arXiv subjects

Simon Cox

Publications and source records attributed to Simon Cox.

At least 19 recordsLinked to original sources

arXiv2026

Quantifying the liquid flow between a soap film and a vertical meniscus

Fluid exchange between a soap film and its bounding menisci governs film drainage and stability, with direct implications for the lifetime of surface bubbles and liquid foams. Despite recent advances, a quantitative characterization of this coupling, associated with the phenomenon of marginal regeneration, remains incomplete. The volumetric flux per unit length of contact follows a well-established scaling law involving geometrical parameters such as the film height and the meniscus radius of curvature. However, the dimensionless prefactor of this relation - the flux coefficient - remains difficult to determine for vertical menisci because of the complex and intermittent flows occurring at the film-meniscus interface. Here, we quantify this flux into the meniscus generated by inserting a solid plate into a vertical soap film. We consider both vertical and inclined plates and further investigate the effects of plate inclination, height, and width. Focusing on the dynamics of the growth of the meniscus driven by liquid supplied by the film, we analyze both steady and transient regimes resulting from the interplay between capillary pressure, gravity, and liquid exchange. Combining experiments, numerical simulations, and theoretical modelling, we determine the flux coefficient using three independent methods and show that it remains constant over the range of parameters explored.

physics.flu-dyn↗

arXiv2025

Mean-field model for the bubble size distribution in coarsening wet foams

Aqueous foams are subject to coarsening, whereby gas from the bubbles diffuses through the liquid phase. Gas is preferentially transported from small to large bubbles, resulting in a gradual decrease of the number of bubbles and an increase in the average bubble size. Coarsening foams are expected to approach a scaling state at late times in which their statistical properties are invariant. However, a model predicting the experimentally observed bubble-size distribution in the scaling state of foams with moderate liquid content, as a function of the liquid fraction $\phi$, has not yet been developed. To this end, we propose a three-dimensional mean-field bubble growth law for foams without inter-bubble adhesion, validated against bubble-scale simulations, and use it to derive a prediction of the scaling-state bubble-size distribution for any $\phi$ from zero up to the unjamming transition $\phi_\text{c} \approx 36\%$. We verify that the derived scaling state is approached from a variety of initial conditions using mean-field simulations implementing the proposed growth law. Comparing our predicted bubble-size distribution with previous simulations and experimental results, we likewise find a large population of small bubbles when $\phi > 0$, but there are qualitative differences from prior results which we attribute to the absence of rattlers, i.e. bubbles not pressed into contact with their neighbours, in our model.

cond-mat.soft↗

arXiv2025

Isoperimetric bubbles in spaces with density $r^p + a$

Least perimeter solutions for a region with fixed mass are sought in ${\mathbb{R}^d}$ on which a density function $\rho(r) = r^p+a$, with $p>0, a>0$, weights both perimeter and mass. On the real line ($d=1$) this is a single interval that includes the origin. For $p \le 1$ the isoperimetric interval has one end at the origin; for larger $p$ there is a critical value of $a$ above which the interval is symmetric about the origin. In the case $p=2$, for $d=2$ and $3$, the isoperimetric region is a circle or sphere, respectively, that includes the origin; the centre moves towards the origin as $a$ increases, with constant radius, and then remains centred on the origin for $a$ above the critical value as the radius decreases.

math.OC↗

arXiv2023

Effects of liquid fraction and contact angle on structure and coarsening in two-dimensional foams

Aqueous foams coarsen with time due to gas diffusion through the liquid. The mean bubble size grows, and small bubbles vanish. However, coarsening is little understood for foams with an intermediate liquid content, particularly in the presence of surfactant-induced attractive forces between the bubbles, measured by the contact angle. Rigorous bubble growth laws have yet to be developed, and the evolution of bulk foam properties is unclear. We present a quasi-static numerical model for coarsening in two-dimensional wet foams, focusing on growth laws and related bubble properties. The deformation of bubbles is modelled using a finite-element approach, and the gas flow through both films and Plateau borders is approximated. We give results for disordered two-dimensional wet foams with 256 to 1024 bubbles, at liquid fractions from $2\%$ to beyond the zero-contact-angle jamming transition, and with contact angles up to $10^\circ$. Simple analytical models are developed to aid interpretation. We find that nonzero contact angle causes a proxy of the initial coarsening rate to plateau at large liquid fractions, and that the individual bubble growth rates are closely related to their effective number of neighbours.

