Random Porous Media Research Articles

Accurate prediction of discontinuous crack paths in random porous media via a generative deep learning model

Pore structures provide extra freedoms for the design of porous media, leading to desirable properties, such as high catalytic rate, energy storage efficiency, and specific strength. This unfortunately makes the porous media susceptible to failure. Deep understanding of the failure mechanism in microstructures is a key to customizing high-performance crack-resistant porous media. However, solving the fracture problem of the porous materials is computationally intractable due to the highly complicated configurations of microstructures. To bridge the structural configurations and fracture responses of random porous media, a unique generative deep learning model is developed. A two-step strategy is proposed to deconstruct the fracture process, which sequentially corresponds to elastic deformation and crack propagation. The geometry of microstructure is translated into a scalar of elastic field as an intermediate variable, and then, the crack path is predicted. The neural network precisely characterizes the strong interactions among pore structures, the multiscale behaviors of fracture, and the discontinuous essence of crack propagation. Crack paths in random porous media are accurately predicted by simply inputting the images of targets, without inputting any additional input physical information. The prediction model enjoys an outstanding performance with a prediction accuracy of 90.25% and possesses a robust generalization capability. The accuracy of the present model is a record so far, and the prediction is accomplished within a second. This study opens an avenue to high-throughput evaluation of the fracture behaviors of heterogeneous materials with complex geometries.

Infiltration and permeability of porous ceramics simulated by random networks

A network computational model for a 3D ceramic structure is developed. The model is applied to study the impact of geometric and material parameters of structure on the liquid metal flow through random porous ceramic medium in pressure infiltration processes. The characteristic geometric features of the ceramic structure favorable for liquid metal flow during the infiltration process are determined. The method of structural approximation and constructive homogenization are applied, and the discrete stationary Stokes equations on random graphs are considered. This approach gives a robust algorithm to determine the macroscopic permeability K of interpenetrating phases. The dependencies of K on the distribution of connections (windows) between the cells (inclusions) are derived. The numerical simulations demonstrate that the permeability K does not depend on the scaled distribution sizes of windows. This implies that K is proportional to the mean value of the window areas. The considered model takes into account a random complex structure of 3D ceramic. Hence, it complements the previous study on the local transport properties of tubes (windows) connecting the cells.

Bending induced polarization charges in non-polar porous polymer for stroke rehabilitation

Owing to the flexibility, lightweight, long-life and low cost, polymers are promising candidates to realize electromechanical conversion in wearable electronics. The flexoelectric effect enables non-piezoelectric materials to achieve electromechanical coupling, thereby broadening application ranges of nonpolar polymers. In this work, the porous samples of polydimethylsiloxane (PDMS) with various pore sizes and porosities are fabricated by the sacrificial salt template method and the chemical gas foaming method. The flexoelectric polarization response can be tuned directly by the structural characters of the porous PDMS. The transverse flexoelectric coefficient of porous PDMS can reach approximately 2.9 times the counterpart of the bulk one. The competitive mechanism between strain gradient and permittivity is proposed on flexoelectricity of random porous media by dielectric impedance spectrums and finite element analyses. The present regulation of flexoelectricity provides an alternative to electromechanical conversion. With the deep learning technique based on one-dimensional convolution neural networks, actions of both sick and normal legs of various stroke patients can be well recognized by the designed device of rehabilitation. The present rehabilitation monitoring system, which is an innovative application of the flexoelectricity in the porous polymers, offers a new approach to support physical therapy for post-stroke patients.

Statistical theory of fluids confined in quenched disordered porous media.

We develop a theory to calculate structural correlations and thermodynamic properties of a fluid confined in a random porous solid medium (matrix). We used density functional formalism to derive an annealed averaged expression for the density profile and excess free energy of fluid arising due to random fields of a particular realization of the matrix. After performing the second average over the quenched-disordered variables, the excess free energy is organized to give one- and two-body potentials for fluid particles. The average over disorder reduces the system to an effective one-component system of fluid in which particles feel one-body (external) potential and interact via effective pair potential. The effective pair potential is a sum of the bare (the one in the pure fluid) and the matrix-induced potential. The resulting partition function involves only fluid variables. Equations are derived for fluid-fluid and fluid-matrix correlation functions and for free energy, pressure, and chemical potential of the fluid. The theory is applied to a model system of hard spheres and results for the effective pair potential, correlation functions, and thermodynamic properties are reported. The effective pair potential is found to be attractive at the contact and develops a repulsive peak before decaying to zero. Results for pair correlation function and structure factor are compared with simulation results for several fluid densities at two matrix densities. In all the cases, a very good agreement has been found.

