arXiv subjects

Julien R. Landel

Publications and source records attributed to Julien R. Landel.

18 recordsLinked to original sources

arXiv2026

Transport and removal of a passive tracer in porous media employing surface washing

This experimental study investigates the dynamics of surface washing to remove a passive tracer from a porous plate by a gravity-driven liquid film across its surface. A disodium fluorescein tracer is introduced at the surface of a water-saturated porous plate and allowed to diffuse into the plate for a number of hours before a film of water solution flows over its surface to extract and transport the tracer away. The removal rate of the tracer is monitored quantitatively by using fluorescence measurements to determine the concentration in the effluent from the washing process. These measurements are supplemented by dye-attenuation imaging, which provides mainly qualitative insights about the tracer's concentration distribution on the porous plate surface. Our findings reveal a three-stage mass-transport process consisting of an initial period of rapid removal of the tracer found within the surface roughness, followed by a period of slower removal, which appears to be limited by vertical diffusion, and a third stage of accelerated advection-dominated removal when the tracer-rich region that was transported downstream during the second stage reaches the downstream boundary of the porous plate. A parametric study explores the influence of the characteristics of the washing film, the permeability of the porous plate, the amount and initial spatial extent of the tracer on the porous plate and the tracer's diffusive penetration depth on the mass removal rates. Our insights offer practical guidance for optimising surface washing protocols for porous systems in industrial and environmental applications.

physics.flu-dyn↗

arXiv2025

Drag reduction in surfactant-contaminated superhydrophobic channels at high Péclet numbers

Motivated by microfluidic applications, we investigate drag reduction in laminar pressure-driven flows in channels with streamwise-periodic superhydrophobic surfaces (SHSs) contaminated with soluble surfactant. We develop a model in the long-wave and weak-diffusion limit, where the streamwise SHS period is large compared to the channel height and the Péclet number is large. Using asymptotic and numerical techniques, we determine the influence of surfactant on drag reduction in terms of the relative strength of advection, diffusion, Marangoni effects and bulk-surface exchange. In scenarios with strong exchange, the drag reduction exhibits a complex dependence on the thickness of the bulk-concentration boundary layer and surfactant strength. Strong Marangoni effects immobilise the interface through a linear surfactant distribution, whereas weak Marangoni effects yield a quasi-stagnant cap. The quasi-stagnant cap has an intricate structure with an upstream slip region, followed by intermediate inner regions, and a quasi-stagnant region that is mediated by weak bulk diffusion. The quasi-stagnant region differs from the immobile region of a classical stagnant cap, observed for instance in surfactant-laden air bubbles in water, by displaying weak slip. As exchange weakens, the bulk and interface decouple: the surfactant distribution is linear when the surfactant is strong, whilst it forms a classical stagnant cap when the surfactant is weak. The asymptotic solutions offer closed-form predictions of drag reduction across much of the parameter space, providing practical utility and enhancing understanding of surfactant dynamics in flows over SHSs.

physics.flu-dyn↗

arXiv2024

Pattern Formation in Crumpled Hydrogel upon Rapid Dehydration with Acetone

From microactuators to biological tissues, non-porous materials with the ability to strongly expand when in contact with a solvent are ubiquitous. Consequently, the swelling of polymer systems such as hydrogel has received recently much research attention. However, the related dehydration of these systems has received much less attention. Here, we present experiments investigating the rapid dehydration of a swollen hydrogel sheet whose surface exhibits a transient crumpling instability characterised by line segments of cusps patterning the surface of the gel into an array of bumps. We perform this dehydration through immersion in acetone, which is highly miscible in water, but poorly miscible in the hydrogel. We report the onset of a fascinating pattern formation where regions of the hydrogel sheet turn turbid. We find that the emerging pattern is independent of the overall extent of the hydrated swollen surface. The pattern wavelength only depends on the duration of hydration before immersion in acetone, growing temporally with a power law behaviour. We conclude through drawing comparisons between features of this dehydration induced pattern and the original crumpling instability in the water swollen hydrogel sheet.

