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• Vargdal, Sigurd; Reis, Paula Kozlowski Pitombeira; Sveinsson, Henrik Andersen & Linga, Gaute (2026). Neural Networks for Predicting Permeability Tensors of 2D Porous Media: Comparison of Convolution- and Transformer-based Architectures. arXiv. doi: 10.48550/ARXIV.2512.01517. Full text in Research Archive
• Linga, Gaute; Pierce, Kevin; Moura, Marcel; Mathiesen, Joachim; Renard, Francois & Borgne, Tanguy Le (2026). Dynamic multiphase flow triggers chaotic mixing in porous media. Proceedings of the National Academy of Sciences of the United States of America (PNAS). ISSN 0027-8424. 123(34). doi: 10.1073/pnas.2612884123. Full text in Research Archive
• Pierce, Kevin; Borgne, Tanguy Le; Renard, Francois & Linga, Gaute (2026). How pore-scale disorder controls fluid stretching in porous media. arXiv. doi: 10.48550/ARXIV.2604.02981. Full text in Research Archive
• Mathias, Klahn,; Linga, Gaute; Borgne, Tanguy Le & Mathiesen, Joachim (2026). Stability of trapped fluid clusters in two-phase porous media flow. Journal of Fluid Mechanics. ISSN 0022-1120. 1039. Full text in Research Archive
• Lanza, Federico; Linga, Gaute; Barras, Fabian & Flekkøy, Eirik Grude (2026). Thermoviscous instability of flow in a weakly heat-conducting channel. Physical Review Fluids. 11(4). doi: 10.1103/gjnj-b4bl. Full text in Research Archive
• Shafabakhsh, Paiman; Cordonnier, Benoit; Borgne, Tanguy Le; Mathiesen, Joachim; Linga, Gaute & Pluymakers, Anne [Show all 9 contributors for this article] (2025). Coupling Neutron and X‐Ray Imaging of Fluid Mixing and Precipitation in Rocks: Challenges and Opportunities. Water Resources Research. ISSN 0043-1397. 61(12). doi: 10.1029/2025wr041911. Full text in Research Archive Show summary

  Solute mixing in rocks plays a central role in a wide range of reactive processes. However, how the complex 3D pore structure of rocks governs mixing rates remains largely unknown. Moreover, some mixing‐driven reactions—such as dissolution and precipitation—can modify the pore space, with poorly understood consequences for mixing itself. Recent advances in X‐ray imaging techniques have significantly enhanced our ability to visualize the pore‐scale rock architecture of rocks and a wide range of fluid processes. However, capturing solute mixing and its impact on chemical reactions—such as mineralization—remains a major challenge. Here, we investigated the potential of coupling time‐lapse 3D neutron and X‐ray imaging to characterize reactive fluid mixing and subsequent calcium carbonate mineralization in porous basalt. Two flow‐through experiments were performed with co‐injected CaCl 2 and Na 2 CO 3 , leading to precipitation. Neutron imaging tracked fluid mixing, while X‐ray imaging distinguished the solid matrix from pore space for fluid analysis. The first experiment showed steady transverse mixing, while a second experiment revealed temporal fluctuations due to trapped air, causing multiphase flow. Neutron images indicated significant fluid mixing driven by these fluctuations. A synchrotron X‐ray image post‐experiment indicated additional mineral precipitates from long‐term diffusive mixing. Despite the promising results, several challenges remain, including resolution limits, temporal synchronization between modalities, and accurate fluid phase segmentation. Overall, our findings highlight both the potential and limitations of integrated neutron and X‐ray imaging for studying pore‐scale reactive transport and mineralization processes.

• Reis, Paula Kozlowski Pitombeira; Linga, Gaute; Moura, Marcel; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Show all 7 contributors for this article] (2025). Interaction between corner and bulk flows during drainage in granular porous media. Advances in Water Resources. ISSN 0309-1708. 198. doi: 10.1016/j.advwatres.2025.104914. Full text in Research Archive
• Shafabakhsh, Paiman; Cordonnier, Benoit; Pluymakers, Anne Marie Henriette; Borgne, Tanguy Le; Mathiesen, Joachim & Linga, Gaute [Show all 9 contributors for this article] (2024). 4D Neutron Imaging of Solute Transport and Fluid Flow in Sandstone Before and After Mineral Precipitation. Water Resources Research. ISSN 0043-1397. 60(3). doi: 10.1029/2023WR036293. Full text in Research Archive Show summary

  In many geological systems, the porosity of rock or soil may evolve during mineral precipitation, a process that controls fluid transport properties. Here, we investigate the use of 4D neutron imaging to image flow and transport in Bentheim sandstone core samples before and after in-situ calcium carbonate precipitation. First, we demonstrate the applicability of neutron imaging to quantify the solute dispersion along the interface between heavy water and a cadmium aqueous solution. Then, we monitor the flow of heavy water within two Bentheim sandstone core samples before and after a step of in-situ mineral precipitation. The precipitation of calcium carbonate is induced by reactive mixing of two solutions containing CaCl2 and Na2CO3, either by injecting these two fluids one after each other (sequential experiment) or by injecting them in parallel (co-flow experiment). We use the contrast in neutron attenuation from time-resolved tomograms to derive three-dimensional fluid velocity field by using an inversion technique based on the advection-dispersion equation. Results show mineral precipitation induces a wider distribution of local flow velocities and leads to alterations in the main flow pathways. The flow distribution appears to be independent of the initial distribution in the sequential experiment, while in the co-flow experiment, we observed that higher initial local fluid velocities tended to increase slightly following precipitation. The outcome of this study contributes to progressing the knowledge in the domain of reactive solute and contaminant transport in the subsurface using the promising technique of neutron imaging.

