Confined flows of a polymer microgel

Visualizing flow dynamics and restart of Carbopol gel solutions in tube and parallel-plates geometries with wall slip

The present study examines the impact of slip in Carbopol solutions during the restart flow in pipelines utilizing in situ visualization techniques. Rheological tests were conducted using smooth and hatched parallel plate geometries to obtain the rheological characteristics of the solutions. The behavior of the solutions in the creep tests is compared with those in the experimental unit. Three flow regimes were identified through rheological and experimental setup tests: non-flow, slip, and yielded. The slip regime allowed the establishment of a slip static yield stress value, indicating significant deformation states, and a restart pressure decrease of about 61% when compared to the static yield stress. The flow dynamics under the wall slip effect is captured by velocity profiles, velocity contour maps and velocity gradient. Transient correlations of the scaling law type were determined, with wall slip in proportion to the velocity gradient and wall shear stress. Additionally, the concentration of viscoplastic material in the solution increased the scaling law index. This research seeks to provide valuable findings by quantifying the effects of apparent wall slip through in situ measurements. Such insights are crucial for designing and managing pipeline transport systems that handle yield stress fluids, applicable across various industries including cosmetics, food processing, and the production of waxy oils.

2.5D printing of a yield-stress fluid

We report on direct ink writing of a model yield-stress fluid and focus on the printability of the first layer, the one in contact with the supporting substrate. We observe a diversity of deposition morphologies that depends on a limited set of operational parameters, mainly ink flow rate, substrate speed and writing density, and also on material properties (e.g., yield-stress). Among these morphologies, one of them does not depend on fluid properties (as long as the fluid displays some yield-stress) and consists of flat films whose thickness is controllable in a significant range, about $$0.1{-}1$$ 0.1 - 1  mm, and tunable in real time during printing. We thus demonstrate the ability to print films with thickness gradients and prove that the printing fidelity is mainly due to a competition between yield-stress and capillarity.

Validation of temperature-controlled rheo-MRI measurements in a submillimeter-gap Couette geometry

A temperature-controlled submillimeter-gap (500 μm) rheo-magnetic resonance imaging (MRI) Couette cell has been developed to measure confined flow of soft structured materials under controlled temperature. The proposed setup enables performing rheo-MRI measurements using (i) a spatially uniform temperature control over the range 15°C to 40°C and (ii) a high spatial resolution up to 10 μm, as a consequence of the improved mechanical stability of the in-house developed rotating elements. Here, we demonstrate the performance of the cell for the rheo-MRI velocimetry study of a thixotropic fat crystal dispersion, a complex fluid commonly used in food manufacturing. The submillimeter-gap geometry and variable temperature capability of the cell enable observing the effects of shear- and temperature-induced fat recrystallization on both wall slip and shear banding under strongly confined flow. Our improved rheo-MRI setup opens new perspectives for the fundamental study of strongly confined flow, cooperative effects, and the underlying interparticle interactions and for ultimately aiding optimization of products involved in spreading/extrusion, such as cosmetics and foods.

Quantifying cooperative flow of fat crystal dispersions

We quantify the cooperative flow behaviour of fat crystal dispersions (FCDs) upon varying crystallization conditions. The latter enabled altering the multiscale microstructure of the FCDs, from the nanometer-sized platelets, and the dispersed fractal aggregates, up to the strength of the mesoscopic weak-link network. To the goal of characterizing strongly-confined flow in these optically-opaque materials, we acquire high-resolution rheo-magnetic-resonance-imaging (rheo-MRI) velocimetry measurements using an in-house developed 500 μm gap Couette cell (CC). We introduce a numerical fitting method based on the fluidity model, which yields the cooperativity length, ξ, in the narrow-gap CC. FCDs with aggregates sizes smaller than the confinement size by an order of magnitude were found to exhibit cooperativity effects. The respective ξ values diverged at the yield stress, in agreement with the Kinetic Elasto-Plastic (KEP) theory. In contrast, the FCD with aggregates sizes in the order of the gap size did not exhibit any cooperativity effect: we attribute this result to the correspondingly decreased mobility of the aggregates. We foresee that our optimized rheo-MRI measurement and fitting analysis approach will propel further similar studies of flow of other multi-scale and optically-opaque materials.

