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In this study, a free energy model of the Lattice Boltzmann Method (LBM) is performed to simulate the motion, deformation, and decomposition of a droplet in the presence of electrohydrodynamic flow in porous media. To simulate the multi-phase flow in the presence of dielectric current by using the LBM, three distribution functions are used. To implement the free energy mode of HCZ, two equilibrium distribution functions are considered, one for solving the Navier-Stokes equation and the other for solving the Cahn-Hillard equation. Initially, the ability of the code to apply surface tension is tested by using the Laplace law and the droplet release test. Results show that there is a linear relation is between surface tension and κ which is a parameter in the HCZ model. The results show that the present numerical program is capable of modeling the regulated surface tension force as well. Then, the Rayleigh–Taylor instability simulation is used to evaluate the code's ability to apply volume forces. Also, the obtained results of the written numerical program are in good agreement with the numerical results of other valid references. Obtained results show that the difference between droplet deformation measured by numerical method and Taylor function is less than 2%. After modeling the droplet motions to investigate the droplet deformation, two electric fields are inserted into the droplet with reverse directions of each other. Then, by various tests, it is shown that at a given potential difference the droplet breaks down after much deformation and is divided into smaller droplets. The decomposition of droplets in a pre-mixed emulsion is a common technique to produce the monodisperse droplets. The presence of monodisperse droplets in an emulsion improves the physical properties of polymer from the science expert's perspective. The results of this study are used to improve the quality of polymer components.

Wettability is one of the key controlling parameters for multiphase flow in porous media, and paramount for various geoscience applications. While a general awareness of the importance of wettability was established decades ago, our fundamental understanding of how wettability influences transport and of how to characterize wettability has improved tremendously in recent years through breakthroughs in imaging technology and modeling techniques. Numerical modeling studies clearly show not only that macroscopic two-phase flow is influenced by the average wettability, but also that the spatial distribution of wetting significantly impacts the macroscopic parameters. Herein, we explore the thermodynamics for porous multiphase systems, and recent breakthroughs in wettability characterization. Our view is that bridging the multiscale characterization of wetting must consider two fundamental perspectives: geometry and energy. Advancing the overall description requires an improved understanding of the operative mechanisms that dominate at various scales, and the development of quantitative approaches to capture these effects. We take a multistage approach, looking at these fundamental perspectives from the sub-pore-to-pore length scales, followed by the pore-to-core length scales using various analytical techniques and numerical simulations. Within this context, there remain many open-ended questions, and we therefore highlight these issues to provide guidance on future research directions. Our overall aim is to provide comprehensive guidance on the multiscale characterization of wettability in porous media, in order to facilitate novel research.

To study the influences of sand and gravel layer and groundwater velocity of Yufuhe River on atrazine migration, adsorption-desorption and sand column experiments were carried out. Results show that the adsorption capacity of montmorillonite, raw sand and washed sand to atrazine sequentially weakens. In different media, the time for atrazine concentrations to peak in washed sand with montmorillonite (WSM), raw sand and washed sand is 60, 135 and 105 minutes respectively, and the peak concentration accounts for 84, 90 and 95% of the initial concentrations. Under different flow rates, the peak time in washed sand at flow rates of 100, 150 and 200 mL/min is 135, 105 and 75 minutes, and the peak time in WSM is 90, 60 and 45 minutes, respectively. Results from this study indicate that increasing flow velocity and suspended colloids concentrations can promote the migration of atrazine in aquifers, while the presence of clay minerals in sand and gravel layers can reduce atrazine migration. Thus, during Yellow River water recharging, the sand and gravel layer of Yufuhe River is helpful to protect the aquifer, but the colloids-associated migration of atrazine can contaminate groundwater in underlying karst aquifer. HIGHLIGHTS Migrations of atrazine in porous media are related to clay minerals and colloids.; Sand and gravel layer can retard the atrazine migration during managed aquifer recharge (MAR).; Increasing groundwater velocity would accelerate atrazine migration.; This study is significant to maintain the long-term operation of the MAR.

Unlike the power-law model, the Ellis model describes the apparent viscosity of a shear-thinning fluid with no singularity in the limit of a vanishingly small shear stress. In particular, this model matches the Newtonian behaviour when the shear stresses are very small. The emergence of the Rayleigh-B\'enard instability is studied when a horizontal pressure gradient, yielding a basic throughflow, is prescribed in a horizontal porous layer. The threshold conditions for the linear instability of this system are obtained both analytically and numerically. In the case of a negligible flow rate, the onset of the instability occurs for the same parametric conditions reported in the literature for a Newtonian fluid saturating a porous medium. On the other hand, when high flow rates are considered, a negligibly small temperature difference imposed across the horizontal boundaries is sufficient to trigger the convective instability., Comment: 13 pages, 5 figures, 2 tables

We explore and develop a Proper Orthogonal Decomposition (POD)-based deflation method for the solution of ill-conditioned linear systems, appearing in simulations of two-phase flow through highly heterogeneous porous media. We accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method achieving speed-ups of factors up to five. The up-front extra computational cost of the proposed method depends on the number of deflation vectors. The POD-based deflation method is tested for a particular problem and linear solver; nevertheless, it can be applied to various transient problems, and combined with multiple solvers, e.g., Krylov subspace and multigrid methods.

This experimental study is an attempt to apply the constriction size concept for determination of hydraulic conductivity of filter material. Five shapes of granular filter material of different gradations were used for the experimental investigations. The controlling constriction size for selected shapes and gradations were worked out and related to the experimental values of hydraulic conductivity. The empirical model for determination of hydraulic conductivity based on controlling constriction size for each shape of granular filter material was developed. Finally, a combined empirical model for the determination of hydraulic conductivity of granular filters was developed based on shape parameters and the controlling constriction size. The model was validated with the experimental data of a past research work; the predicted values of hydraulic conductivity were found in close approximation to the values obtained from the literature. Results of the present work will help in improving the existing design criteria of protective filters, which form an integral part of the safety of hydraulic structures. HIGHLIGHTS Inclusion of constriction size and shape parameters in the hydraulic conductivity determination of granular filters.; Improvement of the effectiveness of the filter design based on permeability.; Enhancement of water resources management in the essential hydraulic structure design where filters form a critical component.

