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This study describes a micromechanics model for estimating the effective vascular permeability for a biological tissue containing parallel microvessels subjected to finite deformations. The representative volume element in the proposed model consists of a hollow cylinder with the inner radius being the microvessel radius and the outer radius determined using the volume fraction of the microvessels in the tissue. The effective vascular permeability is determined using the Poiseuille equation for the microvascular flow, Darcy's law for the homogenized porous tissue, and finite deformation of the tissue matrix modeled as a nonlinear elastic material. The numerical results show that the effective vascular permeability decreases with an increase in the applied pressure on the tissue. The effective permeability can be significantly larger than the reference permeability when the applied pressure is much smaller than the microvascular pressure. On the other hand, the effective permeability becomes less than 30% of the reference permeability when the applied pressure is greater than two times the microvascular pressure. Finally, the effective vascular permeability increases monotonically with an increasing ratio of the deformed volume to the reference volume of the tissue. [ABSTRACT FROM AUTHOR]

Bae, J. and Sherman, D.J., 2025. Microscale morphologic changes caused by groundwater seepage on a macrotidal beach. Journal of Coastal Research, 41(1), 16–26. Charlotte (North Carolina), ISSN 0749-0208. Beach groundwater dynamics and groundwater seepage (exfiltration) are important agents of morphologic change in the intertidal zone and are controlled mainly by the relationships between local water level, the elevation of beach water table, and the permeability of beach sediments. Groundwater seepage can alter sediment transport processes on beaches through regulating saturation on the beach face and generating shear stresses sufficient to initiate sediment transport. This study investigates seepage dynamics in the context of a macrotidal beach and consequent erosion, deposition, and seepage-induced morphologic changes. Data were collected from the west coast of South Korea, at Hakampo Beach, where the spring, mean, and neap tide ranges are 6.5, 4.6, and 2.8 m, respectively. Beach morphology and changes were measured using terrestrial LiDAR. Beach groundwater levels were measured with a series of wells. Sand samples were taken and analyzed to characterize beach face texture and to estimate beach permeability. The water table and sediment data were used to estimate seepage flows at low water, using Darcy's law. The relationship between seepage rates and morphologic changes was examined with geographically weighted regression analysis. The results show that seepage-induced offshore transport occurred in the intertidal zone below groundwater seepage lines during spring tide, whereas transport was concentrated along seepage-induced tidal rills during neap tide. This highlights the importance of recognizing the variability in seepage discharge with different tidal ranges, especially in the context of potential flow rates exceeding the threshold for sediment transport. This study also points to the control of breaks in beach face slope and concomitant changes in grain size in the location of the groundwater seepage line in macrotidal environments. [ABSTRACT FROM AUTHOR]

This paper investigates the stability in a heated fluid-porous system. Darcy's law is used for the flow in the porous medium. Previous studies indicate that the classical Rayleigh–Bénard instability in this flow is independent of the mutual positions of the fluid layer and porous layer. This paper demonstrates that the instability depends on the mutual positions of the fluid layer and porous layer when the liquid density is nonlinearly dependent on temperature. When porous medium is located at the bottom of the system, onset of convection may occur in lower porous layer (pure-porous mode), upper water layer (pure-water mode) or across both layers (porous-water mode). However, onset of convection cannot take place only in the upper porous layer when porous medium is placed at the top of the system. The influence of depth ratio d ˆ and the density inversion parameter θ M on instability of bilayer system are investigated in detail and dependence of critical modes on parameters are summarized in phase diagrams. In addition, direct numerical simulation is used to analyse the instability mechanism and identify subcritical or supercritical instability for bilayer systems. [ABSTRACT FROM AUTHOR]

The article explores how a reaction-driven decrease in viscosity affects viscous fingering patterns at different injection flow rates. Research shows that at high flow rates, the reaction leads to thinner fingers covering a smaller area due to enhanced shielding effects, while at low flow rates, the reaction stabilizes the displacement, resulting in almost stable patterns. The study emphasizes the role of diffusivity in determining the impact of reactions on viscous fingering patterns, particularly in relation to varying Péclet numbers. [Extracted from the article]

The article "Coating thickness prediction for a viscous film on a rough plate" in the Journal of Fluid Mechanics presents a predictive model for determining liquid film thickness on a rough plate using a homogenization approach. The model considers slip and interface permeability terms that vary with the solid fraction of the rough surface, validated by experimental measurements showing decreased slip and permeability with increasing solid fraction. The study highlights the significance of solid fraction in determining slip and permeability values for rough surfaces, exploring the relationship between coating thickness, coating velocity, slip length, and interface permeability. Additionally, the document includes a list of related scientific articles covering topics such as fluid dynamics, porous media, surface interactions, and scientific computing algorithms, offering valuable insights into fluid-solid interactions across different contexts. [Extracted from the article]

ABSTRACT The numerical investigation in this study focuses on the propagation of hydraulically driven fractures in deformable porous media containing two fluid phases. The fully coupled hydro‐mechanical governing equations are discretized and solved using the extended element‐free Galerkin method. The wetting fluid is injected into the initial crack. The pores are filled with both wetting and non‐wetting fluid phases. Essential boundary conditions are enforced using the penalty method. To model the discontinuities in field variables, the extrinsic enrichment strategy is employed. Ridge and Heaviside enrichment functions are utilized to introduce weak and strong discontinuities, respectively. The nonlinear behavior in front of the crack tip is defined by means of a cohesive crack model. Continuity equations for wetting and non‐wetting fluids through the fracture domain are expressed using Darcy's law and cubic law. The coupling terms of fluids are considered in accordance with their mass transfer among the crack and the surrounding domain, simulating the fluid leak‐off phenomenon and the fluid lag zone. The results demonstrate the success of the proposed numerical framework in simulating the intricate aspects of the hydraulic fracturing process. Sensitivity analysis is performed with varying domain permeabilities and wetting fluid viscosities to elucidate their effects on different aspects of hydraulic fracture. [ABSTRACT FROM AUTHOR]

The article explores the development of a predictive macroscopic model for fluid flow across permeable membranes with non-negligible inertia using homogenization theory. It compares constant and variable advection closure approaches to solve microscopic problems and obtain average hydrodynamic tensor components, revealing that inertia decreases permeability. The study offers insights into the impact of inertia on fluid flow and proposes a clustered variable advection closure approach for efficient and accurate modeling in industrial applications. The research highlights the importance of considering inertia in computational modeling of laminar transport across permeable membranes, showing improved accuracy and potential applications in microfluidic circuits and filtration systems. [Extracted from the article]