Continuum modeling of shear startup in soft glassy materials

Yield stress fluids (YSFs) display a dual nature highlighted by the existence of a critical stress σ_{y} such that YSFs are solid for stresses σ imposed below σ_{y}, whereas they flow like liquids for σ>σ_{y}. Under an applied shear rate γ[over ̇], the solid-to-liquid transition is associated with a complex spatiotemporal scenario that depends on the microscopic details of the system, on the boundary conditions, and on the system size. Still, the general phenomenology reported in the literature boils down to a simple sequence that can be divided into a short-time response characterized by the so-called "stress overshoot," followed by stress relaxation towards a steady state. Such relaxation can be either (1) long-lasting, which usually involves the growth of a shear band that can be only transient or that may persist at steady state or (2) abrupt, in which case the solid-to-liquid transition resembles the failure of a brittle material, involving avalanches. In the present paper, we use a continuum model based on a spatially resolved fluidity approach to rationalize the complete scenario associated with the shear-induced yielding of YSFs. A key feature of our model is to provide a scaling for the coordinates of the stress overshoot, i.e., stress σ_{M} and strain γ_{M} as a function of γ[over ̇], which shows good agreement with experimental and numerical data extracted from the literature. Moreover, our approach shows that the power-law scaling σ_{M}(γ[over ̇]) is intimately linked to the growth dynamics of a fluidized boundary layer in the vicinity of the moving boundary. Yet such scaling is independent of the fate of that layer, and of the long-term behavior of the YSF, i.e., whether the steady-state flow profile is homogeneous or shear-banded. Finally, when including the presence of "long-range" correlations, we show that our model displays a ductile to brittle transition, i.e., the stress overshoot reduces into a sharp stress drop associated with avalanches, which impacts the scaling σ_{M}(γ[over ̇]). This generalized model nicely captures subtle avalanche-like features of the transient shear banding dynamics reported in experiments. Our work offers a unified picture of shear-induced yielding in YSFs, whose complex spatiotemporal dynamics are deeply connected to nonlocal effects.

Stress Overshoots in Simple Yield Stress Fluids

Soft glassy materials such as mayonnaise, wet clays, or dense microgels display a solid-to-liquid transition under external shear. Such a shear-induced transition is often associated with a nonmonotonic stress response in the form of a stress maximum referred to as "stress overshoot." This ubiquitous phenomenon is characterized by the coordinates of the maximum in terms of stress σ_{M} and strain γ_{M} that both increase as weak power laws of the applied shear rate. Here we rationalize such power-law scalings using a continuum model that predicts two different regimes in the limit of low and high applied shear rates. The corresponding exponents are directly linked to the steady-state rheology and are both associated with the nucleation and growth dynamics of a fluidized region. Our work offers a consistent framework for predicting the transient response of soft glassy materials upon startup of shear from the local flow behavior to the global rheological observables.

Carbomer microgels as model yield-stress fluids

The review presents current research results for Carbopol-based microgels as yield-stress materials, covering three aspects: chemical, physical and rheological. Such a joint three-aspect study has no analog in the literature. The chemical aspects of Carbopol polymers are presented in terms of a cross-linking polymerization of acrylic acid, their molecular structure, microgel formulation, polyacid dissociation and neutralization, osmotic pressure and associated immense microgel swelling. The physical characterization is focused on models of the shear-induced solid-to-liquid transition of microgels, which are formed of mesoscopic particles typical for soft matter materials. Models that describe interparticle effects are presented to explain the energy states of microgel particles at the mesoscale of scrutiny. Typical representatives of the models utilize attributes of jamming dispersions, micromechanical and polyelectrolyte reactions. Selected relationships that result from the models, such as scaling rules and nondimensional flow characteristics are also presented. The rheological part presents the discussion of problems of yield stress in 2D and 3D deformations, appearance and magnitude of the wall slip. The theory and characteristics of Carbopol microgel deformation in rotational rheometers are presented with graphs for the steady-state measurements, stress-controlled oscillation and two types of transient shear deformation. The review is concluded with suggestions for future research.

