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Eirik Grude Flekkøy

Publications and source records attributed to Eirik Grude Flekkøy.

16 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

Thermo-viscous instability of flow in a weakly heat-conducting channel

An instability may arise when a hot viscous fluid enters a thin gap and cools through heat transfer to a colder surrounding environment. Fluids whose viscosity increases strongly upon cooling create a positive feedback in which warmer regions flow faster and cool more slowly, leading to the formation of thermo-viscous "fingers". Here we investigate this mechanism in the long time, small Biot number regime, where cooling through the plates is weak but acts over sufficiently long times that the temperature becomes nearly uniform across the gap heat. This asymptotic limit enables a depth-averaged description that incorporates both thermal diffusion and hydrodynamic (Taylor) dispersion, allowing us to analyze the dependence of the instability on the Péclet number, viscosity contrast, and wall cooling rate. Using numerical simulations of temperature-dependent viscous flow in a Hele-Shaw geometry, we show that fingering instabilities emerge in response to small inlet perturbations within a range of Péclet numbers and viscosity contrasts. From linear stability analysis we find the dispersion relation and quantify how the fastest growth rate $γ_{\max}$ and corresponding wavenumber $k_{\max}$ depend on the global parameters. We further derive analytical expressions for $γ_{\max}$ and $k_{\max}$ in the limit of high Péclet number and large viscosity contrast, revealing the scaling behavior that controls pattern selection. These results clarify the physical mechanisms driving thermo-viscous fingering in the small Biot number regime and have implications for systems in which temperature-dependent viscous fluids are confined within narrow gaps, such as lubrication flows in mechanical components and magma invasion in small scale fissures.

physics.flu-dyn↗
arXiv2025

Confined colloidal droplets dry to form circular mazes

During drying, particle-laden sessile droplets will leave so-called coffee-stain rings behind. This phenomenon is well-known and well-understood (Deegan et al., Nature 389, 827-829 (1997)). Here we show that when particle-laden droplets confined in a slit are allowed to evaporate very slowly, they do not deposit coffee rings, but form a surprisingly intricate, circular maze-like pattern. We present experiments that illustrate this pattern formation and discuss the factors that determine when such patterns can form. We are not aware of reports of natural examples of the formation of such beautiful patterns under confinement, although it seems likely that they exist.

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↗
arXiv2023

A simplified pore-scale model for slow drainage including film-flow effects

Film flow through networks of corners and capillary bridges can establish connections between seemingly isolated clusters during drainage in porous media. Coupled with drainage through the bulk of pores and throats, the flow through these networks constitutes a secondary drainage mechanism that can significantly affect fluid configurations and residual saturations. In order to investigate the prevalence of this drainage mechanism, we propose a quasi-static pore-network model based on modifying the trapped-cluster-identification algorithm in an invasion-percolation model. With the modification, wetting-phase connectivity could be provided by direct successions of pores and throats, represented by sites and bonds, as well as by chains of interconnected capillary bridges. The advancement of the fluid interface in the porous matrix was determined by the bonds' invasion thresholds, calculated based on local capillary pressure values that could be perturbed to accommodate gravitational effects. With the proposed model, experimentally verified phenomena related to slow drainage in granular porous media were reproduced, showing good qualitative agreement.

physics.flu-dyn↗
arXiv2022

Collective states of active matter with stochastic reversals: emergent chiral states and spontaneous current switching

We study collective dynamical behavior of active particles with topological interactions and directional reversals. Surprising phenomena are shown to emerge as the interaction relaxation time is varied relative to the reversal rate, such as spontaneous formation of collective chiral states due to phase synchronization, and collective directional reversals in the presence of confinement. The results have a direct relevance to modelling and understanding collective reversals and synchronization phenomena in active matter.

cond-mat.soft↗
arXiv2022

Discerning between different 'Oumuamua models by optical and infrared observations

The first interstellar object to be observed in our solar system 1I/2017 U1 'Oumuamua combines the lack of observable cometary activity with an extra-gravitational acceleration. This has given rise to several mutually exclusive explanations based on different assumptions in the material composition of 'Oumuamua. We show how a combination of observations in the infrared and optical spectra may serve to distinguish between these explanations once another object with 'Omuamua-like properties comes close enough to earth. This possibility is linked to the widely different thermal properties of the different material models that have been proposed. Developing a model for the thermal conduction and infrared signal from a fractal model we compare predictions of the infrared signal with that from standard thermal models that assume 'Oumuamua to be either a solid piece of rock/ice or a thin sheet.

