arXiv subjects

Knut Jørgen Måløy

Publications and source records attributed to Knut Jørgen Måløy.

At least 19 recordsLinked to original sources

arXiv2026

A comparison of different image analysis techniques for mapping spatiotemporal pH and carbon dissolution in density-driven convection of CO2 in water

Density-driven convection enhances the carbon dissolution rate, which is significant for the geological carbon storage. This process will also influence the spatiotemporal pH and carbon concentrations of the underground fluid. To illuminate the convection mechanism, it is critical to understand the evolution of those properties within the porous media. However, determining the spatiotemporal pH and concentration within porous media is always challenging. This study employed a combination of three pH indicators that can track a wide range in pH from 4 to 9.5 in a convection experiment. Furthermore, we compared three image-processing techniques: Hue, gray-difference, and angular representation of RGB color space $\mathbf{(ϕ,θ)}$ for quantifying color changes from the universal $\text{pH}$ indicator arising from the carbon convection. The characterized colors were mapped into pH by calibrating against benchmark solutions. The comparative results demonstrate that the color quantified by the Hue technique is most robust, showing invariance to fluid thickness, camera settings, and LED luminance. In the convection experiments, it produces a continuous spatial distribution of pH and concentration level in the system. In contrast, the $\mathbf{(ϕ,θ)}$ and gray-difference techniques were more sensitive to environmental variations. They also have significant limitations for $\text{pH}$ interpolation in the critical range due to their non-monotonic calibration paths. Although all methods ultimately produced similar estimates of total dissolved carbon, the Hue technique offers greater stability and universality for high-resolution, dynamic measurements of pH and carbon concentration in the convection experiments.

physics.flu-dyn↗

arXiv2025

Droplet spreading in a wedge: A route to fluid rheology for power-law liquids

Measuring the rheology of liquids typically requires precise control over shear rates and stresses. Here, we describe an alternative route for predicting the characteristic features of a power-law fluid by simply observing the capillary spreading dynamics of viscous droplets in a wedge-shaped geometry. In this confined setting, capillary and viscous forces interact to produce a spreading dynamics described by anomalous diffusion, a process where the front position grows as a power-law in time with an exponent that differs from the value $1/2$ found in classical diffusion. We derive a nonlinear diffusion equation that captures this behavior, and we show that the diffusion exponent is directly related to the rheological exponent of the fluid. We verify this relationship by using both experiments and simulations for different power-law fluids. As the predictions are independent from flow-specific details, this approach provides a robust tool for inferring rheological properties from the spreading dynamics.

physics.flu-dyn↗

arXiv2025

Interface instability of two-phase flow in a three-dimensional porous medium

We present an experimental study of immiscible, two-phase fluid flow through a three-dimensional porous medium consisting of randomly-packed, monodisperse glass spheres. Our experiments combine refractive-index matching and laser-induced fluorescence imaging to resolve the morphology and stability of the moving interface resulting from the injection of one fluid into another. The imposed injection rate sets a balance between gravitational and viscous forces, producing interface morphologies which range from unstable collections of tangled fingers at low rates to stable sheets at high rates. The image data are complemented by time-resolved pressure measurements. We develop a stability criterion for the fluid interface based on the analysis of the 3D images and the pressure data. This criterion involves the Darcy permeability in each of the two phases and the time derivative of the pressure drop across the medium. We observe that the relative permeability encountered by the invading fluid is modified by the imposed flow rate in our experiment, which impacts the two-phase flow dynamics. We show that, in addition to the balance between the relevant forces driving the dynamics, local regions of crystalline order in the beadpack (crystallites) affect the stability of the invading front. This work provides insights into how disorder on multiple length scales in porous media can interact with viscous, capillary, and gravitational forces to determine the stability and dynamics of immiscible fluid interfaces.

physics.flu-dyn↗

arXiv2025

Drainage front width in a three-dimensional random porous medium under gravitational and capillary effects

A theoretical approach to estimating stable drainage front widths in three-dimensional random porous media under gravitational and capillary effects is presented. Based on the frontier of the infinite cluster in gradient percolation, we propose an expression for the 3D front width dependent on the pore-network topology, the distribution of capillary pressure thresholds for the pore throats, the stabilizing capillary pressure gradient, the average pore size, and the correlation length critical exponent from percolation in three dimensions. Theoretical predictions are successfully compared to numerical results obtained with a bond invasion-percolation model for a wide range of drainage flow parameters.

cond-mat.soft↗

arXiv2024

Interaction between corner and bulk flows during drainage in granular porous media