Interparticle attraction controls flow heterogeneity in calcite gels

We couple rheometry and ultrasonic velocimetry to study experimentally the flow behavior of gels of colloidal calcite particles dispersed in water, while tuning the strength of the interparticle attraction through physico-chemistry. We unveil, for the first time in a colloidal gel, a direct connection between attractive interactions and the occurrence of shear bands, as well as stress fluctuations.

Viscoplastic fingering in rectangular channels

We experimentally study the viscous fingering problem of viscoplastic fluids in channels of rectangular cross section. We find that a yield stress-dependent capillary number (Ca^{*}) and an aspect ratio-dependent Bond number (Bo^{*}) can classify the finger shape into ramified and unified fingering patterns, and the finger flow regime into yield stress, viscosity, and aspect ratio-buoyancy-dominated regimes. For these regimes, we provide the transition boundaries using Ca^{*} and Bo^{*} and propose simple relations to predict the finger width, for a wide range of flow parameters, versus the capillary number, the channel aspect ratio, and the rheology of the viscoplastic fluid.

Unified Theoretical and Experimental View on Transient Shear Banding

Dense emulsions, colloidal gels, microgels, and foams all display a solidlike behavior at rest characterized by a yield stress, above which the material flows like a liquid. Such a fluidization transition often consists of long-lasting transient flows that involve shear-banded velocity profiles. The characteristic time for full fluidization τ_{f} has been reported to decay as a power law of the shear rate γ[over ˙] and of the shear stress σ with respective exponents α and β. Strikingly, the ratio of these exponents was empirically observed to coincide with the exponent of the Herschel-Bulkley law that describes the steady-state flow behavior of these complex fluids. Here we introduce a continuum model, based on the minimization of a "free energy," that captures quantitatively all the salient features associated with such transient shear banding. More generally, our results provide a unified theoretical framework for describing the yielding transition and the steady-state flow properties of yield stress fluids.

Stress Field inside the Bath Determines Dip Coating with Yield-Stress Fluids in Cylindrical Geometry

We study experimentally and theoretically the thickness of the coating obtained by pulling out a rod from a reservoir of yield-stress fluid. Opposite to Newtonian fluids, the coating thickness for a fluid of large enough yield stress is determined solely by the flow inside the reservoir and not by the flow inside the meniscus. The stress field inside the reservoir determines the thickness of the coating layer. The thickness is observed to increase nonlinearly with the sizes of the rod and of the reservoir. We develop a theoretical framework that describes this behavior and allows us to precisely predict the coating thickness.

A mesoscale study of creep in a microgel using the acoustic radiation force

We study the motion of a sphere of diameter 330 μm embedded in a Carbopol microgel under the effect of the acoustic radiation pressure exerted by a focused ultrasonic field. The sphere motion within the microgel is tracked using videomicroscopy and compared to conventional creep and recovery measurements performed with a rheometer. We find that under moderate ultrasonic intensities, the sphere creeps as a power law of time with an exponent α ≃ 0.2 that is significantly smaller than the one inferred from global creep measurements below the yield stress of the microgel (α ≃ 0.4). Moreover, the sphere relaxation motion after creep and the global recovery are respectively consistent with these two different exponents. By allowing a rheological characterization at the scale of the sphere with forces of the order of micronewtons, the present experiments pave the way for acoustic "mesorheology" which probes volumes and forces an intermediate between standard macroscopic rheology and classical microrheology. They also open new questions about the effects of the geometry of the deformation field and of the sphere size and surface properties on the creep behaviour of soft materials.

