Unveiling moisture transport mechanisms in cellulosic materials: Vapor vs. bound water

Natural textiles, hair, paper, wool, or bio-based walls possess the remarkable ability to store humidity from sweat or the environment through "bound water" absorption within nanopores, constituting up to 30% of their dry mass. The knowledge of the induced water transfers is pivotal for advancing industrial processes and sustainable practices in various fields such as wood drying, paper production and use, moisture transfers in clothes or hair, humidity regulation of bio-based construction materials, etc. However, the transport and storage mechanisms of this moisture remain poorly understood, with modeling often relying on an assumption of dominant vapor transport with an unknown diffusion coefficient. Our research addresses this knowledge gap, demonstrating the pivotal role of bound water transport within interconnected fiber networks. Notably, at low porosity, bound water diffusion dominates over vapor diffusion. By isolating diffusion processes and deriving diffusion coefficients through rigorous experimentation, we establish a comprehensive model for moisture transfer. Strikingly, our model accurately predicts the evolution of bound water's spatial distribution for a wide range of sample porosities, as verified through magnetic resonance imaging. Showing that bound water transport can be dominant over vapor transport, this work offers a change of paradigm and unprecedented control over humidity-related processes.

Critical Role of Boundary Conditions in Sorption Kinetics Measurements

In order to characterize the hygroscopic properties of cellulose-based materials, which can absorb large amounts of water from vapor in ambient air, or the adsorption capacity of pollutants or molecules in various porous materials, it is common to rely on sorption-desorption dynamic tests. This consists of observing the mass variation over time when the sample is placed in contact with a fluid containing the elements to be absorbed or adsorbed. Here, we focus on the case of a hygroscopic material in contact with air at a relative humidity (RH) differing from that at which it has been prepared. We show that the vapor mass flux going out of the sample follows from the solution of a vapor convection-diffusion problem along the surface and is proportional to the difference between the RH of the air flux and that along the surface with a multiplicative factor (δ) depending only on the characteristics of the air flux and the geometry of the system, including the surface roughness. This factor may be determined from independent measurements in which the RH along the surface is known while keeping all other variables constant. Then we show that the apparent sorption or desorption kinetics critically depend on the competition between boundary conditions and transport through the material. For sufficiently low air flux intensities or small sample thicknesses, the moisture distribution in the sample remains uniform and evolves toward the equilibrium with a kinetics depending on the value of δ and the material thickness. For sufficiently high air flux intensities or large sample thicknesses, the moisture distribution is highly inhomogeneous, and the kinetics reflect the ability of water transport by diffusion through the material. We illustrate and validate this theoretical description on the basis of magnetic resonance imaging experiments on drying cellulose fiber stacks.

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.

Dynamic NMR Relaxometry as a Simple Tool for Measuring Liquid Transfers and Characterizing Surface and Structure Evolution in Porous Media

Porous media containing voids which can be filled with gas and/or liquids are ubiquitous in our everyday life: soils, wood, bricks, concrete, sponges, and textiles. It is of major interest to identify how a liquid, pushing another fluid or transporting particles, ions, or nutriments, can penetrate or be extracted from the porous medium. High-resolution X-ray microtomography, neutron imaging, and magnetic resonance imaging are techniques allowing us to obtain, in a nondestructive way, a view of the internal processes in nontransparent porous media. Here we review the possibilities of a simple though powerful technique which provides various direct quantitative information on the liquid distribution inside the porous structure and its variations over time due to fluid transport and/or phase changes. It relies on the analysis of the details of the NMR (nuclear magnetic resonance) relaxation of the proton spins of the liquid molecules and its evolution during some process such as the imbibition, drying, or phase change of the sample. This rather cheap technique then allows us to distinguish how the liquid is distributed in the different pore sizes or pore types and how this evolves over time; since the NMR relaxation time depends on the fraction of time spent by the molecule along the solid surface, this technique can also be used to determine the specific surface of some pore classes in the material. The principles of the technique and its contribution to the physical understanding of the processes are illustrated through examples: imbibition, drying or fluid transfers in a nanoporous silica glass, large pores dispersed in a fine polymeric porous matrix, a pile of cellulose fibers partially saturated with bound water, a softwood, and a simple porous inclusion in a cement paste. We thus show the efficiency of the technique to quantify the transfers with a good temporal resolution.