This study deals with a two-dimensional (2D) contaminant transport problem subject to depth varying input source in a finite homogeneous groundwater reservoir. A depth varying input source at the upstream boundary is assumed as the location of disposal site of the pollutant from where the contaminant enters the soil medium and ultimately to the groundwater reservoir. At the extreme boundary of the flow site, the concentration gradient of the contaminant is assumed to be zero. Contaminant dispersion is considered along the horizontal and vertical directions of the groundwater flow. The governing transport equation is the advection–dispersion equation (ADE) associated with linear sorption and first-order biological degradation. The ADE is solved analytically by adopting Laplace transform method. Crank–Nicolson scheme is also adopted for the numerical simulation of the modelled problem. In the graphical comparison of the analytical and numerical solutions, the numerical solution follows very closely with the analytical solution. Also, Root Mean Square (RMS) error and CPU run time are obtained to account for the performance of the numerical solution. HIGHLIGHTS Two-dimensional contaminant transport is discussed in a finite homogeneous porous medium.; Exponentially decaying depth-dependent source is assumed at the upstream of the domain.; The governing equation is solved analytically and numerically.; The RMS error is observed very less.; Verified the input data used in the present study from the existing literature.

Inhomogeneous magnetic fields generated in porous media due to differences in magnetic susceptibility at solid/liquid interfaces and due to intrinsic or artificially doped magnetic impurities can be used to gain insight into the molecular dynamics of fluid in the structure of a porous medium using the concept of NMR modulated gradient spin echo method. We extended the theory of this method to the case of an inhomogeneous magnetic field that cannot be approximated by an uniform gradient, in order to explain the CPMG measurements of self-diffusion in water soaked ceramics, which are doped with magnetic impurities of different contents. The new interpretation provides the spin relaxation times, the average pore size and their distribution, as well as the strength of the internal magnetic gradient fields in the doped ceramics.

RESUMO O objetivo deste trabalho foi apresentar, por meio da técnica dinâmica dos fluidos computacional (CFD), dois métodos utilizados nas representações conceitual e física da vegetação em meio aquático: meio poroso e elementos geométricos simplificados. Três estudos de caso, que incluem um wetland flutuante e manchas de vegetação, exemplificam a aplicação dos métodos, mostrando suas vantagens e desvantagens. Nas etapas da geometria e da malha, a representação da vegetação como meio poroso é mais simples, prática e rápida do que a da vegetação como elementos geométricos simplificados. Porém, na parte da modelagem das equações, o método do meio poroso não consegue capturar os processos de mistura no interior da vegetação, enquanto o método dos elementos geométricos simplificados consegue. ABSTRACT The goal of this work was to present, through computation fluid dynamics (CFD), two methods used in the conceptual and physical representation of vegetation in aquatic environments: the porous media approach and the simplified geometric elements. Three case studies, including a floating wetland and patches of vegetation, exemplify how the methods are applied, showing their advantages and disadvantages. At the geometry and meshing stage, the porous media approach shows to be simpler, faster, and more practical than the simplified geometric elements. However, in the equation modeling, the porous media approach is not able to capture the mixing processes inside the vegetation, while the simplified geometric elements method can capture those processes.

We develop a novel statistical approach to estimate topological information from large, noisy images. Our main motivation is to measure pore microstructure in 2-dimensional X-ray micro-computed tomography (micro-CT) images of ice cores at different depths. The pore space in these samples is where gas can move and get trapped within the ice column and is of interest to climate scientists. While the field of topological data analysis offers tools (e.g. lifespan cutoff and PD Thresholding) for estimating topological information in noisy images, direct application of these techniques to large images often leads to inaccuracies and proves infeasible as image size and noise levels grow. Our approach uses image subsampling to estimate the number of holes of a prescribed size range in a computationally feasible manner. In applications where holes naturally have a known size range on a smaller scale than the full image, this approach offers a means of estimating Betti numbers, or global counts of holes of various dimensions, via subsampling of the image.

We derive high order homogenized models for the incompressible Stokes system in a cubic domain filled with periodic obstacles. These models have the potential to unify the three classical limit problems (namely the ``unchanged' Stokes system, the Brinkman model, and the Darcy's law) corresponding to various asymptotic regimes of the ratio $\eta\equiv a_{\epsilon}/\epsilon$ between the radius $a_{\epsilon}$ of the holes and the size $\epsilon$ of the periodic cell. What is more, a novel, rather surprising feature of our higher order effective equations is the occurrence of odd order differential operators when the obstacles are not symmetric. Our derivation relies on the method of two-scale power series expansions and on the existence of a ``criminal' ansatz, which allows to reconstruct the oscillating velocity and pressure $(\u_{\epsilon},p_{\epsilon})$ as a linear combination of the derivatives of their formal average $(\u_{\epsilon}^{*},p_{\epsilon}^{*})$ weighted by suitable corrector tensors. The formal average $(\u_\epsilon^{*},p_{\epsilon}^{*})$ is itself the solution to a formal, infinite order homogenized equation, whose truncation at any finite order is in general ill-posed. Inspired by the variational truncation method of \cite{smyshlyaev2000rigorous,cherednichenko2016full}, we derive, for any $K\in\N$, a well-posed model of order $2K+2$ which yields approximations of the original solutions with an error of order $O(\epsilon^{K+3})$ in the $L^{2}$ norm. Furthermore, the error improves up to the order $O(\epsilon^{2K+4})$ if a slight modification of this model remains well-posed. Finally, we find asymptotics of all homogenized tensors in the low volume fraction limit $\eta\rightarrow 0$ and in dimension $d\>3$. This allows us to obtain that our effective equations converge coefficient-wise to either of the Brinkman or Darcy regimes which arise when $\eta$ is respectively equivalent, or greater than the critical scaling $\eta_{\mathrm{crit}}\sim\epsilon^{2/(d-2)}$

In this article, we present the Laguerre wavelet exact Parseval frame method (LWPM) for the two-dimensional flow of a rotating micropolar fluid in a porous channel with huge mass transfer. This flow is governed by highly nonlinear coupled partial differential equations (PDEs) are reduced to the nonlinear coupled ordinary differential equations (ODEs) using Berman's similarity transformation before being solved numerically by a Laguerre wavelet exact Parseval frame method. We also compared this work with the other methods in the literature available. Moreover, in the graphs of the velocity distribution and microrotation, we shown that the proposed scheme's solutions are more accurate and applicable than other existing methods in the literature. Numerical results explaining the effects of various physical parameters connected with the flow are discussed.

International audience; The estimation of solid surface energy is generally obtained through the determination of liquid/solid contact angles. Many questions arise in the literature about the appropriate contact angle to use (dynamic, quasi-static or static, measured at a macro or a micro-scale). Theoretically, equilibrium contact angles should be inserted into equations to determine surface energy components. However, for powders or porous materials more issues arise, notably due to the imbibition of the liquid into the medium. An apparent contact angle can be obtained using wicking tests and the modified Washburn equation. Nonetheless, Washburn hypotheses are not always respected or no longer valid during wicking meaning that this procedure could not allow to determine contact angles. This study has the aim to propose a new simple method to determine the surface energy components of powders and porous media. An experimental protocol coupled to a modified Jurin law is proposed. This protocol was applied to lignin particles used as reinforcement in polylactic acid (PLA). Some treatments were performed on lignin to improve the adhesion with PLA and the modifications due to the treatments were characterized. Reliable surface energy and components of untreated and treated lignin were obtained revealing the efficiency of the proposed method.

