum of fluctuations at {\it steady state}. In general, the spectrum and modes differ significantly from those of the linear Rouse model. For a tethered polymer in uniform flow the differences are mainly caused by an inhomogeneous distribution of tension along the chain and are most pronounced due to the finite chain extensibility. Beyond the dynamics of steady state fluctuations we also investigate the nonlinear response of the polymer to a {\em large sudden change} in the flow. This response exhibits several distinct regimes with characteristic decay laws and shows features which are beyond the scope of single mode theories such as the dumbbell model.Comment: 7 pages, 3 figure

Stripes of Partially Fluorinated Alkyl Chains: Dipolar Langmuir Monolayers

Stripe-like domains of Langmuir monolayers formed by surfactants with partially fluorinated lipid anchors (F-alkyl lipids) are observed at the gas-liquid phase coexistence. The average periodicity of the stripes, measured by fluorescence microscopy, is in the micrometer range, varying between 2 and 8 microns. The observed stripe-like patterns are stabilized due to dipole-dipole interactions between terminal -CF3 groups. These interactions are particularly strong as compared with non-fluorinated lipids due to the low dielectric constant of the surrounding media (air). These long-range dipolar interactions tend to elongate the domains, in contrast to the line tension that tends to minimize the length of the domain boundary. This behavior should be compared with that of the lipid monolayer having alkyl chains, and which form spherical micro-domains (bubbles) at the gas-liquid coexistence. The measured stripe periodicity agrees quantitatively with a theoretical model. Moreover, the reduction in line tension by adding traces (0.1 mol fraction) of cholesterol results, as expected, in a decrease in the domain periodicity.Comment: 20 pages, 4 fig

Straightening of Thermal Fluctuations in Semi-Flexible Polymers by Applied Tension

We investigate the propagation of a suddenly applied tension along a thermally excited semi-flexible polymer using analytical approximations, scaling arguments and numerical simulation. This problem is inherently non-linear. We find sub-diffusive propagation with a dynamical exponent of 1/4. By generalizing the internal elasticity, we show that tense strings exhibit qualitatively different tension profiles and propagation with an exponent of 1/2.Comment: Latex file; with three postscript figures; .ps available at http://dept.physics.upenn.edu/~nelson/pull.p

Viscoelastic Effect on Hydrodynamic Relaxation in Polymer Solutions

The viscoelastic effect on the hydrodynamic relaxation in semidilute polymer solutions is investigated. From the linearized two-fluid model equations, we predict that the dynamical asymmetry coupling between the velocity fluctuations and the viscoelastic stress influences on the hydrodynamic relaxation process, resulting in a wave-number-dependent shear viscosity.Comment: 7pages; To be published in Journal of the Physical Society of Japan,Vol 72,No2,(2003

Hydrodynamic Self-Consistent Field Theory for Inhomogeneous Polymer Melts

We introduce a mesoscale technique for simulating the structure and rheology of block copolymer melts and blends in hydrodynamic flows. The technique couples dynamic self consistent field theory (DSCFT) with continuum hydrodynamics and flow penalization to simulate polymeric fluid flows in channels of arbitrary geometry. We demonstrate the method by studying phase separation of an ABC triblock copolymer melt in a sub-micron channel with neutral wall wetting conditions. We find that surface wetting effects and shear effects compete, producing wall-perpendicular lamellae in the absence of flow, and wall-parallel lamellae in cases where the shear rate exceeds some critical Weissenberg number.Comment: Revised as per peer revie