cond-mat.soft↗

arXiv2024

Dye Attenuation Without Dye: Quantifying Concentration Fields with Short-wave Infrared Imaging

Dye attenuation, or photometric imaging, is an optical technique commonly used in fluid dynamics to measure tracer concentration fields and fluid thicknesses under the assumption that the motion of the dye is representative of the fluid motion and that its presence does not affect the behaviour of the system. However, in some systems, particularly living biological systems or those with strong chemical interactions and reactions, the addition of dye may non-trivially influence the system and may not follow the fluid containing it. To overcome this, we demonstrate how short-wave infrared imaging can be used to measure concentration and height profiles of water and other liquids without the introduction of dye for heights down to 0.2mm with spatial and temporal resolutions of the order of 50 microns per pixel and 120 fps respectively. We showcase the utility of this technique by demonstrating its ability to accurately track the temporal evolution of the total water content of two model systems, namely a water drop spreading on a glass slide and spreading within a hydrogel sheet, validating both against an analytical mass balance. Finally, we discuss how the spectral resolution of the present setup could be increased to the point that concentrations within a multi-component system containing more than one type of liquid could be quantified.

physics.flu-dyn↗

arXiv2024

Particle image velocimetry and modelling of horizontal coherent liquid jets impinging on and draining down a vertical wall

The flow patterns created by a coherent horizontal liquid jet impinging on a vertical wall atmoderate flow rates (jet flowrates 0.5-4.0 L min-1, jet velocities 2.6-21 m s-1) are studied withwater on glass, polypropylene and polymethylmethacrylate (acrylic, Perspex(R)) using a novelparticle image velicometry (PIV) technique employing nearly opaque fluid doped withartificial pearlescence to track surface velocity. Flow patterns similar to those reported inprevious studies are observed on each substrate: their dimensions differed owing to theinfluence of wall material on contact angle. The dimensions are compared with models for (i)the radial flow zone, reported by Wang et al. (2013b), and the part of the draining film belowthe jet impingement point where it narrows to a node. For (ii), the model presented by Mertenset al. (2005) is revised to include a simpler assumed draining film shape and an alternativeboundary condition accounting for surface tension effects acting at the film edge. This refinedmodel gives equally good or better fits to the experimental data. The effective contact anglewhich gives good agreement with the data is found to lie between the measured quasi-staticadvancing and receding contact angles, at approximately half the advancing value. The PIVmeasurements confirmed the existence of a thin fast moving film with radial flow surroundingthe point of impingement, and a wide draining film bounded by ropes of liquid below theimpingement point. While these measurements generally support the predictions of existingmodels, these models assume that the flow is steady. In contrast, surface waves were evident inboth regions and this partly explains the difference between the measured surface velocity andthe values estimated from the models.

physics.flu-dyn↗

arXiv2024

Three-dimensional diffusive-thermal instability of flames propagating in a plane Poiseuille flow

The three-dimensional diffusive-thermal stability of a two-dimensional flame propagating in a Poiseuille flow is examined. The study explores the effect of three non-dimensional parameters, namely the Lewis number $Le$, the Damköhler number $Da$, and the flow Peclet number $Pe$. Wide ranges of the Lewis number and the flow amplitude are covered, as well as conditions corresponding to small-scale narrow ($Da \ll 1$) to large-scale wide ($Da \gg 1$) channels. The instability experienced by the flame appears as a combination of the traditional diffusive-thermal instability of planar flames and the recently identified instability corresponding to a transition from symmetric to asymmetric flame. The instability regions are identified in the $Le$-$Pe$ plane for selected values of $Da$ by computing the eigenvalues of a linear stability problem. These are complemented by two- and three-dimensional time-dependent simulations describing the full evolution of unstable flames into the non-linear regime. In narrow channels, flames are found to be always symmetric about the mid-plane of the channel. Additionally, in these situations, shear flow-induced Taylor dispersion enhances the cellular instability in $Le<1$ mixtures and suppresses the oscillatory instability in $Le>1$ mixtures. In large-scale channels, however, both the cellular and the oscillatory instabilities are expected to persist. Here, the flame has a stronger propensity to become asymmetric when the mean flow opposes its propagation and when $Le<1$; if the mean flow facilitates the flame propagation, then the flame is likely to remain symmetric about the channel mid-plane. For $Le>1$, both symmetric and asymmetric flames are encountered and are accompanied by temporal oscillations.