A numerical study is conducted to analyze the effects of a flexible fin on unsteady convective flow in a square enclosure composed of a vertical fluid layer and a porous layer. The fin is attached to the heated left wall of the enclosure. The Brinkman-Forchheimer-extended Darcy flow model is assumed in the porous layer. The governing equations are written in the Arbitrary Lagrangian–Eulerian (ALE) formulation in the fluid and structure domains and then solved using the FEM. The result shows that the fin oscillation impacts the area below the fin rather than the area above the fin or the area in the center. The overall rate of heat transfer is improved as the Darcy number, the fluid layer thickness, and the fin elasticity increase. The overall rate of heat transfer increases exponentially with the rise of the oscillation amplitude. An oscillation amplitude of 0.1 could result in 3.4 percent improvement in the heat transfer rate.

Numerical emulations are conducted to study the physical situation of a variable properties nanofluid inside enclosures with rough boundaries. Two cases are considered based on way of the heating in the enclosures, namely, case1 the enclosure is heated from inside using two heated and cross-section ellipsis at the center of the enclosure and case2 in which differentially heated enclosures are assumed. The numerical procedure which applied to solve the non-homogenous Buongiorno mathematical model is based on the control volume technique with SIMPLE algorithm. Wide ranges for the temperature differences, roughness parameter and Darcy number are considered and the dynamic viscosity of CuO nanofluid is expressed as a mathematical form of the temperature and nanoparticle volume fraction based on experimental results. The main results revealed that the average Nusselt is enhanced by 11% in case 1 and by 30% in case 2 when the temperature differences are increased by 10 °C. Also, the decrease in Darcy number causes that rate of the heat transfer is reduced regardless way of the heating. Moreover the increase in the roughness parameter reduces the maximum values of the stream function in all cases.

Observations of streaming potential for unsaturated conditions do not always show the same trend de10 pending on the hydrodynamic conditions and because of a lake of coherency between the data processing procedures. We combine the data from three studies published in the literature, acquired during non-steady state drainage experiments, and apply the same processing steps. We model the hydrodynamic behaviour of these experiments to confirm that they experienced different flow dynamics. We argue that the raw SP data should not be corrected unless a clear drift of the electrodes stability is observed. The combined hydrody namic behaviour and the streaming potential response show that (a) the observations of one of the experiment (exp #1) are associated to a limited range of water saturation (0.85-1). The corresponding signals could therefore be fairly modelled assuming no saturation dependence of the SPC whatsoever; (b) the observations of exp #3 led to a SPC that can be larger than its value at saturation; (c) the observations of the exp #2 show a non-monotonous behaviour of the SPC as saturation decreases. The underlying physics of a non-monotonous SPC is related to water/air interfaces as shown by the results of the lattice Boltzmann numerical simulations. The main contribution to the SPC behaviour comes from the charged water/air interfaces and depends on the dynamic state of moving or entrapped bubbles. We finally describe the consequences of such a behaviour on the seismoelectric conversions for unsaturated conditions. Facultad de Ciencias Astronómicas y Geofísicas

Significance Solute transport in porous materials is pertinent to many engineering and industrial applications. This research provides direct characterization of spatiotemporal behavior of solute transport in saturated and unsaturated porous media using high-resolution four-dimensional synchrotron X-ray imaging. This research has two key impacts: 1) we demonstrate a workflow for direct characterization of solute transport in any porous material, which allows better design of fabricated porous materials and detailed characterization of natural porous materials, and 2) we evaluate the underlying assumptions used in the existing theories and identify the major gaps in theories that need to be addressed for better predictive modeling., Solute transport in unsaturated porous materials is a complex process, which exhibits some distinct features differentiating it from transport under saturated conditions. These features emerge mostly due to the different transport time scales at different regions of the flow network, which can be classified into flowing and stagnant regions, predominantly controlled by advection and diffusion, respectively. Under unsaturated conditions, the solute breakthrough curves show early arrivals and very long tails, and this type of transport is usually referred to as non-Fickian. This study directly characterizes transport through an unsaturated porous medium in three spatial dimensions at the resolution of 3.25 μm and the time resolution of 6 s. Using advanced high-speed, high-spatial resolution, synchrotron-based X-ray computed microtomography (sCT) we obtained detailed information on solute transport through a glass bead packing at different saturations. A large experimental dataset (>50 TB) was produced, while imaging the evolution of the solute concentration with time at any given point within the field of view. We show that the fluids’ topology has a critical signature on the non-Fickian transport, which yet needs to be included in the Darcy-scale solute transport models. The three-dimensional (3D) results show that the fully mixing assumption at the pore scale is not valid, and even after injection of several pore volumes the concentration field at the pore scale is not uniform. Additionally, results demonstrate that dispersivity is changing with saturation, being twofold larger at the saturation of 0.52 compared to that at the fully saturated domain.

International audience; Highlights • Oil penetrates in parfried frozen products during the first minute of deep-frying, and during cooling, once the product is removed from the oil bath. • The mechanisms of oil penetration during frying involves a Carnot cycle mediated by steam between the crust and the frozen core. • All regions connected by fissures are accessible to oil penetration during deep-frying regardless of their water content. • The deep penetration of oil during cooling and immersion stages are under enthalpic control and requires steam condensation. • Surface oil penetration is conversely under entropic control and is possible only when air (non-condensable phase) can be displaced by oil. Abstract Deep-frying is one of the most used and versatile technique for cooking foods. During immersion stage, it has been well accepted that the internal vaporization created an overpressure across the crust higher than the oil capillary pressure. As a result, oil could penetrate inside the food product only during the very last stages of frying or during cooling. This study shows a * Correspondence: olivier.vitrac@agroparistech.fr more complex picture in parfried frozen French fries with oil being capable of penetrating deep inside the product during the first minute of immersion. The new mechanism invokes a Carnot cycle between hygroscopic and frozen regions mediated by steam along cracks and fissures. Oil labeling and microscopic analysis show that both enthalpic and entropic forces drive oil transport and that oil can replace or be replaced by another phase: new oil, water, air. This work suggests new strategies based on thermodynamics to minimize oil pickup in fried products.

