A key challenge in multiphase flow through porous media is to understand and predict the conditions under which trapped fluid clusters become mobilized. Here, we investigate the stability of such clusters in two-phase flow and present a simple, quasistatic model that accurately determines the critical Bond number (that is, the critical ratio between the average pressure gradient of the flow and the surface tension) for the onset of cluster mobilization. The model is derived by combining elementary geometrical considerations with mass conservation and a mechanical equilibrium condition, resulting in a system of coupled differential equations. Our derivation sheds new light on the mechanisms that govern cluster stability. In addition, since the number of equations equals the number of cluster openings, our model is significantly faster than direct numerical simulations of the same problem and enables efficient exploration of the system's parameter space. Using this approach, we highlight a discrepancy with the prediction of current mean-field theories, which predict that the largest stable cluster size scales in proportion to r/Bo^α, where r is a typical pore size, Bo is the Bond number and α is a fixed exponent. We discuss the mechanisms that explain the breakdown of the mean field theories, and we show that a scaling law of this form can only exist if α is allowed to depend on a broad set of flow and geometric parameters.

The enforcement of global energy conservation in phase-field fracture simulations has been an open problem for the last 25 years. Specifically, the occurrence of unstable fracture is accompanied by a loss in total potential energy, which suggests a violation of the energy conservation law. This phenomenon can occur even with purely quasi-static, displacement-driven loading conditions, where finite crack growth arises from an infinitesimal increase in load. While such behavior is typically seen in crack nucleation, it may also occur in other situations. Initial efforts to enforce energy conservation involved backtracking schemes based on global minimization, however in recent years it has become clearer that unstable fracture, being an inherently dynamic phenomenon, cannot be adequately resolved within a purely quasi-static framework. Despite this, it remains uncertain whether transitioning to a fully dynamic framework would sufficiently address the issue. In this work, we propose a pseudo-dynamic framework designed to enforce energy balance without relying on global minimization. This approach incorporates dynamic effects heuristically into an otherwise quasi-static model, allowing us to bypass solving the full dynamic linear momentum equation. It offers the flexibility to simulate crack evolution along a spectrum, ranging from full energy conservation at one extreme to maximal energy loss at the other. Using data from recent experiments, we demonstrate that our framework can closely replicate experimental load-displacement curves, achieving results that are unattainable with classical phase-field models.

Solute mixing plays a pivotal role in a broad spectrum of chemical and biological processes across natural and engineered porous media. However, current understanding of mixing dynamics remains largely constrained to steady flows in fully or partially water-saturated environments. Multiphase flow systems are generally unsteady, with moving fluid interfaces and flow paths that change in time. Despite the widespread occurrence of dynamic multiphase flows, their impacts on solute mixing are largely unknown. Here, we use experiments and numerical simulations to investigate the effect of dynamic two-phase flow on the stretching and folding of fluid elements, a fundamental mechanism driving solute mixing and reactions in porous media. We find that dynamic two-phase flows induce chaotic mixing, characterized by exponential stretching of fluid elements, leading to strongly enhanced mixing compared to steady single-phase flows. By extensive numerical multiphase flow simulations, we establish dynamic steady states where we reliably measure the mean fluid stretching rate as a function of flow rate. We show that stretching is maximized at an optimum flow rate which balances fluid shear deformation against the frequency of flow reorientation by the intermittent motion of the fluid interface. The findings are rationalized by a mechanistic model linking basic multiphase flow characteristics to the stretching rate, opening perspectives to understand and control mixing and reactions in a wide range of multiphase flow systems.

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 CaCl2 and Na2CO3, 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.

Ice fractures when subject to stress that exceeds the material failure strength. Previous studies have found that a von Mises failure criterion, which places a bound on the second invariant of the deviatoric stress tensor, is consistent with empirical data. Other studies have suggested that a scaling effect exists, such that larger sample specimens have a substantially lower failure strength, implying that estimating material strength from laboratory-scale experiments may be insufficient for glacier-scale modeling. In this paper, we analyze the stress conditions in crevasse onset regions to better understand the failure criterion and strength relevant for large-scale modeling. The local deviatoric stress is inferred using surface velocities and reanalysis temperatures, and crevasse onset regions are extracted from a remotely sensed crevasse density map. We project the stress state onto the failure plane spanned by Haigh-Westergaard coordinates, showing how failure depends on mode of stress. We find that existing crevasse data are consistent with a Schmidt-Ishlinsky failure criterion that places a bound on the absolute value of the maximal principal deviatoric stress, estimated to be 158 +/- 44 kPa. Although the traditional von Mises failure criterion also provides an adequate fit to the data with a von Mises strength of 265 +/- 73 kPa, it depends only on stress magnitude and is indifferent to the specific stress state, unlike Schmidt-Ishlinsky failure which has a larger shear failure strength compared to tensile strength. Implications for large-scale ice flow and fracture modeling are discussed.

