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The increasing appeal of artificial neural networks (ANNs) stems from their remarkable efficiency in dealing with complex and highly nonlinear mathematical concepts. In intricate domains like biological computation, fluid dynamics, and the field of biotechnology, ANNs offer a versatile computational framework that proves immensely valuable. Therefore, the current study employs machine learning techniques to investigate the bioconvective biological transport of Powell–Eyring nanofluid. Various influential factors, including temperature-dependent viscosity, thermal radiation, magnetic field, porous medium, mixed convection, and Ohmic heating, are considered in the analysis. By considering small Reynolds numbers and large wavelengths, the complexity of the system is reduced. A builtin NDSolve function in Mathematica is utilized to numerically address the system of differential equations at hand. Subsequently, the ANN-LMM technique is implemented, utilizing reference datasets for temperature, concentration, and motile microorganism profiles. The dataset is partitioned with 70% allocated for training, 15% for testing, and 15% for verification purposes. The reliability of the developed ANN-LMM is verified by evaluating precision, accuracy, and convergence. This validation is based on efficient fitness demonstrated in terms of mean-squared error (mse), thorough appropriate visualizations of error histograms and regression analysis. The study underscores the capability of ANNs in accurately predicting optimal heat and mass transfer, demonstrating their advantage in designing and improving engineering systems. [ABSTRACT FROM AUTHOR]

Today, mechanical properties and fluid flow dynamic analysis are considered to be two of the most important steps in implant design for bone tissue engineering. The mechanical behavior is characterized by Young's modulus, which must have a value close to that of the human bone, while from the fluid dynamics point of view, the implant permeability and wall shear stress are two parameters directly linked to cell growth, adhesion, and proliferation. In this study, we proposed two simple geometries with a three-dimensional pore network dedicated to a manufacturing route based on a titanium wire waving procedure used as an intermediary step for Mg-based implant fabrication. Implant deformation under different static loads, von Mises stresses, and safety factors were investigated using finite element analysis. The implant permeability was computed based on Darcy's law following computational fluid dynamic simulations and, based on the pressure drop, was numerically estimated. It was concluded that both models exhibited a permeability close to the human trabecular bone and reduced wall shear stresses within the biological range. As a general finding, the proposed geometries could be useful in orthopedics for bone defect treatment based on numerical analyses because they mimic the trabecular bone properties. [ABSTRACT FROM AUTHOR]

The purpose of this study is to systematically examine the basic fluid dynamics associated with a fully liquid region within a porous material. This work has come about as a result of our investigation on the ocular fluid dynamics and transport process in a partially liquefied vitreous humor. The liquid is modeled as a sphere with Stokes flow while the surrounding infinite porous region is described by Brinkman flow. The development here provides basic three-dimensional axisymmetric results on flow characterization and also serves to evaluate the limits of validity of Darcy flow analysis for the same geometry. In the Darcy flow model, the liquid region is also treated as a porous region with a much higher permeability. Therefore, both liquid and porous regions are modeled by Darcy's law. Besides the analytical results from Brinkman–Stokes model, the simpler case of Darcy–Darcy flow for the same geometry has been provided. The results of both cases are compared and the differences between the two sets of results provide the range of validity of our computational model (Khoobyar et al. in J Heat Transf 144:031208, 2022). Some interesting fluid-dynamical aspects of the system are observed through the analysis. For the Darcy–Darcy system, the liquid region velocity is uniform throughout, as expected for potential flow. With the Brinkman–Stokes model, the liquid region has a paraboloidal profile with the maximum possible peak value of six times the far-field velocity in the porous medium. With the liquid region having a lower resistance, the flow tends to converge there for both models as it seeks the path of least resistance. As for the validation of the Darcy–Darcy model, it is a good approximation as far as the exterior flow is concerned. However, the liquid region flow profiles for the two models are different as noted. The current Brinkman–Stokes model has led to explicit analytical solutions for the flow field for both regions. This has permitted an asymptotic analysis giving deeper insight into the flow characterization. [ABSTRACT FROM AUTHOR]

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We derive a class of exact solutions for Stokes flow in infinite and semi‐infinite channel geometries with permeable walls. These simple, explicit, series expressions for both pressure and Stokes flow are valid for all permeability values. At the channel walls, we impose a no‐slip condition for the tangential fluid velocity and a condition based on Darcy's law for the normal fluid velocity. Fluid flow across the channel boundaries is driven by the pressure drop between the channel interior and exterior; we assume the exterior pressure to be constant. We show how the ground state is an exact solution in the infinite channel case. For the semi‐infinite channel domain, the ground‐state solutions approximate well the full exact solution in the bulk and we derive a method to improve their accuracy at the transverse wall. This study is motivated by the need to quantitatively understand the detailed fluid dynamics applicable in a variety of engineering applications including membrane‐based water purification, heat and mass transfer, and fuel cells. [ABSTRACT FROM AUTHOR]