Predicting and controlling the liquid dynamics in a porous medium is of large importance in numerous technological and industrial situations. We derive here a general analytical solution for the dynamics of a flat liquid front in a porous medium, considering the combined effects of capillary imbibition, gravity and evaporation. We highlight that the dynamics of the liquid front in the porous medium is controlled by two dimensionless numbers: a gravity–capillary number G and an evaporation–capillary number E. We analyze comprehensively the dynamics of the liquid front as functions of G and E, and show that the liquid front can exhibit seven kinds of dynamics classified in three types of behaviors. For each limiting case, a simplified expression of the general solution is also derived. Finally, estimations of G and E are computed to evidence the most common regimes and corresponding liquid front dynamics encountered in usual applied conditions. This is realized by investigating the influence of the liquid and porous medium properties, as well as of the atmospheric conditions, on the values of the dimensionless numbers., SCOPUS: ar.j, info:eu-repo/semantics/published

We consider the problem of steady pumping of water from a line drain on the surface of a wet ground. Unlike the classical formulation, which regards the conductivity parameter K as uniformly distributed in the domain, the problem here is solved within a stochastic framework in order to account for the irregular (random), and more realistic, spatial vari- ability of K. Due to the linearity of the problem at stake, we focus on the derivation of the mean Green function G. This is computed by means of an asymptotic expansion. The fundamental result is an analytical (closed form) expression of G which general- izes the classical solution. Based on this, we develop an equivalent conductivity Keq which enables one to tackle the problem similarly to the classical one. In particular, it is shown that the equivalent conductivity grows monotonically with the radial distance r from the drain, and it lies within the range Keq (0) ≤ Keq (r) ≤ Keq (∞) < ∞.

International audience; Electrokinetic and electroosmotic couplings can play important roles in water and ions transport in charged porous media. Electroosmosis is the phenomena explaining the water movement in a porous medium subjected to an electrical field. In this work, a new model is obtained through a new up-scaling procedure, considering the porous medium as a bundle of tortuous capillaries of fractal nature. From the model, the expressions for the electroosmosis pressure coefficient, the relative electroosmosis pressure coefficient, the maximum back pressure, the maximum flow rate, the flow rate-applied back pressure relation and the product of the permeability and formation factor of porous media are also obtained. The sensitivity of the relative electroosmosis pressure coefficient is then analyzed and explained. The model predictions are then successfully compared with published datasets. Additionally, we deduce an expression for the relative streaming potential coefficient and then compare it with a previously published model and experimental data from a dolomite rock sample. We find a good agreement between those models and experimental data, opening up new perspectives to model electroosmotic phenomena in porous media saturated with various fluids.

In the present paper, the free convection oscillatory flow of a micropolar fluid determined by a vertical an infinite surface plane has fluctuates harmonically temperature with a relaxation time is studied. The surface has a constant suction and oscillates free steam velocity, and absorbs the fluid. The Eringen model for micropolar fluid is applied to solve the problem. The components of velocity, induced magnetic field, and concentration profiles have been obtained. The technique of regular perturbation is considered to solve the equations governing to a set of linear coupled and uncoupled ordinary differential equations. The problem has been solved for the small values of the micropolar perturbing parameter χ . The effects of Prandetl number P r , Grashof number G r , material parameter χ , β , γ are discussed. The cooling and heating effect on the fluid has been discussed. The numerical results indicate that the external parameters are affected strongly on the electrically conducting micropolar concentration fluid. If the electrically conducting and thermal relaxation time, the results obtained deduce to the results obtained by Sharma and Gupta (1995) [31].

In this study, mathematical modeling of permeation grouting through fully saturated soil is proposed based on immiscible multiphase flow theory. Grout flow in the medium is modeled together with the existing water as the simultaneous flow of two immiscible fluids. In the model, the porous medium is assumed as isotropic and rigid, fluids are assumed as incompressible and capillary pressure is assumed as negligible. Governing equations are discretized using upstream weighted finite element technique and results show that, proposed models give good results and may be used in the numerical simulation of grouting through fully saturated soils.

Hypothesis The change of wettability toward more water-wet by the injection of low salinity water can improve oil recovery from porous rocks, which is known as low salinity water flooding. To simulate this process at the pore-scale, we propose that the alteration in surface wettability mediated by thin water films which are below the resolution of simulation grid blocks has to be considered, as observed in experiments. This is modeled by a wettability alteration model based on rate-limited adsorption of ions onto the rock surface. Simulations The wettability alteration model is developed and incorporated into a lattice Boltzmann simulator which solves both the Navier-Stokes equation for oil/water two-phase flow and the advection-diffusion equation for ion transport. The model is validated against two experiments in the literature, then applied to 3D micro-CT images of a rock. Findings Our model correctly simulated the experimental observations caused by the slow wettability alteration driven by the development of water films. In the simulations on the 3D rock pore structure, a distinct difference in the mixing of high and low salinity water is observed between secondary and tertiary low salinity flooding, resulting in different oil recoveries.

Most of the existing models for analyzing unconfined flows in hillslope aquifers are based on the Boussinesq (1877) equation. In the development of these models, the assumption of negligible bed-normal velocity was employed, thus restricting their application to shallow groundwater-flow situations. On the basis of a non-hydrostatic pressure approach, a ground-water-flow model that considers the effects of the vertical curvature of the flow streamlines and the three-dimensional geometry of the underlying bedrock was proposed. A dissipative two-four finite-difference scheme was utilized to discretize and solve the model equation. The applicability of the model was assessed by conducting numerical experiments on transient unconfined flows in convergent- and divergent-type hillslope aquifers with non-uniform bedrock slopes. The numerical results for the phreatic-surface profiles and outflow discharges were compared to the experimental data, and a good agreement was obtained. The results of the comparison attested that the dynamics of the hillslope drainage processes were accurately portrayed by the proposed model. This study highlights the necessity of considering the effects of the plan shape and the profile curvature of complex hillslopes in order to improve the overall performance of the computational model.

The growing concerns over desertification have spurred research into technologies aimed at acquiring water from nontraditional sources such as dew, fog, and water vapor. Some of the most promising developments have focused on improving designs to collect water from fog. However, the absence of a shared framework to predict, measure, and compare the water collection efficiencies of new prototypes is becoming a major obstacle to progress in the field. We address this problem by providing a general theory to design efficient fog collectors as well as a concrete experimental protocol to furnish our theory with all the necessary parameters to quantify the effective water collection efficiency. We show in particular that multilayer collectors are required for high fog collection efficiency and that all efficient designs are found within a narrow range of mesh porosity. We support our conclusions with measurements on simple multilayer harp collectors.