The article delves into the behavior of gravity currents in porous media, specifically focusing on the Darcy-Forchheimer regime. The study includes theoretical and experimental analyses, deriving self-similar solutions for different parameters. The results are validated through experiments, exploring the implications of various factors on the propagation of gravity currents. The research also discusses boundary conditions, predictor-corrector schemes, and alternative expressions for current profiles and nose positions over time. Additionally, the document touches on dispersion effects, Forchheimer equation coefficients, and the impact of CO2 compressibility on storage in deep saline aquifers, referencing related works in the field. [Extracted from the article]

The article in the Journal of Fluid Mechanics explores the stability of reactive radial viscous fingering in porous media. It delves into how chemical reactions affect displacement flows' stability through linear stability analysis and nonlinear simulations. The research identifies stable and unstable regions in a phase plane based on Damköhler number (Da) and Péclet number (Pe) values, with a stable region near Rc = Rb regardless of changes in reaction rate. The study sheds light on stability transitions for different reactions, offering valuable insights for applications like enhanced oil recovery and CO2 sequestration. [Extracted from the article]

The article delves into the phenomenon of delayed gravitational collapse in colloidal suspensions, specifically focusing on the resistance of colloidal gels to gravity. Through theoretical modeling, the study examines the delay time, which determines the shelf life of gel-based products, and sedimentation behavior. Factors such as initial volume fraction and particle interactions play a crucial role in understanding the collapse behavior of colloidal gels under gravitational forces. The research sheds light on the time evolution of sedimenting gels, density profiles, colloidal flux, and volume fractions, revealing distinct regimes of delay, linear settling, and exponential compaction. The study underscores the significance of dilatational viscosity and local density variations in comprehending the dynamics of colloidal gels under gravity, suggesting potential modifications to the model for better alignment with experimental findings and advocating for further research to incorporate erosion mechanisms and higher dimensions for a more holistic understanding of colloidal gel behavior. [Extracted from the article]

Traumatic brain injury remains a significant global health concern, requiring advanced understanding and mitigation strategies. In current brain concussion research, there is a significant knowledge gap: the critical role of transient cerebrospinal fluid (CSF) flow in the porous subarachnoid space (SAS) has long been overlooked. To address this limitation, we are developing a simplified mathematical model to investigate the CSF pressurization in the porous arachnoid trabeculae and the resulting motion of brain matter when the head is exposed to a translational impact. The model simplifies the head into an inner solid object (brain) and an outer rigid shell (skull) with a thin, porous fluid gap (SAS). The CSF flow in the impact side (coup region) and the opposite side (contrecoup region) is modeled as porous squeezing and expanding flows, respectively. The flow through the side regions, which connect these regions, is governed by Darcy's law. We found that the porous arachnoid trabeculae network significantly dampens brain motion and reduces pressure variations within the SAS compared to a SAS without the porous arachnoid trabeculae (AT). This effect is particularly pronounced under high-frequency, periodic acceleration impacts, thereby lowering the risk of injury. The dampening effect can be attributed to the low permeability of the AT, which increases resistance to fluid movement and stabilizes the fluid and pressure responses within the SAS, thereby reducing extreme pressure fluctuations and brain displacement under impact. This work provides a foundational understanding of CSF flow dynamics, paving the way for innovative approaches to brain injury prevention and management. [ABSTRACT FROM AUTHOR]

Chemical dissolution along interfaces between solid skeleton and pore fluids tends to alter geomaterials and may cause catastrophic failures. Following the hydrodynamic procedure, this work develops a mathematically rigorous and thermodynamically consistent modelling framework to investigate the impact of chemo-mechanical coupling on the constitutive properties of poroelastic geomaterials. The formulation considers the mass fractions of all the ionic species in the pore fluid as independent state variables that quantify chemical processes. The constitutive and transport relationships are systematically derived from thermodynamic principles, symmetry requirements and conservation laws. To demonstrate its effectiveness, the formulation is adopted to study the dissolution process of saturated calcarenites under acidic environments. Simple density-dependent linear elasticity is being considered whereby stiffness degradation is physically captured in terms of density changes. Without chemical reaction, the stiffness is fixed and the response is purely linearly 'poroelastic'. However, upon reaction the density changes, and thus so also does the stiffness, implying a non-linear response. The model also reveals the connection of densities to chemical potentials and pore fluid pressure, and shows that the latter quantity is governed by both density and osmotic concentration. Simulations of long-term debonding tests of calcarenite samples show good agreement with experimental observations under both uncoupled and coupled testing conditions. Furthermore, considering only a limited number of clearly stated assumptions, the model recovers the form of several empirical laws such as Darcy's law, Fick's law and the law of reaction kinetics. Outside these idealised model assumptions, the newly derived relationships generalise results for field conditions and provide insights into cases where one normally does not have, or technologically cannot reliably obtain experimental data due to challenging loading and boundary conditions. [ABSTRACT FROM AUTHOR]

A comprehensive analysis of the flow in Schwarz‐D triply periodic minimal surfaces (TPMS) structures based on CFD simulations is presented. The pressure drops and friction factor characteristics of the structure are investigated by employing both full‐scale and representative elementary volume (REV)‐scale CFD setups. The results are validated against experimental data from the literature. An analytical model is developed using hydraulic diameter, porosity, and permeability from the CFD simulation results. The findings contribute valuable insights into the optimization and application of Schwarz‐D TPMS structures in engineering systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider an adaptive hybridizable discontinuous Galerkin (HDG) method based on the discrete fracture model for approximation of a single-phase flow in fractured porous media. We are interested in the case that the flow rate in fracture is large enough to justify the use of Forchheimer's law for modeling flow within the fracture, while Darcy's law is applied to the surrounding matrix. The HDG method could be designed to simulate the flow in porous media with reduced fractures which consist of many straight lines or planes. More specifically, we use piecewise polynomials of degree k to approximate the velocity and pressure in fracture and surrounding porous media. The existence and uniqueness of discrete solutions are proved by the Brouwer fixed point theorem, and an efficient and reliable a posteriori error estimator is obtained with respect to an energy norm. Moreover, the HDG scheme, the existence and uniqueness of discrete solutions, and the a posteriori error estimates are also extended to the problem with non-planar, embedded, and intersecting fractures. Finally, several numerical examples are provided to validate the performance of the obtained a posteriori error estimator. [ABSTRACT FROM AUTHOR]

