Slow spreading with a large contact angle on hygroscopic materials.

Water transfer in wood plays a major role during the life time of timber structures but the physics of the various processes involved, such as wetting and imbibition, is not fully understood. Here we show that the angle of contact of a water drop placed in contact with an air dry wood surface is initially larger than 90°, then the drop slowly spreads over the surface, while the apparent (macroscopic) contact angle decreases down to a few tens of degrees. We show that similar results are obtained with a model material, i.e. hydrogel, as soon as a perturbation is induced onto the line of contact. We demonstrate that for the gel the initial large apparent contact angle results from a strong deformation of the gel in a thin softened region below the line of contact resulting from the fast diffusion of water and swelling of this region. This phenomenon ensures a real (local) contact angle close to zero. The spreading then results from the progressive diffusion of water at farther distance and successive perturbations of the line of contact when the drop enters in contact with small liquid droplets dispersed along the surface (residues of the chemical reaction during gel preparation). It is suggested that a similar effect occurs for the water drop over a wood surface and explains the large initial contact angle and slow spreading: the line of contact is initially pinned thanks to a wood surface deformation resulting from the wood surface swelling due to water absorption, thus leading to a large contact angle; it will then unpin when the local conditions have changed as a result of water diffusion at further distance, allowing for a small displacement up to the next pinning point and so on.

Self-Limited Accumulation of Colloids in Porous Media.

We present local direct imaging of the progressive adsorption of colloidal particles inside a 3D model porous medium. By varying the interparticle electrostatic interactions, we observe a large range of particle deposition regimes, from a single layer of particles at the surface of the medium to multiple layers and eventually clogging of the system. We derive the complete deposition dynamics and show that colloid accumulation is a self-limited mechanism towards a deposited fraction associated with a balance between the particle interactions and the imposed flow rate. These trends are explained and predicted using a simple probability model considering the particle adsorption energy and the variation of the drag energy with evolving porosity. This constitutes a direct validation of speculated particle transport mechanisms, and a further understanding of accumulation mechanisms.

Controlled imbibition in a porous medium from a soft wet material (poultice).

We provide a first approach of the mechanisms of liquid imbibition in a porous medium from a wet paste in contact with this substrate. Through Magnetic Resonance Imaging (MRI) we first show that, in contrast with intuition, the liquid can invade the substrate even if it has a larger pore size than the paste, which induces a lower capillary pressure in the substrate. This phenomenon happens because the paste can easily shrink. We then show that the imbibition stops when the capillary pressure in the substrate balances the stress needed to further contract the paste. The dynamics of the process then mainly results from the competition of these two effects plus the pressure gradient associated with the liquid flow through the paste. This in particular shows that the liquid penetration in a porous medium, from a poultice in contact with this medium, may be controlled by adjusting the poultice characteristics.

Convective drying of a porous medium with a paste cover.

The convective drying of a composite system made of a porous medium covered with a paste is a situation often encountered with soils, roads, building and cultural heritage materials. Here we discuss the basic mechanisms at work during the drying of a model composite system made of a homogeneous paste covering a simple granular packing. We start by reviewing the rather well-known case of the convective drying of a simple granular packing (i.e. without paste cover), which serves as a reference for physical interpretations. We show that a simple model assuming homogeneous desaturation followed by a progressive development of a dry front from the sample free surface is in agreement with observations of the internal liquid distribution variations in time. In particular, this model is able to reproduce the saturation vs. time curves of various simple granular systems, which supports our understanding of physical mechanisms at work. Then we show the detailed characteristics of drying of initially saturated model composite systems (with kaolin or cellulose paste) with the help of MRI measurements providing the liquid distribution in the sample at different times during the process up to the very last stages of drying. It appears that the granular medium is unaffected (i.e. remains saturated) during an initial period during which the paste shrinks and finally forms a sufficiently rigid porous structure which will not any more shrink later on. Then the drying process is governed by capillary effects down to very low saturation. Over a wide range of saturations both media desaturate homogeneously (within each medium) at different rates which depend on the specific porous structure of the media, so as to maintain capillary equilibrium throughout the sample. During these different stages the drying rate of the whole system remains constant. For sufficiently low saturation in the paste a dry front can develop, both in the paste and the porous medium below, and the drying rate now decreases. These results show that in a drying composite system liquid extraction can occur more or less simultaneously in the different parts of the material up to the very last stages of drying. The corresponding evolution of the distributions of liquid in the different parts of the sample also provides key information for the prediction of ion or particle transport and accumulation in the different parts of a composite system.