• Dziadkowiec, Joanna; Linga, Gaute; Kalchgruber, Lukas; Kavunga, Sunil; Cheng, Hsiu-Wei & Nilsen, Ola [Show all 9 contributors for this article] (2024). Electrochemically Assisted Growth of Hopper and Tabular Calcite under Confinement. Crystal Growth & Design. ISSN 1528-7483. 24, p. 4930–4943. doi: 10.1021/acs.cgd.3c01433. Full text in Research Archive Show summary

  Crystallization under confinement is commonplace in nature and offers new pathways to engineer crystals with the desired morphologies in a controlled and reproducible manner. In this work, we demonstrate the electrochemically assisted, in situ formation of hopper and tabular calcite crystals within a wedge-like pore formed by confinement induced by the surface force apparatus (SFA). In this geometry, the distance between the confining surfaces decreases continuously from hundreds of micrometers to a few nanometers in a single experimental setup. Calcium carbonate precipitation followed in real-time is triggered by elevating the pH and thus supersaturation directly inside the pore. The pH increase is tracked with a fluorophore tracer and calculated analytically. The unusual calcite crystal habits are obtained in the absence of precipitation-modifying additives and vary as a function of the distance between the confining walls, where at the largest surface separations, hopper crystals form on the gold surface, whereas flat, tabular calcite forms on mica when the confining distance was below 5 μm. Hexagonal or triangular calcite plates exhibit surfaces dominantly defined by rough (001) planes and increase in their surface area-to-volume ratios with decreasing SFA pore thickness. Stabilization of calcite plates bound by (001) faces is a cooperative effect of the oriented growth of calcite on the confining, negatively charged mica walls and the confinement shape, which promotes the development of calcite morphology in the rapid crystal growth directions. The heterogeneous crystallization of calcite is preceded by the nucleation and spreading of a front composed of submicrometer-sized calcium carbonate particles visualized in situ in the SFA pore. Our work demonstrates abundant crystal growth under nanoscale confinement facilitated by elevated pH and a high surface charge of the confining walls.

• Lemoult, Grégoire; Mukund, Vasudevan; Shih, Hong-Yan; Linga, Gaute; Mathiesen, Joachim & Goldenfeld, Nigel [Show all 7 contributors for this article] (2024). Directed percolation and puff jamming near the transition to pipe turbulence. Nature Physics. ISSN 1745-2473. doi: 10.1038/s41567-024-02513-0. Full text in Research Archive Show summary

  The onset of turbulence in pipe flow has defied detailed understanding ever since the first observations of the spatially heterogeneous nature of the transition. Recent theoretical studies and experiments in simpler, shear-driven flows suggest that the onset of turbulence is a directed-percolation non-equilibrium phase transition, but whether these findings are generic and also apply to open or pressure-driven flows is unknown. In pipe flow, the extremely long time scales near the transition make direct observations of critical behaviour virtually impossible. Here we find a technical solution to that limitation and show that the universality class of the transition is directed percolation, from which a jammed phase of puffs emerges above the critical point. Our method is to experimentally characterize all pairwise interactions between localized patches of turbulence puffs and use these interactions as input for renormalization group and computer simulations of minimal models that extrapolate to long length and time scales. The strong interactions in the jamming regime enable us to explicitly measure the turbulent fraction and confirm model predictions. Our work shows that directed-percolation scaling applies beyond simple closed shear flows and underscores how statistical mechanics can lead to profound, quantitative and predictive insights on turbulent flows and their phases.

• Reis, Paula Kozlowski Pitombeira; Linga, Gaute; Moura, Marcel; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Show all 7 contributors for this article] (2024). Interaction between corner and bulk flows during drainage in granular porous media. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2409.05574. Full text in Research Archive
• Shafabakhsh, Paiman; Borgne, Tanguy Le; Renard, Francois & Linga, Gaute (2024). Resolving pore-scale concentration gradients for transverse mixing and reaction in porous media. Advances in Water Resources. ISSN 0309-1708. 192. doi: 10.1016/j.advwatres.2024.104791. Full text in Research Archive Show summary

