arXiv subjects

Joachim Mathiesen

Publications and source records attributed to Joachim Mathiesen.

At least 19 recordsLinked to original sources

arXiv2026

Dynamic multiphase flow triggers chaotic mixing in porous media

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 new perspectives to understand and control mixing and reactions in a wide range of multiphase flow systems.

physics.flu-dyn↗

arXiv2025

Stability of trapped fluid clusters in two-phase porous media flow

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 $r/\text{Bo}^\alpha$, where $r$ is a typical pore size, $\text{Bo}$ is the Bond number and $\alpha$ 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 $\alpha$ is allowed to depend on a broad set of flow and geometric parameters.

physics.flu-dyn↗

arXiv2025

A pseudo-dynamic phase-field model for brittle fracture

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.

cond-mat.mtrl-sci↗

arXiv2021

Enhanced dispersion in intermittent multiphase flow

Transport in multiphase flow through porous media plays a central role in many biological, geological, and engineered systems. Here, we use numerical simulations of transport in immiscible two-phase flow to investigate dispersion in multiphase porous media flow. While dispersion in the main flow direction is similar to that of a single-phase flow and is governed by the porous media structure, we find that transverse dispersion exhibits fundamentally different dynamics. The repeated activation and deactivation of different flow pathways under the effect of capillary forces lead to intermittent flow patterns, strongly enhancing dispersion. We show that the transverse dispersion is controlled by the length scale of fluid clusters, and thus inversely proportional to the square root of the Bond number, the ratio of the force driving the flow and the surface tension. This result leads to a new scaling law relating multiphase flow dynamics to transport properties, opening a range of fundamental and engineering applications.

physics.flu-dyn↗

arXiv2020

Onset of turbulence in channel flows with scale-invariant roughness

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.

physics.flu-dyn↗

arXiv2020

Gender-specific behavior change following terror attacks

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.

cs.SI↗

arXiv2019

Substrate curvature governs texture orientation in thin films of smectic block copolymers

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.

cond-mat.soft↗

arXiv2019

Transient electrohydrodynamic flow with concentration dependent fluid properties: modelling and energy-stable numerical schemes

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 solving 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.

physics.flu-dyn↗

arXiv2019

Self-similar distributions of fluid velocity and stress heterogeneity in a dissolving porous limestone

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 3D 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 towards 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.

physics.geo-ph↗

arXiv2018

Bernaise: A flexible framework for simulating two-phase electrohydrodynamic flows in complex domains

Bernaise (Binary ElectRohydrodyNAmIc SolvEr) is a flexible high-level finite element solver of two-phase electrohydrodynamic flow in complex geometries. Two-phase flow with electrolytes is relevant across a broad range of systems and scales, from 'lab-on-a-chip' devices for medical diagnostics to enhanced oil recovery at the reservoir scale. For the strongly coupled multi-physics problem, we employ a recently developed thermodynamically consistent model which combines a generalized Nernst-Planck equation for ion transport, the Poisson equation for electrostatics, the Cahn-Hilliard equation for the phase field (describing the interface separating the phases), and the Navier-Stokes equations for fluid flow. As an efficient alternative to solving the coupled system of partial differential equations in a monolithic manner, we present a linear, decoupled numerical scheme which sequentially solves the three sets of equations. The scheme is validated by comparison to limiting cases where analytical solutions are available, benchmark cases, and by the method of manufactured solution. The solver operates on unstructured meshes and is therefore well suited to handle arbitrarily shaped domains and problem set-ups where, e.g., very different resolutions are required in different parts of the domain. Bernaise is implemented in Python via the FEniCS framework, which effectively utilizes MPI and domain decomposition, and should therefore be suitable for large-scale/high-performance computing. Further, new solvers and problem set-ups can be specified and added with ease to the Bernaise framework by experienced Python users.

physics.comp-ph↗

arXiv2018

Controlling wetting with electrolytic solutions: phase-field simulations of a droplet-conductor system