Strengthening and drying rate of a drying emulsion layer.

From direct observations and MRI measurements we demonstrate that during the drying of a direct (oil in water) emulsion the whole system essentially concentrates homogeneously, which leads to shrinkage, without air penetration. The structure and mechanical strength (i.e. the elastic modulus) of this concentrated bulk are not significantly different from those of an emulsion directly prepared at this higher concentration. Despite this phenomenon, the drying rate continuously and rapidly decreases as the water content decreases, in contrast with the drying of a simple granular packing. This results from a concentration gradient which develops towards the free surface of the sample where the oil droplets finally coalesce, ultimately forming an oil layer covering the sample through which the water molecules have to diffuse before evaporating. Moreover, as during the process, the liquid is transported towards the free surface where it evaporates, surfactants accumulate and tend to form a thin solid layer below the oil layer, which tends to further reduce the drying rate.

Particle-Size-Exclusion Clogging Regimes in Porous Media.

From observations of the progressive deposition of noncolloidal particles by geometrical exclusion effects inside a 3D model porous medium, we get a complete dynamic view of particle deposits over a full range of regimes from transport over a long distance to clogging and caking. We show that clogging essentially occurs in the form of an accumulation of elements in pore size clusters, which ultimately constitute regions avoided by the flow. The clusters are dispersed in the medium, and their concentration (number per volume) decreases with the distance from the entrance; caking is associated with the final stage of this effect (for a critical cluster concentration at the entrance). A simple probabilistic model, taking into account the impact of clogging on particle transport, allows us to quantitatively predict all these trends up to a large cluster concentration, based on a single parameter: the clogging probability, which is a function of the confinement ratio. This opens the route towards a unification of the different fields of particle transport, clogging, caking, and filtration.

Yielding and Flow of Soft-Jammed Systems in Elongation.

So far, yielding and flow properties of soft-jammed systems have only been studied from simple shear and then extrapolated to other flow situations. In particular, simple flows such as elongations have barely been investigated experimentally or only in a nonconstant, partial volume of material. We show that using smooth tool surfaces makes it possible to obtain a prolonged elongational flow over a large range of aspect ratios in the whole volume of material. The normal force measured for various soft-jammed systems with different microstructures shows that the ratio of the elongation yield stress to the shear yield stress is larger (by a factor of around 1.5) than expected from the standard theory which assumes that the stress tensor is a function of the second invariant of the strain rate tensor. This suggests that the constitutive tensor of the materials cannot be determined solely from macroscopic shear measurements.

Wall Slip of Soft-Jammed Systems: A Generic Simple Shear Process.

From well-controlled long creep tests, we show that the residual apparent yield stress observed with soft-jammed systems along smooth surfaces is an artifact due to edge effects. By removing these effects, we can determine the stress solely associated with steady-state wall slip below the material yield stress. This stress is found to vary linearly with the slip velocity for a wide range of materials whatever the structure, the interaction types between the elements and with the wall, and the concentration. Thus, wall slip results from the laminar flow of some given free liquid volume remaining between the (rough) jammed structure formed by the elements and the smooth wall. This phenomenon may be described by the simple shear flow in a Newtonian liquid layer of uniform thickness. For various systems, this equivalent thickness varies in a narrow range (35±15 nm).

Drying kinetics of deformable and cracking nano-porous gels.

The desiccation of porous materials encompasses a wide range of technological and industrial processes and is acutely sensitive to the hierarchical structure of the porous materials resulting in complex dynamics which are challenging to unravel. Macroscopic observations of the surface and geometry of model colloidal gels during desiccation under controlled air flow highlight the role of crack formation in drying. The density of cracks and their rate of appearance depend on the initial solid fraction of the gels and their adherence to the substrate. While under certain conditions cracking leads to an increase of the drying rate, in other cases cracking allows for its conservation over an extended period of the drying process. Nevertheless, as long as the sample is saturated with water, each piece within the sample shrinks isotropically as if it were an independent drying system. By simulating the airflow around the sample and inside the crack cavities, we show the existence of a perturbation in the air velocity in the vicinity of the crack cavity whose scale depends on the aspect ratio (depth/width) of the latter. On this basis, we propose a simple model which predicts the observed drying rate variations encountered while the sample cracks; and further enables to simulate the desiccation for a designated crack density.

