arXiv subjects

Anne Juel

Publications and source records attributed to Anne Juel.

At least 19 recordsLinked to original sources

arXiv2026

Yielded-region connectivity governs the onset of gravity-driven spreading in elastoviscoplastic drops

The physical mechanisms controlling the onset of gravity-driven spreading of elastoviscoplastic drops remain unclear because yielding, elastic deformation, and viscous dissipation can occur simultaneously in different regions of the material. To isolate these mechanisms, we perform direct numerical simulations of large axisymmetric drops resting on a thin precursor layer of the same material. Each drop is first equilibrated under gravity, $g$, before being subjected to an additional constant downward acceleration of varying magnitude. The drop rheology is described by the Saramito--Herschel--Bulkley model. Once the rate of deformation becomes negligible under the enhanced forcing, the additional acceleration is removed and the drop is allowed to relax again under gravity alone, enabling the global deformation to be separated into recoverable and unrecoverable components. We find that spreading does not occur simply because some portion of the material yields locally. At low imposed accelerations, yielded regions remain confined within a predominantly solid-like viscoelastic matrix, and the resulting deformation is mostly recoverable. Appreciable spreading is observed when these yielded regions connect to form a continuous fluidised pathway from the drop interior to the free surface, allowing radial material transport. The acceleration required for this transition is governed primarily by the yield stress, whereas elasticity controls the partition between recoverable deformation and spreading by regulating the extent and spatial distribution of yielded regions.

physics.flu-dyn↗

arXiv2026

Compaction in a deformable porous cylinder with elastic boundaries

Perfusion of soft materials such as biological tissue or hydrogels is essential for the functioning of organ and laboratory systems such as chromatographic columns and bioreactors. Inspired by these applications, we model fluid-driven compaction in a long, thin cylindrical porous medium bounded by an impermeable elastic membrane and study how flow regimes relate to elastic parameters. Using a Lagrangian formulation of Darcy flow coupled to small-strain linear elasticity with porosity dependent permeability and elastic moduli, we perform an asymptotic reduction in the small aspect ratio limit and obtain a leading-order nonlinear diffusion equation for the porosity, which we solve numerically. Whereas rigid boundaries produce a compaction plateau, compliant walls exhibit, at most, an intermediate plateau beyond which the flow increases once the imposed pressure becomes comparable to the product of membrane stiffness and initial porosity. When the membrane is less stiff than the porous medium, flow rate can exceed that expected for a rigid medium. A parameter space map distinguishes regimes where plateau and breakthrough occur, where the steady flow rate is below (sub-Darcy) or above (super-Darcy) the undeformable-medium prediction, and delineates the small-strain domain in which the theory applies. An asymptotic solution for negligible gravity captures the departure from the plateau and yields compact expressions for effective permeability and flow rate.

physics.flu-dyn↗

arXiv2026

Sub-Yield Dynamics in Yield-Stress Materials

The mechanical response of yield-stress materials below the yield point remains a subject of debate. Two of the most widely used constitutive models for these materials offer fundamentally conflicting views: one permits plastic flow at all stress levels, the other assumes entirely recoverable viscoelasticity below yield. Using parallel superposition rheometry, we test the sub-yield behaviour of a microgel and an emulsion. When residual slip effects are properly accounted for, both fluids exhibit bounded, periodic strain responses, offering compelling evidence that they do not flow in the studied regime. Our results indicate that the sub-yield regime is underpinned by nonlinear viscoelasticity and underscore the need for improved constitutive relations that capture such effects without treating yielding as a precursor for nonlinearity.

physics.flu-dyn↗

arXiv2026

Network modelling of yield-stress fluid flow in randomly disordered porous media

Yield-stress fluid flow through porous media is governed by a strong coupling between rheology and pore-scale geometry, leading to nonlinear, non-Darcy transport and pronounced channelisation near yielding. We develop a pore-network model for Herschel-Bulkley flow in two-dimensional disordered porous media, including optional wall slip. The network is closed by a physics-based pressure-flow relation for a converging-diverging throat, so that yielding and post-yield transport emerge directly from the pore-scale fluid mechanics without fitted resistance parameters. Benchmarking against direct numerical simulations shows that the model captures both the bulk pressure drop and the evolution of the flow topology from spatially distributed transport to strongly channelised flow. The framework also captures the leading effect of wall slip, which lowers the pressure gradient required for transport and reactivates pathways that remain blocked in the no-slip case. Using the model across different porous geometries, we show that near-yield pressure losses are governed by constriction statistics rather than by an obstacle-scale length. In particular, rescaling with the domain-averaged minimum throat width collapses the plastic-dominated response across porosities, identifying the dissipation-relevant geometric scale for viscoplastic transport in this regime.