International audience; The equivalent fluid model (EFM) describes the acoustic properties of rigid porous media by defining the intra-pore fluid phase as a fluid with an effective density and an effective compressibility. Their definitions are based on the dynamic tortuosity α and the normalized dynamic compressibility β. These physical quantities are complex-valued functions depending on the frequency, and can be irrational as in the Johnson-Champoux-Allard-Pride-Lafarge (JCAPL) model. Hence, the system of equations derived from the EFM can involve fractional derivatives in the time domain. This paper presents an approach to formulate the EFM equations described by the JCAPL model in the time domain, leading to an augmented system for which a proof of stability is given. From the EFM, a model for numerical simulation is built with α and β approximated using a multipole model. Sufficient stability conditions are then provided for the multipole-based EFM. Lastly, a numerical analysis is carried out in order to illustrate the theoretical results and a simulation of the impedance tube experiment is presented.

The settling velocity of porous particles in linear stratification is affected by the diffusive exchange between interstitial and ambient water. The extent to which buoyancy and interstitial mass adaptation alters the settling velocity depends on the ratio of the diffusive and viscous time scales. We conducted schlieren experiments and lattice Boltzmann simulations for highly porous (95 %) but impermeable spheres settling in linear stratification. For a parameter range that resembles marine porous particles, 'marine aggregates', i.e. low Reynolds numbers (0.05 0.5 mm) settling is dominated by delayed mass adaptation that diminishes settling velocity by 10 % up to almost 100 %. The derived relationships facilitate the integration of stratification-dependent settling velocities into biogeochemical models., Journal of Fluid Mechanics, 931, ISSN:0022-1120, ISSN:1469-7645

International audience; A two-dimensional axisymmetric model of a solar evaporator was developed, based on a rigid biosourced open-cell foam floating on the surface of water contained in a beaker, including a set of boundary conditions and water transport in the porous medium. Experiments were carried out to validate the model for two cases, with and without a layer of insulating material around the beaker. Several concrete cases of experimental solar evaporation studies recently reported in the literature, with or without insulation, radiation intensification, etc., have then been studied in the light of our model. We have thus been able to compare the observed trends with those of the numerical model in order to explain the results reported in the literature and, in some cases, to find a geometric optimum. The effect of ambient conditions on the evaporation rate was investigated, and significant changes were observed by modifying solar input, air temperature and air humidity. We also showed that increasing the evaporation area and using an insulating layer between the water and the evaporative material increases the evaporation performance.

Porous media filters are used widely to remove bacteria from contaminated water, such as stormwater runoff. Biofilms that colonize filter media during normal function can significantly alter performance, but it is not clear how characteristics of individual populations colonizing porous media combine to affect bacterial retention. We assess how four bacterial strains isolated from stormwater and a laboratory strain, Pseudomonas aeruginosa PAO1, alter Escherichia coli retention in experimental sand columns under conditions of stormwater filtration relative to a clean-bed control. Our results demonstrate that these strains differentially affect E. coli retention, as was previously shown for a model colloid. To determine whether E. coli retention could be influenced by changes in relative abundance of strains within a microbial community, we selected two pairs of biofilm strains with the largest observed differences in E. coli retention and tested how changes in relative abundance of strain pairs in the biofilm affected E. coli retention. The results demonstrate that E. coli retention efficiency is influenced by the retention characteristics of the strains within biofilm microbial community, but individual strain characteristics influence retention in a manner that cannot be determined from changes in their relative abundance alone. This study demonstrates that changes in the relative abundance of specific members of a biofilm community can significantly alter filter performance, but these changes are not a simple function of strain-specific retention and the relative abundance. Our results suggest that the microbial community composition of biofilms should be considered when evaluating factors that influence filter performance. IMPORTANCE The retention efficiency of bacterial contaminants in biofilm-colonized biofilters is highly variable. Despite the increasing number of studies on the impact of biofilms in filters on bacterial retention, how individual bacterial strains within a biofilm community combine to influence bacterial retention is unknown. Here, we studied the retention of an E. coli K-12 strain, as a model bacterium, in columns colonized by four bacterial strains isolated from stormwater and P. aeruginosa, a model biofilm-forming strain. Simplified two-strain biofilm communities composed of combinations of the strains were used to determine how relative abundance of biofilm strains affects filter performance. Our results provide insight into how biofilm microbial composition influences bacterial retention in filters and whether it is possible to predict bacterial retention efficiency in biofilm-colonized filters from the relative abundance of individual members and the retention characteristics of cultured isolates.

The local contact angle distribution within the pore space of a porous medium of mixed wettability is identified by combining pore network simulations and an optimization method. The latter is used to solve the inverse problem consisting of determining the local contact angle distribution from the capillary pressure and relative permeability curves. The inverse optimization method combines a genetic algorithm and the hill-climbing algorithm. The method is illustrated considering a Boolean distribution of the local contact angle in which the pore bodies and throats in the pore space are either hydrophilic or hydrophobic.

Porous materials are widely used in many heat transfer applications. Modeling porous materials at the microscopic level can accurately incorporate the detailed structure and substance parameters and thus provides valuable information for the complex heat transfer processes in such media. In this study, we use the generalized periodic boundary condition for pore-scale simulations of thermal flows in porous materials. A two-dimensional porous model consisting of circular solid domains is considered, and comprehensive simulations are performed to study the influences on macroscopic thermal conductivity from several microscopic system parameters, including the porosity, Reynolds number, and periodic unit aspect ratio and the thermal conductance at the solid–fluid interface. Our results show that, even at the same porosity and Reynolds number, the aspect ratio of the periodic unit and the interfacial thermal conductance can significantly affect the macroscopic thermal behaviors of porous materials. Qualitative analysis is also provided to relate the apparent thermal conductivity to the complex flow and temperature distributions in the microscopic porous structure. The method, findings and discussions presented in this paper could be useful for fundamental studies, material development, and engineering applications of porous thermal flow systems.

International audience; An image-based effective medium approximation (EMA) is developed so as to permit very fast transport properties evaluations of 3D porous media. From an image-based porous network (IBPN) built upon digital image processing of 3D binary images, we focus on throat’s local geometrical properties at the pore scale, for being the most sensible structural units which build up the local pressure. This approach is a 3D image–based extension of the critical point approach proposed in 2D fractures. We show, from analyzing various core rock samples available in the literature, that the asymptotic assumptions associated with the preeminence of critical points in throats are indeed geometrically relevant. We then describe how the image-based EMA evaluated from the conductances computed from the discrete IBPN can be reliably evaluated. The proposed method is evaluated upon the estimation of core sample permeability from binarized image obtained using X-ray tomography. Since it combines digital image treatments with statistical data post-processing without the need of computational fluid dynamics (CFD) computation, it is extremely cost efficient. The results are compared with a micro-scale Stokes flow computation in various rock samples. The sensitivity to the pore discretization also is discussed and illustrated.

