The capillary pressure curves from upscaling interfacial and unsaturated flows in porous layers with vertical heterogeneity

We provide the capillary pressure curves p_(c)(s)as a function of the effective saturation s based on the theoretical framework of upscaling unsaturated flows in vertically heterogeneous porous layers proposed recently(Z.Zheng,Journal of Fluid Mechanics,950,A17,2022).Based on the assumption of vertical gravitational-capillary equilibrium,the saturation distribution and profile shape of the invading fluid can be obtained by solving a nonlinear integral-differential equation.The capillary pressure curves p_(c)(s)can then be constructed by systematically varying the injection rate.Together with the relative permeability curves k_(rn)(s)that are already obtained.One can now provide quick estimates on the overall behaviours of interfacial and unsaturated flows in vertically-heterogeneous porous layers.

Linear stability of a fluid channel with a porous layer in the center

We perform a Poiseuille flow in a channel linear stability analysis of a inserted with one porous layer in the centre, and focus mainly on the effect of porous filling ratio. The spectral collocation technique is adopted to solve the coupled linear stability problem. We investigate the effect of permeability, σ, with fixed porous filling ratio ψ = 1/3 and then the effect of change in porous filling ratio. As shown in the paper, with increasing σ, almost each eigenvalue on the upper left branch has two subbranches at ψ = 1/3. The channel flow with one porous layer inserted at its middle （ψ = 1/3） is more stable than the structure of two porous layers at upper and bottom walls with the same parameters. By decreasing the filling ratio ψ, the modes on the upper left branch are almost in pairs and move in opposite directions, especially one of the two unstable modes moves back to a stable mode, while the other becomes more instable. It is concluded that there are at most two unstable modes with decreasing filling ratio ψ. By analyzing the relation between ψ and the maximum imaginary part of the streamwise phase speed, Cimax, we find that increasing Re has a destabilizing effect and the effect is more obvious for small Re, where ψ a remarkable drop in Cimax can be observed. The most unstable mode is more sensitive at small filling ratio ψ, and decreasing ψ can not always increase the linear stability. There is a maximum value of Cimax which appears at a small porous filling ratio when Re is larger than 2 000. And the value of filling ratio 0 corresponding to the maximum value of Cimax in the most unstable state is increased with in- creasing Re. There is a critical value of porous filling ratio （= 0.24） for Re = 500; the structure will become stable as ψ grows to surpass the threshold of 0.24; When porous filling ratio ψ increases from 0.4 to 0.6, there is hardly any changes in the values of Cimax. We have also observed that the critical Reynolds number is especially sensitive for small ψ where the fastest drop is observed, and there may be a wide range in which the porous filling ratio has less effect on the stability （ψ ranges from 0.2 to 0.6 at σ = 0.002）. At larger permeability, σ, the critical Reynolds number tends to converge no matter what the value of porous filling ratio is.

Three-dimensional consolidation deformation analysis of porous layered soft soils considering asymmetric effects

Long-term settlements for underground structures, such as tunnels and pipelines, are generally observed after the completion of construction in soft clay. The soil consolidation characteristic has great influences on the long-term deformation for underground structures. A three-dimensional consolidation analysis method under the asymmetric loads is developed for porous layered soil based on Biot's classical theory. Time-displacement effects can be fully considered in this work and the analytical solutions are obtained by the state space approach in the Cartesian coordinate. The Laplace and double Fourier integral transform are applied to the state variables in order to reduce the partial differential equations into algebraic differential equations and easily obtain the state space solution. Starting from the governing equations of saturated porous soil, the basic relationship of state space variables is established between the ground surface and the arbitrary depth in the integral transform domain. Based on the continuity conditions and boundary conditions of the multi-layered pore soil model, the multi-layered pore half-space solutions are obtained by means of the transfer matrix method and the inverse integral transforms. The accuracy of proposed method is demonstrated with existing classical solutions. The results indicate that the porous homogenous soils as well as the porous non-homogenous layered soils can be considered in this proposed method. When the consolidation time factor is 0.01, the value of immediate consolidation settlement coefficient calculated by the weighted homogenous solution is 27.4% bigger than the one calculated by the non-homogeneity solution. When the consolidation time factor is 0.05, the value of excess pore water pressure for the weighted homogenous solution is 27.2% bigger than the one for the non-homogeneity solution. It is shown that the material non-homogeneity has a great influence on the long-term settlements and the dissipation process of excess pore water pressure.