This study investigates the interaction between fluid dynamics and electromagnetic fields, a complex problem that has not been extensively studied. The Lorentz force, which arises due to the interaction between magnetic fields and currents in a fluid is considered in this study. This research investigates the effects of a magnetic field, couple stress, and slip velocity on the behavior of a squeeze film (SF) formed between a porous flat and spherical plate. The Stokes equation for couple stress fluids is used to produce a generalized version of the Reynolds equation, which is then used to determine the film pressure. Also, this study considers the impact of a constant magnetic field orthogonal to the plate. The fluid in the porous region is governed by modified Darcy law. The effect of a uniform magnetic field perpendicular to the plate is considered. The bearing characteristics pressure, squeeze film time, and load-carrying capacity are graphically presented. The results revealed that the load-carrying capacity, pressure, and squeeze film time are reduced with a rise in slip and porousness parameters. The slip parameter decreases the values of film pressure, squeeze time, and load-carrying capacity as related to the no-slip case. [ABSTRACT FROM AUTHOR]

Understanding the packing structure and pressure drop across a randomly packed bed of wood particles is essential for the design and control of wood drying, pyrolysis, and gasification processes. This study utilizes experimental and micro-scale simulation methods to explore fluid dynamics within packed bed systems of wood particles and glass spheres. Pressure drop and velocity data from experiments and simulations were fitted using Darcy's law and the Darcy–Forchheimer law to derive key parameters: permeability (K) and Forchheimer coefficient (β), which were then compared with existing correlations. Experiments were conducted in packed beds of wood pellets (R e = 11.5 to 185.1) and glass spheres (R e = 28.3 to 455.7). The Discrete Element Method (DEM) was used to generate packed bed structures of cylindrical and spherical particles, corresponding to the experiments. Flow within the beds was modeled using the incompressible Navier–Stokes equations, with detailed analyses of streamlines and vorticity. CFD results indicated critical Reynolds numbers of 10.1 for glass spheres and 4.1 for wood pellets, marking the transition from Darcy to Forchheimer flow regimes. Beyond these values, the formation of vortices indicated nonlinear effects. Experiments showed that K values were 2. 95 × 1 0 − 7 m 2 and β values 1. 22 × 1 0 3 m−1 for glass spheres; and for wood pellets, K values were 9. 82 × 1 0 − 8 m 2 and β values 3. 04 × 1 0 3 m−1. Using experimental results as references, simulation errors were lower than those from the correlations. Specifically, for wood pellets, simulation errors were 13.54% for K and 10.20% for β , while correlation errors were 42.57% for K and 7.89% for β. This indicates that simulation results are more reliable than existing correlations. [Display omitted] • DEM code generates randomly packed bed systems of wood pellets. • 3D simulations fully resolve the flow through packed beds. • Transition Reynolds number from Darcy to Forchheimer regimes is identified. • Results are discussed and compared with experimental data and existing correlations. [ABSTRACT FROM AUTHOR]

In fluid dynamics applications that involve flow adjacent to a porous medium, there exists some ambiguity in how to model the interface. Despite different developments, there is no agreed upon boundary condition that should be applied at the interface. We present a new analytical solution for laminar boundary layers over permeable beds driven by oscillatory free stream motion where flow in the permeable region follows Darcy's law. We study the fluid boundary layer for two different boundary conditions at the interface between the fluid and a permeable bed that was first introduced in the context of steady flows: a mixed boundary condition proposed by Beavers and Joseph ["Boundary conditions at a naturally permeable bed," J. Fluid Mech. 30, 197–207 (1967)] and the velocity continuity condition proposed by Le Bars and Worster ["Interfacial conditions between a pure fluid and a porous medium: Implications for binary alloy solidification," J. Fluid Mech. 550, 149–173 (2006)]. Our analytical solution based on the velocity continuity condition agrees very well with numerical results using the mixed boundary condition, suggesting that the simpler velocity boundary condition is able to accurately capture the flow physics near the interface. Furthermore, we compare our solution against experimental data in an oscillatory boundary layer generated by water waves propagating over a permeable bed and find good agreement. Our results show the existence of a transition zone below the interface, where the boundary layer flow still dominates. The depth of this transition zone scales with the grain diameter of the porous medium and is proportional to an empirical parameter that we fit to the available data. [ABSTRACT FROM AUTHOR]

This paper delves into the innovative realm of vascularization within concrete, a technique that embeds channel networks into the concrete matrix, mirroring the vascular systems found in living organisms. This approach facilitates the flow of diverse substances throughout the material, significantly expanding the functionalities of concrete beyond its traditional use. The work studies the core principles behind optimizing vascular networks in cementitious materials, from established methods like Constructal Law and Murray's Law to computational approaches and lesser-known theories like Percolation Theory and Darcy's Law. The discussion extends to fundamental fluid dynamics principles - Hagen-Poiseuille, Bernoulli's, Continuity, and Navier-Stokes Equations - and their significance in vascular network design. Additionally, the paper outlines various strategies to construct these vascular networks, addressing the evolution of fabrication methods over time and the challenges encountered. While most existing research focuses on self-healing and thermal regulation capabilities, this paper also explores the potential of vascular networks for a broad spectrum of applications. Through this review, the paper underscores vascularization's transformative potential in shaping concrete technology's future. • An innovative realm of nature-inspired vascularization within concrete was reviewed. • Core principles behind optimizing vascular networks in cementitious materials were summarized. • Fundamental fluid dynamics principles and their significance in vascular network design were reviewed. • Various strategies to construct vascular networks and the challenges encountered were reviewed. • Applications of vascularization in concrete such as self-healing and thermal regulation were discussed. [ABSTRACT FROM AUTHOR]