This study tries to employ the computational fluid dynamics (CFD) approach to investigate the influence of the simultaneous use of the metal foam (porous media) and the water-based nanofluid on the boiling flow regime. For this purpose, boiling flow heat transfer of water-based copper nanofluid inside of both simple pipe and aluminum metal foam pipe is simulated using the Eulerian two-phase CFD model. The nanofluid is supposed to flow inside the pipe with the mass flux of 1927 kg/m2s and the subcooled temperature of 10oc at atmospheric working pressure. The pipe is also under a constant wall heat flux (50–110 KW/m2). Different copper nanoparticle volume fractions (i.e., 0.5, 1, and 1.5%) are considered for this investigation. The porosity and pore density of the metal foam are 0.8 and 10 pore per inch (PPI) respectively. The heat transfer parameters of boiling flow including the wall temperature, the vapor volume fraction on the wall, the onset of the nucleate boiling (ONB), the local heat transfer coefficient, and the mean diameter of the vapor bubble are considered in this study. All heat transfer coefficients predicted by the CFD are compared with the Chen correlation. As far as the authors know, for the first time, the boiling flow of nanofluid-based water inside a metal foam pipe was simulated by the two-phase model of Eulerian. The results reveal that for the metal foam pipe, after happening of the ONB, the wall temperatures suddenly jump over the saturated temperature and the critical heat flux (CHF) happens. But no such sudden increase of the wall temperature is seen along the simple pipe before and after the ONB. Besides, the convective heat transfer coefficient in the metal foam pipe before the beginning of the boiling is more than double the boiling flow in the simple pipe. Although in metal foam pipe, once the boiling happened, the heat transfer coefficient was degraded by 50%, this value is still 25% more than the heat transfer coefficient of the boiling flow in the simple pipe. The results of this study could be practically used for boiling heat transfer analysis of heat exchangers filled by porous media and nanofluid.

The present work introduces numerical simulations based on an incompressible scheme of smoothed particle hydrodynamics (ISPH) method for the thermosolutal convection from an inner I-shaped inside an infinite-shaped cavity embedded by nano-encapsulated phase change materials (NEPCMs). An infinite-shaped enclosure is occupied by a nanofluid and a porous medium. In this work, the heat capacity of a core and shell is used for the overall heat capacity of encapsulated nanoparticles. An inner I-shaped is embedded inside a center of an enclosure and it carries T h and C h . The simulations are performed for different values of a length of an inner I-shaped L 2 ( 0.4 ≤ L 2 ≤ 1.5 ) , a Stefan parameter S t e ( 0.2 ≤ S t e ≤ 0.9 ) , a fusion temperature θ f ( 0.05 ≤ θ f ≤ 0.95 ) , Darcy parameter D a ( 10 − 2 ≤ D a ≤ 10 − 5 ) , an inclination angle γ ( 0 ≤ γ ≤ π / 2 ) and Rayleigh number R a ( 10 3 ≤ R a ≤ 10 6 ) . The numerical simulations showed that a fusion temperature θ f adjust the situations of a melting solidification zone. Further, the intensity of a melting solidification zone is adjusted by a Stefan parameter. Augmentations of an inner I-shaped length and Rayleigh number are powering buoyancy forces and thus the flow speed, and heat & mass transport are enhanced inside an infinite-shaped cavity. Mean Nusselt and Sherwood numbers are enhanced as I-shaped length and Rayleigh number are powered.

The paper is dedicated to numerical simulation based on a mesh-free method for a double-diffusive flow between two different materials inside a porous infinite-shaped enclosure suspended by a nano-encapsulated phase change material (NEPCM). Controlling equations have been solved by the Incompressible Smoothed Particle Hydrodynamics (ISPH) method. The first phase is considered a mixture of water and NEPCMs, and the second phase is formed by solid particles. Inside the novel shape of an infinite-shaped enclosure, the solid phase is carrying T h and C h during the whole simulation and the bottom-wall of an infinite shape is kept at is carrying T c and C c . Variations of Darcy parameter, fusion temperature, buoyancy ratio parameter, Stefan parameter, and Lewis number on the phase change zone, materials tracking, temperature, velocity field, and concentration are discussed. The results have shown that the fusion temperature disciplines the phase change zone within a porous infinite-shaped enclosure. The Stefan number adjusts the intensity of the phase change zone. The buoyancy ratio and the Darcy parameters are representing as essential factors in controlling the distribution of solid particles within the nanofluid phase. The ISPH method is validated by comparison with practical and numerical results.

The dynamic two-phase flow in porous media was theoretically developed based on mass, momentum conservation, and fundamental constitutive relationships for simulating immiscible fluid-fluid retention behavior and seepage in the natural geomaterial. The simulation of transient two-phase flow seepage is, therefore, dependent on both the hydraulic boundaries applied and the immiscible fluid-fluid retention behavior experimentally measured. Many previous studies manifested the velocity-dependent capillary pressure–saturation relationship (Pc-S) and relative permeability (Kr-S). However, those works were experimentally conducted on a continuum scale. To discover the dynamic effects from the microscale, the Computational Fluid Dynamic (CFD) is usually adopted as a novel method. Compared to the conventional CFD methods solving Naiver–Stokes (NS) equations incorporated with the fluid phase separation schemes, the two-phase Lattice Boltzmann Method (LBM) can generate the immiscible fluid-fluid interface using the fluid-fluid/solid interactions at a microscale. Therefore, the Shan–Chen multiphase multicomponent LBM was conducted in this study to simulate the transient two-phase flow in porous media. The simulation outputs demonstrate a preferential flow path in porous media after the non-wetting phase fluid is injected until, finally, the void space is fully occupied by the non-wetting phase fluid. In addition, the inter-relationships for each pair of continuum state variables for a Representative Elementary Volume (REV) of porous media were analyzed for further exploring the dynamic nonequilibrium effects. On one hand, the simulating outcomes reconfirmed previous findings that the dynamic effects are dependent on both the transient seepage velocity and interfacial area dynamics. Nevertheless, in comparison to many previous experimental studies showing the various distances between the parallelly dynamic and static Pc-S relationships by applying various constant flux boundary conditions, this study is the first contribution showing the Pc-S striking into the nonequilibrium condition to yield dynamic nonequilibrium effects and finally returning to the equilibrium static Pc-S by applying various pressure boundary conditions. On the other hand, the flow regimes and relative permeability were discussed with this simulating results in regards to the appropriateness of neglecting inertial effects (both accelerating and convective) in multiphase hydrodynamics for a highly pervious porous media. Based on those research findings, the two-phase LBM can be demonstrated to be a powerful tool for investigating dynamic nonequilibrium effects for transient multiphase flow in porous media from the microscale to the REV scale. Finally, future investigations were proposed with discussions on the limitations of this numerical modeling method.