Carter's model of fluid loss is used in the oil and gas industry performing the numerical approach of leak-off. Its deduction applies some simplifying assumptions, such as the difference between fluid pressure and constant pore pressure and filtration process approximation to a unidirectional flow, perpendicular to the fracture plane. For this paper, the so-called Chimas is an hydromechanical simulator of oil reservoirs, fully coupled and implicit, in a way that considers the poroelastic effects on the propagation of fractures. The leak-off process is explicitly treated in the fracture boundary conditions using Darcy's law. The objective of this work is to validate the filtration phenomenon of Chimas hydromechanical simulator comparing the parameters of length, width and injection pressure with those obtained using an iterative method implemented in MatLab and which includes Carter's analytical equation. Numerical accuracy was validated against asymptotic analytical solutions. The agreement between the iterative method and the analytical solutions was particularly good in relation the length fracture and injection pressure. [ABSTRACT FROM AUTHOR]

This paper presents the numerical study for heat generation and electro-osmotic effects of Carreau model of a fluid in an unsteady channel. This prepared model has many useful applications in microfluidic biological and mechanical research. Modified Darcy's law, viscous dissolution and ciliated walls are also presented. Non-Newtonian fluids play a key role in biological fluids which include the motion of foods within digestive zone, blood circulation, including small bowls and migration of urine. The main findings for the research is to analyze the flow rate change and check the behavior of velocity and temperature by using different parameters. The modeled equations of Carreau fluid flow are depressed into a simple form by employing the long wavelength approximation and small Reynolds number, then the resulting equations are calculated numerically by using MATHEMATICA. Impact of physical factors are graphically figured for velocity, temperature field and streamline distribution. The results show that velocity modifies by applying different values of flow rate and Darcy's number. Temperature profile increases for advanced values of Prandtl number, Eckert number and heat source parameter. For heat source parameter (γ = 0. 5 , 0.6 and 0.7) and Eckert number ( E c = 1. 0 , 1.5 and 2.0) the temperature profile expands at the region (y < 1. 0). [ABSTRACT FROM AUTHOR]

The numerical simulation of reservoir mud invasion is widely used for studying the dynamic invasion process. To investigate the saturation changes of the three phases (water, oil, and mud filtrate) during mud infiltration into intact formations, this study presents a mathematical model for three-phase invasion in cylindrical coordinates. The principle of mud intrusion into the reservoir allows the derivation of the basic equation of three-phase mud seepage from Darcy's law and the law of mass conservation. This is followed by the derivation of the differential equations of pressure and three-phase saturation during mud intrusion. A numerical simulation program for the three-phase seepage flow of mud intrusion is written using the finite-difference method. An adaptive time-step algorithm is developed to address the inadaptability of the intrusion algorithm in the case of mud surges. Additionally, an epithermal effect algorithm is developed to address the problem of mud particles entering the stratum and affecting the absolute permeability. The results show that, as the porosity increases, the radial depth of intrusion decreases, along with a reduction in the invaded annulus range. It can be demonstrated that, when the reservoir pressure is maintained at a constant level, the size of the borehole pressure leads to an increase in the depth of radial intrusion and the extent of the intrusion annulus, under different differential pressure conditions. [ABSTRACT FROM AUTHOR]

Analyzing the mechanisms of soil instability in tunnels due to sudden water ingress is essential for construction safety. This kind of problem belongs to the category of seepage deformation, mostly due to the near tunnel range of water pipeline blowing cracks and heavy rainfall flooding rainwater into the tunnel. Distinguished from general infiltration behavior, the relevant problems have the characteristics of rapid occurrence and short action time. This study develops a 3D fluid–solid coupling model for soil deformation in tunnels with water ingress, grounded in Biot's theory and Darcy's law while considering water level variations within the tunnel. The governing equations are discretized in space and time, and the model's accuracy is validated through comparison with actual measurements from a Zhengzhou subway project. The study analyzes pore pressure, stress-deformation responses, and surface settlement patterns in surrounding soil and rock mass under soil–water coupling. The findings show that (1) the tunnel cavern, as a seepage source, has minimal impact on the lateral settlement trough width, while seepage mainly affects the vertical deformation of surrounding rock; (2) pressure dissipation exhibits hysteresis in clay strata; (3) water ingress increases soil saturation and decreases effective stress, resulting in persistent surface settlement until drainage. There is a minimal discrepancy between model-calculated and measured settlements. [ABSTRACT FROM AUTHOR]

At present, over 2.6 billion people live without access to a continuous water supply, and nearly 900 million people do not obtain drinking water from reliable sources. To solve these problems, one of this study's goals is to come up with a water-supply system that uses a simple, inexpensive, portable ultrafiltration (PUF) unit. To determine the effectiveness of the portable system, water-quality analysis has been carried out to determine if the system produces filtered water from various sources of water, reaching drinking-water standards. A simple model of the system using Darcy's Law was also obtained to predict permeate flux and transmembrane pressure (TMP). Initially, simulation was performed using nominal values taken from the literature for four (4) parameters, i.e., membrane hydraulic resistance, initial rapid fouling constant, mass transfer coefficient, and foulant bulk concentration. By minimizing the error between the model with these nominal values and experimental values, an improved model with updated parameters was obtained using the Evolutionary Programming (EP) approach. With the updated model, the average error between the model and the experiment was reduced from 32% to 9%. This was further validated with new data taken from the experiment. This improved model with the updated parameter was then used to predict the TMP and compared with the experimental value. Contrasting the optimized model with the existing model indicates that the optimized model predicts membrane performance better, leading to a competent and reliable model for the purification of water using a PUF system built in-house. [ABSTRACT FROM AUTHOR]

The article delves into the linear stability analysis of isothermal plane Couette flow over a porous layer using a two-domain approach. It examines the instability of the flow under various conditions, including depth ratio, porosity, Darcy number, and stress-jump coefficient, with numerical methods confirming the results. The study reveals that the flow is linearly stable for specific parameters, with the depth ratio being a key factor in stability determination. The research sheds light on the instability of isothermal plane Couette flow in a superposed fluid-porous system, highlighting three different instability modes and providing valuable insights for engineering applications like ship propeller-induced flow over sedimented porous bottoms. [Extracted from the article]

Comprehending the dynamics of reactive viscoelastic third‐grade fluids (VTGF) in gravity‐driven flows along inclined planes is crucial for numerous engineering and industrial applications. This research focuses to explore the transient behavior of such a fluid under non‐isothermal conditions, with an emphasis on the impact of exothermic reactions. The inclined plane region, filled with a porous material of constant permeability, is modeled using a modified version of Darcy's law to account for resistance to flow. The viscosity‐temperature dependence follows the Nahme‐type principle, while convective cooling at the free surface is simulated using Newton's cooling law. The exothermic chemical reaction of the material is described using Arrhenius kinetics. The resulting mathematical model for energy balanced and momentum comprises a set of non‐homogeneous and nonlinear partial differential equations (PDEs), which are transformed into dimensionless form and solved using semi‐implicit numerical techniques based on finite difference methods (FDM) implemented in Matlab. The study visually examines thermo‐dynamical phenomena such as thermal runaway due to the exothermic reaction and investigates how velocity and temperature respond to variations in system parameters. The numerical findings indicate that the interplay between porous medium, viscosity variation, and thermal effects significantly influences the flow and thermal behavior, providing valuable insights for optimizing and controlling such fluid systems in practical applications. [ABSTRACT FROM AUTHOR]