physics.flu-dyn↗

arXiv2025

Predicting the distribution of yield-stress fluids in branched pipe manifolds

We develop a one-dimensional network model to predict the steady-state distribution of yield-stress fluids in branched pipe manifolds under wall-slip conditions. The model accounts for major friction losses between junctions and incorporates wall slip through a power-law relation calibrated independently via capillary rheometry. Predictions from the model are validated against both bench-scale experiments and fully resolved computational fluid dynamics simulations, showing excellent agreement across a range of flow conditions. Our results demonstrate that wall slip strongly influences the uniformity of fluid distribution by modifying the relative resistance between outlet branches. Furthermore, we show that the problem can be inverted: measured distribution profiles can be used to estimate slip parameters, offering a practical method for slip characterisation without pressure measurement. This modelling framework is computationally inexpensive, robust, and adaptable to various network configurations, making it a valuable tool for the design and analysis of industrial manifold systems involving viscoplastic fluids.

physics.flu-dyn↗

arXiv2025

Dynamics of evaporating, interconnected droplets

We report on the dynamics of a pair of sessile droplets that are connected by a microchannel, yet open to the atmosphere and hence free to evaporate. Our results reveal that fluid exchange between droplets occurs via a pumping flow driven by differences in hydrostatic and Laplace pressure between the two droplets. Evaporation causes the droplets to slowly lose volume and change shape, which subsequently affects the fluid transport between them. We observe that, for equal contact areas, a larger droplet typically feeds a smaller droplet during evaporation and the flow in the connecting channel is unidirectional. However, for unequal contact areas, the flow can reverse in the connecting channel following a sudden switch in dropletshape that occurs during evaporation. A stability,analysis reveals that the dynamics of the exchange flow are underpinned by a supercritical pitchfork bifurcation. Evaporative volume loss permits the droplet pair to step through a sequence of quasi-stationary states determined by the instantaneous volume of the system. Enforcing unequal contact area unfolds the bifurcation such that droplet-shape switching and the associated flow reversal can be understood in terms of a jump from the disconnected to the connected branch of the bifurcation. This establishes symmetry breaking as a mechanism to induce evaporation-driven flow reversal in connected droplets.

physics.flu-dyn↗

arXiv2025

Interface Fragmentation via Horizontal Vibration: A Pathway to Scalable Monodisperse Emulsification

We present a scalable method for producing monodisperse micro-scale emulsions in a rectangular container holding two stably stratified layers of immiscible liquids by applying horizontal vibration. This setup enables the excitation of a single line of ordered Faraday waves along each end wall when viscous forces dominate interfacial dynamics. Our experiments and theoretical modelling show that the critical non-dimensional acceleration for the breakup of the wave tips in a regular array of droplets scales as $N^{-1/2} \omega^{*3/2}$, where $N$ is the kinematic viscosity ratio and $\omega^{*}$ is the frequency of forcing on the viscous-capillary scale. The droplet diameter can be easily tuned by varying the forcing parameters, and the number of droplets generated per cycle is proportional to the width of the container.

cond-mat.soft↗

arXiv2025

On the oscillatory dynamics of a Saffman--Taylor finger with a bubble at its tip

The complex behaviour of air-liquid interfaces driven into Hele-Shaw channels at high speeds could arise from oscillatory dynamics; yet, both the physical and dynamical mechanisms that lead to interfacial oscillations remain unclear. We extend the experiments by Couder \textit{et. al.} (\textit{Phys. Rev. A}, vol. 34, 1986, p. 5175) to present a systematic investigation of the dynamics that result when a small air bubble is placed at the tip of a steadily propagating air finger in a Hele-Shaw channel. The system can exhibit steady and oscillatory behaviour, and we show that these different behaviours each occur in well-defined regions of the phase space defined by flow rate and bubble size. For sufficiently large flow rates, periodic finger oscillations give way to disordered dynamics characterised by an irregular meandering of the finger's tip. We demonstrate that at a fixed flow rate, the oscillations commence when the bubble size is increased sufficiently so that the decreased in-plane curvature of the bubble tip matches the in-plane curvature of the finger tip. The equality between the two in-plane curvatures causes the axial pressure gradient across the bubble, which drives the finger, to vanish, thus rendering the finger susceptible to lateral perturbations. Differing timescales for finger and bubble restoral under perturbation allow sustained oscillations to develop in the finger-bubble system. The oscillations cease when the bubble is sufficiently large that it can act as the tip of a compound finger. The disordered dynamics at high flow rates are consistent with the transient exploration of unstable periodic states, which suggests that similar dynamics may underlie the observed disordered dynamics in viscous fingering.