The wetting properties of immiscible two-phase systems are crucial in a wide range of applications, from lab-on-a-chip devices to field-scale oil recovery. It has long been known that effective wetting properties can be altered by the application of an electric field; a phenomenon coined as electrowetting. Here, we consider theoretically and numerically a single droplet sitting on an (insulated) conductor, i.e., within a capacitor. The droplet consists of a pure phase without solutes, while the surrounding fluid contains a symmetric monovalent electrolyte, and the interface between them is impermeable. Using nonlinear Poisson--Boltzmann theory, we present a theoretical prediction of the dependency of the apparent contact angle on the applied electric potential. We then present well-resolved dynamic simulations of electrowetting using a phase-field model, where the entire two-phase electrokinetic problem, including the electric double layers (EDLs), is resolved. The simulations show that, while the contact angle on scales smaller than the EDL is unaffected by the application of an electric field, an apparent contact angle forms on scales beyond the EDL. This contact angle relaxes in time towards a saturated apparent contact angle. The dependency of the contact angle upon applied electric potential is in good compliance with the theoretical prediction. The only phenomenological parameter in the prediction is shown to only depend on the permeability ratio between the two phases. Based on the resulting unified description, we obtain an effective expression of the contact angle which can be used in more macroscopic numerical simulations, i.e. where the electrokinetic problem is not fully resolved.

physics.flu-dyn↗

arXiv2018

Electrohydrodynamic channeling effects in narrow fractures and pores

In low-permeability rock, fluid and mineral transport occur in pores and fracture apertures at the scale of micrometers and below. At this scale, the presence of surface charge, and a resultant electrical double layer, may considerably alter transport properties. However, due to the inherent non-linearity of the governing equations, numerical and theoretical studies of the coupling between electric double layers and flow have mostly been limited to two-dimensional or axisymmetric geometries. Here, we present comprehensive three-dimensional simulations of electrohydrodynamic flow in an idealized fracture geometry consisting of a sinusoidally undulated bottom surface and a flat top surface. We investigate the effects of varying the amplitude and the Debye length (relative to the fracture aperture) and quantify their impact on flow channeling. The results indicate that channeling can be significantly increased in the plane of flow. Local flow in the narrow regions can be slowed down by up to $5 \%$ compared to the same geometry without charge, for the highest amplitude considered. This indicates that electrohydrodynamics may have consequences for transport phenomena and surface growth in geophysical systems.

physics.flu-dyn↗

arXiv2017

Correlations Between Human Mobility and Social Interaction Reveal General Activity Patterns

A day in the life of a person involves a broad range of activities which are common across many people. Going beyond diurnal cycles, a central question is: to what extent do individuals act according to patterns shared across an entire population? Here we investigate the interplay between different activity types, namely communication, motion, and physical proximity by analyzing data collected from smartphones distributed among 638 individuals. We explore two central questions: Which underlying principles govern the formation of the activity patterns? Are the patterns specific to each individual or shared across the entire population? We find that statistics of the entire population allows us to successfully predict 71\% of the activity and 85\% of the inactivity involved in communication, mobility, and physical proximity. Surprisingly, individual level statistics only result in marginally better predictions, indicating that a majority of activity patterns are shared across {our sample population}. Finally, we predict short-term activity patterns using a generalized linear model, which suggests that a simple linear description might be sufficient to explain a wide range of actions, whether they be of social or of physical character.

cs.SI↗

arXiv2017

Finite Element Lattice Boltzmann Simulations of Contact Line Dynamics

The lattice Boltzmann method has become a standard technique for simulating a wide range of fluid flows. However, the intrinsic coupling of momentum and space discretization restricts the traditional lattice Boltzmann method to regular lattices. Alternative off-lattice Boltzmann schemes exist for both single- and multiphase flows that decouple the velocity discretization from the underlying spatial grid. The current study extends the applicability of these off-lattice methods by introducing a finite element formulation that enables simulating contact line dynamics for partially wetting fluids. This work exemplifies the implementation of the scheme and furthermore presents benchmark experiments that show the scheme reduces spurious currents at the liquid-vapor interface by two orders of magnitude compared to a nodal implementation and allows for predicting the equilibrium states accurately in the range of moderate contact angles.