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. The nature of turbulence that occurs when fluids flow in a pipe is still controversial. Now the onset of turbulence in pipe flow has been shown to be a directed-percolation phase transition.

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. Flow and mixing processes in porous media control many natural and industrial systems, such as microbial clogging, oil extraction, and effluent disposal. In many systems, the porosity may evolve during mineral precipitation, such as in rocks, and control fluid transport properties. Here, we use time-lapsed three-dimensional neutron imaging to explore fluid transport into Berea sandstone core samples during in-situ carbonate precipitation. Neutron imaging can track fluid flow inside the rock, whereas X-ray imaging illuminates the regions where mineral precipitation occurs. We control the precipitation of calcium carbonate in the rock through reactive mixing between solutions containing CaCl2 and Na2CO3. By solving the adverse advection-diffusion equation using the contrast in neutron attenuation from time-lapse images, we derive the 3D velocity field of the injected fluids. Results show that under the effect of mineral precipitation, a wide range of local flow velocities develop in the sample, and we quantify the distribution of flow velocities in the sample. The finding of this experimental study is useful in progressing the knowledge in the domain of reactive solute and contaminant transport in the subsurface. 4D neutron imaging is used to image flow and transport in porous rock and investigate the effect of carbonate precipitation The velocity field of injected fluid is estimated by solving the advection-dispersion equation using the contrast in neutron attenuation Carbonate precipitation widens the distribution of fluid velocities due to local pore-clogging

AbstractFracture networks in rocks and other geomaterials form by seismic and aseismic damage processes that could lead to system‐size failure. Here, we use a multi‐view convolutional neural network model to predict the stress proximity to macroscopic failure of experimentally deformed rock samples using two‐dimensional images. Models are trained on time series of fractures observed in rock samples through dynamic in situ synchrotron X‐ray tomography experiments. The results demonstrate that deep learning models outperform traditional estimates based on fracture density, increasing the accuracy of the predictions. Furthermore, the models provide insights into fundamental characteristics of fracture patterns that may provide precursory information on impending material failure. The trained deep learning models estimate the angle of the fracture plane relative to the principal loading direction, which is a key factor contributing to shear failure. The predicted angle of the fracture plane, in the range of 10°–30° with respect to the direction of maximum compressive stress, is consistent with the established failure criteria used in rock mechanics.

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.

Advances in micro-scale imaging techniques, such as X-ray microtomography, have provided new insights into a broad range of porous media processes. However, direct imaging of flow and transport processes remains challenging due to spatial and temporal resolution limitations. Here, we investigate the use of dynamic three-dimensional 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-lapse 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. These findings suggest that neutron imaging is a promising technique to investigate dynamics processes in porous media.

Ice fractures when subject to stress that exceeds the material failure strength. Previous studies have found that a von Mises failure criterion, which places a bound on the second invariant of the deviatoric stress tensor, is consistent with empirical data. Other studies have suggested that a scaling effect exists, such that larger sample specimens have a substantially lower failure strength, implying that estimating material strength from laboratory-scale experiments may be insufficient for glacier-scale modelling. In this paper, we analyze the stress conditions in crevasse onset regions to better understand the failure criterion and strength relevant for large-scale modelling. The local deviatoric stress is inferred using surface velocities and reanalysis temperatures, and crevasse onset regions are extracted from a remotely sensed crevasse density map. We project the stress state onto the failure plane spanned by Haigh–Westergaard coordinates, showing how failure depends on mode of stress. We find that existing crevasse data is consistent with a Schmidt–Ishlinsky failure criterion that places a bound on the absolute value of the maximal principal deviatoric stress, estimated to be (158 ± 44) kPa. Although the traditional von Mises failure criterion also provides an adequate fit to the data with a von Mises strength of (265 ± 73) kPa, it depends only on stress magnitude and is indifferent to the specific stress state, unlike Schmidt–Ishlinsky failure which has a larger shear failure strength compared to tensile strength. Implications for large-scale ice-flow and fracture modelling are discussed.