Drainage in porous media can be broken down into two main mechanisms: a primary piston-like displacement of the interfaces through the bulk of pore bodies and throats, and a secondary slow flow through corners and films in the wake of the invasion front. In granular porous media, this secondary drainage mechanism unfolds in connected pathways of pendular structures, such as capillary bridges and liquid rings, formed between liquid clusters. To represent both mechanisms, we proposed a dynamic dual-network model for drainage, considering that a gas displaces a wetting liquid from quasi-2D granular porous media. For this model, dedicated analyses of the capillary bridge shapes and hydraulic conductivity were conducted so that the secondary drainage mechanism could be properly quantified at finite speeds. With the model, an investigation of the wetting-phase connectivity and flow during drainage was carried out, covering a broad range of flow conditions. Results indicate that the span of liquid-connected structures in the unsaturated region, as well as their ability to contribute to flow, varies significantly with Capillary and Bond numbers.

cond-mat.soft↗

arXiv2024

Mapping dissolved carbon in space and time: An experimental technique for the measurement of pH and total carbon concentration in density driven convection of CO$_2$ dissolved in water

We present an experimental technique for determining the pH and the total carbon concentration when \ch{CO2} diffuses and flows in water. The technique employs three different pH indicators, which, when combined with an image analysis technique, provides a dynamic range in pH from 4.0 to 9.5. In contrast to usual techniques in which a single pH indicator is used, the methodology presented allows not only to produce a binary classification (pH larger or smaller than a given threshold) but to access a much more complete continuous spatial distribution of pH and concentration levels in the system. We calibrate the method against benchmark solutions and further demonstrate its potential by measuring the pH and total carbon concentration in a density driven convection (DDC) of carbon-enriched water. The motivation for testing the method in this particular experiment comes from the fact that DDC plays a pivotal role in the efficiency of engineered carbon storage processes. The application of the technique presented here provided a direct window for the analysis of the spatial distribution of captured carbon in the DDC flow.

physics.flu-dyn↗

arXiv2022

Competing gravitational and viscous efects in 3D two-phase flow investigated with a table-top optical scanner

We present experiments and theory describing the transition from viscosity-stabilized flow to gravitationally unstable fingering for two-phase flow in a 3D synthetic porous medium. Observation is made possible by the use of our newly developed table-top 3D-scanner based on optical index matching and laser-induced fluorescence, which is described in detail. In the experiment, a more dense, more viscous fluid injected at a fixed flow-rate from a point source at the top of the flow cell displaces a less viscous, less dense fluid. We observe a stable invasion zone near the inlet, which increases in size with increasing flow rates, and presents initially a close to hemispherical shape. At later times, the invasion front transits to an unstable mode and a fingering flow regime. The transition occurs at a predicted critical radius, Rc, corresponding to the zero of the combined viscous and gravitational pressure gradient.

physics.flu-dyn↗

arXiv2022

Stable and unstable capillary fingering in porous media with a gradient in grains size

We present a theoretical and experimental investigation of slow drainage in porous media with a gradient in the grains size (and hence in the typical pores' throats), in an external gravitational field. We mathematically show that such structural gradient and external force have a similar effect on the obtained drainage patterns, when they stabilise the invasion front. With the help of a newly introduced experimental set-up, based on the 3D-print of transparent porous matrices, we illustrate this equivalence, and extend it to the case where the front is unstable. We also present some invasion-percolation simulations of the same phenomena, which are inline with our theoretical and experimental results. In particular, we show that the width of stable drainage fronts mainly scales with the spatial gradient of the average pore invasion threshold and with the local distribution of this (disordered) threshold. The scaling exponent results from percolation theory and is -0.57 for 2D systems. Overall, we propose a unifying theory for the up-scaling of dual fluid flows in most classical scenarii.

cond-mat.soft↗

arXiv2021

Burst dynamics, up-scaling and dissipation of slow drainage in porous media

We present a theoretical and experimental investigation of drainage in porous media. The study is limited to stabilized fluid fronts at moderate injection rates, but it takes into account capillary, viscous, and gravitational forces. In this theory the work applied on the system, the energy dissipation, the final saturation and the width of the stabilized fluid front can all be calculated if we know the dimensionless fluctuation number, the wetting properties, the surface tension between the fluids, the fractal dimensions of the invasion front and the invading structure, and the exponent describing the divergence of the correlation length in percolation. This theoretical description explains how the Haines jumps' local activity and dissipation relate to dissipation on larger scales.

physics.flu-dyn↗

arXiv2021

Thermally activated intermittent dynamics of creeping crack fronts along disordered interfaces