cond-mat.soft↗

arXiv2023

A method for quantifying sectoral optic disc pallor in fundus photographs and its association with peripapillary RNFL thickness

Purpose: To develop an automatic method of quantifying optic disc pallor in fundus photographs and determine associations with peripapillary retinal nerve fibre layer (pRNFL) thickness. Methods: We used deep learning to segment the optic disc, fovea, and vessels in fundus photographs, and measured pallor. We assessed the relationship between pallor and pRNFL thickness derived from optical coherence tomography scans in 118 participants. Separately, we used images diagnosed by clinical inspection as pale (N=45) and assessed how measurements compared to healthy controls (N=46). We also developed automatic rejection thresholds, and tested the software for robustness to camera type, image format, and resolution. Results: We developed software that automatically quantified disc pallor across several zones in fundus photographs. Pallor was associated with pRNFL thickness globally (\b{eta} = -9.81 (SE = 3.16), p < 0.05), in the temporal inferior zone (\b{eta} = -29.78 (SE = 8.32), p < 0.01), with the nasal/temporal ratio (\b{eta} = 0.88 (SE = 0.34), p < 0.05), and in the whole disc (\b{eta} = -8.22 (SE = 2.92), p < 0.05). Furthermore, pallor was significantly higher in the patient group. Lastly, we demonstrate the analysis to be robust to camera type, image format, and resolution. Conclusions: We developed software that automatically locates and quantifies disc pallor in fundus photographs and found associations between pallor measurements and pRNFL thickness. Translational relevance: We think our method will be useful for the identification, monitoring and progression of diseases characterized by disc pallor/optic atrophy, including glaucoma, compression, and potentially in neurodegenerative disorders.

eess.IV↗

arXiv2023

The W3C Data Catalog Vocabulary, Version 2: Rationale, Design Principles, and Uptake

DCAT is an RDF vocabulary designed to facilitate interoperability between data catalogs published on the Web. Since its first release in 2014 as a W3C Recommendation, DCAT has seen a wide adoption across communities and domains, particularly in conjunction with implementing the FAIR data principles (for findable, accessible, interoperable and reusable data). These implementation experiences, besides demonstrating the fitness of DCAT to meet its intended purpose, helped identify existing issues and gaps. Moreover, over the last few years, additional requirements emerged in data catalogs, given the increasing practice of documenting not only datasets but also data services and APIs. This paper illustrates the new version of DCAT, explaining the rationale behind its main revisions and extensions, based on the collected use cases and requirements, and outlines the issues yet to be addressed in future versions of DCAT.

cs.DL↗

arXiv2022

Collapse of a hemicatenoid bounded by a solid wall: instability and dynamics driven by surface Plateau border friction

The collapse of a catenoidal soap film when the rings supporting it are moved beyond a critical separation is a classic problem in interface motion in which there is a balance between surface tension and the inertia of the surrounding air, with film viscosity playing only a minor role. Recently [Goldstein, et al., Phys. Rev. E 104, 035105 (2021)], we introduced a variant of this problem in which the catenoid is bisected by a glass plate located in a plane of symmetry perpendicular to the rings, producing two identical hemicatenoids, each with a surface Plateau border (SPB) on the glass plate. Beyond the critical ring separation, the hemicatenoids collapse in a manner qualitatively similar to the bulk problem, but their motion is governed by the frictional forces arising from viscous dissipation in the SPBs. Here we present numerical studies of a model that includes classical friction laws for SPB motion on wet surfaces and show consistency with our experimental measurements of the temporal evolution of this process. This study can help explain the fragmentation of bubbles inside very confined geometries such as porous materials or microfluidic devices.