We examine the effects of horizontally layered heterogeneities on the spreading of two-phase gravity currents in a porous medium, with application to numerous environmental flows, most notably geological carbon sequestration. Heterogeneities, which are ubiquitous within geological reservoirs, affect the large-scale propagation of two-phase flows through the action of small-scale capillary forces, yet the relationship between these small- and large-scale processes is poorly understood. Here, we derive a simple upscaled model for a gravity current under an impermeable cap rock, which we use to investigate the effect of a wide range of centimetre-scale heterogeneities on kilometre-scale plume migration. By parameterising in terms of different types of archetypal layering, we assess the sensitivity of the gravity current to the distribution and magnitude of these heterogeneities. Furthermore, since field measurements of heterogeneities are often sparse or incomplete, we quantify how uncertainty in such measurements manifests as uncertainty in the macroscale flow predictions. Using realistic parameter values, we demonstrate that heterogeneities can enhance plume migration speeds by as much as 200 %, and that uncertainty in field measurements can have dramatic consequences on flow predictions, particularly in post-injection scenarios where the role of capillary forces in heterogeneities is accentuated.

Having a basic understanding of non-Newtonian fluid flow through porous media, which usually consist of series of expansions and contractions, is of importance for enhanced oil recovery, groundwater remediation, microfluidic particle manipulation, etc. The flow in contraction and/or expansion microchannel is unbounded in the primary direction and has been widely studied before. In contrast, there has been very little work on the understanding of such flow in an expansion–contraction microchannel with a confined cavity. We investigate the flow of five types of non-Newtonian fluids with distinct rheological properties and water through a planar single-cavity microchannel. All fluids are tested in a similarly wide range of flow rates, from which the observed flow regimes and vortex development are summarized in the same dimensionless parameter spaces for a unified understanding of the effects of fluid inertia, shear thinning, and elasticity as well as confinement. Our results indicate that fluid inertia is responsible for developing vortices in the expansion flow, which is trivially affected by the confinement. Fluid shear thinning causes flow separations on the contraction walls, and the interplay between the effects of shear thinning and inertia is dictated by the confinement. Fluid elasticity introduces instability and asymmetry to the contraction flow of polymers with long chains while suppressing the fluid inertia-induced expansion flow vortices. However, the formation and fluctuation of such elasto-inertial fluid vortices exhibit strong digressions from the unconfined flow pattern in a contraction–expansion microchannel of similar dimensions.

There are many studies on the nonlinear relationship between seepage velocity and hydraulic gradient in coarse granular materials, using different approaches and variables to define the resistance formula applicable to that type of granular media. On the basis of an analysis of the existing formulations developed in different studies, we propose an approach for comparing the results obtained by some of the most important studies on state-of-the-art seepage flow in coarse granular media.

Biot's equations describe the physics of hydromechanically coupled systems establishing the widely recognized theory of poroelasticity. This theory has a broad range of applications in Earth and biological sciences as well as in engineering. The numerical solution of Biot's equations is challenging because wave propagation and fluid pressure diffusion processes occur simultaneously but feature very different characteristic time scales. Analogous to geophysical data acquisition, high resolution and three dimensional numerical experiments lately redefined state of the art. Tackling high spatial and temporal resolution requires a high-performance computing approach. We developed a multi- graphical processing units (GPU) numerical application to resolve the anisotropic elastodynamic Biot's equations that relies on a conservative numerical scheme to simulate, in a few seconds, wave fields for spatial domains involving more than 1.5 billion grid cells. We present a comprehensive dimensional analysis reducing the number of material parameters needed for the numerical experiments from ten to four. Furthermore, the dimensional analysis emphasizes the key material parameters governing the physics of wave propagation in poroelastic media. We perform a dispersion analysis as function of dimensionless parameters leading to simple and transparent dispersion relations. We then benchmark our numerical solution against an analytical plane wave solution. Finally, we present several numerical modeling experiments, including a three-dimensional simulation of fluid injection into a poroelastic medium. We provide the Matlab, symbolic Maple, and GPU CUDA C routines to reproduce the main presented results. The high efficiency of our numerical implementation makes it readily usable to investigate three-dimensional and high-resolution scenarios of practical applications., Journal of Geophysical Research: Solid Earth, 126 (7), ISSN:2169-9313, ISSN:0148-0227, ISSN:2169-9356

International audience; We experimentally study the drying of loosely packed wet glass beads at low initial water content. The drying rate is found to decrease at the start, corre- sponding to the decreasing rate period controlled by vapor diffusion, followed by a deviation in drying rate from the diffusion limited evaporation. The prop- agation of drying front associated with a sharp saturation gradient is identified through both image analysis and magnetic resonance imaging technique. The drying-induced collapse of granular medium is observed and quantified. The concentrated collapse at the end of drying suggests the existence of liquid in the form of liquid bridges in the apparent dry region until the end of drying process. Collapse event is found to be local, i.e., a clear boundary can be iden- tified for each collapse event, below which the loosely packed medium remains intact. This indicates the existence of a saturation gradient in the apparent dry region. The drying dynamics and collapse statistics suggest that the observed transition of drying regimes is due to Kelvin effect. This work demonstrates for the first time the drying enhancement phenomenon due to Kelvin effect even for grains with size of hundreds of micrometers, and provides insights on the drying process of partially saturated granular materials, especially near the final period of evaporation.

Ferrofluid is a kind of magnetic fluid, the flow of which is controlled by an external magnetic field. Owing to this property, ferrofluid, as a new function material, has raised extensive concern in the oil industry. In this paper, the issue of ferrofluid flow in complex porous media has been studied by numerical simulation, and the validity and accuracy of the numerical algorithm are demonstrated through a 1-D horizontal tube example. Later, the effects of the magnetic force on ferrofluid flow in complex porous media, such as heterogeneous and fractured porous media, are investigated. The results show that there is basically no flow in low permeability or secondary fracture without a magnetic field, due to the characteristics of porous media and displacement pressure distribution. However, the ferrofluid flow velocity and domain can be changed by applying an external magnetic field. This novel phenomenon may provide a new idea to enhance oil recovery based on controllable flooding technology or meet other industrial needs by using ferrofluid.

International audience; An Eulerian, hyperbolic, multiphase-flow model for dynamic and irreversible compaction of porous materials is constructed. A reversible model for elastic, compressible, porous material is derived. Classical homogenization results are obtained. The irreversible model is then derived in accordance with the following basic principles. First, the entropy inequality is satisfied by the model. Second, the stress coming from the elastic energy decreases in time (the material behaves as Maxwell-type materials). The irreversible model admits an equilibrium state corresponding to a Gurson-type limit which varies with the porosity. The sound velocity at the yield limit is smaller than that of the reversible model. Such an embedded model structure ensures a thermodynamically correct formulation of the porous-material model. The usual model used in the detonation community is recovered. The model is then validated on quasi-static loading-unloading experiments with HMX. The ability of the model to capture strong shock propagation in porous material as well as its ability to deal with interface between a fluid and a porous material is demonstrated and validated on Hugoniot curve of aluminium with various porosities for a unique set of empirical parameters.