physics.flu-dyn↗

arXiv2025

From fluttering to drifting in inertialess sedimentation of achiral particles

There has been much recent interest in the chiral motion of achiral particles that sediment in a viscous fluid in a regime where inertial effects can be neglected. This occurs in a broad range of applications such as those involving biological objects like algae, ultra-thin graphene flakes, or colloidal suspensions. It is known that articles with two planes of symmetry can be categorised as ``settlers'', ``drifters'' or ``flutterers'', where the latter sediment along chiral trajectories despite their achiral shapes. Here we analyse the sedimentation of circular disks bent into a U-shape (``flutterers'') and show how their behaviour changes when we break one of their symmetries by pinching the disks along their axis. The ``fluttering'' behaviour is found to be robust to such shape changes, with the trajectories now evolving towards helical paths. However, the behaviour changes when the degree of pinching becomes too strong, at which point the particles become ``drifters'' which sediment steadily without rotation. We establish criteria for the transition between the two types of behaviour and confirm our predictions in experiments. Finally, we discuss the implications of our observations for the dispersion of dilute suspensions made of such particles.

cond-mat.soft↗

arXiv2025

Advancing sustainable energy solutions with microfluidic porous media

The transition to a sustainable, low-carbon energy future requires transformative advancements in energy and environmental technologies. Carbon capture and sequestration, underground hydrogen storage, and nuclear waste geological disposal will be central aspects of a sustainable energy future, both for mitigating CO2 emissions and providing green energy. A comprehensive understanding of multiphase flow through porous media, along with reactive transport and microbial activities, is essential for assessing the feasibility and managing the risks of these technologies. Microfluidic porous media platforms have emerged as powerful tools for the direct visualization of multiphase reactive flow in porous media and eventually optimizing these multiple physicochemical and biological processes. This review highlights critical scientific challenges associated with these sustainable energy solutions and summarizes the state-of-the-art microfluidic techniques for studying the interplay between multiphase flow, reactive transport, and biological effects in porous media. We provide a comprehensive overview of how these microfluidic approaches enhance the understanding of fundamental pore-scale dynamics and bridge the gap between pore-scale events and large-scale processes. This review is expected to promote both experimental and theoretical understanding of multiphase reactive flow in porous media, thereby informing material design, process optimization, and predictive modeling for scalable implementation. By fostering interdisciplinary collaboration across microfluidics, fluid mechanics, geophysics, materials science, and subsurface engineering, we hope to accelerate innovation and advance sustainable energy solutions.

physics.flu-dyn↗

arXiv2024

Wall-damped Faraday waves in horizontally oscillating two-layer fluid flows

We study experimentally the onset of Faraday waves near the endwalls of rectangular vessel containing two stably-stratified fluid layers, subject to horizontal oscillations. These subharmonic waves (SWs) are excited, because the horizontal inertial forcing drives a harmonic propagating wave which displaces the interface in the vertical direction at the endwalls. We find that the onset of SWs is regulated by a balance between capillary and viscous forces, where the rate of damping is set by the Stokes layer thickness at the wall rather than the wavelength of the SWs. We model the onset of SWs with a weakly-damped Mathieu equation and find that the dimensional critical acceleration scales as $\nu_m^{1/2} \omega^{3/2}$, where $\nu_m$ is the mean viscosity and $\omega$ is the frequency of forcing, in excellent agreement with the experiment over a wide range of parameters.

