Neumann Equation Research Articles

Onset of instability in Darcy–Forchheimer porous layer with power‐law saturating fluid

AbstractThe paper investigates the effects of the Forchheimer term (form drag) and vertical pressure gradient on the buoyancy‐induced instability of power‐law saturating fluid in a porous plane medium. Two isobaric permeable layers are assumed to sandwich the horizontal porous plane. In the meantime, Dirichlet and Neumann equations are the thermal boundary conditions considered for the lower and upper layers. A base flow developed analytically via the governing equations is just in function of the Péclet number , with no dependence on the characteristic parameter of the power law fluid. A linear stability analysis consists of substituting a base flow with a small perturbation into the governing equations leads to a four‐order eigenvalue problem. An analytical solution is performed for the asymptotic cases of an infinite wavelength. The Runge–Kutta solver is applied together with the shooting technique to evaluate numerical solutions for the general case of nonnegligible wave numbers. Among the findings is the contribution of the Forchheimer term in the variation of the threshold Péclet number whose value can switch the wave numbers from zero to nonzero and increase the stability of the system.

Assessment of the interfacial properties of various mineral/hydrogen/water systems

Hydrogen is well known as a medium for clean energy storage. However, storing large amounts of hydrogen in tanks at the surface has many technical, environmental, safety, and economical challenges. Meanwhile, underground formations are good candidates for large-scale storage, but not all subsurface formations are suitable, and the selection of a good subsurface formation is vital. In this respect, the storage capacity and injection/production rate of hydrogen gas are significantly influenced by interfacial characteristics such as the rock-water interfacial tension (γrock-water) and rock-gas interfacial tension (γrock-gas) in the rock/H2/water system. Because these factors cannot be experimentally measured, they are characterized via theoretical methods. Therefore, in the present work, the interfacial properties are calculated by using Young's equation and Neumann's equations of state for various lithologies, including calcite, dolomite, quartz, shale, anhydrite, gypsum, granite, and basalt. The results indicate that γrock-water and γrock-gas are significantly affected by the rock composition and tend to increase with increasing temperature, but are unaffected by changes in pressure. Furthermore, the γrock-water value is found to decrease with increasing salinity for lithologies such as calcite, dolomite, and quartz, but increases with salinity for lithologies such as basalt, granite, and gypsum. Meanwhile, the γrock-gas is found to decrease with increasing pressure, but increase with increasing salinity. However, the variation of γrock-gas with temperature is not straightforward. For example, the interfacial tension in the rock‑hydrogen system is shown to increase with increasing temperature for certain minerals in distilled water, but decreases for other samples, such as anhydrite, granite, and shale, especially in brine. The data presented herein is expected to assist in understanding the suitable subsurface formations and reducing the level of uncertainty for the successful feasibility of underground hydrogen storage projects.

Assessment of rock-hydrogen and rock-water interfacial tension in shale, evaporite and basaltic rocks

Underground hydrogen storage (UHS) is a distinguished method for reducing anthropogenic greenhouse gases (GHGs) and meeting global energy demand. One of the important parameters for subsurface storage of gas is rock-fluid interfacial tension (γrock-fluid) as gas injection and production rate, spread and flow in porous media, storage capacity, and containment security can be derived by this parameter. However, it is impossible to experimentally measure γrock-fluid. Moreover, γrock-fluid data for rock/H2/water systems in various shales, evaporite, and basaltic formations at geo-storage conditions are scarce in the literature. Thus, advancing and receding contact angles data were used to theoretically compute it at various pressures, temperatures, and shale-TOC by the combination of Young's equation and Neumann's equation of state. For all the rocks evaluated in this study, it was found that γrock-gas decreased with pressure, temperature, and shale-TOC. Also, γrock-water decreased with temperature but increased with shale-TOC, assuming that it remained constant with pressure. Thus, this work provides a deep understanding of wetting characteristics at various rock/H2/water systems, leading to a better investigation of hydrogen storage beneath shales, evaporite, and basaltic formations.

Clay-hydrogen and clay-cushion gas interfacial tensions: Implications for hydrogen storage

Rock/fluid interfacial tension (γrock−fluid) govern the fluid flow dynamics, the injection/withdrawal rates, the gas storage capacity, and containment integrity during gas (H2, CO2, N2) geo-storage. Clay-gas interfacial tension (γclay−gas) data, especially for the clay-H2(γclay−H2), the clay-N2(γclay−N2) and the clay-CO2(γclay−CO2) systems, have rarely been reported in the literature due to the challenging nature of these measurements in the laboratory. In this study, Neumann's equation of state and Young-Laplace equation was combined to compute clay-gas and clay-brine interfacial tensions (IFT) parameters at realistic geo-storage temperature (333 K) and pressure (5–20 MPa). Our results show that at similar thermodynamic conditions: γclay−H2>γclay−N2>γclay−CO2. Our calculations also showed that: γkaolinite−N2>γillite−N2>γmontmorillonite−N2, and γkaolinite−CO2>γillite−CO2>γmontmorillonite−CO2. In contrast, for hydrogen a negligible difference in γclay−H2 was obtained for the three clay types, although, the IFT between clay minerals and brine in presence of hydrogen is different for these three clay types. Overall, computed γclay−H2 values were higher than γclay−N2 and γclay−CO2 values, whereas computed clay-brine interfacial tension was lower in presence of hydrogen compared to carbon dioxide and nitrogen. These results suggest that nitrogen and carbon dioxide could be used as favorable cushion gas for maintaining formation pressure during underground hydrogen storage. We also demonstrated a remarkable relationship between clay/gas IFT and gas density that could serve as a helpful tool for quick estimation of rock-fluid interfacial tension.