Wall fluidization in two acts: from stiff to soft roughness

Fluidization of soft glassy materials (SGMs) in microfluidic channels is affected by the wall roughness in the form of microtexturing. When SGMs flow across microgrooves, their constituents are likely trapped within the grooves' gap, and the way they are released locally modifies the fluidization close to the walls. By leveraging a suitable combination of experiments and numerical simulations on concentrated emulsions (a model SGM), we quantitatively report the existence of two physically different scenarios. When the gap is large compared to the droplets in the emulsion, the droplets hit the solid obstacles and easily escape scrambling with their neighbors. Conversely, as the gap spacing is reduced, droplets get trapped inside, creating a "soft roughness" layer, i.e. a complementary series of deformable posts from which overlying droplets are in turn released. In both cases, the induced fluidization scales with the grooves' density, although with a reduced prefactor for narrow gaps, accounting for the softness of the roughness. Both scenarios are also well distinguished via the statistics of the droplets displacement field close to the walls, with large deviations induced by the surface roughness, depending on its stiffness.

Bulk and local rheology in a dense and vibrated granular suspension

In this paper, we investigate experimentally the dynamics of particles in dense granular suspensions when both shear and external vibrations are applied. We study in detail how vibrations affect particle reorganization at the local scale and modify the apparent rheology. The nonlocal nature of the rheology when no vibrations are applied is evidenced, in agreement with previous numerical studies from the literature. It is also shown that vibrations induce structural reorganizations, which tend to homogenize the system and cancel the nonlocal properties.

Scaling description of non-local rheology

The plastic flow of amorphous materials displays non-local effects, characterized by a cooperativity length scale ξ. We argue that these effects enter in the more general description of surface phenomena near critical points. Using this approach, we obtain a scaling relation between exponents that describe the strain rate profiles in shear driven and pressure driven flow, which we confirm both in numerical models and experimental data. We find empirically that the cooperative length follows closely the characteristic length previously extracted in homogenous bulk flows. This analysis shows that the often used mean field exponents fail to capture quantitatively the non-local effects. Our analysis also explains the unusually large finite size effects previously observed in pressure driven flows.

Fluidization and wall slip of soft glassy materials by controlled surface roughness

We present a comprehensive study of concentrated emulsions flowing in microfluidic channels, one wall of which is patterned with micron-size equally spaced grooves oriented perpendicularly to the flow direction. We find a scaling law describing the roughness-induced fluidization as a function of the density of the grooves, thus fluidization can be predicted and quantitatively regulated. This suggests common scenarios for droplet trapping and release, potentially applicable for other jammed systems as well. Numerical simulations confirm these views and provide a direct link between fluidization and the spatial distribution of plastic rearrangements.

Structural and cooperative length scales in polymer gels

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^-1)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.

Spatially dependent diffusion coefficient as a model for pH sensitive microgel particles in microchannels

Solute transport and intermixing in microfluidic devices is strongly dependent on diffusional processes. Brownian Dynamics simulations of pressure-driven flow of model microgel particles in microchannels have been carried out to explore these processes and the factors that influence them. The effects of a pH-field that induces a spatial dependence of particle size and consequently the self-diffusion coefficient and system thermodynamic state were focused on. Simulations were carried out in 1D to represent some of the cross flow dependencies, and in 2D and 3D to include the effects of flow and particle concentration, with typical stripe-like diffusion coefficient spatial variations. In 1D, the mean square displacement and particle displacement probability distribution function agreed well with an analytically solvable model consisting of infinitely repulsive walls and a discontinuous pH-profile in the middle of the channel. Skew category Brownian motion and non-Gaussian dynamics were observed, which follows from correlations of step lengths in the system, and can be considered to be an example of so-called "diffusing diffusivity." In Poiseuille flow simulations, the particles accumulated in regions of larger diffusivity and the largest particle concentration throughput was found when this region was in the middle of the channel. The trends in the calculated cross-channel diffusional behavior were found to be very similar in 2D and 3D.