Hypothesis Control of capillary flow through porous media has broad practical implications. However, achieving accurate and reliable control of such processes by tuning the pore size or by modification of interface wettability remains challenging. Here we propose that the flow of liquid by capillary penetration can be accurately adjusted by tuning the geometry of porous media and develop numerical method to achieve this. Methodologies On the basis of Darcys law, a general framework is proposed to facilitate the control of capillary flow in porous systems by tailoring the geometric shape of porous structures. A numerical simulation approach based on finite element method is also employed to validate the theoretical prediction. Findings A basic capillary component with a tunable velocity gradient is designed according to the proposed framework. By using the basic component, two functional capillary elements, namely, (i) flow amplifier and (ii) flow resistor, are demonstrated. Then, multi functional fluidic devices with controllable capillary flow are realized by integrating the designed capillary elements. All the theoretical designs are validated by numerical simulations. Finally, it is shown that the proposed model can be extended to three dimensional designs of porous media

In the present study, a vertically oriented rectangular-shaped enclosure with triangular shaped double fins filled with PCM was considered as a Latent Thermal Energy Storage (LTES) system. Nine different cases including one pure PCM, three nano-PCM (having different volume fractions), two porous-PCM (having different porosity values) and three nano/porous PCM were considered to conduct the investigation. The PCM material employed for investigations was lauric acid. The copper made porous media was assumed to have porosity values of 98% and 95%. The Al 2 O 3 nano-particles with the volume fractions of 1%, 2% and 4% combined with Lauric acid were considered as nano-PCM. The results presented that the cases with nanoparticles volume fractions of 1% and 2% could improve the melting performance. However, the case with nanoparticle volume fraction of 4% deteriorated the melting performance. In the cases with individual usage of nano-PCM the best case was related to the case with the volume fraction of 1% and resulted in about 184s time-saving. It was found that individual usage of porous media could significantly improve the melting performance; however, adding nanoparticles to the cases with porous media, regardless of volume fraction of nanoparticles deteriorates the melting performance of PCM enclosure.

International audience; This paper presents a new mathematical representation of multiphase thermodynamic equilibrium using so-called repartition coefficients. Combined with a global mass formulation of multiphase Darcy flow in porous media, it allows the derivation of a computationally efficient family of time schemes. The model accounts for the mass conservation of an arbitrary number of components flowing through an arbitrary number of phases, coupled with thermodynamic equilibrium and pore volume conservation. By separating the thermodynamic equilibrium part from the flow part through the repartition coefficients, the formulation removes the need for any specific handling of phase appearance and disappearance within the flow solver. Any “black box” thermodynamic equilibrium solver can then be used to compute the repartition coefficients, from EOS based solvers to tabulated representation of the thermodynamic equilibrium, each specific choice of thermodynamic solver leading to a new scheme. Three numerical experiments, from a simple beam to a real case, illustrate the good behavior of the approach.

A machine learning approach to accelerate convergence of the nonlinear solver in multiphase flow problems is presented here. The approach dynamically controls an acceleration method based on numerical relaxation. It is demonstrated in a Picard iterative solver but is applicable to other types of nonlinear solvers. The aim of the machine learning acceleration is to reduce the computational cost of the nonlinear solver by adjusting to the complexity/physics of the system. Using dimensionless parameters to train and control the machine learning enables the use of a simple two-dimensional layered reservoir for training, while also exploring a wide range of the parameter space. Hence, the training process is simplified and it does not need to be rerun when the machine learning acceleration is applied to other reservoir models. We show that the method can significantly reduce the number of nonlinear iterations without compromising the simulation results, including models that are considerably more complex than the training case.

What are the biomechanical implications in the dynamics and evolution of a growing solid tumor? Although the analysis of some of the biochemical aspects related to the signaling pathways involved in the spread of tumors has advanced notably in recent times, their feedback with the mechanical aspects is a crucial challenge for a global understanding of the problem. The aim of this paper is to try to illustrate the role and the interaction between some evolutionary processes (growth, pressure, homeostasis, elasticity, or dispersion by flux-saturated and porous media) that lead to collective cell dynamics and defines a propagation front that is in agreement with the experimental data. The treatment of these topics is approached mainly from the point of view of the modeling and the numerical approach of the resulting system of partial differential equations, which can be placed in the context of the Hele-Shaw-type models. This study proves that local growth terms related to homeostatic pressure give rise to retrograde diffusion phenomena, which compete against migration through flux-saturated dispersion terms., MINECO-Feder (Spain) research grant numbers RTI2018-098850-B-I00 (J.C., J.S.) & EQC2018-004508-P (B.B., J.M.), Junta de Andalucía (Spain) Projects PY18-RT-2422 (J.C., J.S.), A-FQM-311-UGR18 (J.C., J.S.) & IE2017-5537 (B.B., J.M.), Instituto de Salud Carlos III, project number DTS17/00087 (J.M., J.S.), Ministry of Science, Innovation and Universities of Spain, project numbers DPI2017-85359-R (B.B., J.M.) & PID2019-106947RA-C22 (B.B., J.M.), Consejería de Economía, Conocimiento, Empresas y Universidad and European Regional Development Fund (ERDF), ref. SOMM17/6109/UGR (J.C., J.M., J.S.), Ministry of Science, Innovation and Universities of Spain, FPU2017/01415

Unidirectional unsteady flows of the incompressible Burgers’ fluids between two infinite horizontal parallel plates are analytically studied when the magnetic and porous effects are taken into consideration. The fluid motion is induced by the two plates, which move in their planes with time-dependent velocities. Exact general expressions are established both for the dimensionless velocity and shear stress fields as well as the corresponding Darcy’s resistance in the channel using the Laplace transform. If both plates move with equal velocities in the same direction, the fluid motion becomes symmetric with respect to the mid-plane between them. Otherwise, its motion is non-symmetric. To bring to light the behavior of the fluid, the dimensionless velocity profiles versus the spatial variable as well as its time evolution are presented both for the symmetric and asymmetric case. Finally, for comparison, similar graphical representations are presented together for the velocities of the incompressible Oldroyd-B and Burgers’ fluids. For large values of the time t, as expected, the behavior of the two different fluids is almost identical. The Darcy’s resistance against y is also graphically represented for the symmetric flow at different values of the time t. The influence of the magnetic field on the fluid motion is graphically revealed and discussed.