In this study, finite element software was used to simulate seepage at the core scale, the stress sensitivity of the shale core of the stripe layer and fractures was evaluated, and the production optimization design of reservoir C in block B of the oilfield under different fracturing parameters and wellbore parameters was simulated. The coupled finite element model of reservoir seepage stress was established; the pore elasticity model was used to determine the reservoir deformation; the seepage followed Forchheimer's law and Darcy's law; and finally, the liquid production was calculated to optimize the production plan. The results showed that the permeability under the same stress conditions increased nonlinearly with the increase in the striatal angle at the core scale, the permeability under the same effective stress conditions decreased gradually with the increase in the shale/fringe thickness ratio, and the elastic modulus and Poisson's ratio of the proppant decreased. The permeability stress sensitivity was stronger. In the reservoir-scale model, the production pressure difference was the most significant factor affecting shale oil production, followed by the number of fractures and the length of the horizontal zone wellbore, and the elastic modulus of the proppant and Poisson's ratio had the least impact on production. [ABSTRACT FROM AUTHOR]

The article in the Journal of Fluid Mechanics explores the dynamics of fluid flow in a three-layer Hele-Shaw problem driven by a sink. Using numerical methods, the study investigates the interaction between interfaces and the sink, leading to rich pattern formation phenomena. The research emphasizes the influence of parameters such as the width of the annular region, sink location, and fluid mobilities on the system's dynamics, with potential applications in fields like oil recovery and porous media flow. The document contains a collection of scientific research articles authored by a diverse group of researchers, offering valuable insights into complex fluid dynamics phenomena in Hele-Shaw cells, including bubble motion, finger selection in viscous fingering, and pattern formation. [Extracted from the article]

To investigate the development of temperature fields under seepage conditions for pipe curtain freezing method, drawing on the Sanya River Estuary Trench Tunnel freezing project, combined with Darcy's law and heat transfer theory in porous media, using finite element software to establish a coupled water-heat numerical model, the study employs varying seepage rates in the model and a method for creating temperature measurement paths, and analyzes the evolution of the frozen soil curtain, circulation time, and wall thickness. The results indicate that the frozen soil curtain develops along the seepage direction, with the soil on the downstream side freezing earlier than the upstream side, and attaining a lower final temperature； when the flow rate is approximately 2. 87 m/d, the impact of low seepage rates on the overall circulation time of the frozen soil curtain is relatively minor； as the seepage rate increases, the overall circulation time of the frozen soil curtain grows significantly, accompanied by increased regional unevenness and a decrease in thickness； when the flow rate increases to approximately 10. 02 m/d, local non-circulation occurs in the frozen soil curtain. Considering the original freezing plan to be conservative, an optimized design is proposed： reducing the number of inner circle freezing pipes from 80 to 56, the simulated average thickness of the frozen soil curtain is approximately 4. 28 m, a decrease of 0. 195 m compared to the original plan. This optimized design still meets the freezing design specifications. [ABSTRACT FROM AUTHOR]

This work considers the isothermal process of incompressible viscous fluid filtration in an oil-saturated, fractured-porous reservoir. A study of the pressure and water saturation distribution process is carried out for a case in which a production well is put into operation. For this problem, i.e., a mathematical model in a two-dimensional formulation, a numerical method and a parallel algorithm are proposed. The mathematical model of two-phase filtration is written in accordance with the classical laws of continuum mechanics and Darcy's law and also includes a function of fluid exchange between low-permeability pores and high-permeability natural fractures within the framework of the Warren–Root model. The numerical solution is based on the finite-difference method and a splitting scheme of physical processes and spatial coordinates. For a split system with respect to piezoconductivity, an implicit finite-difference scheme with fixed saturations is constructed, and with respect to saturation transfer, explicit and implicit difference schemes are constructed. For parallel implementation of the developed numerical approach, a method based on geometric parallelism is selected. Testing of the developed method is performed using the example of calculating liquid mass transfer for a wide range of parameters. To verify the model, the obtained calculated pressure curves are compared with field data recorded by a deep-well measuring device. The results allow for estimation of the distribution of reservoir pressure and water saturation depending on the permeability of the fracture set and the pore part. The obtained results allow for monitoring of well operations, reducing unexpected accident risks and optimizing the development system in order to increase oil production in fractured-porous reservoirs. Computational experiments confirm the efficiency of the developed numerical algorithm and its parallel implementation. [ABSTRACT FROM AUTHOR]

The utilization of lattice-based scaffolds emerging as an advance technique over conventional bio-implants in Bone Tissue Engineering. In this study, totally six lattice structures are considered for permeability and wall shear stress (WSS) investigation. Namely triply periodic minimal surfaces (TPMS)-based Gyroid, Schwarz-P, Schwarz-D, and two beam-based structure—Cubic and Fluorite are compared with the proposed new lattice structure at porosity level of 80%, 75%, and 70%. The proposed new lattice has combine characteristic of Gyroid and Schwarz-D TPMS lattice. The permeability is determined through Darcy's law, where the pressure drop across the lattice structure is calculated using a computational fluid dynamics (CFD) tool at flowrate between 0.2 and 10 ml/min. The Cubic and Schwarz-P lattice structures exhibited the highest permeability but at the cost of a lower active surface area for WSS, measuring below 155 mm², means least cell proliferation occurs while the permeability value in New Lattice structure is in the ideal range with the enhanced active surface area for WSS (514 mm²). The complex internal curvatures of New Lattice promote the cell proliferation while the through-pore holes allow the efficient cell seeding.The utilization of lattice-based scaffolds emerging as an advance technique over conventional bio-implants in Bone Tissue Engineering. In this study, totally six lattice structures are considered for permeability and wall shear stress (WSS) investigation. Namely triply periodic minimal surfaces (TPMS)-based Gyroid, Schwarz-P, Schwarz-D, and two beam-based structure—Cubic and Fluorite are compared with the proposed new lattice structure at porosity level of 80%, 75%, and 70%. The proposed new lattice has combine characteristic of Gyroid and Schwarz-D TPMS lattice. The permeability is determined through Darcy's law, where the pressure drop across the lattice structure is calculated using a computational fluid dynamics (CFD) tool at flowrate between 0.2 and 10 ml/min. The Cubic and Schwarz-P lattice structures exhibited the highest permeability but at the cost of a lower active surface area for WSS, measuring below 155 mm², means least cell proliferation occurs while the permeability value in New Lattice structure is in the ideal range with the enhanced active surface area for WSS (514 mm²). The complex internal curvatures of New Lattice promote the cell proliferation while the through-pore holes allow the efficient cell seeding. [ABSTRACT FROM AUTHOR]

