Polymer Flow Through Porous Media: Numerical Prediction of the Contribution of Slip to the Apparent Viscosity.

The flow of polymer solutions in porous media is often described using Darcy’s law with an apparent viscosity capturing the observed thinning or thickening effects. While the macroscale form is well accepted, the fundamentals of the pore-scale mechanisms, their link with the apparent viscosity, and their relative influence are still a matter of debate. Besides the complex effects associated with the rheology of the bulk fluid, the flow is also deeply influenced by the mechanisms occurring close to the solid/liquid interface, where polymer molecules can arrange and interact in a complex manner. In this paper, we focus on a repulsive mechanism, where polymer molecules are pushed away from the interface, yielding a so-called depletion layer in the vicinity of the wall. This depletion layer acts as a lubricating film that may be represented by an effective slip boundary condition. Here, our goal is to provide a simple mean to evaluate the contribution of this slip effect to the apparent viscosity. To do so, we solve the pore-scale flow numerically in idealized porous media with a slip length evaluated analytically in a tube. Besides its simplicity, the advantage of our approach is also that it captures relatively well the apparent viscosity obtained from core-flood experiments, using only a limited number of inputs. Therefore, it may be useful in many applications to rapidly estimate the influence of the depletion layer effect over the macroscale flow and its relative contribution compared to other phenomena, such as non-Newtonian effects

Interference microscopy on thin diblock copolymer films

At equilibrium thin films of symmetric diblock copolymers exhibit a morphology where the lamellar microdomains are oriented parallel to the external surfaces. Interference microscopy has been used to investigate this orientation which results in a quantization of the film thickness. Solution cast films of the symmetric polystyrene/polymethylmethacrylate P(S-b-MMA) diblock copolymers exhibit a single interference color characteristic of a film of uniform thickness with a free surface that is flat and smooth. Interference microscopy on these films annealed at 170°C for 24 hours and more shows the development of two distinct interference colors. The variations in the colors are discrete rather than continuous indicating step discontinuities in the film thickness with a height equal to one period of the underlying oriented lamellar multilayer. The free surface topology is such there are patches of one color spread across the surface on a uniform background, i.e., there are islands or depressions on the surface. The average size and spatial distribution of these islands or depressions are found to vary with annealing time ; the appearance of the free surface is reminiscent of a two-dimensional phase coarsening process. The time dependent change in the case of depressions is reported herein.A l'équilibre thermodynamique, les films minces de copolymères diblocs, symétriques, se présentent sous la forme d'un empilement lamellaire orienté parallèlement aux surfaces externes. L'observation des couleurs d'interférence par microscopie optique a été utilisée ici pour étudier ce processus d'orientation et la quantification de l'épaisseur du film qui en résulte. L'observation de films non recuits de copolymères diblocs, symétriques polystyrène/polyméthylméthacrylate P(S-b-MMA) révèle la présence d'une seule couleur d'interférence (bleu), ce qui indique que l'épaisseur du film est uniforme et que sa surface libre est plane. Si on recuit ces films à 170°C pendant 24 heures et plus, on constate l'existence de deux couleurs d'interférence (bleu indigo et marron clair). Les variations de couleur sont discrètes et non pas continues ; elles correspondent à des marches d'épaisseur de hauteur égale à la période de l'empilement lamellaire. La surface libre du film se présente comme un fond uniforme bleu indigo constellé de taches marron clair réparties uniformément ; ces taches correspondent à des trous. La taille moyenne et la distribution spatiale de ces trous varient avec le temps de recuit. Le comportement observé semble présenter des analogies avec une transition de phase à deux dimensions

Surface Evolution of Copolymer thin Films as Revealed by Atomic Force Microscopy

AbstractAtomic Force Microscopy has been used to study the early stage evolution of the free surface of annealed symmetric poly(styrene-b-n-butylmethacrylate) diblock copolymer thin films. As the lamellar ordering propagates through the film thickness, Islands or holes are formed on the free surface. It Is shown that, depending on the Initial film thickness, I.e. on the fraction of the film surface occupied by the islands (or holes) In the ordered state, the existence or non-existence of spatial correlations characterizes the ordering kinetics of both islands and holes. However, the limit between these two regimes is not the same in the two cases : in the case of holes, spatial correlations occur for a higher value of the surface coverage than In the case of islands.</jats:p

Static wetting behaviour of diblock copolymers

Thin liquid films of ordered diblock copolymers deposited on a solid substrate form a multilayer stacking parallel to the solid surface. A multilayer with a finite extend can be stable, metastable, or unstable, depending on the relative values of the surface energies of the various interfaces. The spreading parameter and chemical potential of a $n$-layer are derived, and used for classifying all possible situations. It is shown that only mono- and bilayers can be stable, and that non-wetting multilayers are subjected to a long-time piling up instability, leading in practice to the formation of characteristic ziggourat-like structures

Islands and holes on the free surface of thin diblock copolymer films. I. Characteristics of formation and growth

When deposited on a silicon substrate, symmetric polystyrene/polymethylmethacrylate P(S-b-MMA) diblock copolymers form, at equilibrium, a multilayer structure parallel to the substrate. If the top layer is incomplete, islands or holes are formed in this layer. The kinetics of formation and growth of islands or holes is investigated, here, by in situ interference microscopy. The present study is focused on dense systems (≃ 30 % of islands (or holes) in area coverage). In the early stage, the way of formation of elevations and holes appears to be different. For longer times, the growth of islands and holes is controlled by the same mechanisms : individual growth, coalescence and dissolution.Les copolymères diblocs symétriques polystyrènejpolyméthylméthacrylate P(S-b-MMA), déposés sur un substrat de silicium, forment à l'équilibre thermodynamique, une structure multicouche parallèle au substrat. Si la couche supérieure est incomplète, des ilôts ou des trous se forment dans celle-ci. La cinétique de formation et de croissance des ilôts et des trous est étudiée ici, par microscopie interférométrique in situ. Seuls les systèmes denses (= 30 % d'ilôts ou de trous en taux de couverture) sont envisagés. Aux temps courts, la formation des ilôts est différente de celle des trous. Aux temps longs, la croissance des ilôts et des trous est contrôlée par les mêmes mecanismes : croissance individuelle, coalescence et disparition