physics.flu-dyn↗

arXiv2024

U-shaped disks in Stokes flow: Chiral sedimentation of a non-chiral particle

We study the sedimentation of U-shaped circular disks in the Stokes limit of vanishing inertia. We simulate the flow past such disks using a finite-element-based solution of the 3D Stokes equations, accounting for the integrable singularities that develop along their edges. We show that the purely vertical sedimentation of such disks in their upright- [upside-down-] U orientation is unstable to perturbations about their pitching [rolling] axes. The instability is found to depend only weakly on the size of the container in which the disks sediment, allowing us to analyse their behaviour based on the resistance matrix which governs the evolution of the disk's six rigid-body degrees of freedom in an unbounded fluid. We show that the governing equations can be reduced to two ODEs which describe the disk's inclination against the direction of gravity. A phase-plane analysis, results of which are in good agreement with experiments, reveals that the two instabilities generally cause the disk to sediment along complex spiral trajectories while it alternates between pitching- and rolling-dominated motions. The chirality of the trajectories is set by the initial conditions rather than the (non-chiral) shape of the disk. For certain initial orientations, the disk retains its inclination and sediments along a perfectly helical path. The observed behaviour is fundamentally different from that displayed by flat circular disks which sediment without any reorientation. We therefore study the effect of variations in the disk's curvature to show how in the limit of vanishing curvature the behaviour of a flat disk is recovered.

physics.flu-dyn↗

arXiv2024

Periodic dynamics in viscous fingering

The displacement of a viscous liquid by air in the narrow gap between two parallel plates - a Hele-Shaw channel - is an exemplar of complex pattern formation. Typically, bubbles or fingers of air propagate steadily at low values of the driving parameter. However, as the driving parameter increases, they can exhibit disordered pattern-forming dynamics. In this paper, we demonstrate experimentally that a remote perturbation of the bubble's tip can drive time-periodic bubble propagation: a fundamental building block of complex unsteady dynamics. We exploit the propensity of a group of bubbles to self-organise into a fixed spatial arrangement in a Hele-Shaw channel with a centralised depth-reduction in order to apply a sustained perturbation to a bubble's shape as it propagates. We find that the bubble with a perturbed shape begins to oscillate after the system undergoes a supercritical Hopf bifurcation upon variation of the tip perturbation and dimensionless flow rate. The oscillation cycle features the splitting of the bubble's tip and advection of the resulting finger-like protrusion along the bubble's length until it is absorbed by the bubble's advancing rear. The restoral of the bubble's tip follows naturally because the system is driven by a fixed flow rate and the perturbed bubble is attracted to the weakly unstable, steadily propagating state that is set by the ratio of imposed viscous and capillary forces. Our results suggest a generic mechanism for time-periodic dynamics of propagating curved fronts subject to a steady shape perturbation.

physics.flu-dyn↗

arXiv2023

Light-scattering reconstruction of transparent shapes using neural networks

The accurate characterisation of the 3D deformations of slender fibres and thin sheets in flow, is a key experimental challenge in the study of particle-laden flows. We propose a high-resolution, single-camera method to visualise non-intrusively the shape of a transparent crumpled sheet, as it translates, rotates and deforms. We perform periodic scans of the crumpled shape by illuminating it with a sequence of stacked light sheets at a rate much faster than its deformation and image the scattered light signal in a plane near-orthogonal to the plane of lighting. Processing of the data using a pinhole camera model yields a noisy spatio-temporal dataset of the strongly deformed time-evolving surface of the sheet, which we reconstruct in 3D using a neural autoencoder. We validate the robustness of the shape reconstruction algorithm to noise using synthetic data sets, and demonstrate the accurate reconstruction of laboratory sedimentation experiments with elastic disks. We find that the inclusion of isometricity-enforcing penalties into the cost function of the autoencoder enables us to robustly reconstruct highly folded shapes, where different regions of the sheet overlap.

physics.flu-dyn↗

arXiv2023

Robust fabrication of ultra-soft tunable PDMS microcapsules as a biomimetic model for red blood cells

Microcapsules with liquid cores encapsulated by thin membranes have many applications in science, medicine and industry. In this paper, we design a suspension of microcapsules which flow and deform like red blood cells (RBCs), as a valuable tool to investigate microhaemodynamics. A reconfigurable and easy-to-assemble 3D nested glass capillary device is used to robustly fabricate water-oil-water double emulsions which are then converted into spherical microcapsules with hyperelastic membranes by cross-linking the polydimethylsiloxane (PDMS) layer coating the droplets. The resulting capsules are monodisperse to within 1% and can be made in a wide range of size and membrane thickness. We use osmosis to deflate by 36% initially spherical capsules of diameter 350 {\mu}m and a membrane thickness of 4% of their radius, in order to match the reduced volume of biconcave RBCs. We compare the propagation of initially spherical and deflated capsules under constant volumetric flow in cylindrical capillaries of different confinements. We find that only deflated capsules deform broadly similarly to RBCs over a similar range of capillary numbers (Ca) -- the ratio of viscous to elastic forces. Similarly to the RBCs, the microcapsules transition from a symmetric 'parachute' to an asymmetric 'slipper'-like shape as Ca increases within the physiological range, demonstrating intriguing confinement-dependent dynamics. In addition to biomimetic RBC properties, high-throughput fabrication of tunable ultra-soft microcapsules could be further functionalized and find applications in other areas of science and engineering