  Mixing-limited reactions are central to a wide range of processes in natural and engineered porous media. Recent advances have shown that concentration gradients sustained by flow at the pore-scale influence macroscopic reaction rates over a large range of reactive transport regimes. Yet, resolving concentration gradients driven by fluid mixing at the pore-scale is challenging with current simulation methods. Here, we introduce a computational methodology to resolve concentration gradients at the pore scale in mixing-limited reactions. We consider a steady-state reactive transport problem characterized by reactive fluids flowing in parallel in a porous material. Given a mesh representation of the pore space and a steady velocity field, we solve the steady advection-diffusion equation for conservative scalar transport using a stabilized finite-element method combined with mesh refinement adapted to local scalar gradients. Based on this solution and assuming instantaneous reaction kinetics in the fluid, we infer the distribution of species involved in an irreversible bi-molecular reaction. We validate the method by comparing our results for uniform flow with analytical solutions and then apply it to simulate mixing-limited reactions in a three-dimensional random bead pack and Berea sandstone sample. Chaotic flow within the pore space leads to sustained concentration gradients, which are captured by our numerical framework. The results underscore the ability of the methodology to simulate transverse mixing and mixing-limited reactions in complex porous media and to provide bottom-up numerical data to improve the prediction of effective reaction rates at larger scales.

• Linga, Gaute; Mathiesen, Joachim; Renard, Francois & Borgne, Tanguy Le (2023). Fingerprints of Chaos in a Two-Phase Porous Media Flow. In Médici, Ezequiel F. & Otero, Alejandro D. (Ed.), Album of Porous Media. Springer. ISSN 9783031238000. doi: 10.1007/978-3-031-23800-0_64. Full text in Research Archive
• Mathiesen, Joachim; Linga, Gaute; Misztal, Marek; Renard, Francois & Borgne, Tanguy Le (2023). Dynamic Fluid Connectivity Controls Solute Dispersion in Multiphase Porous Media Flow. Geophysical Research Letters. ISSN 0094-8276. 50(16). doi: 10.1029/2023GL105233. Full text in Research Archive Show summary

  Abstract Solute transport in multiphase flow through porous media plays a central role in many natural systems and geoengineering applications. The interplay between fluid flow and capillary forces leads to transient flow dynamics and phase distributions. However, it is not known how such dynamic flow affects the dispersion of transported species. Here, we use highly resolved numerical simulations of immiscible two‐phase flow to investigate dispersion in multiphase flows. We show that repeated activation and deactivation of different flow pathways under the effect of capillary forces accelerates the spreading of solutes compared to single phase flow. We establish the transport laws under dynamic multiphase flows by linking the dispersion coefficient to the Bond number, the ratio of the force driving the flow and the surface tension. Our results determine the controlling factors for solute dispersion in porous media, opening a range of applications for understanding and controlling transport in porous geological systems.

• Reis, Paula Kozlowski Pitombeira; Moura, Marcel; Linga, Gaute; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Show all 7 contributors for this article] (2023). A simplified pore-scale model for slow drainage including film-flow effects. Advances in Water Resources. ISSN 0309-1708. 182. doi: 10.1016/j.advwatres.2023.104580. Full text in Research Archive Show summary

  Liquid-filled corners and capillary bridges can establish networks connecting 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 is 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 is determined by the bonds’ invasion thresholds and local capillary pressure values, calculated taking into consideration gravitational effects. With the proposed model, experimentally verified phenomena related to slow drainage in granular porous media are reproduced, showing good qualitative agreement.

• Baldelli, Beatrice; Linga, Gaute & Flekkøy, Eirik Grude (2022). Thermal conduction through a cool well. Physical Review Fluids. 7(10). doi: 10.1103/PhysRevFluids.7.103503. Full text in Research Archive Show summary

  We study a differentially heated square cavity with inlet and outlet ports at the top of the side walls, quantifying how the effective thermal conductivity changes with the temperature difference across the system. The side walls are insulating, the top surface is kept at a fixed high temperature, and the bottom surface at a fixed low temperature, leading to buoyancy-stabilized flow. We visualize the flow pattern for Reynolds number, Re=1, and Prandtl number, Pr=50, and characterize the heat transfer at the bottom surface using the Nusselt number, Nu, for Re=0.1,1,10 and Pr=1,50. As the Richardson number, Ri, is increased, we observe the formation of a series of system-spanning vortices through the merging of Moffatt eddies growing from the bottom corners of the cavity. We find that the convection, which enhances the transport of heat, is strongly suppressed by increasing the temperature drop. As a result Nu drops by a factor 1–3 depending on the Reynolds number.

• Linga, Gaute; Angheluta, Luiza & Mathiesen, Joachim (2022). Onset of turbulence in channel flows with scale-invariant roughness. Physical Review Research (PRResearch). 4(3). doi: 10.1103/PhysRevResearch.4.033086. Full text in Research Archive Show summary

  Using 3D direct numerical simulations of the Navier–Stokes equations, we study the effect of a self-affine wall roughness on the onset of turbulence in channel flow. We quantify the dependence of the turbulent intensity (proportional to the mean-squared velocity fluctuations) on the Reynolds number Re for different roughness amplitudes A. We find that for sufficiently high amplitudes, A>Ab, the transition changes its nature from being subcritical (as is known at A=0) to supercritical, i.e., the boundary roughness renders the flow unstable for Re>Rel, where the critical Rel decays nontrivially with increasing A. The dependence of the friction factor on Re is found to follow a generalized Forchheimer law, which interpolates between the laminar and inertial asymptotes. The transition between these two asymptotes occurs at a second critical Rec which is comparable in magnitude to Rel. This implies that transitional flow is an integral part of flow in open fractures when Re is sufficiently high, and should be accounted for in effective modeling approaches.