physics.flu-dyn↗

arXiv2024

Confinement-induced drift in Marangoni-driven transport of surfactant: a Lagrangian perspective

Successive drops of coloured ink mixed with surfactant are deposited onto a thin film of water to create marbling patterns in the Japanese art technique of Suminagashi. To understand the physics behind this and other applications where surfactant transports adsorbed passive matter at gas-liquid interfaces, we investigate the Lagrangian trajectories of material particles on the surface of a thin film of a confined viscous liquid under Marangoni-driven spreading by an insoluble surfactant. We study a model problem in which several deposits of exogenous surfactant simultaneously spread on a bounded rectangular surface containing a pre-existing endogenous surfactant. We derive Eulerian and Lagrangian formulations of the equations governing the Marangoni-driven surface flow. Both descriptions show how confinement can induce drift and flow reversal during spreading. The Lagrangian formulation captures trajectories without the need to calculate surfactant concentrations; however, concentrations can still be inferred from the Jacobian of the map from initial to current particle position. We explore a link between thin-film surfactant dynamics and optimal transport theory to find the approximate equilibrium locations of material particles for any given initial condition by solving a Monge-Ampère equation. We find that, as the endogenous surfactant concentration $δ$ vanishes, the equilibrium shapes of deposits using the Monge-Ampère approximation approach polygons with corners curving in a self-similar manner over lengths scaling as $δ^{1/2}$. We explore how Suminagashi patterns may be produced by using computationally efficient successive solutions of the Monge-Ampère equation.

physics.flu-dyn↗

arXiv2024

Unsteady evolution of slip and drag in surfactant-contaminated superhydrophobic channels

Recognising that surfactants can impede the drag reduction resulting from superhydrophobic surfaces (SHSs), we investigate the impact of spatio-temporal fluctuations in surfactant concentration on the drag-reduction properties of SHSs. We model the unsteady transport of soluble surfactant in a channel flow bounded by two SHSs. The flow is laminar, pressure-driven, and the SHSs are periodic in the streamwise and spanwise directions. We assume that the channel length is much longer than the streamwise period, the streamwise period is much longer than the channel height and spanwise period, and bulk diffusion is sufficiently strong for cross-channel concentration gradients to be small. By combining long-wave and homogenisation theories, we derive an unsteady advection-diffusion equation for surfactant-flux transport over the length of the channel, which is coupled to a quasi-steady advection-diffusion equation for surfactant transport over individual plastrons. As diffusion over the length of the channel is typically small, the surfactant flux is governed by a nonlinear wave equation. In the fundamental case of the transport of a bolus of surfactant, we predict its propagation speed and describe its nonlinear evolution via interaction with the SHS. The propagation speed can fall below the average streamwise velocity as the surfactant adsorbs and rigidifies the plastrons. Smaller concentrations of surfactant are advected faster than larger ones, so that wave-steepening effects can lead to shock formation in the surfactant-flux distribution. Our asymptotic results reveal how unsteady surfactant transport can affect the spatio-temporal evolution of the slip velocity, drag reduction and effective slip length in SHS channels.

physics.flu-dyn↗

arXiv2023

Exogenous-endogenous surfactant interaction yields heterogeneous spreading in complex branching networks