Two-step diffusion in cellular hygroscopic (vascular plant-like) materials

Vascular plants, a vast group including conifers, flowering plants, etc., are made of a cellular hygroscopic structure containing water in the form of either free (i.e., in a standard liquid state) or bound (i.e., absorbed in the cell walls) water. From nuclear magnetic resonance techniques, we distinguish the dynamics of bound water and free water in a typical material (softwood) with such a structure, under convective drying. We show that water extraction relies on two mechanisms of diffusion in two contiguous regions of the sample, in which respectively the material still contains free water or only contains bound water. However, in any case, the transport is ensured by bound water. This makes it possible to prolong free water storage despite dry external conditions and shows that it is possible to extract free water in depth (or from large heights) without continuity of the free water network.

Brittle solid collapse to simple liquid for a waxy suspension

We show that thanks to the existence of a continuous (percolating) network of weak interparticle bonds in a liquid, wax suspensions behave as "soft breakable (brittle) solids". It appears that, under the action of either a large stress over a short time or oscillating low stress (fatigue test), the initially solid network of these materials is broken and dispersed in the liquid, which makes them turn abruptly ("collapse") and irreversibly into a low viscous fluid. This collapse is more dramatic as the concentration increases. These phenomena are related to the evolution of the microstructure directly observed after different flow histories. The interpretation of these results provides new perspectives for understanding the physical origin of the brittleness or plasticity of solid or pasty materials, and suggests such materials might be used as model systems to simulate and explain natural catastrophic events such as landslides and avalanches.

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.

Synergistic actions of mixed small and large pores for capillary absorption through biporous polymeric materials

Water absorption in porous media is an important process involved in numerous materials for various applications, such as in the building industry, food processing and bioengineering. Designing new materials with appropriate absorption properties requires an understanding of how absorption behavior depends on both the material's morphology and the properties of the solid matrix, i.e. hydrophilic/hydrophobic nature and swelling/deformation properties. Although the basic principles of imbibition are well-known for simple porous systems, much less is known about absorption in complex porous systems, in particular those containing several coexisting porous phases, such as wood for example. Here, water absorption is studied for model porous organic materials exhibiting several degrees of hydrophobicity and two pore size levels, either as monoporous materials (large or small pores) or as biporous materials (mixed large and small pores). The interconnected biporous structure is designed via a double porogen templating approach using cubic sodium chloride particles as templates for the generation of the larger pore size (250-400 μm) and i-PrOH as a porogenic solvent for the smaller pore size (2-5 μm). While absorption for the small pore material is well described by the classical Washburn theory, the large pore material shows a drastic reduction in the imbibition rate. This behavior is attributed to the slow breakthrough mechanism for the water interface at sharp edge connections between pores. Remarkably, this slow regime is suppressed for the biporous material and the imbibition rate is even higher than the sum of rates obtained for its monoporous counterparts, which highlights the synergistic action of mixed small and large pores.

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).

Drying kinetics driven by the shape of the air/water interface in a capillary channel

We look at the drying process in a simple glass channel with dominant capillary effects as is the case in microfluidics. We find drying kinetics commonly observed for confined geometry, namely a constant period followed by a falling rate period. From visualization of the air/water interface with high resolution, we observe that the drying rate decreases without a drying front progression although this is the usually accepted mechanism for confined geometries. We show with FEM that in our specific geometry the falling rate period is due to changes in the shape of the air-water interface at the free surface where most evaporation occurs. Our simulations show that the sensitivity of the drying rate to the shape of the first air-water interface from the sample free surface implies that slight changes of the wetting or pinning conditions can significantly modify the drying rate.

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.

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.

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.

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.

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.

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.

Drying of a model soil

Drying experiments have been carried out with model soils made of different pastes filling granular packings. A detailed information concerning the time evolution of the water saturation distribution inside the sample was obtained from magnetic resonance imaging measurements. This study makes it possible to understand the physical origin of the drying characteristics of these materials. The drying curves exhibit a constant-rate period (CRP) and a falling-rate period (FRP) but the relative durations of these periods depend on the paste structure. With a kaolin suspension the CRP lasts down to very low water densities and is associated with a homogeneous drying of the paste throughout the sample. With a bentonite suspension the CRP is shorter and the drying in the FRP results from a complex process involving fractures progressing downward through the pasty matrix. With a gel the CRP period is even shorter and the drying in the FRP results from the progression of a dry front through the packing as a result of the shrinkage of the gel matrix. This provides an overview of the main possible processes at work when drying a soil as a function of its components along with some practical means for slowing down drying from soils.