High‐dimensional models typically require a large computational overhead for multiphysics applications, which hamper their use for broad‐sweeping domain interrogation. Herein, we develop a modeling framework to capture the through‐plane fluid dynamic response of electrodes and flow fields in a redox flow cell, generating a computationally inexpensive two‐dimensional (2D) model. We leverage a depth‐averaging approach that also accounts for variations in out‐of‐plane fluid motion and departures from Darcy's law that arise from averaging across three‐dimensions (3D). Our resulting depth‐averaged 2D model successfully predicts the fluid dynamic response of arbitrary in‐plane flow field geometries, with discrepancies of <5% for both maximum velocity and pressure drop. This corresponds to reduced computational expense, as compared to 3D representations (<1% of duration and 10% of RAM usage), providing a platform to screen and optimize a diverse set of cell geometries. [ABSTRACT FROM AUTHOR]

In the present study, the diffraction and the radiation problems of water waves by a surfacepiercing porous cylindrical body are considered. The idea conceived is based on the capability of porous structures to dissipate the wave energy and to minimize the environmental impact, developing wave attenuation and protection. In the context of linear wave theory, a three-dimensional solution based on the eigenfunction expansion method is developed for the determination of the velocity potential of the flow field around the cylindrical body. Numerical results are presented and discussed concerning the wave elevation and the hydrodynamic forces on the examined body for various values of porosity coefficients. The results revealed that porosity plays a key role in reducing/controlling the wave loads on the structure and the wave run-up, hence porous barriers can be set up to protect a marine structure against wave attack. [ABSTRACT FROM AUTHOR]

The Darcy-Forchheimer relation is a key concept utilized in the analysis of fluid dynamics, specifically in understanding the pressure drop experienced by a fluid as it traverses a porous medium or a conduit with added resistance. This resistance may stem from various factors such as turbulence and viscosity. The Forchheimer coefficient serves as a metric to quantify this resistance and is typically determined through empirical studies or computational modeling. Its value is influenced by parameters like the porosity of the medium and the characteristics of the particles within it. Grasping the intricacies of the Darcy-Forchheimer relation empowers engineers and researchers to make precise predictions regarding pressure differentials and to devise efficient fluid flow systems. This knowledge is particularly vital in sectors such as oil and gas, chemical manufacturing, and environmental management. The aim of this study is to explore the application of the Darcy-Forchheimer relation within the domain of electro-magneto-hydro-dynamics flow of Micropolar nanofluid over a deformable surface. The investigation considers the impact of bio-convection (microorganisms) and the presence of a first-order chemical reaction. The energy equation accounts for phenomena like viscous dissipation, nonlinear thermal radiation, convective heat transfer, and the Soret and Dufour effects. Additionally, the research delves into the stochastic and thermophoretic attributes of the system. The governing equations of the problem were transformed into a dimensionless system and solved using the ND-solve technique. Graphical analyses were conducted to examine fluid flow, microrotation velocity, microorganism distribution, concentration, particle behavior, and temperature in relation to key flow variables. The findings indicate that higher Hartman numbers have a reverse effect on temperature and velocity profiles. An increase in the material variable results in a decrease in microrotation velocity. Temperature is influenced by vector radiation. Concentration shows contrasting trends for random and thermophoresis variables. The presence of motile microorganisms reduces the bioconvection Lewis and Peclet numbers. [ABSTRACT FROM AUTHOR]

Purpose: Many monoclonal antibodies (mAbs) are administered via subcutaneous (SC) injection. Local transport and absorption kinetics and mechanisms, however, remain poorly understood. A multiphysics computational model was developed to simulate the injection and absorption processes of a protein solution in the SC tissue. Methods: Quantitative relationships among tissue properties and transport behaviors of an injected solution were described by respective physical laws. SC tissue was treated as a 3-dimensional homogenous, poroelastic medium, in which vasculatures and lymphatic vessels were implicitly treated. Tissue deformation was considered, and interstitial fluid flow was modeled by Darcy's law. Transport of the drug mass was described based on diffusion and advection, which was integrated with tissue mechanics and interstitial fluid dynamics. Results: Injection and absorption of albumin and IgG solutions were simulated. Upon injection, a sharp rise in tissue pressure, porosity, and fluid velocity could be observed at the injection tip. Largest tissue deformation appeared at the model surface. Transport of drug mass out of the injection zone was minimal. Absorption by local lymphatics was found to last several weeks. Conclusions: A bottom-up method was developed to simulate drug transport and absorption of protein solutions in skin tissue base on physical principles. The results appear to match experimental observations. [ABSTRACT FROM AUTHOR]