Experiments have shown that surfactant introduced to a liquid-filled maze can find the solution path. We reveal how the maze-solving dynamics arise from interactions between the added surfactant and endogenous surfactant present at the liquid surface. We simulate the dynamics using a nonlinear model solved with a discrete mimetic scheme on a graph. Endogenous surfactant transforms local spreading into a non-local problem with an omniscient view of the maze geometry, key to the maze-solving dynamics. Our results offer insight into surfactant-driven transport in complex networks such as lung airways.

physics.flu-dyn↗

arXiv2023

Laminar drag reduction in surfactant-contaminated superhydrophobic channels

While superhydrophobic surfaces (SHSs) show promise for drag reduction applications, their performance can be compromised by traces of surfactant, which generate Marangoni stresses that increase drag. This question is addressed for soluble surfactant in a three-dimensional laminar channel flow, with periodic SHSs on both walls. We assume that diffusion is sufficiently strong for cross-channel concentration gradients to be small. Exploiting a long-wave theory that accounts for a rapid transverse Marangoni-driven flow, we derive a one-dimensional model for surfactant evolution, which allows us to predict the drag reduction across the parameter space. The system exhibits multiple regimes, involving competition between Marangoni effects, bulk and interfacial diffusion, advection and shear dispersion. We map out asymptotic regions in the high-dimensional parameter space, deriving approximations of the drag reduction in each region and comparing them to numerical simulations. Our atlas of maps provides a comprehensive analytical guide for designing surfactant-contaminated channels with SHSs, to maximise the drag reduction in applications.

physics.flu-dyn↗

arXiv2023

A single parameter can predict surfactant impairment of superhydrophobic drag reduction

Recent experimental and computational investigations have shown that trace amounts of surfactants, unavoidable in practice, can critically impair the drag reduction of superhydrophobic surfaces (SHSs), by inducing Marangoni stresses at the air-liquid interface. However, predictive models for realistic SHS geometries do not yet exist, which has limited the understanding and mitigation of these adverse surfactant effects. To address this issue, we derive a model for laminar, three-dimensional flow over SHS gratings as a function of geometry and soluble surfactant properties, which together encompass 10 dimensionless groups. We establish that the grating length $g$ is the key geometric parameter and predict that the ratio between actual and surfactant-free slip increases with $g^2$. Guided by our model, we perform synergistic numerical simulations and microfluidic experiments, finding good agreement with the theory as we vary surfactant type and SHS geometry. Our model also enables the estimation, based on velocity measurements, of a priori unknown properties of surfactants inherently present in microfluidic systems. For SHSs, we show that surfactant effects can be predicted by a single parameter, representing the ratio between the grating length and the interface length scale beyond which the flow mobilizes the air-water interface. This mobilization length is more sensitive to the surfactant chemistry than to its concentration, such that even trace-level contaminants may significantly increase drag if they are highly surface active. These findings advance the fundamental understanding of realistic interfacial flows and provide practical strategies to maximize superhydrophobic drag reduction.

physics.flu-dyn↗

arXiv2023

A model for slip and drag in turbulent flows over superhydrophobic surfaces with surfactant

Superhydrophobic surfaces (SHSs) can reduce the friction drag in turbulent flows. In the laminar regime, it has been shown that trace amounts of surfactant can negate this drag reduction, at times rendering these surfaces no better than solid walls (Peaudecerf et al., Proc. Natl. Acad. Sci. USA 114(28), 7254-9, 2017). However, surfactant effects on the drag-reducing properties of SHSs have not yet been studied under turbulent flow conditions, where predicting the effects of surfactant in direct numerical simulations remains expensive by today's standards. We present a model for turbulent flow inclusive of surfactant, in either a channel or boundary-layer configuration, over long but finite-length streamwise ridges that are periodic in the spanwise direction, with period $P$ and gas fraction $φ$. We adopt a technique based on a shifted log law to acquire an expression for the drag reduction. The average streamwise and spanwise slip lengths are derived by introducing a local laminar model within the viscous sublayer, whereby the effect of surfactant is modelled by modifying the average streamwise and spanwise slip lengths. Our model agrees with available laboratory experimental data from the literature when conditions are clean (surfactant-free), or when there are low surfactant levels. However, we find an appreciable drag increase for larger background surfactant concentrations that are characteristic of turbulent flows over SHSs for marine applications.