Three-dimensional jamming and flows of soft glassy materials

Various disordered dense systems, such as foams, gels, emulsions and colloidal suspensions, undergo a jamming transition from a liquid state (they flow) to a solid state below a yield stress. Their structure, which has been thoroughly studied with powerful means of three-dimensional characterization, shows some analogy with that of glasses, which led to them being named soft glassy materials. However, despite its importance for geophysical and industrial applications, their rheological behaviour, and its microscopic origin, is still poorly known, in particular because of its nonlinear nature. Here we show from two original experiments that a simple three-dimensional continuum description of the behaviour of soft glassy materials can be built. We first show that when a flow is imposed in some direction there is no yield resistance to a secondary flow: these systems are always unjammed simultaneously in all directions of space. The three-dimensional jamming criterion seems to be the plasticity criterion encountered in most solids. We also find that they behave as simple liquids in the direction orthogonal to that of the main flow; their viscosity is inversely proportional to the main flow shear rate, as a signature of shear-induced structural relaxation, in close similarity to the structural relaxations driven by temperature and density in other glassy systems.

Solid-liquid transition and rejuvenation similarities in complex flows of thixotropic materials studied by NMR and MRI

We study the flow of a typical thixotropic material subjected to very different deformation histories (squeeze, shear, and extrusion) with either local (proton NMR and magnetic resonance imaging) or macroscopic measurements after different times of rest. Specifically, we measure the velocity fields and the spin-spin NMR relaxation of the material after different flow histories. The relaxation data exhibits a long relaxing component revealing information about the reversible microstructural evolution of the sample during aging-rejuvenation cycles. We show that for each deformation process, the evolution of the viscosity during the solid-liquid transition is similar by a factor related to the initial state of the material. Moreover, results examining the impact of the rate at which the deformation is imposed suggest that the state of the material during this transition may be described by a single parameter reflecting the average size and deformation of the material's flocs. These results also show that localization of flow occurs as a result of a progressive differential evolution of the material in different regions of the flow, and thus are determined by the boundary conditions of the flow.

Wide-gap Couette flows of dense emulsions: local concentration measurements, and comparison between macroscopic and local constitutive law measurements through magnetic resonance imaging

Flows of dense emulsions show many complex features among which long range nonlocal effects pose a problem for macroscopic characterization. In order to get around this problem, we study the flows of several dense emulsions, with droplet size ranging from 0.3to40microm , in a wide-gap Couette geometry. We couple macroscopic rheometric experiments and local velocity measurements through magnetic resonance imaging (MRI) techniques. As concentration heterogeneities are expected in the wide-gap Couette flows of multiphase materials, we also designed a method to measure the local droplet concentration in emulsions with a MRI device. In contrast to dense suspensions of rigid particles where very fast migration occurs under shear in wide-gap Couette flows, we show that no migration takes place in dense emulsions even for strains as large as 100 000 in our systems. As a result of the absence of migration and of finite size effect, we are able to determine very precisely the local rheological behavior of several dense emulsions. As the materials are homogeneous, this behavior can also be inferred from purely macroscopic measurements. We thus suggest that properly analyzed purely macroscopic measurements in a wide-gap Couette geometry can be used as a tool to study the local constitutive laws of dense emulsions. All behaviors are basically consistent with Herschel-Bulkley laws of index 0.5. The existence of a constitutive law accounting for all flows contrasts with previous results obtained within a microchannel by Goyon [Nature (London) 454, 84 (2008)]: the use of a wide-gap Couette geometry is likely to prevent here from nonlocal finite size effects; it also contrasts with the observations of Bécu [Phys. Rev. Lett. 96, 138302 (2006)]. We also evidence the existence of discrepancies between a perfect Herschel-Bulkley behavior and the observed local behavior at the approach of the yield stress due to slow shear flows below the apparent yield stress in the case of a strongly adhesive emulsion.

Gelation on the microscopic scale

Particle-tracking methods are used to study gelation in a colloidal suspension of Laponite clay particles. We track the motion of small fluorescent polystyrene spheres added to the suspension, and obtain the micron-scale viscous and elastic moduli of the material from their mean-squared displacement. The fluorescent spheres move subdiffusively due to the microstructure of the suspension, with the diffusive exponent decreasing from close to one at early times to near zero as the material gels. The particle-tracking data show that the system becomes more heterogeneous on the microscopic scale as gelation proceeds. We also determine the bulk-scale moduli using small-amplitude oscillatory shear rheometry. Both the macroscopic and microscopic moduli increase with time, and on both scales we observe a transition from a primarily viscous fluid to an elastic gel. We find that the gel point, determined as the time at which the viscous and elastic moduli are equal, is length-scale dependent--gelation occurs earlier on the bulk scale than on the microscopic scale.