Magnetic resonance imaging measurements evidence weak dispersion in homogeneous porous media.

We measure the dispersion coefficient through homogeneous bead or sand packings at different flow rates from direct magnetic resonance imaging (MRI) visualizations of the transport characteristics of a pulse of paramagnetic nanoparticles. Through two-dimensional imaging we observe homogeneous dispersion inside the sample, but we show that entrance effects may induce significant radial heterogeneities, which would affect the interpretation of the breakthrough curve. Another MRI approach then provides quantitative measurements of the evolution in time of the longitudinal particle distribution in the sample. These data can be analyzed to deduce the coefficient of dispersion independently of entrance effects. The values obtained for this "effective" dispersion coefficient are almost ten times lower than the commonly accepted values.

Water retention against drying with soft-particle suspensions in porous media.

Polymers suspended in granular packings have a significant impact on water retention, which is important for soil irrigation and the curing of building materials. Whereas the drying rate remains constant during a long period for pure water due to capillary flow providing liquid water to the evaporating surface, we show that it is not the case for a suspension made of soft polymeric particles called microgels: The drying rate decreases immediately and significantly. By measuring the spatial water saturation and concentration of suspended particles with magnetic resonance imaging, we can explain these original trends and model the process. In low-viscosity fluids, the accumulation of particles at the free surface induces a recession of the air-liquid interface. A simple model, assuming particle transport and accumulation below the sample free surface, is able to reproduce our observations without any fitting parameters. The high viscosity of the microgel suspension inhibits flow towards the free surface and a drying front appears. We show that water vapor diffusion over a defined and increasing length sets the drying rate. These results and model allow for better controlling the drying and water retention in granular porous materials.

Rayleigh-Taylor Instability in Elastoplastic Solids: A Local Catastrophic Process.

We show that the Rayleigh-Taylor instability in elastoplastic solids takes the form of local perturbations penetrating the material independently of the interface size, in contrast with the theory for simple elastic materials. Then, even just beyond the stable domain, the instability abruptly develops as bursts rapidly moving through the other medium. We show that this is due to the resistance to penetration of a finger which is minimal for a specific finger size and drops to a much lower value beyond a small depth (a few millimeters).

Water transfer and crack regimes in nanocolloidal gels.

Direct observations of the surface and shape of model nanocolloidal gels associated with measurements of the spatial distribution of water content during drying show that air starts to significantly penetrate the sample when the material stops shrinking. We show that whether the material fractures or not during desiccation, as air penetrates the porous body, the water saturation decreases but remains almost homogeneous throughout the sample. This air invasion is at the origin of another type of fracture due to capillary effects; these results provide insight into the liquid dynamics at the nanoscale.

Breaking of non-Newtonian character in flows through a porous medium.

From NMR measurements we show that the velocity field of a yield stress fluid flowing through a disordered well-connected porous medium is very close to that for a Newtonian fluid. In particular, it is shown that no arrested regions exist even at very low velocities, for which the solid regime is expected to be dominant. This suggests that these results obtained for strongly nonlinear fluid can be extrapolated to any nonlinear fluid. We deduce a generalized form of Darcy's law for such materials and provide insight into the physical origin of the coefficients involved in this expression, which are shown to be moments of the second invariant of the strain rate tensor.

Breakage of non-Newtonian character in flow through a porous medium: evidence from numerical simulation.

We study the flow, through a model two-dimensional porous medium, of Newtonian fluids, power-law fluids, and viscoplastic fluids in the laminar regime and with moderate or dominant effects of the yielding term. A numerical technique able to take properly into account yielding effects in viscoplastic flows without any regularization is used to determine the detailed flow characteristics. We show that as soon as the distance between the disks forming the porous medium is sufficiently small, the velocity field and in particular the distribution function of the velocity of these different fluids in a wide range of flow regimes are similar. Moreover, the volume fraction of fluid at rest is negligible even at low flow rate. Thus the non-Newtonian character of a fluid flowing through such a complex geometry tends to be broken. We suggest that this is due to the fact that in a flow through a channel of rapidly varying cross section, the deformation, and thus the flow field, is imposed on the fluid, a situation that is encountered almost everywhere in a porous medium. These results make it possible to deduce a general expression for Darcy's law of these fluid types and estimate the parameters appearing in this expression.

