Flow of foam through a convergent channel

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.

Three-dimensional liquid foam flow through a hopper resolved by fast X-ray microtomography

We probe the complex rheological behaviour of liquid foams flowing through a conical constriction. With fast X-ray tomographic microscopy we measure in situ the displacement and deformation of up to fifty thousand bubbles at any single time instance while varying systematically the foam liquid fraction, the bubble size and the flow direction - convergent vs. divergent. The large statistics and high spatio-temporal resolution allows to observe and quantify the deviations from a purely viscous flow. We indeed reveal an asymmetry between the convergent and divergent flows associated to the emergence of elastic stresses in the latter case, and enhanced as the liquid fraction is reduced. Such effect is related to the reorientation of the deformed bubbles flowing out of the constriction, from a prolate to an oblate shape in average, while they pass through the hopper waist.

Dislocation mechanisms in the plastic deformation of monodisperse wet foams within an expansion-contraction microfluidic geometry

Densely packed wet foam was subjected to gradual expansion and contraction in a wide (1400-1800 μm) microfluidic channel to study localized plastic deformation events within the monodisperse bubble matrix. Dislocation glide, reflection, nucleation, and dipole transformations from extensional and compressive stresses were observed across a range of fluid flow rates and bubble packing densities. Disparate, cyclic reflections occur in two independent regions of the flowing foam, and the mechanisms of dislocation reflection under tension are expanded. The use of an asymmetric channel created a dichotomy in the model crystalline system between straighter, aligned bubble rows and curved, misaligned rows due to the corresponding streamlines within the channel. The resulting gradient in crystalline alignment had numerous effects on dislocation mobility and plastic deformation. 7/7 dipoles were found to rearrange to a more stable configuration aligned with the foam flow before dissociating. Dislocations comprising 5/5 dipoles (resembling the inverse-Stone-Wales defect in carbon nanostructures) were discovered to pass through one another via intermediate ring structures, which most commonly consisted of three dislocation pairs around a triangular-shaped central bubble.

Ultrasonic measurements of the bulk flow field in foams

The flow field of moving foams is relevant for basic research and for the optimization of industrial processes such as froth flotation. However, no adequate measurement technique exists for the local velocity distribution inside the foam bulk. We have investigated the ultrasound Doppler velocimetry (UDV), providing the first two-dimensional, non-invasive velocity measurement technique with an adequate spatial (10mm) and temporal resolution (2.5Hz) that is applicable to medium scale foam flows. The measurement object is dry aqueous foam flowing upward in a rectangular channel. An array of ultrasound transducers is mounted within the channel, sending pulses along the main flow axis, and receiving echoes from the foam bulk. This results in a temporally and spatially resolved, planar velocity field up to a measurement depth of 200mm, which is approximately one order of magnitude larger than those of optical techniques. A comparison with optical reference measurements of the surface velocity of the foam allows to validate the UDV results. At 2.5Hz frame rate an uncertainty below 15 percent and an axial spatial resolution better than 10mm is found. Therefore, UDV is a suitable tool for monitoring of industrial processes as well as the scientific investigation of three-dimensional foam flows on medium scales.

Non-trivial rheological exponents in sheared yield stress fluids

In this work we discuss possible physical origins of non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. A key ingredient in our scenario is the presence of a self-consistent mechanical noise that stems from the spatial superposition of long-range elastic responses to localized plastically deforming regions. We study analytically a mean-field model, in which this mechanical noise is accounted for by a stress diffusion term coupled to the plastic activity. Within this description we show how a dependence of the shear modulus and/or the local relaxation time on the shear rate introduces corrections to the usual mean-field prediction, concerning the Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the mean-field picture is then shown to be robust with respect to structural disorder and partial relaxation of the local stress. We test this prediction numerically on a mesoscopic lattice model that implements explicitly the long-range elastic response to localized shear transformations, and we conclude on how our scenario might be tested in rheological experiments.

Lamella Division in a Foam Flowing through a Two-Dimensional Porous Medium: A Model Fragmentation Process

We flow a 2D foam through a model 2D porous medium and study experimentally and numerically how the bubble size distribution evolves along the medium. The dominant mechanism of bubble creation is a fragmentation process occurring when bubbles pinched against obstacles are split in two smaller bubbles. We infer the statistics of these individual and local fragmentation events from the experimental data and propose a fragmentation equation to relate that statistics to the evolution of the global size distribution. The predicted evolution shows very good agreement with direct experimental measurements of the bubble size distribution.