In this paper, we probe the influence of confinement on the flows of a polymer microgel, namely Carbopol. We compare its bulk rheological behavior, measured with a rheometer and well described by a Hershel-Bulkley law, to velocity profiles measured in rough microchannels, obtained with a particle tracking velocimetry technique. We show a strong disagreement between the bulk prediction for the velocity profiles and the measured ones in the microchannels. Velocity profiles in confined conditions are successfully analyzed within the framework of a non-local fluidity model introduced recently (J. Goyon et al. Nature, 454, 84 (2008)). This allows to determine a cooperativity length ξ, whose order of magnitude compares with the structure size of the microgel. Moreover, we measure flow curves using a rheometer for different gap conditions and also show that this set of data exhibit a strong effect of the confinement on the measured rheological properties. This is again characterized by a typical length of the same order as the cooperativity length scale ξ. We thus evidence confinement effects with two complementary experiments which both give the same typical length for the rearrangements in the flows.

International audienceFoams have been used for decades as displacing fluids for enhanced oil recovery and aquifer remediation, and more recently, for remediation of the vadose zone, in which case foams carry chemical amendments. Foams are better injection fluids than aqueous solutions due to their low sensitivity to gravity and because they are less sensitive to permeability heterogeneities, thus allowing a more uniform sweep. The latter aspect results from their peculiar rheology, whose understanding motivates the present study. We investigate foam flow through a two-dimensional porous medium consisting of circular obstacles positioned randomly in a horizontal transparent Hele-Shaw cell. The local foam structure is recorded in situ, which provides a measure of the spatial distribution of bubble velocities and sizes at regular time intervals. The flow exhibits a rich phenomenology including preferential flow paths and local flow nonstationarity (intermittency) despite the imposed permanent global flow rate. Moreover, the medium selects the bubble size distribution through lamella division-triggered bubble fragmentation. Varying the mean bubble size of the injected foam, its water content, and mean velocity, we characterize those processes systematically. In particular, we measure the spatial evolution of the distribution of bubble areas, and infer the efficiency of bubble fragmentation depending on the various control parameters. We furthermore show that the distributions of bubble sizes and velocities are correlated. This study sheds new light on the local rheology of foams in porous media and opens the way toward quantitative characterization of the relationship between medium geometry and foam flow properties. It also suggests that large-scale models of foam flows in the subsurface should account for the correlation between bubble sizes and velocities

Understanding the relationship between the material structural details, the geometrical confining constraints, the local dynamical events and the global rheological response is at the core of present investigations on complex fluid properties. In the present article, this problem is addressed on a model yield stress fluid made of highly entangled polymer gels of Carbopol which follows at the macroscopic scale the well-known Herschel-Bulkley rheological law. First, performing local rheology measurements up to high shear rates ([Formula: see text] s)and under confinement, we evidence unambiguously the breakdown of bulk rheology associated with cooperative processes under flow. Moreover, we show that these behaviors are fully captured with a unique cooperativity length [Formula: see text] over the whole range of experimental conditions. Second, we introduce an original optical microscopy method to access structural properties of the entangled polymer gel in the direct space. Performing image correlation spectroscopy of fluorophore-loaded gels, the characteristic size D of carbopol gels microstructure is determined as a function of preparation protocol. Combining both dynamical and structural information shows that the measured cooperative length [Formula: see text] corresponds to 2-5 times the underlying structural size D, thus providing a strong grounding to the "Shear Transformation Zones" modeling approach.