Velocity distributions in confined flows of some complex fluids: sequence, sample and hardware issues.

The present work addresses the problem of using Pulsed Field Gradient (PFG) experiments to measure velocity probability density functions and/or distributions in restricted flows, without being subjected to the blurring due to diffusive molecular motions. It especially focuses on two important classes of complex yield-stress fluids, i.e. water based colloidal suspensions or polymeric gels, and concentrated emulsions. Taking into account the many constraints owing to fluid diffusive properties, flow rate, hardware characteristics and pore size, it is found that the existence of suitable and optimised sequence parameters can be discussed in a graphical way. To do so, it also shown that Murday and Cotts formula describing diffusion inside emulsion droplets can be efficiently approximated by means of a set of asymptotic expressions. Different tuning regimes are identified for both kind of fluids, highlighting the influence of each of the various constraints on measuring possibilities. A method is given to build quantitative diagrams indicating pore sizes and flow rates allowing pure velocity assessment for a given fluid and Nuclear Magnetic Resonance (NMR) hardware. Measurements are found to be mainly constrained by fluid self-diffusivity and microstructure at low flow rates, and hardware characteristics at high flow rates. Although high gradient strengths can be made necessary to decrease achievable velocities and pore sizes in some specific cases, low gradient systems turn out suitable in many situations thanks to optimised sequence tuning. Due to their larger size, the latter also appear to offer the widest variety of workable experimental conditions. The use of these results is finally exemplified on the practical case of an emulsion flow in a model porous system.

Solid-solid transition in Landau-Levich flow with soft-jammed systems.

We study the Landau-Levich problem, i.e., withdrawal of a plate from a bath of fluid, in the case of a soft-jammed system, which involves a transition from a solid bath to a solid layer stuck on the plate. We show that this solid-solid transition is prepared inside the bath before the emersion from the fluid, through the existence of a uniform (boundary) layer in the liquid regime along the plate. This layer controls the original characteristics of the (solid) coated layer, whose thickness is almost independent of the velocity but proportional to the material yield stress.

Enhanced displacement of a liquid pushed by a viscoelastic fluid.

We consider the displacement, in a rectangular channel, of a Newtonian oil pushed by different types of liquids (Newtonian, shear-thinning, viscoelastic) of slightly higher apparent viscosity. In the absence of viscoelastic effects the interface between the two fluids becomes sharper at larger velocities, so that the thickness of the lateral film left behind increases with the flow rate. On the contrary, with a viscoelastic fluid, the shape of the interface is almost independent of the velocity so that the thickness of the lateral film is approximately constant. Moreover this thickness decreases when the ratio of normal to tangential stresses increases, suggesting that this effect can be attributed to normal stress differences. A heuristic theoretical approach tends to confirm this statement.

MRI evidence for a receding-front effect in drying porous media.

After drying colloidal particles suspended in a porous medium a concentration gradient appears. Using ^{1}H MRI we propose a protocol to observe simultaneously the distributions of air, liquid, and colloid through the unsaturated solid porous structure. Thus we show that the above phenomenon comes from a receding-front effect: The elements migrate towards the free surface of the sample and accumulate in the remaining liquid films. Our understanding of the process makes it possible to establish a simple model without diffusion predicting the drying rate and the concentration distribution in time, in excellent agreement with the experimental observations.

Physical origin of shear-banding in jammed systems.

Jammed systems all have a yield stress. Among these materials some have been shown to shear-band but it is as yet unclear why some materials develop shear-band and some others do not. In order to rationalize existing data concerning the flow characteristics of jammed systems and in particular understand the physical origin of such a difference, we propose a simple approach for describing the steady flow behaviour of yield stress fluids, which retains only basic physical ingredients. Within this framework we show that in the liquid regime the behaviour of jammed systems turns from that of a simple yield stress fluid (exhibiting homogeneous flows) to a shear-banding material when the ratio of a characteristic relaxation time of the system to a restructuring time becomes smaller than 1, thus suggesting a possible physical origin of these trends.