We present a subcritical fracture growth model, coupled with the elastic redistribution of the acting mechanical stress along rugous rupture fronts. We show the ability of this model to quantitatively reproduce the intermittent dynamics of cracks propagating along weak disordered interfaces. To this end, we assume that the fracture energy of such interfaces (in the sense of a critical energy release rate) follows a spatially correlated normal distribution. We compare various statistical features from the hence obtained fracture dynamics to that from cracks propagating in sintered polymethylmethacrylate (PMMA) interfaces. In previous works, it has been demonstrated that such approach could reproduce the mean advance of fractures and their local front velocity distribution. Here, we go further by showing that the proposed model also quantitatively accounts for the complex self-affine scaling morphology of crack fronts and their temporal evolution, for the spatial and temporal correlations of the local velocity fields and for the avalanches size distribution of the intermittent growth dynamics. We thus provide new evidence that Arrhenius-like subcritical growth laws are particularly suitable for the description of creeping cracks.

cond-mat.mtrl-sci↗

arXiv2021

Heat emitting damage in skin: a thermal pathway for mechanical algesia

Mechanical pain (or mechanical algesia) can both be a vital mechanism warning us for dangers or an undesired medical symptom important to mitigate. Thus, a comprehensive understanding of the different mechanisms of this type of pain is paramount. In this work, we study the tearing of porcine skin in front of an infrared camera, and show that mechanical injuries in biological tissues can generate enough heat to stimulate the neural network. In particular, we report local temperature elevations of up to 24 degrees Celsius around fast cutaneous ruptures, which shall exceed the threshold of the neural nociceptors usually involved in thermal pain. Slower fractures exhibit lower temperature elevations, and we characterise such dependency to the damaging rate. Overall, we bring experimental evidence of a novel - thermal - pathway for direct mechanical algesia. In addition, the implications of this pathway are discussed for mechanical hyperalgesia as well, in which a role of the cutaneous thermal sensors has long been suspected. We also show that thermal dissipation shall actually account for a significant portion of the total skin's fracture energy, making temperature monitoring an efficient way to detect biological damages.

physics.bio-ph↗

arXiv2021

Thermal dissipation as both the strength and weakness of matter. A material failure prediction by monitoring creep

In any domain involving some stressed solids, that is, from seismology to general engineering, the strength of matter is a paramount feature to understand. We here discuss the ability of a simple thermally activated sub-critical model, that includes the auto-induced thermal evolution of cracks tips, to predict the catastrophic failure of a vast range of materials. It is in particular shown that the intrinsic surface energy barrier, for breaking the atomic bonds of many solids, can be easily deduced from the slow creeping dynamics of a crack. This intrinsic barrier is however higher than the macroscopic load threshold at which brittle matter brutally fails, possibly as a result of thermal activation and of a thermal weakening mechanism. We propose a novel method to compute the macroscopic critical energy release rate of rupture, G_a, solely from monitoring slow creep, and show that this reproduces the experimental values within 50% accuracy over twenty different materials, and over more than four decades of fracture energy.

cond-mat.mtrl-sci↗

arXiv2020

How heat controls fracture: the thermodynamics of creeping and avalanching cracks

While of paramount importance in material science, the dynamics of cracks still lacks a complete physical explanation. The transition from their slow creep behavior to a fast propagation regime is a notable key, as it leads to full material failure if the size of a fast avalanche reaches that of the system. We here show that a simple thermodynamics approach can actually account for such complex crack dynamics, and in particular for the non-monotonic force-velocity curves commonly observed in mechanical tests on various materials. We consider a thermally activated failure process that is coupled with the production and the diffusion of heat at the fracture tip. In this framework, the rise in temperature only affects the sub-critical crack dynamics and not the mechanical properties of the material. We show that this description can quantitatively reproduce the rupture of two different polymeric materials (namely, the mode I opening of polymethylmethacrylate (PMMA) plates, and the peeling of pressure sensitive adhesive (PSA) tapes), from the very slow to the very fast fracturing regimes, over seven to nine decades of crack propagation velocities. In particular, the fastest regime is obtained with an increase of temperature of thousands of kelvins, on the molecular scale around the crack tip. Although surprising, such an extreme temperature is actually consistent with different experimental observations that accompany the fast propagation of cracks, namely, fractoluminescence (i.e., the emission of visible light during rupture) and a complex morphology of post-mortem fracture surfaces, which could be due to the sublimation of bubbles.