physics.flu-dyn↗

arXiv2022

Droplet absorption and spreading into thin layers of polymer hydrogels

From biological tissues to layers of paint, macroscopic non-porous materials with the capacity to swell when brought in contact with an appropriate solvent are ubiquitous. Here, we study experimentally and theoretically one of the conceptually simplest of such systems, the swelling of a thin hydrogel layer by a single water drop. Using a bespoke experimental setup, we observe fast absorption leading to a radially spreading axisymmetric blister. Employing a linear poroelastic framework and thin-layer scalings, we develop a non-linear one-dimensional diffusion equation for the evolution of the blister height profile, which agrees well with experimental observations.

cond-mat.soft↗

arXiv2021

Surfactant spreading in a two-dimensional cavity and emergent contact-line singularities

We model the advective Marangoni spreading of insoluble surfactant at the free surface of a viscous fluid that is confined within a two-dimensional rectangular cavity. Interfacial deflections are assumed small, with contact lines pinned to the walls of the cavity, and inertia is neglected. Linearizing the surfactant transport equation about the equilibrium state allows a modal decomposition of the dynamics, with eigenvalues corresponding to decay rates of perturbations. Computation of the family of mutually orthogonal two-dimensional eigenfunctions reveals singular flow structures near each contact line, resulting in spatially oscillatory patterns of wall shear stress and a pressure field that diverges logarithmically. These singularities at a stationary contact line are associated with dynamic compression of the surfactant monolayer; we show how they can be regularized by weak surface diffusion. Their existence highlights the need for careful treatment in computations of unsteady advection-dominated surfactant transport in confined domains.

physics.flu-dyn↗

arXiv2020

Three-dimensional advective--diffusive boundary layers in open channels with parallel and inclined walls

We study the steady laminar advective transport of a diffusive passive scalar released at the base of narrow three-dimensional longitudinal open channels with non-absorbing side walls and rectangular or truncated-wedge-shaped cross-sections. The scalar field in the advective--diffusive boundary layer at the base of the channels is fundamentally three-dimensional in the general case, owing to a three-dimensional velocity field and differing boundary conditions at the side walls. We utilise three-dimensional numerical simulations and asymptotic analysis to understand how this inherent three-dimensionality influences the advective-diffusive transport as described by the normalised average flux, the Sherwood $Sh$ or Nusselt numbers for mass or heat transfer, respectively. We show that $Sh$ is well approximated by an appropriately formulated two-dimensional calculation, even when the boundary layer structure is itself far from two-dimensional. This important result can significantly simplify the modelling of many laminar advection--diffusion scalar transfer problems: the cleaning or decontamination of confined channels, or transport processes in chemical or biological microfluidic devices.

physics.flu-dyn↗

arXiv2019

A theory for the slip and drag of superhydrophobic surfaces with surfactant

Superhydrophobic surfaces (SHSs) have the potential to reduce drag at solid boundaries. However, multiple independent studies have recently shown that small amounts of surfactant, naturally present in the environment, can induce Marangoni forces that increase drag, at least in the laminar regime. To obtain accurate drag predictions, one must solve the mass, momentum, bulk surfactant and interfacial surfactant conservation equations. This requires expensive simulations, thus preventing surfactant from being widely considered in SHS studies. To address this issue, we propose a theory for steady, pressure-driven, laminar, two-dimensional flow in a periodic SHS channel with soluble surfactant. We linearise the coupling between flow and surfactant, under the assumption of small concentration, finding a scaling prediction for the local slip length. To obtain the drag reduction and interfacial shear, we find a series solution for the velocity field by assuming Stokes flow in the bulk and uniform interfacial shear. We find how the slip and drag depend on the nine dimensionless groups that together characterize the surfactant transport near SHSs, the gas fraction and the normalized interface length. Our model agrees with numerical simulations spanning orders of magnitude in each dimensionless group. The simulations also provide the constants in the scaling theory. Our model significantly improves predictions relative to a surfactant-free one, which can otherwise overestimate slip and underestimate drag by several orders of magnitude. Our slip length model can provide the boundary condition in other simulations, thereby accounting for surfactant effects without having to solve the full problem.