Transition from a simple yield-stress fluid to a thixotropic material

From magnetic resonance imaging rheometry we show that a pure emulsion can be turned from a simple yield stress fluid to a thixotropic material by adding a small fraction of colloidal particles. The two fluids have the same behavior in the liquid regime but the loaded emulsion exhibits a critical shear rate below which no steady flows can be observed. For a stress below the yield stress, the pure emulsion abruptly stops flowing, whereas the viscosity of the loaded emulsion continuously increases in time, which leads to an apparent flow stoppage. This phenomenon can be very well represented by a model assuming a progressive increase of the number of droplet links via colloidal particles.

Physical age of soft-jammed systems

We study experimentally the liquid-solid transition in a soft-jammed system and focus on its aging in the solid regime. We investigate the impact of temperature, density, and load changes on the material behavior. We show that all elastic modulus versus time curves fall on a single master curve when rescaled by an appropriate factor function of the density, the temperature, the load, and the time elapsed since preshear. This allows us to distinguish the effect of temperature and density on the mechanical properties and their effect on aging. Since the time evolutions of the elastic modulus under various conditions are similar within a factor, we suggest that the rescaled time reflects the physical age of the material; i.e., it describes the degree of progress of the structural organization relative to a state of reference of the system in the solid regime and constitutes a means for characterizing the effective state of such systems.

Rheophysics of pastes: a review of microscopic modelling approaches

Pastes are materials intermediate between solids and liquids which are of great practical interest as they keep the shape they have been given. Despite their various internal structures it is possible to draw up a generic rheophysical scheme from which one qualitatively understands, from a physical point of view, their main mechanical characteristics, solid regime, solid-liquid transition, liquid regime, thixotropy and aging. Here we review in detail these different properties as they are generally observed with most pasty materials and the attempts to describe them using microscopic structure-based theoretical models. For real systems a unified, qualitative, conceptual description is provided. For some model systems (, foams, colloidal gels…) there exist consistent microscopic approaches providing quantitative relationships between rheological parameters in the solid regime and physical parameters of the system. For the liquid regime and thixotropy the situation is more complex.

General probabilistic approach to the filtration process

We show experimentally that clogging is basically a matter of the probability of the presence of particles. We describe this process as a function of the main variables of the process, namely, the ratio of particle to mesh hole size, the solid fraction, and the number of grains arriving at each mesh hole during one test, with the help of a simple model, the predictions of which are in very good agreement with our experimental data.

Gravity flow instability of viscoplastic materials: the ketchup drip

In contrast with simple liquids such as water, milk, honey, which easily flow as a continuous jet when poured from a vessel, pasty materials such as mayonnaise, mustard, ketchup, puree, etc., fall by fits and starts in a wide range of flow rates. This may, for example, be observed when ketchup or mayonnaise is pushed from a tube at a sufficient height over a plate: although surface tension effects are generally negligible because of its high viscosity the material drops as successive droplets of more or less similar size (except at large flow rates). Here we demonstrate that this effect is a kind of flow instability which develops when the weight of material becomes larger than a force due to its yield stress, namely a critical stress below which it cannot flow steadily. Furthermore, we show that depending on the exact material behavior surprising phenomena may be observed: the size of the droplet may remain constant or even decrease (for thixotropic materials) as the flow rate increases. This approach, for example, provides tools for controlling the shape of droplets in cooking and the size of extrudates in food and mineral industries.

Model for Brownian motion in soft-jammed systems

Brownian motion in soft-jammed systems (pastes) is directly described by taking into account the specific mechanical characteristics of the material surrounding the moving object. In particular we obtain explicit forms for the fluctuation-dissipation equation and the specific characteristics of diffusion through a soft-jammed system.

Flow of wet granular materials

The transition from frictional to lubricated flows of a dense suspension of non-Brownian particles is studied. The pertinent parameter characterizing this transition is the Leighton number Le=eta(s)gamma / sigma, the ratio of lubrication to frictional forces. Le defines a critical shear rate below which no steady flow without localization exists. In the frictional regime the shear flow is localized. The lubricated regime is not simply viscous: the ratio of shear to normal stresses remains constant and the velocity profile has a universal form in both frictional and lubricated regimes. Finally, a discrepancy between local and global measurements of viscosity is identified, which suggests inhomogeneity of the material under flow.