We measure the pressure difference during two‐phase flow across a sandstone sample for a range of injection rates and fractional flows of water, the wetting phase, during an imbibition experiment. We quantify the onset of a transition from a linear relationship between flow rate and pressure gradient to a nonlinear power‐law dependence. We show that the transition from linear (Darcy) to nonlinear flow and the exponent in the power‐law is a function of fractional flow. We use energy balance to accurately predict the onset of intermittency for a range of fractional flows, fluid viscosities, and different rock types. Plain Language Summary: Multiphase flow in porous media is described by an empirical extension of Darcy's law where flow rate is proportional to pressure gradient. Darcy's law is used to quantify and design a wide variety of processes including carbon dioxide storage in the subsurface, and air and moisture flows through materials as diverse as soils and surgical masks. However, as flow rate increases, this linear Darcy law breaks down with a transition to a nonlinear intermittent flow regime. Through an extensive set of experimental measurements, we quantify the relationship between flow rate and pressure gradient. A theory based on energy balance accurately predicts the transition to intermittency. Our work quantifies multiphase flow over a wide range of conditions. Key Points: Flow rate and pressure gradient during steady‐state multiphase flow are measured experimentallyThe transition to a non‐Darcy flow regime is quantified and predicted theoreticallyThe theory makes accurate predictions for several rock types, fractional flows, and mobility ratios [ABSTRACT FROM AUTHOR]

Fourier neural operators (FNOs) have recently been proposed as an effective framework for learning operators that map between infinite-dimensional spaces. We prove that FNOs are universal, in the sense that they can approximate any continuous operator to desired accuracy. Moreover, we suggest a mechanism by which FNOs can approximate operators associated with PDEs efficiently. Explicit error bounds are derived to show that the size of the FNO, approximating operators associated with a Darcy type elliptic PDE and with the incompressible Navier-Stokes equations of fluid dynamics, only increases sub (log)-linearly in terms of the reciprocal of the error. Thus, FNOs are shown to efficiently approximate operators arising in a large class of PDEs. [ABSTRACT FROM AUTHOR]

The problem of convection in a fluid-saturated porous medium is reviewed with a focus on 'vigorous' convective flow, when the driving buoyancy forces are large relative to any dissipative forces in the system. This limit of strong convection is applicable in numerous settings in geophysics and beyond, including geothermal circulation, thermohaline mixing in the subsurface and heat transport through the lithosphere. Its manifestations range from 'black smoker' chimneys at mid-ocean ridges to saltdesert patterns to astrological plumes, and it has received a great deal of recent attention because of its important role in the long-term stability of geologically sequestered CO2. In this review, the basic mathematical framework for convection in porous media governed by Darcy's Law is outlined, and its validity and limitations discussed. The main focus of the review is split between 'two-sided' and 'one-sided' systems: the former mimics the classical Rayleigh--Bénard set-up of a cell heated from below and cooled from above, allowing for detailed examination of convective dynamics and fluxes; the latter involves convection from one boundary only, which evolves in time through a series of regimes. Both set-ups are reviewed, accounting for theoretical, numerical and experimental studies in each case, and studies that incorporate additional physical effects are discussed. Future research in this area and various associated modelling challenges are also discussed. [ABSTRACT FROM AUTHOR]

In the paper, a mathematical model for the filtration of two-component suspensions in a dual-zone porous medium is considered. The model consists of the mass balance equations, the kinetic equations for active and passive zones of porous medium for each component of the suspension and Darcy's law. To solve the problem, a numerical algorithm for computer experimentation is developed on the basis of finite difference method. Based on numerical results, the main characteristics of suspension filtration in a porous medium are established. Influences of model parameters on transport and deposition of suspended particles of two-component suspension in porous media are analysed. It is shown that the polydispersity of suspension and multistage nature of the deposition kinetics can lead to various effects that are not characteristic for the transport of one-component suspensions with one-stage particle deposition kinetics. In particular, in distribution of the concentration of suspended particles in a moving fluid non-monotonic dynamics are obtained at individual points in the medium. It is shown that at the points of the medium near to the input section, the concentration of deposited particles can reach partial capacities in the passive zone. [ABSTRACT FROM AUTHOR]

In this paper, a comprehensive framework is proposed to estimate the anisotropic permeability matrix in trabecular bone specimens based on micro-computed tomography (microCT) imaging combined with pore-scale fluid dynamics simulations. Two essential steps in the proposed methodology are the selection of (i) a representative volume element (RVE) for calculation of trabecular bone permeability and (ii) a converged mesh for accurate calculation of pore fluid flow properties. Accurate estimates of trabecular bone porosities are obtained using a microCT image resolution of approximately 10 μm. We show that a trabecular bone RVE in the order of 2×2×2 mm3 is most suitable. Mesh convergence studies show that accurate fluid flow properties are obtained for a mesh size above 125,000 elements. Volume averaging of the pore-scale fluid flow properties allows calculation of the apparent permeability matrix of trabecular bone specimens. For the four specimens chosen, our numerical results show that the so obtained permeability coefficients are in excellent agreement with previously reported experimental data for both human and bovine trabecular bone samples. We also identified that bone samples taken from long bones generally exhibit a larger permeability in the longitudinal direction. The fact that all coefficients of the permeability matrix were different from zero indicates that bone samples are generally not harvested in the principal flow directions. The full permeability matrix was diagonalized by calculating the eigenvalues, while the eigenvectors showed how strongly the bone sample's orientations deviated from the principal flow directions. Porosity values of the four bone specimens range from 0.83 to 0.86, with a low standard deviation of ± 0.016, principal permeability values range from 0.22 to 1.45 ⋅ 10−8 m2, with a high standard deviation of ± 0.33. Also, the anisotropic ratio ranged from 0.27 to 0.83, with high standard deviation. These results indicate that while the four specimens are quite similar in terms of average porosity, large variability exists with respect to permeability and specimen anisotropy. The utilized computational approach compares well with semi-analytical models based on homogenization theory. This methodology can be applied in bone tissue engineering applications for generating accurate pore morphologies of bone replacement materials and to consistently select similar bone specimens in bone bioreactor studies.