cond-mat.soft↗

arXiv2020

Thermal weakening of cracks and brittle-ductile transition: a phase model

We present a model for the thermally activated propagation of cracks in elastic matrices. The propagation is considered as a subcritical phenomenon, the kinetics of which being described by an Arrhenius law. In this law, we take the thermal evolution of the crack front into account, assuming that a portion of the released mechanical energy is transformed into heat in a plastic process zone. We show that such a model leads to a two-phase crack propagation: a first phase at low velocity in which the temperature elevation is of little effect and the propagation is mainly governed by the mechanical load and by the toughness of the medium, and a second phase in which the crack is thermally weakened and propagates at greater velocity. Such a dual behavior can potentially explain the usual stick-slip in brittle fracturing, and we illustrate how with numerical simulations of mode I cracks propagating in thin disordered media. In addition, we predict the existence of a limiting ambient temperature above which the weakened phase ceases to exist and we propose this critical phenomenon as a novel explanation for the brittle-ductile transition of solids.

cond-mat.mtrl-sci↗

arXiv2018

Pressure evolution and deformation of confined granular media during pneumatic fracturing

By means of digital image correlation, we experimentally characterize the deformation of a dry granular medium confined inside a Hele-Shaw cell due to air injection at a constant overpressure high enough to deform it (from 50 to 250 kPa). Air injection at these overpressures leads to the formation of so called pneumatic fractures, i.e. channels empty of beads, and we discuss the typical deformations of the medium surrounding these structures. In addition we simulate the diffusion of the fluid overpressure into the medium, comparing it with the Laplacian solution over time, and relating pressure gradients with corresponding granular displacements. In the compacting medium we show that the diffusing pressure field becomes similar to the Laplace solution on the order of a characteristic time given by properties of the pore fluid, granular medium and the system size. However, before the diffusing pressure approaches the Laplace solution on system scale, we find that it resembles the Laplacian field near the channels, with the highest pressure gradients on the most advanced channel tips and a screened pressure gradient behind them. We show that the granular displacements more or less always move in the direction against the local pressure gradients, and when comparing granular velocities with pressure gradients in the zone ahead of channels, we observe a Bingham type of rheology for the granular paste (the mix of air and beads), with an effective viscosity $μ\_B$ and displacement thresholds $\nabla P\_c$ evolving during mobilization and compaction of the medium. Such a rheology, with disorder in the displacement thresholds, could be responsible for placing the pattern growth at moderate injection pressures in a universality class like the Dielectric Breakdown Model with $η=2$, where fractal dimensions are found between 1.5 and 1.6 for the patterns.

cond-mat.soft↗

arXiv2017

Verification of a dynamic scaling for the pair correlation function during the slow drainage of a porous medium

We give experimental grounding for the remarkable observation made by Furuberg et al. in Ref. [furuberg1988] of an unusual dynamic scaling for the pair correlation function $N(r,t)$ during the slow drainage of a porous medium. The authors of that paper have used an invasion percolation algorithm to show numerically that the probability of invasion of a pore at a distance $r$ away and after a time $t$ from the invasion of another pore, scales as $N(r,t)\propto r^{-1}f\left(r^{D}/t\right)$, where $D$ is the fractal dimension of the invading cluster and the function $f(u)\propto u^{1.4}$, for $u \ll 1$ and $f(u)\propto u^{-0.6}$, for $u \gg 1$. Our experimental setup allows us to have full access to the spatiotemporal evolution of the invasion, which was used to directly verify this scaling. Additionally, we have connected two important theoretical contributions from the literature to explain the functional dependency of $N(r,t)$ and the scaling exponent for the short-time regime ($t \ll r^{D}$). A new theoretical argument was developed to explain the long-time regime exponent ($t \gg r^{D}$).

physics.flu-dyn↗

arXiv2017

Critical behavior in porous media flow

The intermittent burst dynamics during the slow drainage of a porous medium is studied experimentally. We have shown that this system satisfies a set of conditions known to be true for critical systems, such as intermittent activity with bursts extending over several time and length scales, self-similar macroscopic fractal structure and $1/f^α$ power spectrum. Additionally, we have verified a theoretically predicted scaling for the burst size distribution, previously assessed via numerical simulations. The observation of $1/f^α$ power spectra is new for porous media flows and, for specific boundary conditions, we notice the occurrence of a transition from $1/f$ to $1/f^2$ scaling. An analytically integrable mathematical framework was employed to explain this behavior.

physics.flu-dyn↗

arXiv2017

Pattern formation of frictional fingers in a gravitational potential

Aligned finger structures, with a characteristic width, emerges during the slow drainage of a liquid/granular mixture in a tilted Hele-Shaw cell. A transition from vertical to horizontal alignment of the finger structures is observed as the tilting angle and the granular density are varied. An analytical model is presented, demonstrating that the alignment properties is the result of the competition between fluctuating granular stresses and the hydrostatic pressure. The dynamics is reproduced in simulations. We also show how the system explains patterns made during dyke formations.

physics.flu-dyn↗