• Haugerud, Ivar Svalheim; Linga, Gaute & Flekkøy, Eirik Grude (2022). Solute dispersion in channels with periodic square boundary roughness. Journal of Fluid Mechanics. ISSN 0022-1120. 944. doi: 10.1017/jfm.2022.522. Full text in Research Archive Show summary

  Transport of solutes through channels with rough boundaries is abundant in natural and engineered settings. However, it is not known currently what the consequences of an abruptly alternating boundary are for the solute dispersion, in particular when advected by inertial fluid flow. To investigate this, we compute numerically the time-asymptotic longitudinal dispersion coefficient of a passive solute advected by fluid flow through a two-dimensional channel with square boundary roughness. We determine how the effective diffusion coefficient depends on the boundary amplitude, Péclet number and Reynolds number. For creeping flow, the effective diffusion coefficient is found to be enhanced significantly through the recirculation zones. Increasing fluid inertia reduces the effective diffusion coefficient by up to a factor of two for high Péclet numbers. We interpret this behaviour by analysing residence times computed from Lagrangian particle simulations.

• Linga, Gaute; Møyner, Olav; Nilsen, Halvor Møll; Arthur, Moncorgé & Lie, Knut-Andreas (2020). An implicit local time-stepping method based on cell reordering for multiphase flow in porous media. Journal of Computational Physics: X. 6. doi: 10.1016/j.jcpx.2020.100051. Full text in Research Archive Show summary

  We discuss how to introduce local time-step refinements in a sequential implicit method for multiphase flow in porous media. Our approach relies heavily on causality-based optimal ordering, which implies that cells can be ordered according to total fluxes after the pressure field has been computed, leaving the transport problem as a sequence of ordinary differential equations, which can be solved cell-by-cell or block-by-block. The method is suitable for arbitrary local time steps and grids, is mass-conservative, and reduces to the standard implicit upwind finite-volume method in the case of equal time steps in adjacent cells. The method is validated by a series of numerical simulations. We discuss various strategies for selecting local time steps and demonstrate the efficiency of the method and several of these strategies by through a series of numerical examples.

• Linga, Gaute; Bolet, Asger & Mathiesen, Joachim (2020). Transient electrohydrodynamic flow with concentration-dependent fluid properties: Modelling and energy-stable numerical schemes. Journal of Computational Physics. ISSN 0021-9991. 412. doi: 10.1016/j.jcp.2020.109430. Full text in Research Archive Show summary

  Transport of electrolytic solutions under influence of electric fields occurs in phenomena ranging from biology to geophysics. Here, we present a continuum model for single-phase electrohydrodynamic flow, which can be derived from fundamental thermodynamic principles. This results in a generalized Navier–Stokes–Poisson–Nernst–Planck system, where fluid properties such as density and permittivity depend on the ion concentration fields. We propose strategies for constructing numerical schemes for this set of equations, where the electrochemical and the hydrodynamic subproblems are decoupled at each time step. We provide time discretizations of the model that suffice to satisfy the same energy dissipation law as the continuous model. In particular, we propose both linear and non-linear discretizations of the electrochemical subproblem, along with a projection scheme for the fluid flow. The efficiency of the approach is demonstrated by numerical simulations using several of the proposed schemes.

• Nielsen, Bjarke Frost; Linga, Gaute; Christensen, Amalie & Mathiesen, Joachim (2020). Substrate curvature governs texture orientation in thin films of smectic block copolymers. Soft Matter. ISSN 1744-683X. 16(14), p. 3395–3406. doi: 10.1039/c9sm02389e. Full text in Research Archive Show summary

  Self-assembly of ordered nanometer-scale patterns is interesting in itself, but its practical value depends on the ability to predict and control pattern formation. In this paper we demonstrate theoretically and numerically that engineering of extrinsic as well as intrinsic substrate geometry may provide such a controllable ordering mechanism for block copolymers films. We develop an effective two-dimensional model of thin films of striped-phase diblock copolymers on general curved substrates. The model is obtained as an expansion in the film thickness and thus takes the third dimension into account, which crucially allows us to predict the preferred orientations even in the absence of intrinsic curvature. We determine the minimum-energy textures on several curved surfaces and arrive at a general principle for using substrate curvature as an ordering field, namely that the stripes will tend to align along directions of maximal curvature.