cond-mat.soft↗

arXiv2023

Stable bubble formations in a Hele-Shaw channel

Deformable bubbles propagated by the flow of a viscous liquid in a planar Hele-Shaw channel of uniform depth tend to travel steadily along the channel's streamwise axis and pairs of neighbouring bubbles will either separate or coalesce because an individual bubble's propagation speed increases monotonically with its size. Thus, any group of bubbles will eventually rearrange itself in order of decreasing size and all of the bubbles will separate. We show that, by introducing a small geometric perturbation to the channel in the form of an axially-uniform depth reduction along its centreline, the system supports a multitude of stable bubble formations and this can disrupt the usual reordering by bubble size. The constituent bubbles of a stable formation lie in alternation on opposite sides of the depth-perturbation, retain fixed shapes and propagate steadily at the same speed. A stable formation is always led by the smallest of its constituent bubbles, which would be the slowest bubble in isolation. The leading bubble propagates as if it were isolated and the trailing bubbles reduce their speeds by adjusting their shapes and overlaps of the depth-perturbation in the perturbation fields of their preceding nearest-neighbours in order to match that of the leading bubble. The trailing bubbles can be arranged in any order and, hence, the number of stable formations increases factorially as the number of bubbles is increased.

physics.flu-dyn↗

arXiv2022

The propagation of air fingers into an elastic branching network

We study experimentally the propagation of an air finger through the Y-bifurcation of an elastic, liquid-filled Hele-Shaw channel, as a benchtop model of airway reopening. With channel compliance provided by an elastic upper boundary, we can impose collapsed channel configurations into which we inject air with constant volume-flux. We typically observe steady finger propagation in the main channel, which is lost ahead of the Y-bifurcation but subsequently recovered in the daughter channels. At low levels of initial collapse, steady finger shapes and bubble pressure in the daughter channels map onto those in the main channel, despite small differences in initial collapse in different parts of the Y-channel. However, at higher levels of initial collapse where the elastic sheet almost touches the bottom boundary of the channel, experimentally indistinguishable fingers in the main channel can lead to multiple states of reopening of the daughter channels. The downstream distance at which steady propagation is recovered in the daughter channels also varies considerably with injection flow rate and initial collapse because of a transition in the mechanics regulating finger propagation. We find that the characteristic time and length-scales of this recovery are largest in the regime where viscous and surface tension forces dominate at low flow rate and/or low initial collapse, and that they decrease towards a constant plateau reached in the limit where elastic and surface tension forces balance at high flow rate and/or high initial collapse. Our findings suggest that practical networks are unlikely to comprise long enough channels for steady state propagation to remain established.

physics.flu-dyn↗

arXiv2020

Sorting of capsules according to their stiffness: from principle to application

We assess experimentally the ability of a simple flow-based sorting device, recently proposed numerically by [Zhu et al., Soft Matter, 2014, 10, 7705-7711], to separate capsules according to their stiffness. The device consists of a single pillar with a half-cylinder cross-section which partially obstructs a flow channel so that initially centred, propagating capsules deform and circumvent the obstacle into an expanding channel (or diffuser). We perform experiments with millimetric capsules of fixed size which indicate that the deviation of the capsule in the diffuser varies monotonically with a capillary number - the ratio of viscous to elastic stresses - where the elastic stresses are measured independently to include the effects of pre-inflation, membrane thickness and material properties. We find that soft capsules with resistance to deformation differing by a factor of 1.5 can be reliably separated in the diffuser but that experimental variability increases significantly with capsule stiffness. We extend the study to populations of microcapsules with size polydispersity. We find that the combined effects of increasing capsule deformability and relative constriction of the device with increasing capsule size enable the tuning of the imposed flow so that capsules can be separated based on their shear modulus but irrespectively of their size.

cond-mat.soft↗