Fluid flow through geologic porous media is represented by Darcy's law and its inertial and nonlinear extension, the Forchheimer equation. These relationships equate the product of the driving potential gradient and phenomenological coefficients representing momentum resistance and dissipation to flux. From decades of research, the coefficient of viscous permeability (kv) in Darcy's law is largely predictable, but this is not the case for the coefficient of inertial permeability (ki) in the Forchheimer equation. Synthesizing results from thousands of laboratory and field flow tests and pore‐scale flow model results, we show that ki can be predicted from kv via the equation ki = 1010kv3/2 across 12 and 20 orders of magnitude in kv and ki, respectively. Since it is related with ki, kv is thus sufficient for predicting flow across viscous to inertial regimes for most geologic porous media. Plain Language Summary: Fluid flow through geologic porous media is dictated by permeability which is the resistance imparted by the medium. Flows in porous media are described by either Darcy's law or its extension for high flow rates, the Forchheimer equation. In both models, permeability represents the dissipation of mechanical energy by inertial losses and by fluid viscosity. Thus, permeability depends on both fluid properties and the configuration of pores. Decades of research has made the permeability in Darcy's law predictable from medium properties such as porosity and grain size, but the additional permeability in the Forchheimer equation has remained almost impossible to predict. This has hindered the application of the Forchheimer equation for many settings where it is potentially more appropriate. Through a broad synthesis of published data and through computational simulations, we were able to relate the permeability in Darcy's law to the permeability in the Forchheimer equation for the diversity of geologic porous media representing varied pore geometries and configurations. Thus, both kinds of permeability are now predictable and linked. This knowledge will help in many geophysical and engineering applications where it is necessary to consider flows at high rates. Key Points: We analyzed and synthesized viscous and inertial permeability data for different types of geologic porous mediaA universal visco‐inertial permeability model is established using the compiled dataThe parameter in the universal model is attributed to local surface roughness and void distribution pattern [ABSTRACT FROM AUTHOR]

An accurate quantitative description of the diffusion coefficient in a porous medium is essential for predictive transport modeling. Well-established relations, such as proposed by Buckingham, Penman, and Millington-Quirk, relate the scalar diffusion coefficient to the porous medium’s porosity. To capture the porous medium’s structure in more detail, further models include fitting parameters, geometric, or shape factors. Some models additionally account for the tortuosity, e.g., via Archie’s law. A validation of such models has been carried out mainly via experiments relating the proposed description to a specific class of porous media (by means of parameter fitting). Contrary to these approaches, upscaling methods directly enable calculating the full, potentially anisotropic, effective diffusion tensor without any fitting parameters. As input only the geometric information in terms of a representative elementary volume is needed. To compute the diffusion-porosity relations, supplementary cell problems must be solved numerically and their (flux) solutions must be integrated. We apply this approach to provide easy-to-use quantitative diffusion-porosity relations that are based on representative single grain, platy, blocky, prismatic soil structures, porous networks, or random porous media. As a discretization method, we use the discontinuous Galerkin method on structured grids. To make the relations explicit, interpolation of the obtained data is used. We furthermore compare the obtained diffusion-porosity relations with the well-established relations mentioned above and also with the well-known Voigt-Reiss or Hashin-Shtrikman bounds. We discuss the ranges of validity and further provide the explicit relations between the diffusion and surface area and comment on the role of a tortuosity-porosity relation. [ABSTRACT FROM AUTHOR]

We study the structural stability for the Brinkman fluid interfacing with a Darcy fluid in an unbounded domain. We show that the solutions depend continuously on the interface coefficient α 1 by using the method of a second order differential inequality. We have never seen any paper deal with the structural stability for the interface fluids in an unbounded domain. Our method would be useful in studying the structural stability for other interface fluid equations in porous media in an unbounded domain. [ABSTRACT FROM AUTHOR]

Serpentine flow fields and other flow fields with partial under-land cross-flow are commonly used in various energy devices, such as proton exchange membrane (PEM) fuel cells and redox flow batteries, due to their higher mass transfer rate to reaction sites and better product removal capability. Accurately predicting the under-land cross-flow rate and pressure drop in such flow fields is crucial in flow field design optimizations. Darcy's law is the most commonly used model in predicting the under-land cross-flow and pressure drop in such flow fields. However, since the Darcy's law neglects inertial effect, its validity in different designs and operating conditions needs to be carefully studied. In this work, mathematical models for a serpentine flow field are developed based on both the Darcy's law and a modified Darcy's law that includes the inertial effect. Both models are solved and analytical solutions are obtained. The predicted pressure drops and under-land cross-flow rates from the two models are compared with experimental data and the results show that under some conditions, both the Darcy's law and the modified Darcy's law can predict pressure drop and under-land cross-flow rate reasonably well. However, under other conditions the Darcy's law can result in significantly large errors in predicting both pressure drop and under-land cross-flow rates. Further studies provide the variations of errors from the Darcy's law with different parameters, including channel length, gas diffusion layer (GDL) thickness, land width, inlet flow rate, GDL permeability and GDL inertial coefficient. [ABSTRACT FROM AUTHOR]