• Linga, Gaute; Bolet, Asger & Mathiesen, Joachim (2019). Bernaise: A flexible framework for simulating two-phase electrohydrodynamic flows in complex domains. Frontiers in Physics. 7. doi: 10.3389/fphy.2019.00021. Full text in Research Archive
• Linga, Gaute & Flåtten, Tore Halsne (2019). A Hierarchy of Non-Equilibrium Two-Phase Flow Models. ESAIM: Proceedings and Surveys. 66, p. 109–143. doi: 10.1051/proc/201966006. Full text in Research Archive Show summary

  We review and extend a hierarchy of relaxation models for two-phase flow. The models are derived from the non-equilibrium Baer–Nunziato model, which is endowed with relaxation source terms to drive it towards equilibrium. The source terms cause transfer of volume, heat, mass and momentum due to differences between the phases in pressure, temperature, chemical potential and velocity, respectively. In the context of two-phase flow models, the subcharacteristic condition implies that the sound speed of an equilibrium system can never exceed that of the relaxation system. Here, previous work by Flåtten and Lund [Math. Models Methods Appl. Sci., 21 (12), 2011, 2379–2407] and Lund [SIAM J. Appl. Math. 72, 2012, 1713–1741] is extended to encompass two-fluid models, i.e. models with separately governed velocities for the two phases. Each remaining model in the hierarchy is derived, and analytical expressions for the sound speeds are presented. Given only physically fundamental assumptions, the subcharacteristic condition is shown to be satisfied in the entire hierarchy, either in a weak or in a strong sense.

• Linga, Gaute; Bolet, Asger & Mathiesen, Joachim (2018). Controlling wetting with electrolytic solutions: Phase-field simulations of a droplet-conductor system. Physical Review E (PRE). ISSN 2470-0045. 98(1). doi: 10.1103/PhysRevE.98.013101. Full text in Research Archive
• Bolet, Asger; Linga, Gaute & Mathiesen, Joachim (2018). Electrohydrodynamic channeling effects in narrow fractures and pores. Physical Review E (PRE). ISSN 2470-0045. 97(4). doi: 10.1103/PhysRevE.97.043114. Full text in Research Archive
• Wilhelmsen, Øivind; Aasen, Ailo; Skaugen, Geir; Aursand, Peder; Austegard, Anders & Aursand, Eskil [Show all 10 contributors for this article] (2017). Thermodynamic modeling with equations of state: present challenges with established methods. Industrial & Engineering Chemistry Research. ISSN 0888-5885. 56(13), p. 3503–3515. doi: 10.1021/acs.iecr.7b00317. Full text in Research Archive Show summary

  Equations of state (EoS) are essential in the modeling of a wide range of industrial and natural processes. Desired qualities of EoS are accuracy, consistency, computational speed, robustness and predictive ability outside of the domain where they have been fitted. In this work, we review present challenges associated with established models, and give suggestions on how to overcome them in the future. The most accurate EoS available, multiparameter EoS, have a second artificial Maxwell loop in the two-phase region that gives problems in phase-equilibrium calculations and exclude them from important applications such as treatment of interfacial phenomena with mass based density functional theory. Suggestions are provided on how this can be improved. Cubic EoS are among the most computationally efficient EoS, but they often lack sufficient accuracy. We show that extended corresponding state EoS are capable of providing significantly more accurate single-phase predictions than cubic EoS with only a doubling of the computational time. In comparison, the computational time of multiparameter EoS can be orders of magnitude larger. For mixtures in the two-phase region, however, the accuracy of extended corresponding state EoS has a large potential for improvement. The molecular-based SAFT family of EoS are preferred when predictive ability is important, e.g. for systems with strongly associating fluids or polymers where few experimental data are available. We discuss some of their benefits and present challenges. A discussion is presented on why predictive thermodynamic models for reactive mixtures such as CO2-NH3 and CO2-H2O-H2S must be developed in close combination with phase- and reaction equilibrium theory, regardless of the choice of EoS. After overcoming present challenges, a next-generation thermodynamic modeling framework holds the potential to improve the accuracy and predictive ability in a wide range of applications such as process optimization, computational fluid dynamics, treatment of interfacial phenomena and processes with reactive mixtures.

• Linga, Gaute; Mathiesen, Joachim & Renard, Francois (2017). Self-similar distributions of fluid velocity and stress heterogeneity in a dissolving porous limestone. Journal of Geophysical Research (JGR): Solid Earth. ISSN 2169-9313. 122(3), p. 1726–1743. doi: 10.1002/2016JB013536. Full text in Research Archive Show summary

  In a porous rock, the spatial distribution of the pore space induces a strong heterogeneity in fluid flow rates and in the stress distribution in the rock mass. If the rock microstructure evolves through time, for example, by dissolution, fluid flow and stress will evolve accordingly. Here we consider a core sample of porous limestone that has undergone several steps of dissolution. Based on 3‐D X‐ray tomography scans, we calculate numerically the coupled system of fluid flow in the pore space and stress in the solid. We determine how the flow field affects the stress distribution both at the pore wall surface and in the bulk of the solid matrix. We show that during dissolution, the heterogeneous stress evolves in a self‐similar manner as the porosity is increased. Conversely, the fluid velocity shows a stretched exponential distribution. The scalings of these common master distributions offer a unified description of the porosity evolution, pore flow, and the heterogeneity in stress for a rock with evolving microstructure. Moreover, the probability density functions of stress invariants (mechanical pressure or von Mises stress) display heavy tails toward large stresses. If these results can be extended to other kinds of rocks, they provide an additional explanation of the sensitivity to failure of porous rocks under slight changes of stress. This research was originally published in Journal of Geophysical Research. Solid Earth. © 2017 American Geophysical Union