Effect of Magnetic Field on Kelvin-Helmholtz Instability in a Couple-Stress Fluid Layer Bounded Above by a Porous Layer and Below by a Rigid Surface

Kelvin-Helmholtz instability (KHI) appears in stratified two-fluid flow at surface. When the relative velocity is higher than the critical relative velocity, the growth of waves occurs. It is found that magnetic field has a stabilization effect whereas the buoyancy force has a destabilization effect on the KHI in the presence of sharp inter-face. The RT instability increases with wave number and flow shear, and acts much like a KHI when destabilizing effect of sheared flow dominates. It is shown that both of ablation velocity and magnetic field have stabilization effect on RT instability in the presence of continued interface. In this paper, we study the effect of magnetic field on Kelvin-Helmholtz instability (KHI) in a Couple-stress fluid layer above by a porous layer and below by a rigid surface. A simple theory based on fully developed flow approximations is used to derive the dispersion relation for the growth rate of KHI. We replace the effect of boundary layer with Beavers and Joseph slip condition at the rigid surface. The dispersion relation is derived using suitable boundary and surface conditions and results are discussed graphically. The stabilization effect of magnetic field takes place for whole waveband and becomes more significant for the short wavelength. The growth rate decreases as the density scale length increases. The stabilization effect of magnetic field is more significant for the short density scale length.

Stress dependence of elastic wave dispersion and attenuation in fluid-saturated porous layered media

The fluid-saturated porous layered(FSPL)media widely exist in the Earth's subsurface and their overall mechanical properties,microscopic pore structure and wave propagation characteristics are highly relevant to the in-situ stress.However,the effect of in-situ stress on wave propagation in FSPL media cannot be well explained with the existing theories.To fill this gap,we propose the dynamic equations for FSPL media under the effect of in-situ stress based on the theories of poroacoustoelasticity and anisotropic elasticity.Biot loss mechanism is considered to account for the stress-dependent wave dispersion and attenuation induced by global wave-induced fluid flow.Thomsen's elastic anisotropy parameters are used to represent the anisotropy of the skeleton.A plane-wave analysis is implemented on dynamic equations yields the analytic solutions for fast and slow P waves and two S waves.Modelling results show that the elastic anisotropy parameters significantly determine the stress dependence of wave velocities.Vertical tortuosity and permeability have remarkable effects on fast and slow P-wave velocity curves and the corresponding attenuation peaks but have little effect on S-wave velocity.The difference in velocities of two S waves occurs when the FSPL medium is subjected to horizontal uniaxial stress,and the S wave along the stress direction has a larger velocity,which implies that the additional anisotropy other than that induced by the beddings appears due to horizontal stress.Besides,the predicted velocity results have the reasonable agreement with laboratory measurements.Our equations and results are relevant to a better understanding of wave propagation in deep strata,which provide some new theoretical insights in the rock physics,hydrocarbon exploration and stress detection in deep-strata shale reservoirs.

Effect of porous surface layer on wave propagation in elastic cylinder immersed in fluid

To study the damage to an elastic cylinder immersed in fluid, a model of an elastic cylinder wrapped with a porous medium immersed in fluid is designed. This structure can both identify the properties of guided waves in a more practical model and address the relationship between the cylinder damage degree and the surface and surrounding medium. The principal motivation is to perform a detailed quantitative analysis of the longitudinal mode and flexural mode in an elastic cylinder wrapped with a porous medium immersed in fluid. The frequency equations for the propagation of waves are derived each for a pervious surface and an impervious surface by employing Biot theory. The influences of the various parameters of the porous medium wrapping layer on the phase velocity and attenuation are discussed. The results show that the influences of porosity on the dispersion curves of guided waves are much more significant than those of thickness,whereas the phase velocity is independent of the static permeability. There is an apparent “mode switching” between the two low-order modes. The characteristics of attenuation are in good agreement with the results from the dispersion curves.This work can support future studies for optimizing the theory on detecting the damage to cylinder or pipeline.

High-Throughput Growth of Hexagonal Boron Nitride Film Using Porous-Structure Isolation Layer

Chemical vapor deposition is considered as the most hopeful method for the synthesis of large-area high-quality hexagonal boron nitride on the substrate of catalytic metal. However, the size the hexagonal boron nitride films are limited to the size of growth chamber, which indicates a lower production efficiency. In this paper, the utilization efficiency of growth chamber is highly improved by alternately stacking multiple pieces of Cu foils and carbon fiber surface felt with porous structure. Uniform and continuous hexagonal boron nitride films are prepared on Cu foils through chemical vapor deposition utilizing ammonia borane as the precursor. This work develops a simple and practicable method for high-throughput preparation of hexagonal boron nitride films, which could contribute to the industrial application of hexagonal boron nitride. .