cond-mat.soft↗

arXiv2022

Effect of Contact Angle on Capillary Pressure and Liquid Recovery from Angular Pore Channels

We predict the volume of liquid recovered from different-shaped prismatic channels following gas displacement. This recovery factor depends strongly on the contact angle at which the gas-liquid interfaces meet the walls of the channel. We show that scaling the contact angle by a critical value, dependent on the channel shape, leads to a master curve for the recovery factor.} Our numerical simulations with the Surface Evolver are supported by theoretical calculations for the capillary entry pressure in a channel with a triangular or rectangular cross-section and for the interface shape in a "scalloped" triangular channel formed between three parallel cylinders.

physics.flu-dyn↗

arXiv2021

Prediction of the capillary pressure of fluid surrounding a cylinder representing an idealized rock structure in porous media

Liquids in oil-bearing porous media assume complex shapes that depend on the reservoir characteristics and the wetting properties of the liquid. The wide variation in the geometry of rock formations makes it difficult to accurately predict the capillary pressure of small volumes of liquid and hence the likelihood of being able to move it. Here we consider the situation in which a small volume of liquid surrounds an upright cylinder on a flat substrate and predict the shape that the liquid takes and its capillary pressure. We validate our predictions by comparing with Surface Evolver simulations for a range of contact angles and cylinder radii.

physics.flu-dyn↗

arXiv2019

Least-perimeter partition of the disc into $N$ regions of two different areas

We present conjectured candidates for the least perimeter partition of a disc into $N \le 10$ regions which take one of two possible areas. We assume that the optimal partition is connected, and therefore enumerate all three-connected simple cubic graphs for each $N$. Candidate structures are obtained by assigning different areas to the regions: for even $N$ there are $N/2$ regions of one area and $N/2$ regions of the other, and for odd $N$ we consider both cases, i.e. where the extra region takes either the larger or the smaller area. The perimeter of each candidate is found numerically for a few representative area ratios, and then the data is interpolated to give the conjectured least perimeter candidate for all possible area ratios. At larger $N$ we find that these candidates are best for a more limited range of the area ratio.

cond-mat.soft↗

arXiv2017

A viscous froth model adapted to wet foams

We describe the extension of a "viscous froth" model to the dynamics of a wet foam in a Hele-Shaw cell. The two-dimensional model includes the friction experienced by the soap films as they are dragged along the cell walls, while retaining accurate geometrical information. To explore the consequences of changing the liquid content in this situation, we consider a simple foam geometry known as a bubble lens: a bubble partially filling a narrow, straight channel with a single film spanning the gap between the bubble and the opposite wall. The triple vertices of this structure are decorated with Plateau borders whose area determines the liquid fraction of the foam. We derive new expressions to allow the pressure in the Plateau borders to be calculated, and determine numerically the range of driving velocities for which the system reaches a steady state. As the liquid fraction increases, the lens moves more slowly and the spanning film is more greatly distorted, reducing the range of stable driving velocities. For higher velocities, the spanning film moves so quickly that it leaves the bubble behind, a situation which must be avoided in any particular application.

cond-mat.soft↗

arXiv2012

Deformation of a free interface pierced by a tilted cylinder

We investigate the interaction between an infinite cylinder and a free fluid-fluid interface governed only by its surface tension. We study the deformation of an initially flat interface when it is deformed by the presence of a cylindrical object, tilted at an arbitrary angle, that the interface "totally wets". Our simulations predict all significant quantities such as the interface shape, the position of the contact line, and the force exerted by the interface on the cylinder. These results are compared with an experimental study of the penetration of a soap film by a cylindrical liquid jet. This dynamic situation exhibits all the characteristics of a totally wetting interface. We show that whatever the inclination, the force is always perpendicular to the plane of the interface, and its amplitude diverges as the inclination angle increases. Such results should bring new insights in both fluid and solid mechanics, from animal locomotion to surface micro-processing.-processing.

