Boundary conditions for soft glassy flows: slippage and surface fluidization

Directional Fluidity of Dense Emulsion Activated by Transverse Wedge-Shaped Microroughness

The handling and fluidization of amorphous soft solids, such as emulsions, foams, or gels, is crucial in many technological processes. This is generally achieved by applying mechanical stress that overcomes a critical threshold, known as yield stress, below which these systems behave as elastic solids. However, the interaction with the walls can facilitate the transition from solid to fluid by activating rearrangements of the fluid constituents close to the wall, resulting in increased fluidity of the system up to distances greater than the spatial scale of the rearrangements. We address the impact of wedge-shaped microroughness on activating the fluidization of emulsion droplets in pressure-driven flow through microfluidic channels. We realize the micro wedges by maskless photolithography to texture one wall of the channel and measure the velocity profiles for flow directed accordingly and against the increasing ramp of the wedge-shaped grooves. We report the enhancement of the emulsion flow in the direction of the climbing ramp of the wedge activated by increasing the magnitude of the pressure gradient. A gain for the volumetric flow rate is registered with respect to the opposite direction as being to 30%, depending on the pressure drop.

Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

Interplay between wall slip and shear banding in a thixotropic yield stress fluid

We study the local dynamics of a thixotropic yield stress fluid that shows a pronounced non-monotonic flow curve. This mechanically unstable behavior is generally not observable from standard rheometry tests, resulting in a stress plateau that stems from the coexistence of a flowing band with an unyielded region below a critical shear rate c. Combining ultrasound velocimetry with standard rheometry, we discover an original shear-banding scenario in the decreasing branch of the flow curve of model paraffin gels, in which the velocity profile of the flowing band is set by the applied shear rate  instead of c. As a consequence, the material slips at the walls with a velocity that shows a non-trivial dependence on the applied shear rate. To capture our observations, we propose a differential version of the so-called lever rule, describing the extent of the flowing band and the evolution of wall slip with shear rate. This phenomenological model holds down to very low shear rates, at which the dimension of the flowing band becomes comparable to the size of the individual wax particles that constitute the gel microstructure, leading to cooperative effects. Our approach provides a framework where constraints imposed in the classical shear-banding scenario can be relaxed, with wall slip acting as an additional degree of freedom.

Emulsions in microfluidic channels with asymmetric boundary conditions and directional surface roughness: stress and rheology

The flow of emulsions in confined microfluidic channels is affected by surface roughness. Directional roughness effects have recently been reported in channels with asymmetric boundary conditions featuring a flat wall, and a wall textured with directional roughness, the latter promoting a change in the velocity profiles when the flow direction of emulsions is inverted [D. Filippi et al., Adv. Mater. Technol., 2023, 8, 2201748]. An operative protocol is needed to reconstruct the stress profile inside the channel from velocity data to shed light on the trigger of the directional response. To this aim, we performed lattice Boltzmann numerical simulations of the flow of model emulsions with a minimalist model of directional roughness in two dimensions: a confined microfluidic channel with one flat wall and the other patterned by right-angle triangular-shaped posts. Simulations are essential to develop a protocol based on mechanical arguments to reconstruct stress profiles. Hence, one can analyze data to relate directional effects in velocity profiles to different rheological responses close to the rough walls associated with opposite flow directions. We finally show the universality of this protocol by applying it to other realizations of directional roughness by considering experimental data on emulsions in a microfluidic channel featuring a flat wall and a wall textured by herringbone-shaped roughness.

Controlling rheology via boundary conditions in dense granular flows

Boundary shape, particularly roughness, strongly controls the amount of wall slip in dense granular flows. In this paper, we aim to quantify and understand which aspects of a dense granular flow are controlled by the boundary conditions, and to incorporate these observations into a cooperative nonlocal model characterizing slow granular flows. To examine the influence of boundary properties, we perform experiments on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall; the latter is selected among 6 walls with various roughnesses, local concavity, and compliance. We find that we can successfully capture the full flow profile using a single set of empirically determined model parameters, with only the wall slip velocity set by direct observation. Through the use of photoelastic particles, we observe how the internal stresses fluctuate more for rougher boundaries, corresponding to a lower wall slip, and connect this observation to the propagation of nonlocal effects originating from the wall. Our measurements indicate a universal relationship between dimensionless fluidity and velocity.

Deformation profiles and microscopic dynamics of complex fluids during oscillatory shear experiments

Oscillatory shear tests are widely used in rheology to characterize the linear and non-linear mechanical response of complex fluids, including the yielding transition. There is an increasing urge to acquire detailed knowledge of the deformation field that is effectively present across the sample during these tests; at the same time, there is mounting evidence that the macroscopic rheological response depends on the elusive microscopic behavior of the material constituents. Here we employ a strain-controlled shear-cell with transparent walls to visualize and quantify the dynamics of tracers embedded in various cyclically sheared complex fluids, ranging from almost-ideal elastic to yield stress fluids. For each sample, we use image correlation processing to measure the macroscopic deformation field, and echo-differential dynamic microscopy to probe the microscopic irreversible sample dynamics in reciprocal space; finally, we devise a simple scheme to spatially map the rearrangements in the sheared sample, once again without tracking the tracers. For the yield stress sample, we obtain a wave-vector dependent characterization of shear-induced diffusion across the yielding transition, which is accompanied by a three-order-of-magnitude speed-up of the dynamics and by a transition from localized, intermittent rearrangements to a more spatially homogeneous and temporally uniform activity. Our tracking free approach is intrinsically multi-scale, can successfully discriminate between different types of dynamics, and can be automated to minimize user intervention. Applications are many, as it can be translated to other imaging modes, including fluorescence, and can be used with sub-resolution tracers and even without tracers, for samples that provide intrinsic optical contrast.