Abrupt transition from viscoelastic solidlike to liquidlike behavior in jammed materials

Using a new rheometrical technique, which makes it possible to determine both the velocity field in steady state and the strain field in the very first instants of the flow, we show that, beyond a critical deformation, typical pasty materials (a foam and a polymeric gel) turn abruptly from a viscoelastic solidlike behavior to a steady liquidlike behavior at a shear rate larger than a critical value.

Practical determination of the rheological behavior of pasty biosolids

In this paper, we demonstrate that the rheological behavior of pasty sewage sludges, regardless of origin, treatment or composition, follows a Herschel-Bulkley model. The yield stress and solid volume fraction are found to be the only two distinctive rheological characteristics of these materials. By scaling the shear rate and the shear stress with two parameters depending only on the yield stress and the solid fraction, the flow curves of 48 pasty sludges all fall along a unique dimensionless master curve. This result may be used in practice to determine, from simple, independent measurements, the rheological behavior of any pasty sludge: the yield stress can be measured with the help of the 'slump test' and the solid concentration determined from the organic and mineral matter contents. The results obtained with this technique are in very good agreement with those obtained by direct rheometry.

Viscosity bifurcation in granular materials, foams, and emulsions

We show that the rheological properties of dry granular materials, as well as foams and emulsions, are similar to typical thixotropic fluids: under a sufficiently strong shear the viscosity decreases in time, leading to a hysteresis in an up-and-down stress ramp. This leads to a viscosity bifurcation around a critical stress: for smaller stresses, the viscosity increases in time and the material eventually stops flowing, whereas for slightly larger stresses the viscosity decreases continuously with time and the flow accelerates. These results show that all jammed systems exhibit strong mechanical similarities around the transition between a "fluid" and a "solid" state, and that the transition between these states is discontinuous. This similarity is further emphasized by the fact that both a simple model for the dynamics of a grain on a sandpile [Quartier et al., Phys. Rev. E 62, 8299 (2000)] and a simple model for the thixotropic behavior of (colloidal) pastes [Coussot et al., Phys. Rev. Lett. 88, 175501 (2002)] extrapolated to granular flows qualitatively predict this viscosity bifurcation.

Coexistence of liquid and solid phases in flowing soft-glassy materials

Magnetic-resonance-imaging rheometrical experiments show that concentrated suspensions or emulsions cannot flow steadily at a uniform rate smaller than a critical value (gamma(c)). As a result, a "liquid" region (sheared rapidly, i.e., at a rate larger than gamma(c)) and a "solid" region (static) coexist. The behavior of the fluid in the liquid region follows a simple power-law model, while the extent of the solid region increases with the degree of jamming of the material.

Avalanche behavior in yield stress fluids

We show that, above a critical stress, typical yield stress fluids (gels and clay suspensions) and soft glassy materials (colloidal glasses) start flowing abruptly and subsequently accelerate, leading to avalanches that are remarkably similar to those of granular materials. Rheometrical tests reveal that this is associated with a bifurcation in rheological behavior: for small stresses, the viscosity increases in time; the material eventually stops flowing. For slightly larger stresses the viscosity decreases continuously in time; the flow accelerates. Thus the viscosity jumps discontinuously to infinity at the critical stress. We propose a simple physical model capable of reproducing these effects.

Viscous fingering in a yield stress fluid

We study the Saffman-Taylor or viscous fingering instability in yield stress fluids. The theory for yield stress fluids shows that the dispersion equation of the instability is similar to that for Newtonian fluids; however, the capillary number governing the instability now contains the yield stress. Experiments using gels and foams reveal very branched fingers in the gel. The results are in excellent agreement with theory for the gel, with, in addition, a crossover from yield stress dominated to viscous behavior. The results for foams are very different due to the existence of wall slip.

Pore size NMR imaging

Magnetic resonance imaging (MRI) experiments with industrial or civil engineering materials do not in general aim at determining more than water density distribution or profile. Nevertheless, it is fundamental to know more about their internal structure in relation to their macroscopic behaviour. Two techniques make possible such studies. They involve magnetic resonance imaging coupled with an analysis of respectively freezing and relaxation effects. These techniques do not have the usual magnetic resonance imaging resolution limitations. We present a mathematical treatment of data obtained by these techniques that directly provides spatial maps of the different moments of the pore size distribution.