astro-ph.EP↗
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↗
arXiv2020

The escape problem for active particles confined to a disc

We study the escape problem for interacting, self-propelled particles confined to a disc, where particles can exit through one open slot on the circumference. Within a minimal 2D Vicsek model, we numerically study the statistics of escape events when the self-propelled particles can be in a flocking state. We show that while an exponential survival probability is characteristic for non-interaction self-propelled particles at all times, the interacting particles have an initial exponential phase crossing over to a sub-exponential late-time behavior. We propose a new phenomenological model based on non-stationary Poisson processes which includes the Allee effect to explain this sub-exponential trend and perform numerical simulations for various noise intensities.

cond-mat.stat-mech↗
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↗
arXiv2013

A General Criterion for Liquefaction in Granular Layers with Heterogeneous Pore Pressure

Fluid-saturated granular and porous layers can undergo liquefaction and lose their shear resistance when subjected to shear forcing. In geosystems, such a process can lead to severe natural hazards of soil liquefaction, accelerating slope failure, and large earthquakes. Terzaghi's principle of effective stress predicts that liquefaction occurs when the pore pressure within the layer becomes equal to the applied normal stress on the layer. However, under dynamic loading and when the internal permeability is relatively small the pore pressure is spatially heterogeneous and it is not clear what measurement of pore pressure should be used in Terzaghi's principle. Here, we show theoretically and demonstrate using numerical simulations a general criterion for liquefaction that applies also for the cases in which the pore pressure is spatially heterogeneous. The general criterion demands that the average pore pressure along a continuous surface within the fluid-saturated granular or porous layer is equal to the applied normal stress.

physics.geo-ph↗
arXiv2013

Influence of asperities on fluid and thermal flow in a fracture: a coupled Lattice Boltzmann study

The characteristics of the hydro-thermal flow which occurs when a cold fluid is injected into a hot fractured bedrock depend on the morphology of the fracture. We consider a sharp triangular asperity, invariant in one direction, perturbing an otherwise flat fracture. We investigate its influence on the macroscopic hydraulic transmissivity and heat transfer efficiency, at fixed low Reynolds number. In this study, numerical simulations are done with a coupled lattice Boltzmann method that solves both the complete Navier-Stokes and advection-diffusion equations in three dimensions. The results are compared with those obtained under lubrication approximations which rely on many hypotheses and neglect the three-dimensional (3D) effects. The lubrication results are obtained by analytically solving the Stokes equation and a two-dimensional (integrated over the thickness) advection-diffusion equation. We use a lattice Boltzmann method with a double distribution (for mass and energy transport) on hypercubic and cubic lattices. Beyond some critical slope for the boundaries, the velocity profile is observed to be far from a quadratic profile in the vicinity of the sharp asperity: the fluid within the triangular asperity is quasi-static. We find that taking account of both the 3D effects and the cooling of the rock, are important for the thermal exchange. Neglecting these effects with lubrication approximations results in overestimating the heat exchange efficiency. The evolution of the temperature over time, towards steady state, also shows complex behavior: some sites alternately reheat and cool down several times, making it difficult to forecast the extracted heat.

physics.geo-ph↗
arXiv2013

History-independence of steady-state in simultaneous two-phase flow through porous media

It is well known that the transient behavior during drainage or imbibition in multiphase flow in porous media strongly depends on the history and initial condition of the system. However, when the steady-state regime is reached and both drainage and imbibition take place at the pore level, the influence of the evolution history and initial preparation is an open question. Here, we present an extensive experimental and numerical work investigating the history dependence of simultaneous steady-state two-phase flow through porous media. Our experimental system consists of a Hele-Shaw cell filled with glass beads which we model numerically by a network of disordered pores transporting two immiscible fluids. From the measurements of global pressure evolution, histogram of saturation and cluster-size distributions, we find that when both phases are flowing through the porous medium, the steady state does not depend on the initial preparation of the system or on the way it has been reached.

physics.flu-dyn↗
arXiv2012

Family-Vicsek scaling of detachment fronts in Granular Rayleigh Taylor Instabilities during sedimenting granular/fluid flows

When submillimetric particles are confined in a fluid such that a compact cluster of particles lie above the clear fluid, particles will detach from the lower boundary of the cluster and form an unstable separation front giving rise to growing fingers of falling particles. We study this problem using both experiments and hybrid granular/fluid mechanics models. In the case of particles from 50 to 500 microns in diameter falling in air, we study the horizontal density fluctuations at early times: the amplitude of the density difference between two points at a certain horizontal distance grows as a power law of time. This happens up to a saturation corresponding to a power law of the distance. The way in which the correlation length builds up to this saturation also follows a power law of time. We show that these decompaction fronts in sedimentation problems follow a Family-Vicsek scaling, characterize the dynamic and Hurst exponent of the lateral density fluctuations, respectively z \sim 1 and ζ\sim 0.75, and show how the prefactors depend on the grain diameter. We also show from similar simulations with a more viscous and incompressible fluid, that this feature is independent of the fluid compressibility or viscosity, ranging from air to water/glycerol mixtures.

physics.flu-dyn↗