The water table fluctuation (WTF) method is popular for groundwater recharge (GR) estimation, but its accuracy is challenged when applied in areas with thick vadose zones because of the signal lag and attenuation with depth and uncertainties from barometric pressure effect and lateral flow. Improvement of the WTF method used the linear regression method and Darcy's law, and has been assessed to give satisfactory results. In particular, the improved method presented lower GR (20–34%) relative to the conventional method. GR decreased from the centre to the edge of the tableland. The regional average GR was 63–81 mm year−1, equivalent to 11–14% of annual average rainfall. Lag times between recharge and rainfall ranged from 1 to 9 months. Rainfall and vegetation dominated the spatiotemporal variability of GR. Our study provides reference and technical support for GR estimation with the WTF method in regions with a thick vadose zone. [ABSTRACT FROM AUTHOR]

The creeping flow of a tangent hyperbolic liquid via a channel of porous walls is discussed in this article. For the formulation of problem, the laws of conservation of mass, momentum, and energy are used. A description of fluid leakage through channel walls is provided by Darcy's law. An analytical solution to the equations of motion is determined with appropriate physical approximations by applying the perturbation technique. Expressions for the hydrostatic pressure, velocity field, and temperature are found. The flow characteristics of tangent hyperbolic fluid are affected by the filtration coefficient and inlet pressure, which are also discussed. Graphs are used to discuss the effects of the inlet pressure, the Wiessenberg number, the magnetic field, the law index, the Brickman number, and the wall filtration parameter on the flow characteristics. The mean pressure difference is shown to be increased by the magnetic field. The derived data are used in a flat plate hemodialyzer to investigate the filtrate flow. The theoretical values for the hemodialyzer's mean pressure difference and filtration rate are computed using the derived solutions. A reasonable agreement is established between the calculated results and the experimental data. It is determined that the fluid flow in a flat plate hemodialyzer can be studied hydrodynamically using the model that is presented. A flat plate hemodialyzer's filtrate flow is examined by using the results that were obtained. [ABSTRACT FROM AUTHOR]

Gas‐water flow in propped fractures can be commonly observed in various practical applications, including hydrocarbon development, geothermal exploitation, contaminant transport, and geological carbon storage. The fluid flow in a propped fracture can be regarded as Darcy type if only the resistance from the propping materials (e.g., cement in natural fractures and proppant‐pack in hydraulic fractures) accounts. However, if the fracture width is sufficiently small, the extra resistance from the viscous shear of fracture walls cannot be neglected, resulting in the appearance of Brinkman flow. In practice, during the development of a naturally fractured aquifer or a hydraulicly fractured hydrocarbon reservoir, the fracture width will be significantly reduced as the production proceeds. Therefore, the Brinkman flow can impose a strong effect on the fluid transportation within the fractures. However, the existing study about the two‐phase Brinkman flow in propped fractures is still far from adequate. In this work, on the basis of a modified two‐phase Brinkman equation, the authors derive a novel analytical formulation to correct the relative permeability of gas‐water two‐phase flow in propped fractures to account for the Brinkman effect. With the aid of the proposed formulation, the authors carry out a comprehensive investigation of the influence of Brinkman flow on the effective gas‐water relative permeability and well performance. The calculated results show that the effect of Brinkman flow on the water phase (or gas phase) transportation is more significant with a larger water (or gas) saturation. A narrower propped fracture is more likely to induce Brinkman flow, thus leading to a lower relative permeability for both water and gas phases. As the propping‐material permeability is increased, the fluid transportation bears more severe viscous drag from fracture walls, and the relative permeability will be consequently reduced. Only if the fracture width is significantly reduced during the production, the Brinkman flow demonstrates its influence on the well performance. Otherwise, Darcy's law can provide sufficiently accurate results in characterizing the two‐phase flow in propped fractures. Key Points: The viscous shear from fracture walls and the resistance from propping materials induce Brinkman flow in propped fracturesNeglecting the effect of Brinkman flow can cause significant errors in evaluating the gas‐water relative permeability in propped fracturesAn analytical formulation is proposed to correct the relative permeability of gas‐water flow in propped fractures considering Brinkman flow [ABSTRACT FROM AUTHOR]

Bentonite grouting is utilized widely in geotechnical engineering to stabilize the excavation and prevent seepage in sandy soils. However, the infiltration behavior of bentonite slurry in sandy soil is not well understood, primarily due to rheological blocking and the formation of a filter cake. This study performed infiltration column tests to investigate the infiltration behavior under various conditions, including slurry concentration, sand properties, grouting pressure, and infiltration duration. Monitoring included infiltrated distances (calculated from drainage volume), pore pressure at different depths, and bentonite distribution using methylene blue titration. Results indicate that rheological blocking occurs during the infiltration process as bentonite slurry, which is a shear-thinning fluid, increases in viscosity with a decreased shear rate. This phenomenon is more pronounced with higher slurry concentrations, leading to reduced infiltration distances. Additionally, in soils with pore throats smaller than bentonite particles, a filter cake forms above the surface of the grouted soil, decreasing the pore pressure and further reducing infiltration distance. The distribution of bentonite content remains consistent across the infiltrated zone, resulting in a linear pressure drop. Based on these findings, the study proposes a novel model that combines the generalized Darcy's law, the Herschel–Bulkley rheological model, and mass conservation of slurry to predict the spatiotemporal progression of the infiltration front. This model, which was validated using experimental data, accurately predicts the effects of rheological properties and filter cake formation on infiltration. The results of this study provide valuable insights into infiltration processes and enhance the application of bentonite slurry in grouting. [ABSTRACT FROM AUTHOR]