This paper reports an analytical investigation of non-isothermal fluid flow in a thin (or long) vertical pipe filled with porous medium via asymptotic analysis. We assume that the fluid inside the pipe is cooled (or heated) by the surrounding medium and that the flowis governed by the prescribed pressure drop between pipe's ends. Starting from the dimensionlessDarcy-Brinkman-Boussinesq system, we formally derive amacroscopic model describing the effective flow at small Brinkman-Darcy number. The asymptotic approximation is given by the explicit formulae for the velocity, pressure and temperature clearly acknowledging the effects of the cooling (heating) and porous structure. The theoretical error analysis is carried out to indicate the order of accuracy and to provide a rigorous justification of the effective model. [ABSTRACT FROM AUTHOR]

This study presents analytical models for naturally fractured tectonic reservoirs (NFTRs), which essentially correspond to type I fractured reservoirs, including the effects of the nonlinear gradient term for radial flow, single phase (oil), for constant rate in an infinite reservoir. Using an exact solution of Navier-Stokes equation and Cole-Hopf transform, NFTRs have been modeled. Our models are applied for fissured formations with extensive fractures. Smooth and rough extension fractures were analyzed using single and slab flow geometries. The motivation for this study was to develop a real and representative model of a NFTR, with extension fractures to describe its pressure behavior. A discussion is also presented with field examples, regarding the effect of a quadratic gradient term and the difference between the nonlinear and linear pressure solutions, comparing the Darcy laminar flow equation, with the exact solution of the Navier-Stokes equation applied to the diffusion equation and boundary conditions in wellbore. [ABSTRACT FROM AUTHOR]

In the context of flow and transport in porous and fractured media, Darcy-based continuum models, while computationally inexpensive, are of limited use when the scale of interest is of similar size or smaller than the characteristic network connection length. Recently, we have outlined a non-local Darcy model that bridges the gap between network and Darcy-based descriptions. This formulation is able to account for non-local pressure effects that are not accounted for in a classical Darcy description. At the heart of this non-local flow formulation is a conductivity distribution or kernel that is related to the scalar permeability in the classical Darcy law. In this paper, ensembles of flow networks are considered, of which the necessary statistical information is assumed to be known. In order to relate the conductivity distribution with the flow statistics, a stochastic transport model for fluid particles, termed generalized continuous time random walk (g-CTRW), which is a generalization of correlated continuous time random walk, is introduced. Note that similar assumptions as for correlated CTRW are made, i.e., that lengths and velocities of connections between successive nodes along the trajectories can be described by Markov processes. In order to proceed with a theoretical analysis, a Boltzmann equation is presented, which is consistent with the particle time marching algorithm based on g-CTRW. An important outcome of the analysis is an expression relating the joint probability density function of velocity and connection length in the networks with the conductivity kernel. A numerical, stationary flow example demonstrates how the kernel can be extracted. Further, an algorithm is proposed to compute consistent velocity statistics, mean pressure distribution, and spatially varying conductivity kernel in the case of non-stationary flow. This coupled iterative approach is an attempt to consistently compute stochastic flow and transport in large network ensembles. [ABSTRACT FROM AUTHOR]

Most suspension descriptions nowadays employed are based on Jeffery model and some of its phenomenological adaptations that do not take into account the possible existence of a relative velocity between the fibres and the suspending fluid when the fibre interactions increase. It is expected that at very low density of contacts, as predicted by standard suspension models, fibres move with the suspending fluid velocity. When the density of fibre interactions becomes extremely high and a percolated network of fibre contacts is established within the suspension, fibres cannot move anymore and then the fluid flows throughout the rigid or moderately deformable entangled fibre skeleton, like a fluid flowing through a porous medium. In between these two limit cases, one could expect that fibres move but with a velocity lower than the one of the suspending fluid. Thus, two contributions are expected, one coming from standard suspension theory in which fibres and fluid move with the same velocity, and the other resulting in a Darcy contribution consisting of the relative fibre/fluid velocity. In this paper, we elaborate a general model able to adapt continuously to all these flow regimes. [ABSTRACT FROM AUTHOR]