• Linga, Gaute & Lund, Halvor (2016). A Two-Fluid Model for Vertical Flow Applied to CO2 Injection Wells. International Journal of Greenhouse Gas Control. ISSN 1750-5836. 51, p. 71–80. doi: 10.1016/j.ijggc.2016.05.009. Full text in Research Archive Show summary

  Flow of CO2 in wells is associated with substantial variations in thermophysical properties downhole, due to the coupled transient processes involved: complex flow patterns, density changes, phase transitions, and heat transfer to and from surroundings. Large temperature variations can lead to thermal stresses and subsequent loss of well integrity, and it is therefore crucial to employ models that can predict this accurately. In this work, we present a model for vertical well flow that includes both two-phase flow and heat conduction. The flow is described by a two-fluid model, where mass transfer between the phases is modelled by relaxation source terms that drive the phases towards thermodynamic equilibrium. We suggest a new formulation of the mass transfer process that satisfies the second law of thermodynamics, and that is also continuous in the single-phase limit. This provides a more robust transition from two-phase to single-phase flow than the previous formulation. The model predicts which flow regimes are present downhole, and calculates friction and heat transfer depending on this. Moreover, the flow model is coupled with a heat conduction model for the layers that comprise the well, including tubing, packer fluid, casing, cement or drilling mud, and rock formation. This enables prediction of the temperature in the well fluid and in each layer of the well. The model is applied to sudden shut-in and blowout cases of a CO2 injection well, where we employ the highly accurate Span-Wagner reference equation-of-state to describe the thermodynamics of CO2. We predict pressure, temperature and flow regimes during these cases and discuss implications for well integrity. © 2016 Elsevier Ltd.

• Linga, Gaute; Ballone, Pietro & Hansen, Alex (2015). Creep rupture of fiber bundles: A molecular dynamics investigation. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. ISSN 1539-3755. 92(2). doi: 10.1103/PhysRevE.92.022405. Full text in Research Archive
• Linga, Gaute; Aursand, Peder & Flåtten, Tore (2015). Two-phase nozzle flow and the subcharacteristic condition. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. 426(2), p. 917–934. doi: 10.1016/j.jmaa.2015.01.065. Full text in Research Archive Show summary

  We consider nozzle flow models for two-phase flow with phase transfer. Such models are based on energy considerations applied to the frozen and equilibrium limits of the underlying relaxation models. In this paper, we provide an explicit link between the mass flow rate predicted by these models and the classical subcharacteristic condition of Chen, Levermore and Liu. In particular, we demonstrate that for sufficiently small pressure differences, the equilibrium nozzle model will predict a lower mass flow rate than the frozen model when the subcharacteristic condition is satisfied. An application to tank leakage of CO2 is presented, indicating that the frozen and equilibrium models provide significantly different predictions. This difference is comparable in magnitude to the modeling error introduced by applying simple ideal-gas/incompressible-liquid equations-of-state for CO2.

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• Reis, Paula Kozlowski Pitombeira; Moura, Marcel; Pierce, Kevin; Måløy, Knut Jørgen & Linga, Gaute (2026). Secondary imbibition in 2D porous media: The role of flow direction in trapping. Full text in Research Archive
• Moura, Marcel; Brodin, Joachim Falck; Reis, Paula Kozlowski Pitombeira; Pierce, Kevin; Jankov, Mihailo & Rikvold, Per Arne [Show all 11 contributors for this article] (2026). From Thin Films to Stable Fronts: Tabletop Experimental Approaches to 2D and 3D Porous Media Flows. doi: https:/www.youtube.com/live/bSQ-sHK6FTU?si=W9_rbJ5BkyRPHP0m. Full text in Research Archive
• Moura, Marcel; Reis, Paula Kozlowski Pitombeira; Rikvold, Per Arne; Linga, Gaute; Flekkøy, Eirik Grude & Schäfer, Gerhard [Show all 8 contributors for this article] (2026). Thin Film Flow: Fluid Transport via Thin Liquid Films in Slow Porous Media Flows. Full text in Research Archive
• Dziadkowiec, Joanna; Linga, Gaute; Dunkel, Kristina G.; Valtiner, Markus & Renard, Francois (2026). In-situ, real-time replacement of calcite under geometrical confinement. doi: 10.5194/egusphere-egu26-3925. Full text in Research Archive Show summary

  Mineral replacement by dissolution-precipitation reactions that occur under confinement critically influences subsurface deformation by modifying rock porosity, permeability, and cohesion, and by inducing fracturing. Yet real-time, experimental observations of these phenomena at the nano- to microscale remain insufficient. In this work, we follow the in-situ replacement of confined calcite crystal using a surface force apparatus (SFA) technique. Calcite undergoes dissolution under low pH conditions, followed by replacement into three various Ca-minerals: calcium oxalate, calcium sulfate (gypsum), or calcium phosphate (brushite), depending on the initial composition of the solution. We monitor these reactions in real time, map the spatial distribution of precipitates as a function of confinement gap size, and evaluate how epitaxy between the secondary phases and the parent calcite governs preferred nucleation and growth sites. In addition, we measure forces that act on the confining pore wall during the replacement and estimate the associated crystallization pressures. This work contributes to the understanding of the mineral growth under confinement and its consequences for porous rock integrity, with immediate relevance to subsurface fluid and gas storage operations, where rapid mineralization is common.

