C. Allain

Flow induced by a sphere settling in an aging yield-stress fluid

We have studied the flow induced by a macroscopic spherical particle settling in a Laponite suspension that exhibits a yield stress, thixotropy, and shear thinning. We show that the fluid thixotropy (or aging) induces an increase with time of both the apparent yield stress and shear-thinning properties but also a breaking of the flow fore-aft symmetry predicted in Hershel-Bulkley fluids (yield-stress, shear-thinning fluids with no thixotropy). We have also varied the stress exerted by the particles on the fluid by using particles of different densities. Although the stresses exerted by the particles are of the same order of magnitude, the velocity field presents utterly different features: whereas the flow around the lighter particle shows a confinement similar to the one observed in shear-thinning fluids, the wake of the heavier particle is characterized by an upward motion of the fluid (“negative wake”), whatever the fluid’s age. We compare the features of this negative wake to the one observed in visco...

Glass transition induced by solvent desorption for statistical MMA/nBMA copolymers : Influence of copolymer composition

Abstract An experimental study of the glass transition induced by solvent desorption has been performed for a series of Methyl methacrylate (MMA)/n-butyl methacrylate (nBMA) statistical copolymer films. The glass transition temperature of the dry homopolymers, PMMA and PnBMA, are, respectively, about 105 and 7°C above the temperature of the experiment, so that the glass transition domain can be analyzed in detail by varying the solvent concentration and the copolymer composition. A strong coupling was found between drying dynamic and stress relaxation. In particular, the quantitative analysis of the desorption isotherms based on the Leibler–Sekimoto approach led to a bulk modulus K that increases as the proportion of nBMA increases, contrary to the behavior of dry annealed samples.

Mesophase formation in high molecular-weight xanthan solutions

After a short review of theoretical background on mesophase formation in polymer solutions, this paper describes the liquid crystal phase transition and the corresponding rheological properties for aqueous solutions of a high-molecularweight xanthan sample (Mw ≈ 1.8 ⋅ 106). The formation of mesophases has been studied using polarizing microscopy and viscometry. The effects of the presence of salts, bacteria cells and proteins have been investigated. The variations in the viscosity, due to mesophase formation, are in qualitative agreement with the predictions of Mathesons theory, but the onset of the ordered phase occurs at very low polymer concentrations and the diphasic domain is much broader than predicted by thermodynamic models. These characteristics of the phase transition are related to the very high molecular weight of the sample studied and can be explained mainly by the effects of cooperative interactions between xanthan chains and of chain flexibility reducing translational entropy.

Scaling of boundary-layer flows driven by double-diffusive convection

The objective of this paper is to investigate natural convection driven by two buoyancy sources, such as heat and mass, in vertical boundary layers. Starting from the integral equations and using scale analysis, we derive the different asymptotic flow regimes encountered with different buoyancy forces and diffusion coefficients. Each type of flow is characterized by a set of scaling relations yielding the velocity, temperature and concentration distributions inside the fluid, and the heat and mass transfer coefficients. All our results are perfectly corroborated by numerical investigations in a wide range of parameters.

Analysis of the solvent diffusion in glassy polymer films using a set inversion method

Abstract Within the framework of solvent diffusion in glassy polymers, this paper concerns an experimental study of toluene sorption and desorption in P(MMA/nBMA) copolymer films. Gravimetric experiments (quartz microbalance) are performed in a pressure and temperature controlled chamber. Coupling between solvent diffusion and viscoelastic relaxation is taken into account through the time-dependent solubility model, based on the Fick diffusion equation inside the film and a time variable boundary condition at the film/vapor interface. Viscoelastic relaxation is described by a first order model or by a stretched exponential. In the present paper, a special focus is given on the set inversion method used to analyze the data and to derive well-defined uncertainty intervals upon each determined quantity, taking all the uncertainties on the weight measurements into account. We find that the mutual diffusion coefficient strongly decreases in the glassy state, of about two orders of magnitude for a 0.05 decrease in the solvent weight fraction.

Drying of Glassy Polymer Varnishes: a Quartz Resonator Study

We report on desorption measurements on polymeric thin films coated onto quartz crystal resonators. Due to the high sensitivity of quartz crystal microbalances, the experiments can be performed on very thin films, which have small diffusion time constants even in the glassy state. When drying is performed slowly enough, diffusion equilibrium can be maintained through the whole process of desorption, including the glassy domain. From these quasi-stationary pressure ramps, we derived the solvent chemical potential as a function of polymer volume fraction μ(o). The results fit well to a model recently proposed by Leibler and Sekimoto. 1 In addition, we have derived the mutual diffusion coefficient D(o) from pressure step experiments. We observe a strong decrease of D(o) for high polymer concentrations typical of hypodiffusive systems like polymers. We investigated the drying of an industrial varnish that is a blend of 2 copolymers as well as the drying of its components separately. Both the solvent chemical potential μ(o) and the mutual diffusion coefficient D(o) of the blend interpolate between the respective quantities of the components.

Pore scale mixing and macroscopic solute dispersion regimes in polymer flows inside two-dimensional model networks

A change of solute dispersion regime with the flow velocity has been studied both at the macroscopic and pore scales in a transparent array of capillary channels, using an optical technique allowing for simultaneous local and global concentration mappings. Two solutions of different polymer concentrations (500 and 1000ppm) have been used at different Peclet numbers. At the macroscopic scale, the displacement front displays a diffusive spreading: for Pe≤10, the dispersivity ld is constant with Pe and increases with the polymer concentration; for Pe>10, ld increases as Pe1.35 and is similar for the two concentrations. At the local scale, a time lag between the saturations of channels parallel and perpendicular to the mean flow has been observed and studied as a function of the flow rate. These local measurements suggest that the change of dispersion regime is related to variations of the degree of mixing at the junctions. For Pe≤10, complete mixing leads to pure geometrical dispersion enhanced for shear thi...

OPTICAL FOURIER TRANSFORMS OF FRACTALS

Diffraction experiments are performed on one and two dimensional deterministic fractals. We show that this method allows a direct determination of several geometrical characteristics of fractals among these, the Hausdorffs dimension D. Applications to experimentally obtained objects are discussed.

Scaling in flows driven by heat and mass convection in a porous medium

In this paper, we report on a scale analysis of natural-convection boundary layers driven simultaneously by thermal and mass diffusion. We derive the scaling laws followed by the temperature and the concentration fields. These are corroborated by numerical investigations in a wide range of parameters. In particular, we predict the existence of flows which are heatdriven even though the amplitude of the solutal convection is dominant.

Gravity driven instabilities in miscible non-Newtonian fluid displacements in porous media

Gravity driven instabilities in model porous packings of 1mm diameter spheres are studied by comparing the broadening of the displacement front between fluids of slightly different densities in stable and unstable configurations. Water, water–glycerol and water–polymer solutions are used to vary independently viscosity and molecular diffusion and study the influence of shear-thinning properties. Both injected and displaced solutions are identical but for a different concentration of NaNO3 salt used as an ionic tracer and to introduce the density contrast. Dispersivity in stable configuration increases with polymer concentration – as already reported for double porosity packings of porous grains. Gravity-induced instabilities are shown to develop below a same threshold Peclet number Pe for water and water–glycerol solutions of different viscosities and result in considerable increases of the dispersivity. Measured threshold Pe values decrease markedly on the contrary with polymer concentration. The quantitative analysis demonstrates that the development of the instabilities is controlled by viscosity through a characteristic gravity number G (ratio between hydrostatic and viscous pressure gradients). A single threshold value of G accounts for results obtained on Newtonian and non-Newtonian solutions.