Large scale flow visualization and anemometry applied to lab-on-a-chip models of porous media

The following is a report on an experimental technique that allows one to quantify and map the velocity field with very high resolution and simple equipment in large 2D devices. Illumination through a grid is proposed to reinforce the contrast in the images and allow one to detect seeded particles that are pixel-sized or even smaller. The velocimetry technique that we have reported is based on the auto-correlation functions of the pixel intensity, which we have shown are directly related to the magnitude of the local average velocity. The characteristic time involved in the decorrelation of the signal is proportional to the tracer size and inversely proportional to the average velocity. We have reported on a detailed discussion about the optimization of relevant involved parameters, the spatial resolution and the accuracy of the method. The technique is then applied to a model porous medium made of a random channel network. We show that it is highly efficient to determine the magnitude of the flow in each of the channels of the network, opening the door to the fundamental study of the flows of complex fluids. The latter is illustrated with a yield stress fluid, in which the flow becomes highly heterogeneous at small flow rates.

Cooperativity flows and shear-bandings: a statistical field theory approach

Cooperativity effects have been proposed to explain the non-local rheology in the dynamics of soft jammed systems. Based on the analysis of the free-energy model proposed by L. Bocquet, A. Colin and A. Ajdari, Phys. Rev. Lett., 2009, 103, 036001, we show that cooperativity effects resulting from the non-local nature of the fluidity (inverse viscosity) are intimately related to the emergence of shear-banding configurations. This connection materializes through the onset of inhomogeneous compact solutions (compactons), wherein the fluidity is confined to finite-support subregions of the flow and strictly zero elsewhere. The compacton coexistence with regions of zero fluidity ("non-flowing vacuum") is shown to be stabilized by the presence of mechanical noise, which ultimately shapes up the equilibrium distribution of the fluidity field, the latter acting as an order parameter for the flow-noflow transitions occurring in the material.

Wall slip across the jamming transition of soft thermoresponsive particles

Flows of suspensions are often affected by wall slip, that is, the fluid velocity v(f) in the vicinity of a boundary differs from the wall velocity v(w) due to the presence of a lubrication layer. While the slip velocity v(s)=|v(f)-v(w)| robustly scales linearly with the stress σ at the wall in dilute suspensions, there is no consensus regarding denser suspensions that are sheared in the bulk, for which slip velocities have been reported to scale as a v(s)∝σ(p) with exponents p inconsistently ranging between 0 and 2. Here we focus on a suspension of soft thermoresponsive particles and show that v(s)) actually scales as a power law of the viscous stress σ-σ(c), where σ(c) denotes the yield stress of the bulk material. By tuning the temperature across the jamming transition, we further demonstrate that this scaling holds true over a large range of packing fractions ϕ on both sides of the jamming point and that the exponent p increases continuously with ϕ, from p=1 in the case of dilute suspensions to p=2 for jammed assemblies. These results allow us to successfully revisit inconsistent data from the literature and pave the way for a continuous description of wall slip above and below jamming.

Slip of Spreading Viscoplastic Droplets

The spreading of axisymmetric viscoplastic droplets extruded slowly on glass surfaces is studied experimentally using shadowgraphy and swept-field confocal microscopy. The microscopy furnishes vertical profiles of the radial velocity using particle image velocimetry (PIV) with neutrally buoyant tracers seeded in the fluid. Experiments were conducted for two complex fluids: aqueous solutions of Carbopol and xanthan gum. On untreated glass surfaces, PIV demonstrates that both fluids experience a significant amount of effective slip. The experiments were repeated on glass that had been treated to feature positive surface charges, thereby promoting adhesion between the negatively charged polymeric constituents of the fluids and the glass surface. The Carbopol and xanthan gum droplets spread more slowly on the treated surface and to a smaller radial distance. PIV demonstrated that this reduced spreading was associated with a substantial reduction in slip. For Carbopol, the effective slip could be eliminated entirely to within the precision of the PIV measurements; the reduction in slip was less effective for xanthan gum, with a weak slip velocity remaining noticeable.