As an effective reinforcement technology for seepage prevention, penetration grouting has been widely used in geotechnical and underground engineering. Because grouting is a hidden project, the extent of slurry spread is often estimated theoretically and through experience. Therefore, it is important to understand the diffusion pattern and scope of penetration grouting in reinforcement engineering. Based on the generalized Darcy's law, a penetration grouting model considering the gravity and the time-varying nature of the slurry viscosity is proposed in this study. Its validity and effectiveness are verified through a comparison with existing penetration grouting tests. Based on the established penetration grouting model, the effects of the grouting pressure, permeability coefficient, water–cement ratio, and other factors on penetration grouting are analyzed. The penetration and diffusion process of a Bingham fluid considering gravity and time-variable slurry viscosity is computationally simulated using a finite-element software. The research results show that the proposed penetration grouting model is more accurate than the traditional one that does not consider the two aforementioned factors, and its results are more in line with the experimental ones. The rate of error calculated from the experimental value is about 11%. The diffusion radius of the slurry increases with increasing grouting pressure, permeability coefficient, and water–cement ratio, and decreases with increasing groundwater pressure. With the elapse of the grouting time, the increase rate of the diffusion radius exhibits a trend of increasing first and then decreasing and tending to level off. These research results can provide certain theoretical support for penetration grouting research in geotechnical and underground engineering. [ABSTRACT FROM AUTHOR]

The aim of this study is to present forced convective nanofluid flow over a moving plate embedded in an absorbent medium. Following Darcy law's for porous medium, the flow analysis is explored in attendance of warmth basis/drop. The main objective of this study is to explore the effects of Brownian motion and thermophoresis. The plate is considered to move in both directions: in the way of movement of fluid and in the opposite route of fluid movement. Similarity alterations have been applied to alter the leading partial differential equations (PDEs) to ordinary differential equations (ODEs). Numerical solutions have been obtained with the help of MATHEMATICA software. Dual solutions have been obtained when the plate and liquid go in reverse ways. Wall shear stress, Nusselt and Sherwood numbers all are found to rise with the rising permeability parameter of absorbent medium. For Nusselt and Sherwood numbers, ranges of dual solutions diminish by the mounting values of permeability parameter K. The critical values for porosity parameter K = 0. 0 1 , 0.02, 0.03 are R c 1 = 1. 8 7 2 9 0 9 , R c 2 = 1. 9 2 7 2 1 1 , R c 3 = 1. 9 8 2 4 2 8 4 , respectively. For decreasing values of s, range of dual solutions decreases. For s = − 0. 4 5 , dual solutions exist in the range (1. 1 9 , 1. 2 0). [ABSTRACT FROM AUTHOR]

The article delves into the development of a macroscopic model for perfect-slip flow in porous media through the use of the adjoint method and Green's formula. It highlights the symmetric and positive nature of the permeability tensor, Kps, obtained from solving the closure problem, and establishes relationships between Kps, Ks, and K. Numerical simulations validate the macroscopic model and the connection between Kps and K, while also exploring the symmetry and positivity of Ks and K. The document provides a thorough examination of various studies and models in fluid mechanics, particularly focusing on slip flow in porous media, with contributions from researchers like Lasseux and Valdés-Parada. References to microfluidics, numerical simulations, and boundary conditions in fluid mechanics are also included, offering valuable insights into fluid behavior in porous media and enhancing the understanding of fluid dynamics. [Extracted from the article]

Controlling the microclimate condition inside a greenhouse is very important to ensure the best indoor conditions for both crop growth and crop production. To this regard, this paper provides the results of a novel approach to study a greenhouse, aiming to define a porous media model simulating the crop presence. As first, an experimental campaign has been carried out to evaluate air temperature and air velocity distributions in a naturally ventilated greenhouse with sweet pepper plants cultivated in pots. Then, the main aspects of energy balance, in terms of mass transfer and heat exchange, and both indoor and outdoor climate conditions have been combined to set up a computational fluid dynamics model. In the model, in order to simulate the crop presence and its effects, an isotropic porous medium following Darcy's law has been defined based on the physical characteristics of the crops. The results show that the porous medium model could accurately simulate the heat and mass transfer between crops, air, and soil. Moreover, the adoption of this model helps to clarify the mechanism of thermal exchanges between crop and indoor microclimate and allows to assess in more realistic ways the microclimate conditions close to the crops. [ABSTRACT FROM AUTHOR]

The article "Closed equation model for cavity evolution in granular media" in the Journal of Fluid Mechanics presents a closed three-equation model for predicting cavity evolution in granular media, particularly in explosion-driven gas-particle flows. The study extends the classical Rayleigh-Plesset model to include gas expansion and non-Darcy gas-penetration effects, examining both symmetric and asymmetric gas injection scenarios. By non-dimensionalizing the equations, key dimensionless numbers are derived to characterize cavity expansion response time and non-Darcy effects intensity. The model's predictions were validated through refined numerical simulations, revealing discrepancies attributed to neglecting inertial effects and a buffer mechanism in the granular medium. The study further explores the impact of dimensionless numbers on cavity evolution processes and conducts additional tests to enhance the model's predictive accuracy. [Extracted from the article]

China's coal seam permeability is low, and the original coal seam gas extraction is difficult. CO2 displacement of coal seam CH4 technology is an effective gas extraction technology. CO2 is injected into the coal seam under pressure, and competitive adsorption occurs with CH4 in the pores. The gas composition is nonuniformly distributed, and its viscosity μ is the dynamic parameter. As the gas is compressible, the pressure drops, and migration distance does not satisfy a linear relationship. Therefore, the gas transport does not conform to Darcy's law. The mass transfer process and a multicomponent gas competitive adsorption were investigated theoretically and experimentally. The adsorption characteristics and gas compressibility determine the distribution of the gas components in pores and change the gas dynamic viscosity in different regions. The change in the gas dynamic viscosity in the channel is the direct reason for the nonlinear pressure gradient and gas flow curve. The permeability and gas component affect the degree of nonlinear deviation of the gas flow and pressure gradient curve. This affects the nonlinear deviation degree of the curve by changing the gas dynamic viscosity in the pore channel during displacement. The reasonable displacement pressure is the critical pressure (PO) through experimental and theoretical analysis. [ABSTRACT FROM AUTHOR]

Magnesium phosphate cement (MPC) has a promising application in grouting. This study drew on the traditional cement-waterglass two-liquid grouting model. Creatively, the two main reaction components of MPC, dead-burned magnesium oxide and phosphate, were applied to the grouting field in a two-component liquid form. At the same time, through proportioning adjustment and experimental testing, we obtained A\B liquid components, which can be stabilized. In addition, MPC slurry was compared with the traditional grouting material, silicate cement slurry, to demonstrate its superiority. Finally, we simulated the grout diffusion process of the mixed slurry using the two-phase Darcy's law module of COMSOL Multiphysics subsurface fluids. The results show that the mixed slurry with a magnesium phosphate ratio of 1/3, a magnesium–boron ratio between 5% and 10%, and a water–cement ratio of 0.2–0.5 has better stability and mobility. Under the same fluidity, its strength is much higher than that of common silicate cement slurry and has good injectability. MPC was subjected to two-fluid grouting to take advantage of its fast-hardening and early-strengthening properties, while also improving its stability and fluidity. This study provided a theoretical foundation for the application of MPC. [ABSTRACT FROM AUTHOR]