Size-dependence of the flow threshold in dense granular materials

The flow threshold in dense granular materials is typically modeled by local, stress-based criteria. However, grain-scale cooperativity leads to size effects that cannot be captured with local conditions. In a widely studied example, flows of thin layers of grains down an inclined surface exhibit a size effect whereby thinner layers require more tilt to flow. In this paper, we consider the question of whether the size-dependence of the flow threshold observed in inclined plane flow is configurationally general. Specifically, we consider three different examples of inhomogeneous flow - planar shear flow with gravity, annular shear flow, and vertical chute flow - using two-dimensional discrete-element method calculations and show that the flow threshold is indeed size-dependent in these flow configurations, displaying additional strengthening as the system size is reduced. We then show that the nonlocal granular fluidity model - a nonlocal continuum model for dense granular flow - is capable of quantitatively capturing the observed size-dependent strengthening in all three flow configurations.

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.

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.

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.

Avalanche-like fluidization of a non-Brownian particle gel

We report on the fluidization dynamics of an attractive gel composed of non-Brownian particles made of fused silica colloids. Extensive rheology coupled to ultrasonic velocimetry allows us to characterize the global stress response together with the local dynamics of the gel during shear startup experiments. In practice, after being rejuvenated by a preshear, the gel is left to age for a time tw before being subjected to a constant shear rate [small gamma, Greek, dot above]. We investigate in detail the effects of both tw and [small gamma, Greek, dot above] on the fluidization dynamics and build a detailed state diagram of the gel response to shear startup flows. The gel may display either transient shear banding towards complete fluidization or steady-state shear banding. In the former case, we unravel that the progressive fluidization occurs by successive steps that appear as peaks on the global stress relaxation signal. Flow imaging reveals that the shear band grows until complete fluidization of the material by sudden avalanche-like events which are distributed heterogeneously along the vorticity direction and correlated to large peaks in the slip velocity at the moving wall. These features are robust over a wide range of tw and [small gamma, Greek, dot above] values, although the very details of the fluidization scenario vary with [small gamma, Greek, dot above]. Finally, the critical shear rate [small gamma, Greek, dot above]* that separates steady-state shear-banding from steady-state homogeneous flow depends on the width of the shear cell and exhibits a nonlinear dependence with tw. Our work brings about valuable experimental data on transient flows of attractive dispersions, highlighting the subtle interplay between shear, wall slip and aging whose modeling constitutes a major challenge that has not been met yet.

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.

Non-local rheology in dense granular flows: Revisiting the concept of fluidity

The aim of this article is to discuss the concepts of non-local rheology and fluidity, recently introduced to describe dense granular flows. We review and compare various approaches based on different constitutive relations and choices for the fluidity parameter, focusing on the kinetic elasto-plastic model introduced by Bocquet et al. (Phys. Rev. Lett 103, 036001 (2009)) for soft matter, and adapted for granular matter by Kamrin et al. (Phys. Rev. Lett. 108, 178301 (2012)), and the gradient expansion of the local rheology μ(I) that we have proposed (Phys. Rev. Lett. 111, 238301 (2013)). We emphasise that, to discriminate between these approaches, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics.

Effective Wall Friction in Wall-Bounded 3D Dense Granular Flows

We report numerical simulations on granular shear flows confined between two flat but frictional sidewalls. Novel regimes differing by their strain localization features are observed. They originate from the competition between dissipation at the sidewalls and dissipation in the bulk of the flow. The effective friction at sidewalls is characterized (effective friction coefficient and orientation of the friction force) for each regime, and its interdependence with slip and force fluctuations is pointed out. We propose a simple scaling law linking the slip velocity to the granular temperature in the main flow direction which leads naturally to another scaling law for the effective friction.

Apparent wall slip in non-Brownian hard-sphere suspensions

We analyze apparent wall slip, the reduction of particle concentration near the wall, in hard-sphere suspensions at concentrations well below the jamming limit utilizing a continuum level diffusion model. The approach extends a constitutive equation proposed earlier with two additional potentials describing the effects of gravitation and wall-particle repulsion. We find that although both mechanisms are shear independent by nature, due to the shear-rate-dependent counter-balancing particle migration fluxes, the resulting net effect is non-linearly shear dependent, causing larger slip at small shear rates. In effect, this shows up in the classically measured flow curves as a mild shear thickening regime at the transition from small to intermediate shear rates.

Poiseuille flow of soft glasses in narrow channels: from quiescence to steady state

Using numerical simulations, the onset of Poiseuille flow in a confined soft glass is investigated. Starting from the quiescent state, steady flow sets in at a time scale which increases with a decrease in applied forcing. At this onset time scale, a rapid transition occurs via the simultaneous fluidization of regions having different local stresses. In the absence of steady flow at long times, creep is observed even in regions where the local stress is larger than the bulk yielding threshold. Finally, we show that the time scale to attain steady flow depends strongly on the history of the initial state.