Experimental Study on Jet Impingement Boiling Heat Transfer in Brass Beads Packed Porous Layer

Jet impingement boiling has been widely used in industrial facilities as its higher heat transfer coefficient(HTC)and critical heat flux(CHF)can be achieved in comparison with the pool boiling.By covering beads packed porous layer on the heated wall surface,the enlarged heat transfer area and rise of nucleation sites for boiling occur,thus,the heat transfer performance of boiling can be enhanced.For the jet impingement boiling with brass bead packed porous layers,the heat transfer performance is crucially influenced by the characteristics of porous layer and working fluid flow,so the experiments were conducted to investigate the effects of the jet flow rate,fluid inlet subcooling,number of porous layer and brass bead diameter of porous layer.Comparison study shows that impingement boiling promotes the HTC and CHF as 1.5 times and 2.5 times respectively as pool boiling at similar conditions.Higher heat transfer performance can be obtained in the cases of a higher jet flow rate and a higher fluid inlet subcooling,and there exist the optimal layer number and bead diameter for heat transfer.Particularly,a double-layer porous layer results in an increase of 39%in heat flux at superheat of 30 K compared with a single-layer case;a single porous layer at d=8 mm brings an increase of 23%in heat flux at superheat of 30 K compared with that of bare plain surface.Besides,the actual scene of jet impingement boiling was recorded with a camera to investigate the behavior evolution of vapor bubbles which is highly correlated to the heat transfer process.

Axially Oriented Structured Porous Layers for Heat Transfer Enhancement in a Solar Receiver Tube

The present work reports a numerical investigation of heat transfer and pressure drop characteristics in a solar receiver tube with different shaped porous media for laminar and low Reynolds number turbulent flow regimes.Numerical simulations have been performed with finite volume-based code ANSYS(v-2017)for different shapes of porous layers axially oriented in the tube.The plain-shaped porous medium fitted up to 50%of the tube shows better performance than other-shaped porous layers.Simulations have also been performed for axially oriented structured porous media with different sizes.Axially oriented structured porous medium develops a lateral flow disturbance enhancing the intermixing of the liquid and porous medium at their interface.Structured porous medium with a 3-crest configuration shows the best heat transfer performance among all the shapes of porous media.It offers a maximum of 148%heat transfer enhancement compared to a half-filled plain porous layer,whereas it reports a maximum of 564%enhancement compared to the flow without a porous layer.The lateral flow tendency or the swirling effect helps better heat transfer performance in the axially oriented structured porous media.Performance evaluation criterion(PEC)in all types of porous media is more in the transitional flow regime than in the laminar and turbulent flow regimes.For the same operating conditions,the maximum value of the PEC in the present work is 120%higher than the maximum value of PEC for other-shaped porous media reported in the literature.Correlations for Nusselt number have been developed for both laminar and turbulent flow regimes for three crests shaped porous medium.

Model of formation and roughness calculation of the porous layer on the heated surface during nanofluids boiling

The article contains developed by authors model of the porous layer formation.This layer forms on the heated surface during nanofluids boiling.It has a great influence on boiling characteristics,particularly,on critical heat flux value;and it is very important to have clear knowledge about its formation and properties.The main goal of current step of our investigations was to find out correlations:for calculation of porous layer with definite thickness creation time and for its roughness.

A novel dual-functional layer exhibiting exceptional protection and photocatalytic activity by organic functionalization of plasma electrolyzed layer

The formation of inorganic-organic hybrids(IOH)on the metallic substrates would play a decisive role in improving their structural and functional features.In this work,the growth of organic coating(OC)consisting of coumarin-3-carboxylic acid(3-CCA)and albumin(ALB)on the inorganic layer(IC),produced by plasma electrolysis of AZ31 Mg alloy,led to enabling organically synergistic reactions on the porous inorganic surface,forming a flake-like structure sealing the structural defects of IC.Synergistic actions between OC and IC endow the flake-like structures with chemical protection and photocatalytic performance.Upon contact with a corrosive solution,the IOH layer possesses stable morphologies that delay the corrosive degradation of the whole structure.The electrochemical stability of the sample produced by immersion IC in the organic solution for 10 h(IOH2 sample)was superior to the other samples as it had the lowest corrosion current density(1.69×10^(−10)A·cm^(−2))and the highest top layer resistance(1.2×10^(7)Ω·cm^(2)).Moreover,the IOH layer can photodegrade the organic pollutants in model wastewater,where the highest photocatalytic efficiency of 99.47%was found in the IOH2 sample.Furthermore,computational calculations were performed to assess the relative activity of different parts of the ALB and 3-CCA structures,which provide helpful information into the formation mechanism of the IOH materials.