A machine learning based-method to generate random circle-packed porous media with the desired porosity and permeability

The generation of digital porous media facilitates the fabrication of artificial porous media and the analysis of their properties. The past random digital porous medium generation methods are unable to generate a porous medium with a specified permeability. In this work, a new method is proposed to generate a random circle-packed digital porous medium with a specified porosity and permeability. Firstly, the process of generating the random circle-packed digital porous medium with a specified porosity is detailed. Secondly, the permeability of the digital porous medium is calculated by the multi-relaxation time lattice Boltzmann method. A total of 3,000 digital porous medium samples are generated, and their microstructure data and permeabilities are prepared for the training of a convolutional neural network (CNN) model, which is then applied to effectively predict the permeability of a digital porous medium. Finally, our method is elaborated and the choice of target permeability in this method is discussed. Our approach has the potential to be applied to the generation of other types of porous media.

Stochastic dynamics construction of a three-dimensional microstructure of red clay

Constructing a microstructure of red clay is an important part of studying the physical and mechanical properties of red clay. The study of red clay microstructure is generalized. The red clay matrix and pores are regarded as two types of randomly moving particles, and the microstructure model of three-dimensional red clay random porous media is established from the Langevin equation of the phase separation process in stochastic dynamics, using the separation and aggregation of the two particles. The model controls the evolution process of the porous medium by artificially controlling the particle placement. Here, the trends of porosity, average pore length, Euler’s number, and the fractal dimension of the porous medium during the evolution process under different parameter conditions (smooth length Δ and rise and fall term η) are calculated, and a feasible method for surviving the microstructure of red clay is summarized. Due to the consideration of the interaction forces between the solid- and void-phase particles, the porous media generated by this model are more similar to the real porous media in nature, with connected and unconnected pore structures and tortuous pore channels. Finally, the red clay of Bijie, Guizhou, is modeled as an example to prove the feasibility of the method.

Homogenization of the linearized ionic transport equations in random porous media

In this paper we obtain the homogenization results for a system of partial differential equations describing the transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid random disperse porous medium. We present a study of the nonlinear Poisson–Boltzmann equation in a random medium, establish convergence of the stochastic homogenization procedure and prove well-posedness of the two-scale homogenized equations. In addition, after separating scales, we prove that the effective tensor satisfies the so-called Onsager properties, that is the tensor is symmetric and positive definite. This result shows that the Onsager theory applies to random porous media. The strong convergence of the fluxes is also established. In the periodic case homogenization results for the mentioned system have been obtained in Allaire et al (2010 J. Math. Phys. 51 123103).

The impact of random porosity distribution on the composite metal foam-phase change heat transfer for thermal energy storage

The goal of this work is to investigate the phase change material (PCM) embedded with a high thermal conductive solid structure (metal foam). In order to boost the effective heat conductivity and therefore quicken the storage process, metal foam is incorporated. The resultant storage medium is handled as a porous material. Most of earlier investigations of a similar type assumed that the medium's porosity in the porous zone is uniform. However, a random porosity is more accurate and realistic. Various sets of random structures were created using a pseudo-random generator. The mathematical formulation utilizes the Darcy-Brinkman model and volume-averaging method. The governing equations are numerically solved using the control-volume-based finite element approach. Various samples with high random porosity distributions were simulated and compared to the case of uniform porosity. The results were reported in the form of isotherms, liquid fractions, and streamlines. The outcomes revealed that a random porous medium could provide a lower rate of PCM melting (up to 10 %) for a similar average porosity compared to a uniform porous medium.