<p>Flow and mixing processes in porous media control many natural and industrial systems, such as microbial clogging, oil extraction, and effluent disposal. In many systems, the porosity may evolve during mineral precipitation, such as in rocks, and control fluid mixing and fluid transport properties. Here, we use three-dimensional in situ dynamic neutron and X-ray micro-tomography imaging to explore fluid transport into Berea sandstone core samples during in-situ carbonate precipitation. Neutron imaging can track fluid flow inside the rock, whereas X-ray imaging illuminates the regions where mineral precipitation occurs. We control the precipitation of calcium carbonate in the rock through reactive-mixing between solutions containing CaCl<sub>2</sub> and Na<sub>2</sub>CO<sub>3</sub>. By solving the advection-diffusion equation using the contrast in neutron attenuation from time-lapse images, we derive the 3D velocity field of the injected fluids and characterize the evolution of the permeability field into the rock during mineral precipitation. We also investigate the mixing between heavy water and a cadmium solution under the influence of mineral precipitation. Results show that, under the effect of mineral precipitation, a wide range of local flow velocities develop in the sample, under the same fluid injection rate, and we quantify the distribution of flow velocities in the sample. Moreover, we observe more efficient mixing between heavy water and a cadmium solution after mineral precipitation. The finding of this experimental study is useful in progressing the knowledge in the domain of reactive solute and contaminant transport in the subsurface.</p>

Solute mixing in porous media is a complex and often beautiful process. Here, a tiny strip of dye is injected numerically (at the right) into a simulated two-phase (leftward) flow through an array of solid spheres.

Terrorists use violence in pursuit of political goals. While terror often has severe consequences for victims, it remains an open question how terror attacks affect the general population. We study the behavioral response of citizens of cities affected by $7$ different terror attacks. We compare real-time mobile communication patterns in the first $24$ hours following a terror attack to the corresponding patterns on days with no terror attack. On ordinary days, the group of female and male participants have different activity patterns. Following a terror attack, however, we observe a significant increase of the gender differences. Knowledge about citizens' behavior response patterns following terror attacks may have important implications for the public response during and after an attack.

Muscles and tendons, actuators in robotics, and various sports implements are examples that exploit elasticity to accelerate objects. Tuning the mechanical properties of elastic elements connecting objects can greatly enhance the transfer of mechanical energy between the objects. Here, we study experimentally the throw of rigid projectiles by an actuator, which has a soft elastic element added to the distal end. We vary the thickness of the elastic layer and suggest a simple mass-spring chain model to find the properties of the elastic layer, which will maximize the energy transfer from the actuator to the projectile. The insertion of a soft layer, impedance matched to the ejection frequency of the projectile mass, can increase the throwing efficiency by over 400%. Finally, we identify that very thick and very soft compliant layers could potentially lead to high efficiency and flexibility simultaneously.

Using 3D direct numerical simulations of the Navier--Stokes equations, we study the effect of wall roughness on the onset of turbulence in channel flow. The dependence of the friction factor on the Reynolds number, $\mathrm{Re}$, 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 first critical $\mathrm{Re}$, $\mathrm{Re}_{\mathrm{c}}$, that depends nontrivially on the roughness amplitude. We identify the transition from subcritical to supercritical onset by looking at the dependence of the velocity fluctuations on Re for different roughness amplitudes. We find that this second critical $\mathrm{Re}$ is comparable in magnitude to $\mathrm{Re}_{\mathrm{c}}$, implying that transitional flow is an integral part of flow in open fractures when $\mathrm{Re}$ and the roughness amplitude are sufficiently high.

Digital contact tracing has been suggested as an effective strategy for controlling an epidemic without severely limiting personal mobility. Here, we use smartphone proximity data to explore how social structure affects contact tracing of COVID-19. We model the spread of COVID-19 and find that the effectiveness of contact tracing depends strongly on social network structure and heterogeneous social activity. Contact tracing is shown to be remarkably effective in a workplace environment and the effectiveness depends strongly on the minimum duration of contact required to initiate quarantine. In a realistic social network, we find that forward contact tracing with immediate isolation can reduce an epidemic by more than 70%. In perspective, our findings highlight the necessity of incorporating social heterogeneity into models of mitigation strategies. Graphic abstract

Epidemics are regularly associated with reports of superspreading: single individuals infecting many others. How do we determine if such events are due to people inherently being biological superspreaders or simply due to random chance? We present an analytically solvable model for airborne diseases which reveal the spreading statistics of epidemics in socio-spatial heterogeneous spaces and provide a baseline to which data may be compared. In contrast to classical SIR models, we explicitly model social events where airborne pathogen transmission allows a single individual to infect many simultaneously, a key feature that generates distinctive output statistics. We find that diseases that have a short duration of high infectiousness can give extreme statistics such as 20% infecting more than 80%, depending on the socio-spatial heterogeneity. Quantifying this by a distribution over sizes of social gatherings, tracking data of social proximity for university students suggest that this can be a approximated by a power law. Finally, we study mitigation efforts applied to our model. We find that the effect of banning large gatherings works equally well for diseases with any duration of infectiousness, but depends strongly on socio-spatial heterogeneity.