Self-assembly of coumarin molecules on plasma electrolyzed layer for optimizing the electrochemical performance of AZ31 Mg alloy

A novel inorganic-organic layer with outstanding corrosion resistance in a 3.5wt.% NaCl solution was fabricated by taking advantage of the unique interactions between coumarin (COM) molecules and the porous layer formed on Mg alloy. To achieve this aim, the AZ31 Mg alloy coated via microarc oxidation (MAO) coating was placed in an ethanolic solution of COM for 6 and 12 h at 25 ℃. By reducing the surface area exposed to the corrosive species, the donor-acceptor complexes produced by the particular interactions between the COM and MAO surface would successfully prevent the corrosion of Mg alloy substrate. The MAO layer would provide the ideal sites for the charge-transfer-induced physical and chemical locking, leading to uneven organic layer nucleation and crystal growth with a thatch-like structure. To evaluate the formation mechanism of such hybrid composites and highlight the key bonding modes between the COM and MAO, theoretical simulations were conducted.

Non-Darcy flows in layered porous media(LPMs)with contrasting pore space structures

Compared to single layer porous media,fluid flow through layered porous media(LPMs)with contrasting pore space structures is more complex.This study constructed three-dimensional(3-D)pore-scale LPMs with different grain size ratios of 1.20,1.47,and 1.76.The flow behavior in the constructed LPMs and single layer porous media was numerically investigated.A total of 178 numerical experimental data were collected in LPMs and single layer porous media.In all cases,two different flow regimes(i.e.,Darcy and Non-Darcy)were observed.The influence of the interface of layers on Non-Darcy flow behavior in LPMs was analyzed based pore-scale flow data.It was found that the available correlations based on single layer porous media fail to predict the flow behavior in LPMs,especially for LPM with large grain size ratio.The effective permeability,which incorporated the influence of the interface is more accurate than the Kozeny-Carman equation for estimating the Darcy permeability of LPMs.The inertial pressure loss in LPMs,which determines the onset of the Non-Darcy flow,was underestimated when using a power law expression of mean grain size.The constant B,an empirical value in the classical Ergun equation,typically equals 1.75.The inertial pressure loss in LPMs can be significantly different from it in single lager porous media.For Non-Darcy flow in LPMs,it is necessary to consider a modified larger constant B to improve the accuracy of the Ergun empirical equation.

Experimental investigation on rainfall infiltration and solute transport in layered porous and fractured media

Layered structures with upper porous and lower fractured media are widely distributed in the world. An experimen- tal investigation on rainfall infiltration and solute transport in such layered structures can provide the necessary foundation for effectively preventing and forecasting water bursting in mines, controlling contamination of mine water, and accomplishing ecological restoration of mining areas. A typical physical model of the layered structures with porous and fractured media was created in this study. Then rainfall infiltration experiments were conducted after salt solution was sprayed on the surface of the layered structure. The volumetric water content and concentration of chlorine ions at different specified positions along the profile of the experiment system were measured in real-time. The experimental results showed that the lower fractured media, with a considerably higher permeability than that of the upper porous media, had significant effects on preventing water infil- tration. Moreover, although the porous media were homogeneous statistically in the whole domain, spatial variations in the features of effluent concentrations with regards to time, or so called breakthrough curves, at various sampling points located at the horizontal plane in the porous media near the porous-fractured interface were observed, indicating the diversity of solute transport at small scales. Furthermore, the breakthrough curves of the outflow at the bottom, located beneath the underlying fractured rock, were able to capture and integrate features of the breakthrough curves of both the upper porous and fractured media, which exhibited multiple peaks, while the peak values were reduced one by one with time.