Rose water in random porous media: Associative replica Ornstein-Zernike theory study

The properties of water are vastly affected by its local environment or in other words the system in which water is present. There are many systems in which water is confined in pores of different sizes and shapes. We studied the system in which porous media consisted of quenched Lennard-Jones disks and water modelled as rose water which was allowed to move inside pores. Associative replica Ornstein–Zernike theory was used to calculate the properties of the system. The accuracy of the theory under different conditions was tested against Monte Carlo simulations. The advantage of the theory is that it is magnitudes faster than computer simulations. From pair distribution functions calculated with the theory, the effects of different conditions on the structure of the system was investigated. We also studied how different conditions such as fluid temperature, fluid density, matrix density and matrix particle size affect a fraction of bonded molecules, excess internal energy and isothermal compressibility.

Microgel dynamics within the 3D porous structure of transparent PEG hydrogels

We report an investigation on the effects of the confinement imposed by application-relevant poly(ethylene glycol) (PEG) hydrogel matrices with controlled porosity on the dynamics of soft microgels. Through a detailed characterization of the internal structure of the hydrogels at the nano and microscale, we were able to link the microgel dynamics, measured by particle tracking, to the 3D geometrical confinement imposed by the porous matrices. PEG hydrogels with a high degree of transparency and tunable pore sizes and volume fractions were obtained using freeze-thawing. We found that the porosity of the hydrogel networks is characterized by elongated channels having asymmetric sections, with the average size decreasing from about 7 to about 2 particle diameters, and the size distribution becoming narrower with increasing PEG content in the pre-reaction mixture. The microgel dynamics slowdown and change from diffusive to sub-diffusive as a result of the increasing confinement. The observed decrease in diffusivity is consistent with models of diffusion in cylindrical pores and can be attributed to hydrodynamic and steric effects in addition to geometrical constriction. A dependence of the effective diffusion coefficient on the pore volume fraction, which is unusually pronounced, suggests the presence of microgel-hydrogel interactions. Our results demonstrate that a detailed characterization of the 3D geometry of the porous network is of primary importance for the understanding of transport properties in complex, random porous media.

Kaniadakis Functions beyond Statistical Mechanics: Weakest-Link Scaling, Power-Law Tails, and Modified Lognormal Distribution

Probabilistic models with flexible tail behavior have important applications in engineering and earth science. We introduce a nonlinear normalizing transformation and its inverse based on the deformed lognormal and exponential functions proposed by Kaniadakis. The deformed exponential transform can be used to generate skewed data from normal variates. We apply this transform to a censored autoregressive model for the generation of precipitation time series. We also highlight the connection between the heavy-tailed -Weibull distribution and weakest-link scaling theory, which makes the -Weibull suitable for modeling the mechanical strength distribution of materials. Finally, we introduce the -lognormal probability distribution and calculate the generalized (power) mean of -lognormal variables. The -lognormal distribution is a suitable candidate for the permeability of random porous media. In summary, the -deformations allow for the modification of tails of classical distribution models (e.g., Weibull, lognormal), thus enabling new directions of research in the analysis of spatiotemporal data with skewed distributions.

Effective Diffusivity From Analytical Solution for Banks of Cylinders

Abstract Benchmarks are provided for the evaluation of the effective coefficient for species diffusion, or electrical/thermal conduction, in structured porous media. The cases considered corresponding to doubly periodic rows of circular cylinders, for which a power series solution has been previously obtained, from complex variable theory. Both inline and staggered geometries are considered for three common configurations: inline-square, rotated-square, and equilateral geometries. From these mathematical solutions, values for the effective conduction/diffusion coefficient are readily constructed. The results are presented in terms of correlations for the ratio of effective-to-bulk conductivity/diffusivity or microstructural parameter, as a function of porosity. It is shown that near identical results with the present analytical analysis are obtained using calculations based on a finite-volume method and also with a previous mathematical analysis for the case of inline-square geometry. The present analytical solutions are also compared with two well-known correlations for random porous media, based on effective medium and percolation theory. It is shown that agreement with the analytical solution is not in general particularly good and depends on the choice of fitting parameters. The present results may be used as canonical data for comparative studies with numerical procedures to enumerate microstructural parameters for arbitrary-shaped occlusions in random geometries.

Migration of active rings in porous media.

Inspired by how the shape deformations in active organisms help them to migrate through disordered porous environments, we simulate active ring polymers in two-dimensional random porous media. Flexible and inextensible active ring polymers navigate smoothly through the disordered media. In contrast, semiflexible rings undergo transient trapping inside the pore space; the degree of trapping is inversely correlated with the increase in activity. We discover that flexible rings swell while inextensible and semiflexible rings monotonically shrink upon increasing the activity. Together, our findings identify the optimal migration of active ring polymers through porous media.