An upscaling approach for multi-porosity media is developed and demonstrated on a three-scale porous medium. The three-scale porous medium problem is analyzed using the so-called MultiSPH approach, which is a sequential smooth particle hydrodynamics (SPH) solver at multiple scales. By this approach, upscaling introduces drag forces on the SPH particles at coarser scales. The resulting permeabilities obtained by the MultiSPH approach are validated against available analytical solutions for simple microstructures. For complex microstructures, the MultiSPH approach is validated against detailed single-scale SPH simulations and experimental data. Sensitivities of fluid-structure interaction on the permeability is investigated. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We consider a non-stationary Stokes system in a thin porous medium Ω ϵ of thickness ϵ which is perforated by periodically solid cylinders of size a ϵ. We are interested here to give the limit behavior when ϵ goes to zero. To do so, we apply an adaptation of the unfolding method. Time-dependent Darcy's laws are rigorously derived from this model depending on the comparison between a ϵ and ϵ. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We extend here a “bottleneck” flow model derived earlier for incompressible fluids flowing under creeping flow conditions [Despois, J. and Mortensen, A: Acta Materialia 53 (2005) 1381] to flow regimes where inertial losses are no longer negligible, causing the governing flow law to deviate from Darcy's law and become the Darcy-Forchheimer law. The proposed law is compared with measurements of the Darcian permeability K D and of the Forchheimer coefficient C in forced-flow of air through microcellular aluminium made by the replication process. The geometrical features of the cellular medium are varied in terms of volume fraction of porosity (in the range of 0.66–0.86) and the average cell diameter from (108–425 μm). As found previously in measurements with water, the Darcy permeability of the foams for airflow is also reasonably well captured by the model. In the Forchheimer-regime the model gives good quantitative agreement with data if one assumes that the amount of air kinetic energy that is dissipated when passing across each bottleneck linking one pore to its neighbour along the fluid flow path corresponds to the difference, in a stream of constant cross-sectional area, between a uniform fluid velocity profile and the non-uniform profile that is created by the no-slip condition along the window boundary. [ABSTRACT FROM AUTHOR]

This article continues the study in [4] of generalized Forchheimer flows in heterogeneous porous media. Such flows are used to account for deviations from Darcy's law. In heterogeneous media, the derived nonlinear partial differential equation for the pressure can be singular and degenerate in the spatial variables, in addition to being degenerate for large pressure gradient. Here we obtain the estimates for the L ∞ -norms of the pressure and its time derivative in terms of the initial and the time-dependent boundary data. They are established by implementing De Giorgi–Moser's iteration in the context of weighted norms with the weights specifically defined by the Forchheimer equation's coefficient functions. With these weights, we prove suitable weighted parabolic Poincaré–Sobolev inequalities and use them to facilitate the iteration. Moreover, local in time L ∞ -bounds are combined with uniform Gronwall-type energy inequalities to obtain long-time L ∞ -estimates. [ABSTRACT FROM AUTHOR]

Main theme of present investigation is to model and analyze the peristaltic activity of Carraeu-Yasuda nanofluid saturating porous space in a curved channel. Unlike the traditional approach, the porous medium effects are characterized by employing modified Darcy’s law for Carreau-Yasuda fluid. To our knowledge this is first attempt in this direction for Carreau-Yasuda fluid. Heat and mass transfer are further considered. Simultaneous effects of heat and mass transfer are examined in presence of mixed convection, viscous dissipation and thermal radiation. The compliant characteristics for channel walls are taken into account. The resulting complex mathematical system has been discussed for small Reynolds number and large wavelength concepts. Numerical approximation to solutions are thus plotted in graphs and the physical description is presented. It is concluded that larger porosity in a medium cause an enhancement in fluid velocity and reduction in concentration. [ABSTRACT FROM AUTHOR]

Based on the theory of fluid dynamics in porous media, combined with the gas state equation, Darcy's law and the discriminant equation of one-dimensional seepage instability, a mathematical model of one-dimensional penetration stability failure is established to study the seepage damage law of coal seam. Assuming that the background pressure of the coal wall is attenuated according to the exponential law, the mathematical equation is solved by using the finite difference method. Furthermore, the process of coal bed instability which is supposed as a form of a 'sublayer' pushing forward was analysed. That is, the coal bed loses its stability layer by layer. The calculation results showed that the thickness of the failure sublayer decreases with the reduction of coal permeability and the acceleration of dissipation rate of the background pressure. The model provides a method which can analyse the outburst process and its intensity quantitatively. [ABSTRACT FROM AUTHOR]

Pervious concrete (PC) mixtures were designed and prepared to measure and study permeability characteristics at varying head levels using a falling head permeameter. A total of 1092 readings was used to study the permeability properties of eighteen PC mixtures whose porosity was in the range of 15–37%, and permeability in the realm of 0.076–3.5 cm/s. The permeability reduced as the head of water increased, and gradually attained an asymptotic relation with the head. Cement-to-aggregate ratio had largest contribution in controlling permeability of PC mixtures. Nonlinearity in Darcy’s law was observed in respect of permeability of PC mixes, which was modelled using Izbash/power law, and was prominent for gradations consisting of larger sized aggregates due to inconsequential tortuous pore structure. Modified Kozeny-Carman equation was fitted for PC gradations to compare the results with Izbash law, which showed good agreement. This study is deemed to assist in understanding the hydrodynamics of water flow in pervious concrete, which in turn will aid in rational pervious concrete pavement system designs. [ABSTRACT FROM AUTHOR]

This technical note describes an effective and inexpensive field technique for measuring the saturated hydraulic conductivity of both undisturbed cores and repacked soil samples. The method requires no specialized equipment; everything that is required can be obtained in a hardware store. The method is a straightforward field implementation of the widely used falling-head laboratory analysis directly derived from Darcy's law. As such, it sidesteps the need for empirical assumptions about soil texture and the relationship between saturated and unsaturated flow components which many permeameter-based methods rely upon. The method is shown to produce results that are consistent with K values obtained elsewhere in the same homogeneous sand formation. Furthermore, the proposed method is useful for measuring hydraulic conductivity in drill cuttings obtained from direct push or auguring drill techniques, which cannot be done with any other field method. The range of hydraulic conductivity values that this test is appropriate for is on the order of 1E − 7 m/s to 1E − 3 m/s. [ABSTRACT FROM AUTHOR]