physics.flu-dyn↗

arXiv2017

Traces of surfactants can severely limit the drag reduction of superhydrophobic surfaces

Superhydrophobic surfaces (SHSs) have the potential to achieve large drag reduction for internal and external flow applications. However, experiments have shown inconsistent results, with many studies reporting significantly reduced performance. Recently, it has been proposed that surfactants, ubiquitous in flow applications, could be responsible, by creating adverse Marangoni stresses. Yet, testing this hypothesis is challenging. Careful experiments with purified water show large interfacial stresses and, paradoxically, adding surfactants yields barely measurable drag increases. This suggests that other physical processes, such as thermal Marangoni stresses or interface deflection, could explain the lower performance. To test the surfactant hypothesis, we perform the first numerical simulations of flows over a SHS inclusive of surfactant kinetics. These simulations reveal that surfactant-induced stresses are significant at extremely low concentrations, potentially yielding a no-slip boundary condition on the air--water interface (the "plastron") for surfactant amounts below typical environmental values. These stresses decrease as the streamwise distance between plastron stagnation points increases. We perform microchannel experiments with thermally-controlled SHSs consisting of streamwise parallel gratings, which confirm this numerical prediction. We introduce a new, unsteady test of surfactant effects. When we rapidly remove the driving pressure following a loading phase, a backflow develops at the plastron, which can only be explained by surfactant gradients formed in the loading phase. This demonstrates the significance of surfactants in deteriorating drag reduction, and thus the importance of including surfactant stresses in SHS models. Our time-dependent protocol can assess the impact of surfactants in SHS testing and guide future mitigating designs.

cond-mat.soft↗

arXiv2015

Convective mass transfer from a submerged drop in a thin falling film

We study the fluid mechanics of removing a passive tracer contained in small, viscous drops attached to a flat inclined substrate using thin gravity-driven film flows. A convective mass transfer establishes across the drop-film interface and the tracer in the drop diffuses into the film flow. The Peclet number for the tracer in the film is large. The Peclet number Pe_d in the drop varies from 0.01 to 1. The characteristic transport time in the drop is much larger than in the film. We model the mass transfer of the tracer from the drop bulk into the film using an empirical model based on Newton's law of cooling. This model is supported by a theoretical model solving the quasi-steady 2D advection-diffusion equation in the film coupled with a time-dependent 1D diffusion equation in the drop. We find excellent agreement between our experimental data and the 2 models, which predict an exponential decrease in time of the tracer concentration in the drop. The results are valid for all drop and film Peclet numbers studied. The transport characteristic time is related to the drop diffusion time scale, as diffusion within the drop is the limiting process. Our theoretical model predicts the well-known relationship between the Sherwood and Reynolds numbers in the case of a well-mixed drop Sh~Re_L^{1/3}=γL^2/ν_f, based on the drop length L, film shear rate γand film kinematic viscosity ν_f. We show that this relationship is mathematically equivalent to a more physically intuitive relationship Sh~Re_δ, based on the diffusive boundary layer thickness δ. The model also predicts a correction in the case of a non-uniform drop concentration, which depends on Re_δ, the Schmidt number, the drop aspect ratio and the diffusivity ratio. This prediction is in agreement with experiments at low Pe_d. It also agrees as Pe_d approaches 1, although the influence of Re_δincreases.

physics.flu-dyn↗