• Pierce, Kevin; Lamblin, Marc; Borgne, Tanguy Le; Heyman, Joris & Linga, Gaute (2025). Mixing enhancement by dynamic multiphase flow through 3D porous media. Transactions of the American Geophysical Union. Full text in Research Archive
• Linga, Gaute (2025). Mixing by interfaces: How does water infiltration control mixing and reactions in soils? Full text in Research Archive
• Linga, Gaute (2025). Pore-scale modelling of solute mixing in unsteady flows. Full text in Research Archive
• Linga, Gaute (2025). Enhanced mixing triggered by unsteady flow at the pore-scale. Full text in Research Archive
• Lanza, Federico; Linga, Gaute; Barras, Fabian; Khobaib, Khobaib; Flekkøy, Eirik Grude & Måløy, Knut Jørgen (2025). From Carbopol to magma: challenges in complex flows through porous and confined media. Full text in Research Archive
• Moura, Marcel; Reis, Paula Kozlowski Pitombeira; Rikvold, Per Arne; Linga, Gaute; Flekkøy, Eirik Grude & Schäfer, Gerhard [Show all 8 contributors for this article] (2025). Thin Film Flow: Fluid Transport via Thin Liquid Films in Slow Porous Media Flows. Full text in Research Archive
• Pierce, James Kevin; Lamblin, Marc; Borgne, Tanguy Le; Heyman, Joris & Linga, Gaute (2025). Enhanced mixing in dynamic multiphase flow through 3D porous media. Full text in Research Archive
• Pierce, James Kevin; Borgne, Tanguy Le & Linga, Gaute (2025). Burst-enhanced mixing in multiphase flows through porous media. Full text in Research Archive
• Pierce, James Kevin; Borgne, Tanguy Le & Linga, Gaute (2025). Impact of structural disorder on mixing in porous media. Full text in Research Archive
• Linga, Gaute (2025). Security in Physics. Full text in Research Archive
• Linga, Gaute (2025). Mixing by interfaces. Full text in Research Archive
• Reis, Paula Kozlowski Pitombeira; Moura, Marcel; Linga, Gaute; Toussaint, Renaud; Rikvold, Per Arne & Flekkøy, Eirik Grude [Show all 7 contributors for this article] (2025). Modeling Gas-Liquid Drainage in Porous Media with Network Models. Full text in Research Archive
• Linga, Gaute; Borgne, Tanguy Le & Heyman, Joris (2024). New light on a classical push-pull experiment. Full text in Research Archive Show summary

  A series of push-pull experiments by Oxaal, Flekkøy et al. [1, 2] three decades ago elegantly singled out the effect of stagnation points on pore-scale mixing. In these experiments, a line of tracer dye was injected into a Hele-Shaw cell containing a single cylindrical obstacle. The line was then advected by creeping flow towards the obstacle. After a time T/2, the flow field was reversed and the strip was advected back until a time T. The final state of the tracer line was then identical to the initial one, except near the middle, where the width could locally be orders of magnitude larger than the molecular diffusivity. Until now, a quantitative theory for this enhancement was missing. Here, we provide a complete theory for mixing by push-pull flow near stagnation points by employing the Lagrangian stretching framework. [1] U. Oxaal, E.G. Flekkøy, and J. Feder. Irreversible dispersion at a stagnation point: Experiments and lattice Boltzmann simulations. Phys. Rev. Lett. 72 (1994). [2] E.G. Flekkøy, U. Oxaal, J. Feder, and T. Jøssang. Hydrodynamic dispersion at stagnation points: Simulations and experiments. Phys. Rev. E 52 (1995).

