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

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

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

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

Contact line motion for partially wetting fluids

We study the flow close to an advancing contact line in the limit of small capillary number. To take into account wetting effects, both long and short-ranged contributions to the disjoining pressure are taken into account. In front of the contact line, there is a microscopic film corresponding to a minimum of the interaction potential. We compute the parameters of the contact line solution relevant to the matching to a macroscopic problem, for example a spreading droplet. The result closely resembles previous results obtained with a slip model

Monomer dynamics of a wormlike chain

We derive the stochastic equations of motion for a tracer that is tightly attached to a semiflexible polymer and confined or agitated by an externally controlled potential. The generalised Langevin equation, the power spectrum, and the mean-square displacement for the tracer dynamics are explicitly constructed from the microscopic equations of motion for a weakly bending wormlike chain by a systematic coarse-graining procedure. Our accurate analytical expressions should provide a convenient starting point for further theoretical developments and for the analysis of various single-molecule experiments and of protein shape fluctuations.Comment: 6 pages, 4 figure

Non-monotonous crossover between capillary condensation and interface localisation/delocalisation transition in binary polymer blends

Within self-consistent field theory we study the phase behaviour of a symmetric binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A component and the corresponding semi-infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surface fields to the interface localisation/delocalisation transition for antisymmetric surface fields. In the former case the phase diagram has a single critical point close to the bulk critical point. In the latter case the phase diagram exhibits two critical points which correspond to the prewetting critical points of the semi-infinite system. The crossover between these qualitatively different limiting behaviours occurs gradually, however, the critical temperature and the critical composition exhibit a non-monotonic dependence on the surface field.Comment: to appear in Europhys.Let

Generic morphologies of viscoelastic dewetting fronts

A simple model is put forward which accounts for the occurrence of certain generic dewetting morphologies in thin liquid coatings. It demonstrates that by taking into account the elastic properties of the coating, a morphological phase diagram may be derived which describes the observed structures of dewetting fronts. It is demonstrated that dewetting morphologies may also serve to determine nanoscale rheological properties of liquids.Comment: 4 pages, 2 figure