The characteristics of gas seepage in broken coal and rock composed of different particle sizes and grades were investigated in this study. On the basis of Darcy's law and non‐Darcy seepage theory, equations of gas permeability in the nonlinear seepage of broken coal and rock, as well as the porosity of broken coal and rock, under triaxial compression were determined. The stress loading path of gas seepage in broken coal and rock was developed. The characteristics of gas seepage in broken coal and rock composed of different particle sizes and grades were analyzed, and the results showed that the gas permeability after compression was proportional to the particle size of the broken coal and rock. Under triaxial compression, the gas permeability of the broken coal and rock composed of graded‐particle sizes was lower than that of the broken coal and rock composed of different single‐particle sizes. The gas permeability of the broken coal was lower than that of the broken rock mass, and the gas permeability and porosity of the broken coal and rock can be described by the exponential decay function. At a constant porosity, the gas permeability of the broken coal and rock was proportional to the size grading index under triaxial compression. The coefficient of viscosity and gravity of the flow are key factors influencing the flow permeability in broken coal and rock. This study provides a reference for on‐site practice such as the efficient extraction of gas in goafs. [ABSTRACT FROM AUTHOR]

The paper presents a simulation-based approach for optimizing CO2 injection into depleted gas reservoirs, with the goal of enhancing underground CO2 storage. The research employs a two-dimensional dynamic reservoir model, developed using Darcy's law, to describe gas flow in a pressure-homogeneous porous medium, along with real gas equations. The model integrates the Du Fort–Frenkel and finite-difference methods to accurately simulate the behavior of CO2 during injection and storage. Real data from an operational gas storage facility were used to calibrate the model. CO2sim v1 software, specifically developed for this purpose, simulates CO2 injection cycles and quiescence phases, enabling the optimization of storage capacity and energy efficiency. The reservoir model, based on the engineering of the geological structure, is discretized into approximately 16,000 cells and solved using the finite-difference method, allowing for rapid simulation of CO2 injection and quiescence processes. The average computation time for a 150-day cycle is approximately 5 min. Simulation results indicate that increasing the number of injection wells and carefully controlling the injection rates significantly improves the distribution of CO2 within the reservoir, thereby enhancing storage efficiency. Additionally, appropriate well placement and prolonged quiescence periods lead to better CO2 dispersion, increasing the storage potential while reducing energy costs. The study concludes that further development of the software, along with comprehensive technical and economic assessments, is required to fully optimize CO2 storage on a commercial scale. [ABSTRACT FROM AUTHOR]

In this paper, the coupled linear theory of thermoelasticity for nanomaterials with triple porosity is considered in which the combination of Darcy's law and the volume fraction concept for three levels of pores (macro-, meso- and micropores) is provided. The 3D basic boundary value problems (BVPs) of steady vibrations of this theory are formulated and these BVPs are investigated using the potential method (boundary integral equation method) and the theory of singular integral equations. Namely, the formula of integral representation of regular vectors is obtained. The surface (single-layer and double-layer) and volume potentials are introduced and their basic properties are given. Some useful singular integral operators are defined for which Noether's theorems are valid. The symbolic determinants and indexes of these operators are calculated. The BVPs of steady vibrations are reduced to the equivalent singular integral equations. Finally, with the help of the potential method, we prove the existence theorems for classical solutions of the aforementioned BVPs. [ABSTRACT FROM AUTHOR]

Radiation of ocean water waves for (i) a system consisting of a hollow porous cylinder at the top, (ii) another system comprising a solid porous cylinder at the top; with a rigid solid cylinder considered at the bottom, is studied. Translational motions in the x-, and z-directions, surge and heave, are considered. Subsequently, the associated added mass and damping coefficients are investigated. The present configuration can be observed to be a wave energy device which taps ocean wave energy. Continuity conditions for pressure and velocity across the linear interfaces are used for setting up a system of linear equations. To validate the model, result of damping coefficients is compared with a result of Miloh [Wave loads on a floating solar pond. In: Proceedings of the international workshop on ship and platform motions. Berkeley: Department of Naval Architecture and Ocean Engineering; 1983] for the first case and with that of Yeung [Added mass and damping of a vertical cylinder in finite-depth waters. Appl Ocean Res. 1981;3(3):119–133] for the second case, both showing a good agreement. It is found that the variation of porous coefficient, radii, and depth has immense influence on the coefficients for such a cylindrical system. [ABSTRACT FROM AUTHOR]

We study surface gravity waves for viscous fluid flows governed by Darcy's law. The free boundary is acted upon by an external pressure posited to be in traveling wave form with a periodic profile. It has been proven that for any given speed, small external pressures generate small periodic traveling waves that are asymptotically stable. In this work, we construct a class of slowly traveling waves that are of arbitrary size and asymptotically stable. Our results are valid in all dimensions and for both the finite and infinite depth cases. [ABSTRACT FROM AUTHOR]

Most numerical simulations for modeling acid reactive fluid transport and wormhole propagation during matrix acidizing, waterflooding, and CO2 sequestration in carbonate formations are computationally expensive, limiting real-time reservoir management and deep learning training datasets generation for inverse modeling research. Therefore, there is a need for less computationally expensive acid-reactive fluid flow models with adequate accuracy. This study developed and validated a simplified acid reactive-transport model by integrating a simplified Stokes–Brinkman model (as opposed to Darcy's law), an averaged continuum model, and a pseudo-fracture model. Using FEniCS, the model effectively simulates acid-reactive fluid transport and wormhole propagation in carbonate rocks, achieving a high R-square value of about 0.97 based on a quantitative comparison of the breakthrough volume with other models. The simplified model can also simulate wormhole propagation for the reciprocal of the Damköhler number (1/Da) ranging from 0.001 to 1 with adequate accuracy. Sensitivity studies on the natural fracture parameters such as orientation, length, width, and density showed that higher fracture density, wider fracture aperture, longer fracture length, and orientation aligned with the direction of acid injection contribute to lower pore volume to breakthrough ratio but may not increase long-term acid stimulation efficiency. Also, the presence or absence of fractures in the matrix does not alter the dissolving patterns and optimum injection rate. This simple acid reactive-transport model can generate large training datasets for developing surrogate models in deep learning research. Finally, the FEniCS code in this paper is shared so future researchers can reproduce the results or extend the research work. [ABSTRACT FROM AUTHOR]