Unsteady natural convection of nano-encapsulated phase change materials (NEPCMs) inside a random porous medium considering local thermal non-equilibrium condition

A local thermal non-equilibrium analysis is undertaken to simulate unsteady free convective heat transfer inside a square enclosure filled with a random porous medium. There is a time-varying temperature profile at the hot wall. The fluid is a suspension comprising nano-encapsulated phase change materials (NEPCM) particles dispersed in water while aluminum foam, copper foam, or glass balls are considered for the solid matrix. It is found that when the hot wall temperature reaches its minimum value during one oscillation period, most of the cavity is occupied by the NEPCM particles in the solidious phase. For the metallic foams, the heat transfer of the medium is substantially higher than the NEPCM particles. Meanwhile, the Nusselt number of the glass balls is much lower than the suspension. A rise in the dimensionless frequency or amplitude of the temperature profile as well as approaching the dimensionless fusion temperature to 0.5 elevates Nusselt number of the suspension. However, no general conclusion can be drawn for their consequences on the heat transfer in the solid matrix. Among the current alterable parameters, only the contributions of the non-dimensional interface heat transfer coefficient and the non-dimensional amplitude of the temperature profile are found significant.

A 3D random porous media model for cement mortar based on X-ray computed tomography

Cement-based materials are typical porous media in which the spatial pores are of vital importance to flow problems, such as chloride ion penetration. This study proposes a three-dimensional (3D) random porous media model to characterize the spatial distribution associated with the porosity in cement mortar. The proposed model addresses the random heterogeneity in material properties using a Weibull random field and an exponential correlation function. The spatial distribution data associated with the porosity of the cement mortar, including the marginal distribution of the porosity and correlation structure of the Weibull random field, are obtained via X-ray computed tomography (XCT). The results indicate that the isotropic exponential correlation function is adequate for characterizing the correlation structure of the Weibull field with a maximum correlation length of 5.7515 mm. Moreover, a comparison of the simulated and measured porosity fields suggests that the proposed model can capture the characteristics of the porosity distribution in cement mortar. Considering the correlation in the porosity leads to a larger variance in the mean porosity of the mortar in the Monte Carlo simulation (MCS). In the example, the chloride diffusion in the cement mortar is illustrated using the proposed 3D random porous media model coupled with finite element (FE) analysis. The effect of the spatial correlation of the porosity on chloride diffusion in cement mortar was discussed from a probabilistic perspective. The proposed model provides insights into considering the properties of heterogeneous materials.

Empty liquid state and re-entrant phase behavior of the patchy colloids confined in porous media.

Patchy colloids with three and four equivalent patches, confined in an attractive random porous medium, undergo re-entrant gas-liquid phase separation with the liquid phase density approaching zero at low temperatures. The (bonding) colloid-colloid interaction causes the liquid-gas phase separation, which is modulated by the presence of the randomly distributed hard-sphere obstacles, attracting the colloids via Yukawa potential. Due to this interaction, a layer of mutually bonded colloids around the obstacles is formed. The network becomes nonuniform, with colloid particles locally centered on the obstacles. Features described in this article may open possibilities to produce equilibrium gels with predefined nonuniform distribution of particles and indicate how complicated the phase behavior of biological macromolecules in a crowded environment may be.

Behaviour of the model antibody fluid constrained by rigid spherical obstacles: Effects of the obstacle-antibody attraction.