cond-mat.soft↗

arXiv2012

Instability of stretched and twisted soap films in a cylinder

A soap film, or a flexible membrane without bending and torsional stiffness, that is confined in a cylinder is shown to be susceptible to a surface-tension-driven instability when it is stretched or twisted. This leads to its breakdown and places an upper limit on the aspect ratio of such structures. A simple analysis confirms the values for the critical aspect ratio of the stretched film found in both simulations and experiments on soap films, and this threshold decreases with increasing twist of the film.

cond-mat.soft↗

arXiv2012

Elasto-plastic flow of a foam around an obstacle

We simulate quasistatic flows of an ideal two-dimensional monodisperse foam around different obstacles, both symmetric and asymmetric, in a channel. We record both pressure and network contributions to the drag and lift forces, and study them as a function of obstacle geometry. We show that the drag force increases linearly with the cross section of an obstacles. The lift on an asymmetric aerofoil-like shape is negative and increases with its arc length, mainly due to the pressure contribution.

cond-mat.soft↗

arXiv2010

Discrete rearranging disordered patterns: Prediction of elastic and plastic behaviour, and application to two-dimensional foams

We study the elasto-plastic behaviour of materials made of individual (discrete) objects, such as a liquid foam made of bubbles. The evolution of positions and mutual arrangements of individual objects is taken into account through statistical quantities, such as the elastic strain of the structure, the yield strain and the yield function. The past history of the sample plays no explicit role, except through its effect on these statistical quantities. They suffice to relate the discrete scale with the collective, global scale. At this global scale, the material behaves as a continuous medium; it is described with tensors such as elastic strain, stress and velocity gradient. We write the differential equations which predict their elastic and plastic behaviour in both the general case and the case of simple shear. An overshoot in the shear strain or shear stress is interpreted as a rotation of the deformed structure, which is a purely tensorial effect that exists only if the yield strain is at least of order 0.3. We suggest practical applications, including: when to choose a scalar formalism rather than a tensorial one; how to relax trapped stresses; and how to model materials with a low, or a high, yield strain.

cond-mat.soft↗

arXiv2008

Remarks on the accuracy of algorithms for motion by mean curvature in bounded domains

Simulations of motion by mean curvature in bounded domains, with applications to bubble motion and grain growth, rely upon boundary conditions that are only approximately compatible with the equation of motion. Three closed form solutions for the problem exist, governing translation, rotation and expansion of a single interface [1], providing the only benchmarks for algorithm verification. We derive new identities for the translation solution. Then we estimate the accuracy of a straightforward algorithm to recover the analytical solution for different values of the velocity V given along the boundary. As expected, for large V the error can reach unacceptable levels especially near the boundary. We discuss factors influencing the accuracy and propose a simple modification of the algorithm which improves the computational accuracy.

cond-mat.soft↗

arXiv2008

Screening in two-dimensional foams

Using the Surface Evolver software, we perform numerical simulations of point-like deformations in a two-dimensional foam. We study perturbations which are infinitesimal or finite, isotropic or anisotropic, and we either conserve or do not conserve the number of bubbles. We measure the displacement fields around the perturbation. Changes in pressure decrease exponentially with the distance to perturbation, indicating a screening over a few bubble diameters.

cond-mat.soft↗

arXiv2008

Topological and geometrical disorder correlate robustly in two-dimensional foams

A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the disorder. The former is a geometrical measurement, while the latter is purely topological. We discuss the common points and differences between both quantities. We measure them in a foam which is sheared, so that bubbles move past each other and the foam is "shuffled" (a notion we discuss). Both quantities are strongly correlated; in this case (only) it thus becomes sufficient to use either one or the other to characterize the foam disorder. We suggest applications to the analysis of other systems, including biological tissues.

cond-mat.soft↗