• Pierce, James Kevin; Borgne, Tanguy Le & Linga, Gaute (2024). Impact of heterogeneity on solute mixing in porous media flows. Full text in Research Archive
• Pierce, James Kevin; Linga, Gaute & Borgne, Tanguy Le (2024). Experimental imaging of pore scale stretching and coalescence as drivers for solute mixing in porous media. Full text in Research Archive
• Lanza, Federico; Baldelli, Beatrice; Linga, Gaute; Barras, Fabian & Flekkøy, Eirik Grude (2024). The Cooling Instability. Full text in Research Archive
• Lanza, Federico; Baldelli, Beatrice; Linga, Gaute; Barras, Fabian & Flekkøy, Eirik Grude (2024). Dynamic instability of a temperature-dependent viscous fluid in a Hele-Shaw cell. Full text in Research Archive
• Moura, Marcel; Måløy, Knut Jørgen; Flekkøy, Eirik Grude; Brodin, Joachim Falck; Reis, Paula Kozlowski Pitombeira & Linga, Gaute [Show all 7 contributors for this article] (2024). A pool of two-phase flows experiments: films, bursts, patterns and avalanches. Full text in Research Archive
• Moura, Marcel; Måløy, Knut Jørgen; Flekkøy, Eirik Grude; Brodin, Joachim Falck; Reis, Paula Kozlowski Pitombeira & Linga, Gaute [Show all 7 contributors for this article] (2024). A little bit of our activity at PoreLab and Njord. Full text in Research Archive
• Reis, Paula Kozlowski Pitombeira; Linga, Gaute; Moura, Marcel; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Show all 7 contributors for this article] (2024). Investigation of liquid connectivity and drainage in granular porous media. Full text in Research Archive
• Reis, Paula Kozlowski Pitombeira; Linga, Gaute; Moura, Marcel; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Show all 7 contributors for this article] (2024). Investigation of liquid connectivity and drainage in granular porous media. Full text in Research Archive
• Reis, Paula Kozlowski Pitombeira; Linga, Gaute; Moura, Marcel; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Show all 7 contributors for this article] (2024). Network modeling of corner and bulk flows during drainage in granular porous media. Full text in Research Archive
• Linga, Gaute (2024). Mixing by interfaces: Impact of unsteady flow on solute transport in porous media. Full text in Research Archive
• Linga, Gaute (2024). Mixing by interfaces. Full text in Research Archive
• Lanza, Federico; Baldelli, Beatrice; Linga, Gaute; Barras, Fabian & Flekkøy, Eirik Grude (2024). Simulating finger structures that may form when a warm liquid (lava) cools and becomes more viscous during flow through a fracture. Full text in Research Archive
• Linga, Gaute (2024). Capillarity drives chaotic mixing in porous media flow. Full text in Research Archive
• Linga, Gaute (2024). How does capillarity control mixing in porous media? Full text in Research Archive
• Reis, Paula Kozlowski Pitombeira; Moura, Marcel; Linga, Gaute; Rikvold, Per Arne; Flekkøy, Eirik Grude & Måløy, Knut Jørgen (2023). A simplified pore-scale model for drainage including film flow effects. Full text in Research Archive
• Reis, Paula Kozlowski Pitombeira; Moura, Marcel; Linga, Gaute; Rikvold, Per Arne; Flekkøy, Eirik Grude & Måløy, Knut Jørgen (2023). A modified-invasion-percolation model for drainage in quasi-2D porous media. Full text in Research Archive
• Reis, Paula Kozlowski Pitombeira; Moura, Marcel; Linga, Gaute; Rikvold, Per Arne; Flekkøy, Eirik Grude & Måløy, Knut Jørgen (2023). A simplified pore-scale model for slow drainage including film-flow effects. Full text in Research Archive
• Reis, Paula Kozlowski Pitombeira; Moura, Marcel; Linga, Gaute; Rikvold, Per Arne; Toussaint, Renaud & Flekkøy, Eirik Grude [Show all 7 contributors for this article] (2023). Numerical analysis of drainage in porous media using network models. Full text in Research Archive
• Pierce, James Kevin; Moura, Marcel & Linga, Gaute (2023). Chaotic mixing in two-dimensional unsteady porous media flow. Full text in Research Archive
• Pierce, James Kevin; Linga, Gaute & Moura, Marcel (2023). Hallmarks of chaotic mixing in two dimensional unsteady porous media flow. Full text in Research Archive
• Pierce, James Kevin & Linga, Gaute (2023). Chaos in flatland: mixing in unsteady two dimensional porous media flow. Full text in Research Archive
• Pierce, James Kevin; Linga, Gaute & Moura, Marcel (2023). Impact of the solid structure on solute mixing in porous media flow. Full text in Research Archive
• Linga, Gaute (2023). Chaotic mixing in time-dependent porous media flows. Full text in Research Archive
• Linga, Gaute & Borgne, Tanguy Le (2023). Chaotic mixing due to oscillatory flow in porous media. Full text in Research Archive
• Linga, Gaute; Mathiesen, Joachim; Renard, Francois & Borgne, Tanguy Le (2022). Chaotic mixing in intermittent two-phase porous media flows. Full text in Research Archive
• Linga, Gaute (2022). Chaotic mixing in intermittent two-phase porous media flows. Full text in Research Archive
• Linga, Gaute (2022). Chaotic mixing in unsteady porous media flows. Full text in Research Archive
• Linga, Gaute; Mathiesen, Joachim; Renard, Francois & Borgne, Tanguy Le (2020). Stretching and Folding in Intermittent Two-Phase Porous Media Flows. Full text in Research Archive
• Nielsen, Bjarke Frost; Linga, Gaute; Olsen, Kristian Stølevik & Simonsen, Lone (2020). Vejen til frihed. Weekendavisen. ISSN 0106-4142. Full text in Research Archive Show summary

  https://www.weekendavisen.dk/2020-19/ideer/vejen-til-frihed

• Linga, Gaute (2020). Stretching and mixing in two-phase flow in porous media. Full text in Research Archive
• Linga, Gaute (2019). Two-phase electrohydrodynamics in complex geometries – modelling and simulation. Full text in Research Archive
• Linga, Gaute (2019). Influence of roughness, inertia and surface charge on fluid transport in fractures and pores: Insights from direct numerical simulations. Full text in Research Archive
• Lie, Knut-Andreas; Linga, Gaute; Møyner, Olav; Nilsen, Halvor Møll & Moncorge, A (2019). An implicit local time-stepping method based on cell reordering for multiphase flow in porous media. Full text in Research Archive

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