A non-Darcy flow develops in porous media when the velocity of reservoir fluids becomes extremely high because of the continuous narrowing of the cross section area of the flow and the convergence of flow streamlines. Therefore, the inertial effect increases significantly and the total pressure drop, required by fluids to move from the outer drainage area towards the wellbore increases significantly due to the extra pressure drop caused by the non-Darcy flow. The extra pressure drop is described by the Forchheimer equation in which the deviation from Darcy's law is proportional to the inertial factor which in turn is a function of porous media characteristics such as permeability and porosity. This paper introduces a new technique for estimating rate dependent skin factors ( DQ sc ) and non-Darcy flow coefficients ( D ). The new technique uses dimensionless pressure for steady state flow to determine these two parameters. A set of plots has been developed for the term ( DQ sc ) based on reservoir configurations i.e. reservoir boundaries (2 x e & 2 y e ), wellbore length, and anisotropy. All the plots have been developed based on the fact that the rate dependent skin factor represents the difference between the total pressure drop and the pressure drop caused by Darcy flow only when non-Darcy coefficient equals to zero. Dimensionless pressure drops for horizontal wells producing from finite acting reservoirs have been calculated for steady state flow when the impact of dimensionless time can be eliminated. The calculated pressure drops have been used in reservoir performance models to estimate rate dependent skin factors and non-Darcy coefficients. A point of special interest in this study is the ability to estimate these two parameters without the need for experimental work or the need to use currently proposed empirical models for calculating them. This new technique requires knowing reservoir configurations (reservoir width and length), the length of the wellbore, and the height of the formation in addition to the anisotropy. The study indicates that rate dependent skin factors and non-Darcy coefficients have the minimum values when the reservoirs having square-shape drainage area. It has also been found that both parameters have great impact on wells with short wellbore length. Additionally, isotropic formations and symmetrical wells perform better than anisotropic formations and asymmetrical wells in terms of extra pressure drop caused by non-Darcy flow. [ABSTRACT FROM AUTHOR]

In this paper, the mixed Navier–Stokes/Darcy problem which describes a fluid flow filtrating through porous media is considered. Based on two-grid discretizations, two local and parallel finite element algorithms for solving this mixed model are proposed. Numerical analysis and experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithms. [ABSTRACT FROM AUTHOR]

Within the framework of the theory of plane steady filtration of an incompressible fluid according to Darcy's law, two limiting schemes modeling the filtration flows under the Joukowski tongue through a soil massif spread over an impermeable foundation or strongly permeable confined water-bearing horizon are considered. [ABSTRACT FROM AUTHOR]

This paper presents a model to describe the propagation of waves in a poroelastic medium saturated by a three-phase viscous, compressible fluid. Two capillary relations between the three fluid phases are included in the model by introducing Lagrange multipliers in the principle of virtual complementary work. This approach generalizes that of Biot for single-phase fluids and allows to determine the strain energy density, identify the generalized strains and stresses, and derive the constitutive relations of the system. The kinetic and dissipative energy density functions are obtained assuming that the relative flow within the pore space is of laminar type and obeys Darcy's law for three-phase flow in porous media. After deriving the equations of motion, a plane wave analysis predicts the existence of four compressional waves, denoted as type I, II, III, and IV waves, and one shear wave. Numerical examples showing the behavior of all waves as function of saturation and frequency are presented. [ABSTRACT FROM AUTHOR]

The incompressible Brinkman equation represents the homogenized fluid flow past obstacles that comprise a small volume fraction. In nondimensional form, the Brinkman equation can be characterized by a single parameter that represents the friction or resistance due to the obstacles. In this work, we derive an exact fundamental solution for 2D Brinkman flow driven by a regularized point force and describe the numerical method to use it in practice. To test our solution and method, we compare numerical results with an analytic solution of a stationary cylinder in a uniform Brinkman flow. Our method is also compared to asymptotic theory; for an infinite-length, undulating sheet of small amplitude, we recover an increasing swimming speed as the resistance is increased. With this computational framework, we study a model swimmer of finite length and observe an enhancement in propulsion and efficiency for small to moderate resistance. Finally, we study the interaction of two swimmers where attraction does not occur when the initial separation distance is larger than the screening length. [ABSTRACT FROM AUTHOR]

The process of injecting chemical grout into cohesionless soil and its permeation by water are simulated by using a transparent soil model and a finite element model (FEM). The urea-formaldehyde resin is used as the grouting material in the transparent soil modelling. Two black and white charge-coupled device cameras are mounted in an orthogonal position to provide a three dimensional view of the groundwater-grout interface. The groundwater-grout interface is primarily influenced by the advection of the flowing water with increasing distance from the injection point owing to the reduction in the grouting pressure. An equation based on fluid dynamics in porous media and Darcy's law is then proposed to predict the displacement of the groundwater-grout interface in flowing water. A numerical model based on the FEM is also developed to simulate this process. The numerical simulation results are found to match the physical modelling well. [ABSTRACT FROM AUTHOR]