This study investigates the behaviour of a fluid of monoclonal antibodies (mAbs) when trapped in a confinement represented by rigid spherical obstacles that attract antibodies. The antibody molecule is depicted as an assembly of seven hard spheres (7-bead model), organized to resemble a Y-shaped object. The model antibody has two Fab and one Fc domains located in the corners of letter Y. In this calculation, only the Fab-Fab and Fab-Fc attractive pairs of interactions are effective. The confinement is formed by the randomly distributed hard-spheres fixed in space. The spherical obstacles, besides the size exclusion, interact with beads of the antibody molecules via the Yukawa attractive potential. We applied the combination of the scaled particle theory, replica Ornstein-Zernike equations, Wertheim's thermodynamic perturbation approach and the Flory-Stockmayer theory to calculate: (i) the phase diagram of the liquid-liquid phase separation and the percolation threshold, (ii) the cluster size distributions, and (iii) the second virial coefficient of the protein fluid distributed among the obstacles. All these quantities were calculated as functions of the strength of the attraction between the monoclonal antibodies, and the monoclonal antibodies and obstacles. The conclusion is that while the hard-sphere obstacles decrease the critical density and the critical temperature of the mAbs fluid, the effect of the protein-obstacle attraction is more complex. Adding an attractive potential to the obstacle-mAbs interaction first increases the wideness of the T*-ρ envelope. However, with the further increase of the obstacle-mAbs attraction intensity, we observe reversal of the effect, the T*-ρ curves become narrower. At some point, depending on the obstacle-mAbs interaction, the situation is observed where two different temperatures have the same fluid density (re-entry point). In all the cases shown here the critical point decreases below the value for the neat fluid, but the behaviour with respect to an increase of the strength of the obstacle-mAbs attraction is not monotonic. Yet another interesting phenomenon, known in the literature as an approach toward the "empty liquid" state, is observed. The stability of the "protein droplets", formed by the liquid-liquid phase separation, depends on their local environment and temperature.

An assessment of turbulence transportation near regular and random permeable interfaces

Turbulent channel flow with a porous wall is investigated using direct numerical simulation, where the porous media domain consists of regular or random circular cylinder arrays. We compare the statistics and structure of the mean flow and turbulence in the channel flow with a bulk Reynolds number of 2500 and two porosities (φ=0.6 and 0.8) for the porous media. It is shown that the random interface significantly affects the dynamics of turbulence and the time-averaged flow. More intense mixing is observed near the random interface due to augmented form-induced shear stresses. Due to the strong dependence of induced flow direction on the interface geometry, we segmented the flow field into two types of areas based on the slope angle formed by the top-layer cylinders: the windward area and leeward area. The conditional average of turbulence kinematic energy budget over each type of area reveals their respective role in turbulence transportation more explicitly. In addition, we use finite-time Lyapunov exponents to inspect the Lagrangian coherent structures in the flow fields, which reveal the preferential fluid trajectories in the random porous medium geometry.

Homogenization of immiscible compressible two–phase flow in random porous media

The paper deals with stochastic homogenization of a system modeling immiscible compressible two-phase, such as water and gas, flow in random porous media. The problem is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. This formulation leads to a coupled system consisting of a nonlinear degenerate parabolic equation for the gas pressure and a nonlinear degenerate parabolic diffusion-convection equation for the liquid saturation, subject to appropriate boundary and initial conditions. We consider the behavior of compressible two-phase flow in heterogeneous reservoirs with permeability and porosity being realizations of given statistically homogeneous random fields. We derive the effective (macroscopic) problem and prove the convergence of solutions. Our approach relies on stochastic two-scale convergence techniques, the realization-wise notion of stochastic two-scale convergence being used. Also, we exploit various a priori estimates as well as monotonicity and compactness arguments. To our best knowledge, this is the first stochastic homogenization result in the case of compressible two-phase flow in random porous media.

Pore scale study on capillary pumping process in three-dimensional heterogeneous porous wicks using Lattice Boltzmann method

Quartet structure generation set (QSGS) method is improved to numerically reconstruct three-dimensional heterogeneous porous wicks with uniform pore size distribution. The capillary pumping processes of the reconstructed random porous wicks are simulated at pore scale by using a three-dimensional two-phase lattice Boltzmann model. The evolutions of two-phase interface and the variations of the imbibed liquid volume fraction with time are analyzed under the conditions of different porosity, pore structure, and surface wettability. The comparisons between the LBM results and those predicted by a macroscopic scale homogenous model are also conducted. It is found that due to the pore scale effects, the two-phase interface in a random porous media is very irregular, especially at the earlier stages of capillary pumping process when the liquid penetration is faster, and the imbibed liquid does not increase exponentially with time as predicted by the macroscopic scale model. Meanwhile, the liquid penetration rate does not decrease monotonously, but exhibits different degrees of fluctuations. The pore scale effects are more prominent in the cases of lower porosity, smaller pore size and better surface wettability. In the parametric range of the present study, the capillary performance increases with the decreasing of porosity, average pore radius (when porosity is fixed) and contact angle.