physics.flu-dyn↗

arXiv2017

Characterization of phase transitions in a model ecosystem of sessile species

We consider a model ecosystem of sessile species competing for space. In particular, we consider the system introduced in [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011)] where species compete according to a fixed interaction network with links determined by a Bernoulli process. In the limit of a small introduction rate of new species, the model exhibits a discontinuous transition from a high-diversity state to a low-diversity state as the interaction probability between species, $γ$, is increased from zero. Here we explore the effects of finite introduction rates and system-size on the phase transition by utilizing efficient parallel computing. We find that the low state appears for $γ>γ_c$. As $γ$ is increased further, the high state approaches to the low state, suggesting the possibility that the two states merge at a high $γ$. We find that the fraction of time spent in the high state becomes longer with higher introduction rates, but the availability of the two states is rather insensitive to the value of the introduction rate. Furthermore we establish a relation between the introduction rate and the system size, which preserves the probability for the system to remain in the high-diversity state.

q-bio.PE↗

arXiv2016

Evaluation of the Finite Element Lattice Boltzmann Method for Binary Fluid Flows

In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex boundaries. The current work combines characteristic-based integration of the streaming step with the free-energy based multiphase model by Lee et. al. [Journal of Computational Physics, 206 (1), 2005 ]. This allows for simulation time steps more than an order of magnitude larger than the relaxation time. Unlike previous work by Wardle et. al. [Computers and Mathematics with Applications, 65 (2), 2013 ] that integrated intermolecular forcing terms in the advection term, the current scheme applies collision and forcing terms locally for a simpler finite element formulation. A series of thorough benchmark studies reveal that this does not compromise stability and that the scheme is able to accurately simulate flows at large density and viscosity contrasts.

physics.flu-dyn↗

arXiv2016

Measure of Node Similarity in Multilayer Networks

The weight of links in a network is often related to the similarity of the nodes. Here, we introduce a simple tunable measure for analysing the similarity of nodes across different link weights. In particular, we use the measure to analyze homophily in a group of 659 freshman students at a large university. Our analysis is based on data obtained using smartphones equipped with custom data collection software, complemented by questionnaire-based data. The network of social contacts is represented as a weighted multilayer network constructed from different channels of telecommunication as well as data on face-to-face contacts. We find that even strongly connected individuals are not more similar with respect to basic personality traits than randomly chosen pairs of individuals. In contrast, several socio-demographics variables have a significant degree of similarity. We further observe that similarity might be present in one layer of the multilayer network and simultaneously be absent in the other layers. For a variable such as gender, our measure reveals a transition from similarity between nodes connected with links of relatively low weight to dis-similarity for the nodes connected by the strongest links. We finally analyze the overlap between layers in the network for different levels of acquaintanceships.

cs.SI↗

arXiv2016

The Dynamics of Initiative in Communication Networks

Human social interaction is often intermittent. Two acquainted persons can have extended periods without social interaction punctuated by periods of repeated interaction. In this case, the repeated interaction can be characterized by a seed initiative by either of the persons and a number of follow-up interactions. The tendency to initiate social interaction plays an important role in the formation of social networks and is in general not symmetric between persons. In this paper, we study the dynamics of initiative by analysing and modeling a detailed call and text message network sampled from a group of 700 individuals. We show that in an average relationship between two individuals, one part is almost twice as likely to initiate communication compared to the other part. The asymmetry has social consequences and ultimately might lead to the discontinuation of a relationship. We explain the observed asymmetry by a positive feedback mechanism where individuals already taking initiative are more likely to take initiative in the future. In general, people with many initiatives receive attention from a broader spectrum of friends than people with few initiatives. Lastly, we compare the likelihood of taking initiative with the basic personality traits of the five factor model.

cs.SI↗