Yield stress and elasticity influence on surface tension measurements

We have performed surface tension measurements on carbopol gels of different concentrations and yield stresses. Our setup, based on the force exerted by a capillary bridge on two parallel plates, allows us to measure an apparent surface tension of the complex fluid and to investigate the influence of flow history. More precisely the apparent surface tension measured after stretching the bridge is always higher than after compressing it. The difference between the two values is due to the existence of a yield stress in the fluid. The experimental observations are successfully reproduced with a simple elasto-plastic model. The shape of successive stretching-compression cycles can be described by taking into account the yield stress and the elasticity of the gel. We show that the surface tension γLV of yield stress fluids is the mean of the apparent surface tension values only if the elastic modulus is high compared to the yield stress. This work highlights that measurements of thermodynamic quantities are challenged by the fluid out-of-equilibrium state implied by jamming, even at small scales where the shape of the bridge is driven by surface energy. Therefore setups allowing for deformation in opposite directions are relevant for surface tension measurements on yield stress fluids.

Universal and non-universal features in coarse-grained models of flow in disordered solids

We study the two-dimensional (2D) shear flow of amorphous solids within variants of an elastoplastic model, paying particular attention to spatial correlations and time fluctuations of, e.g., local stresses. The model is based on the local alternation between an elastic regime and plastic events during which the local stress is redistributed. The importance of a fully tensorial description of the stress and of the inclusion of (coarse-grained) convection in the model is investigated; scalar and tensorial models yield similar results, while convection enhances fluctuations and breaks the spurious symmetry between the flow and velocity gradient directions, for instance when shear localisation is observed. Besides, correlation lengths measured with diverse protocols are discussed. One class of such correlation lengths simply scale with the spacing between homogeneously distributed, simultaneous plastic events. This leads to a scaling of the correlation length with the shear rate as γ̇(-1/2) in 2D in the athermal regime, regardless of the details of the model. The radius of the cooperative disk, defined as the near-field region in which plastic events induce a stress redistribution that is not amenable to a mean-field treatment, notably follows this scaling. On the other hand, the cooperative volume measured from the four-point stress susceptibility and its dependence on the system size and the shear rate are model-dependent.

Dynamical role of slip heterogeneities in confined flows

We demonstrate that flows in confined systems are controlled by slip heterogeneities below a certain size. To show this we image the motion of soft glassy suspensions in microchannels whose inner walls impose different slip velocities. As the channel height decreases, the flow ceases to have the symmetric shape expected for yield-stress fluids. A theoretical model accounts for the role of slip heterogeneities and captures the velocity profiles. We generalize these results by introducing a length scale, valid for all fluids, below which slip heterogeneities dominate the flow in confined systems. General implications of this notion, concerning the interplay between slip and confinement, are presented.

Comprehensive review on additives of topical dosage forms for drug delivery

Skin is the largest organ of the human body and plays the most important role in protecting against pathogen and foreign matter. Three important modes such as topical, regional and transdermal are widely used for delivery of various dosage forms. Among these modes, the topical dosage forms are preferred because it provides local therapeutic activity when applied to the skin or mucous membranes. Additives or pharmaceutical excipients (non-drug component of dosage form) are used as inactive ingredients in dosage form or tools for structuring dosage forms. The main use of topical dosage form additives are controling the extent of absorption, maintaining the viscosity, improving the stability as well as organoleptic property and increasing the bulk of the formulation. The overall goal of this article is to provide the clinician with information related to the topical dosage form additives and their current major applications against various diseases.

A mesoscopic model for the rheology of soft amorphous solids, with application to microchannel flows

We have studied a mesoscopic model for the flow of amorphous solids. The model is based on key features identified at the microscopic level, namely periods of elastic deformation interspersed with localised rearrangements of particles that induce long-range elastic deformations. These long-range deformations are derived following a continuum mechanics approach, in the presence of solid boundaries, and are included in full in the model. Indeed, they mediate spatial cooperativity in the flow, whereby a localised rearrangement may lead a distant region to yield. In particular, we have simulated a channel flow and found manifestations of spatial cooperativity that are consistent with published experimental observations for concentrated emulsions in microchannels. Two categories of effects are distinguished. On the one hand, the coupling of regions subject to different shear rates, for instance, leads to finite shear rate fluctuations in the seemingly unsheared "plug" in the centre of the channel. On the other hand, there is convincing experimental evidence of a specific rheology near rough walls. We discuss the diverse possible physical origins for this effect, and we suggest that it may be associated with the bumps of particles into surface asperities as they slide along the wall.