Self-Assembled Porous-Reinforcement Microstructure-Based Flexible Triboelectric Patch for Remote Healthcare

Realizing real-time monitoring of physiological signals is vital for preventing and treating chronic diseases in elderly individuals. However,wearable sensors with low power consumption and high sensitivity to both weak physiological signals and large mechanical stimuli remain challenges.Here, a flexible triboelectric patch(FTEP) based on porous-reinforcement microstructures for remote health monitoring has been reported. The porousreinforcement microstructure is constructed by the self-assembly of silicone rubber adhering to the porous framework of the PU sponge. The mechanical properties of the FTEP can be regulated by the concentrations of silicone rubber dilution. For pressure sensing, its sensitivity can be effectively improved fivefold compared to the device with a solid dielectric layer, reaching 5.93 kPa^(-1) under a pressure range of 0–5 kPa. In addition, the FTEP has a wide detection range up to 50 kPa with a sensitivity of 0.21 kPa^(-1). The porous microstructure makes the FTEP ultra-sensitive to external pressure, and the reinforcements endow the device with a greater deformation limit in a wide detection range. Finally, a novel concept of the wearable Internet of Healthcare(Io H) system for real-time physiological signal monitoring has been proposed, which could provide real-time physiological information for ambulatory personalized healthcare monitoring.

FORMATION AND PROPERTIES 0F POROUS SILICON LAYER ON HEAVILY DOPED n-Si

The anodic voltammetric curves of heavily doped n-Si in HF solution, on which three different regions have emerged, and were plotted, A porous silicon layer with fine morphology was formed in linear region.

Effects of Solid Matrix and Porosity of Porous Medium on Heat Transfer of Marangoni Boundary Layer Flow Saturated with Power-Law Nanofluids

The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.

Flow through a Variable Permeability Brinkman Porous Core

In this work, we consider the flow through composite porous layers of variable permeability, with the middle layer representing a porous core bounded by two Darcy layers. Brinkman’s equation is valid in the middle layer and has been reduced to an Airy’s inhomogeneous differential equation. Solution is obtained in terms of Airy’s functions and the Nield-Kuznetsov function.

3D Fe-MOF embedded into 2D thin layer carbon nitride to construct 3D/2D S-scheme heterojunction for enhanced photoreduction of CO_(2)

Regulating charge transfer to achieve specific transfer path can improve electron utilization and complete efficient photoreduction of CO_(2).Here,we fabricated a S-scheme heterojunction of CN/Fe-MOF by an in-situ assembly strategy.The S-scheme charge transfer mechanism was confirmed by band structure,electron spin resonance(ESR)and work function(Φ)analysis.On the one hand,the response of Fe-MOF in the visible region improved the utilization of light energy,thus increasing the ability of CN/Fe-MOF to generate charge carriers.On the other hand,CN,as the active site,not only had strong adsorption capacity for CO_(2),but also retained photogenerated electrons with high reduction capacity because of S-scheme charge transfer mechanism.Hence,in the absence of any sacrificial agent and cocatalyst,the optimized 50CN/Fe-MOF obtained the highest CO yield(19.17μmol g^(–1))under UV-Vis irradiation,which was almost 10 times higher than that of CN.In situ Fourier transform infrared spectra not only revealed that the photoreduction of CO_(2) occurred at the CN,but also demonstrated that the S-scheme charge transfer mechanism enabled 50CN/Fe-MOF to have a stronger ability to generate HCOO–than CN.

Improving the electrochemical stability of AZ31 Mg alloy in a 3.5wt.%NaCl solution via the surface functionalization of plasma electrolytic oxidation coating

The unique interactions between hexadecanoic acid(HA)and albumin(ALB)molecules on the surface of the porous layer of AZ31 Mg alloy were exploited to fabricate a novel hybrid composite film with excellent electrochemical stability in a 3.5 wt.%Na Cl solution.Herein,the inorganic layer(IL)obtained by plasma electrolytic oxidation of AZ31 Mg alloy in an alkaline-phosphate-WO_(3)electrolyte was soaked in an organic solution composed of ALB and HA for 10 and 24 h at 60℃.Although albumin and HA may coexist on the same surface of IL,the higher reactivity of ALB molecules would prevent the formation of a thick layer of HA.The donor-acceptor complexes formed due to the unique interactions between ALB and/or HA and IL surface would reduce the area exposed to the corrosive species which in turn would efficiently protect the substrate from corrosion.The porous structure of the IL would provide preferable sites for the physical and chemical locking triggered by charge-transfer phenomena,leading to the inhomogeneous nucleation and crystal growth of a flowery flakes-like organic layer.DFT calculations were performed to reveal the primary bonding modes between the ALB,HA,and IL and to assess the mechanistic insights into the formation of such novel hybrid composites.