Saturated hydraulic conductivity (Ks) is a crucial parameter that influences water flow in saturated soils, with applications in various fields such as surface water runoff, soil erosion, drainage, and solute transport. However, accurate determination of Ks is challenging due to temporal and spatial uncertainties. This study addresses the knowledge gap regarding the long‐term behavior of Ks in sandy soils with less than 10% fine particles. The research investigates the changes in Ks over a long period of constant head tests and examines the factors influencing its variation. Two sandy samples were tested using a hydraulic conductivity cell, and the hydraulic head and discharge were recorded for over 50 days. The results show a general decline in Ks throughout the test, except for brief periods of increase. At the end of both tests, there are noticeable reductions in the saturated hydraulic conductivities of the samples, with one sample being 96% and the other sample 91% less than the maximum recorded saturated hydraulic conductivity during the tests. Furthermore, the relationship between flow rate and hydraulic head gradient does not follow the expected linear correlation from Darcy's law, highlighting the complex nature of sandy soil saturated hydraulic conductivity. The investigation of soil properties in three different sections of the samples before and after the tests revealed a decrease in the percentage of fine particles and a shift in specific gravity from the bottom to the top of the sample, suggesting particle migration along the flow direction. Factors such as clogging by fine particles and pore pressure variation contribute to the changes in Ks. The findings of this research show the importance of considering changes of saturated hydraulic conductivity during constant‐head laboratory tests. Therefore, this study provides evidence for the requirement to further assess the laboratory methods for measurement of the saturated hydraulic conductivity in sandy soil mixtures. Key Points: The estimation of saturated hydraulic conductivity through constant head tests demonstrates sensitivity to the duration of the testsObservations indicate an alteration in particle size distribution before and after testing within different sections of the samplesFlow rate and hydraulic gradient vary over the test duration, emphasizing the complex hydraulic system within the samples [ABSTRACT FROM AUTHOR]

Shelterbelts provide essential protection against wind erosion and soil degradation, as well as protection for fruit-bearing plants and crops from strong winds. Enhancing their sheltering capabilities requires optimizing their pattern and orientation, as well as defining their height and desired canopy shape, according to the desired performance. In this work, Large Eddy Simulation is employed to investigate the flow field and windbreak effectiveness of single and double-arranged shelterbelts characterized by different geometry and resistance to the air passage for neutral atmospheric condition. In particular, the canopy of the shelterbelts is modeled as an isotropic porous medium immersed in atmospheric boundary layer flow using the Darcy–Forchheimer model. Results show that a shelterbelt with a rectangular-shaped cross-section and a large canopy height results in the most significant reduction in mean wind speed and TKE, thus providing a large wind-protection region. As the spacing distance of double-arranged shelterbelts increases, the protection zones formed by both shelterbelts are reduced. The systematic comparisons of flow patterns, drag force coefficients, and windbreak effectiveness indicators of a series of single and double-arranged shelterbelts are essential for optimizing the design and management of shelterbelts. [ABSTRACT FROM AUTHOR]

The primary aim of this study was to examine the peristaltic flow of an unsteady non-Newtonian TiO2 nanofluid through a uniformly symmetric channel under the influence of electro-osmosis. The fluid behavior was modeled by the Sutterby model. Furthermore, the flow took place through a porous medium, following a modified form of Darcy's law. Additionally, the impacts of Dufour and Soret effects, chemical reaction, activation energy, viscous dissipation, heat generation, and thermal radiation were considered. A wave transformation was used to simplify the governing equations describing the velocity, temperature, and nanoparticle concentration. These simplified equations were then solved analytically using the homotopy perturbation method. Additionally, set figures were employed to illustrate and discuss the impact of the physical parameters involved in the problem on the obtained solutions. It is found that the presence of a modified Darcy's medium in the Navier–Stokes equation results in a porous term that is dependent on the index of the Sutterby model. Furthermore, it is found that as the thermophoresis parameter increases, the nanoparticles are more concentrated, and their flow from the hot region to the cold region is more effective. Additionally, it is observed that in the presence of thermal radiation, the activation energy and the Brownian motion parameter have similar effects on the concentration profile. [ABSTRACT FROM AUTHOR]

Porous ionic electrospray emitters have received significant interest for space propulsion due to their performance and operational simplicity. We have developed a diffusion equation for describing the transient flow response in a porous electrospray emitter, which allows for the prediction of the settling time for flow in the porous emitter. This equation accounts for both the change in liquid storage at exposed pores on the emitter with pressure and viscous diffusion through Darcy's law. Transient flow solutions are provided for the most common emitter topologies: pillar, cone, and wedge. Transient flow solutions describe the settling time and magnitude of current overshoot from porous electrosprays, while providing useful guidelines for reducing transient response time through emitter design. Comparing diffusion of pressure to the onset delay model for electrospray emission shows that diffusion is most relevant at higher voltages and when a porous reservoir is used. Accounting for multiple emission sites on the wedge geometry shows that emission sites settle in proportion to emission site spacing to the power − 1.74. Article Highlights: The transient response of porous electrosprays is affected by fluid storage in exposed pores. Pressure diffuses into a porous electrospray through depletion of fluid in exposed pores. Diffusion of pressure complements the existing onset delay model for porous electrosprays. [ABSTRACT FROM AUTHOR]

In this article, a two-level overlapping domain decomposition preconditioner is developed for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite element method for discretizing the partial differential equation by Darcy's law with the no-flux boundary condition and is then followed by a velocity elimination technique to yield a linear algebraic system with only unknowns of pressure. Then, our main objective is to design a robust and efficient domain decomposition preconditioner for this system, which is accomplished by engineering a multiscale coarse space that is capable of characterizing high-contrast features of the permeability field. A generalized eigenvalue problem is solved in each nonoverlapping coarse element in a communication-free manner to form the global solver, which is accompanied by local solvers originated from additive Schwarz methods but with a non-Galerkin discretization to derive the two-level preconditioner. We provide a rigorous analysis that indicates that the condition number of the preconditioned system could be bounded above with several assumptions. Extensive numerical experiments with various types of three-dimensional high-contrast models are exhibited. In particular, we study the robustness against the contrast of the media as well as the influences of numbers of eigenfunctions, oversampling sizes, and subdomain partitions on the efficiency of the proposed preconditioner. Strong and weak scalability performances are also examined. [ABSTRACT FROM AUTHOR]