Effect of organic acids on CO2-rock and water-rock interfacial tension: Implications for CO2 geo-storage

A small concentration of organic acid in carbon dioxide (CO2) storage formations and caprocks could significantly alter the wettability of such formations into less water-wet conditions, decreasing the CO2-storage potential and containment security. Recent studies have attempted to infer the influence of the organic acid concentration on the wettability of rock–CO2–brine systems by measuring advancing and receding contact angles. However, no studies have investigated the influence of organic acid contamination on CO2-storage capacities from rock-fluid interfacial tension (IFT) data because solid-brine and solid-CO2 IFT values cannot be experimentally measured. Equilibrium contact angles and rock-fluid IFT datasets were used to evaluate the viability of CO2 storage in storage rocks and caprocks. First, the contact angles of rock in brine-CO2 systems were measured to compute Young's equilibrium contact angles. Subsequently, rock-brine and rock-gas IFT values at CO2 geo-storage conditions were computed via a modified form of Neumann's equation of state. For two storage-rock minerals (quartz and calcite) and one caprock mineral (mica), the results demonstrated high CO2-brine equilibrium contact angles at high pressure (0.1–25 MPa) and increasing concentrations of stearic acid (10−5 to 10−2 mol/L). Rock-brine IFT increased with the increased stearic acid concentration but remained constant with increased pressure. In all conditions, the order of increasing hydrophobicity of the mineral surfaces is calcite > mica > quartz. At 323 K, 25 MPa, and a stearic acid concentration of 10−2 mol/L, quartz became intermediate-wet with a CO2-brine equilibrium contact angle of 89.8°, whereas mica and calcite became CO2-wet with CO2-brine equilibrium contact angles of 117.5° and 136.5°, respectively. This work provides insight into the effects of organic acids inherent in CO2 geo-storage formations and caprocks on rock wettability and rock-fluid interfacial interactions.

Assessment of wettability and rock-fluid interfacial tension of caprock: Implications for hydrogen and carbon dioxide geo-storage

Underground hydrogen (H 2 ) storage (UHS) and carbon dioxide (CO 2 ) geo-storage (CGS) are prominent methods of meeting global energy needs and enabling a low-carbon global economy. The pore-scale distribution, reservoir-scale storage capacity, and containment security of H 2 and CO 2 are significantly influenced by interfacial properties, including the equilibrium contact angle ( θ E ) and solid-liquid and solid-gas interfacial tensions ( γ S L and γ S G ). However, due to the technical constraints of experimentally determining these parameters, they are often calculated based on advancing and receding contact angle values. There is a scarcity of θ E , γ S L , and γ S G data, particularly related to the hydrogen structural sealing potential of caprock, which is unavailable in the literature. Young's equation and Neumann's equation of state were combined in this study to theoretically compute these three parameters ( θ E , γ S L , and γ S G ) at reservoir conditions for the H 2 and CO 2 geo-storage potential. Pure mica, organic-aged mica, and alumina nano-aged mica substrates were investigated to explore the conditions for rock wetting phenomena and the sealing potential of caprock. The results reveal that θ E increases while γ S G decreases with increasing pressure, organic acid concentration, and alkyl chain length. However, γ S G decreases with increasing temperatures for H 2 gas, and vice versa for CO 2 . In addition, θ E and γ S L decrease, whereas γ S G increases with increasing alumina nanofluid concentration from 0.05 to 0.25 wt%. Conversely, θ E and γ S L increase, whereas γ S G decreases with increasing alumina nanofluid concentration from 0.25 to 0.75 wt%. The hydrogen wettability of mica (a proxy of caprock) was generally less than the CO 2 wettability of mica at similar physio-thermal conditions. The interfacial data reported in this study are crucial for predicting caprock wettability alterations and the resulting structural sealing capacity for UHS and CGS. • The equilibrium contact angle ( θ E ) increases with pressure and organic concentration but decreases with temperature. • The solid-gas interfacial tension ( γ S G ) decreases with pressure and organic concentration but increases with temperature. • The solid-liquid interfacial tension ( γ S L ) and θ E decreases, whereas γ S G increases with increasing alumina nanofluid concentration. • Mica hydrogen wettability is less than mica CO 2 wettability in all physio-thermal conditions.

Group velocity dispersion in terahertz frequency combs within a generalized Maxwell-Bloch framework

As many molecules have their rotovibrational resonance frequencies in the mid-infrared or terahertz regime, efficient generation of corresponding frequency combs may lead to large progress in gas spectroscopy and sensing. Quantum cascade lasers (QCLs) are among the most promising candidates for a compact and cheap radiation source in this frequency range. This contribution presents a full-wave numerical solution of the Maxwell-Liouville-von Neumann equations, thus avoiding the limited applicability of the rotating wave approximation to moderate field strengths and spectral bandwidths. We include losses and chromatic dispersion of the optically active material in the QCL. The semiclassical approach uses the finite-difference time-domain (FDTD) method to derive update equations for the electric field, starting from the one-dimensional Maxwell equations. There, the optical full-wave propagation is coupled to the electronic quantum system via a polarization term that arises from the evolution of the density matrix. Furthermore, dispersion effects are considered through a classical polarization term and losses are introduced by a finite material conductivity. This work mainly focuses on the integration of group velocity dispersion (GVD) due to the bulk material and, if applicable, the waveguide geometry into the update equations. It is known to be one of the main degradation mechanisms of terahertz frequency combs, but has not yet been added to the existing full-wave solver. The implementation is carried out as Lorentz model and is applied to an experimentally investigated QCL frequency comb setup from the literature. The reported results are in good agreement with the experimental data. Especially, they confirm the need for dispersion compensation for the generation of terahertz frequency combs in QCLs.

PH effect on wettability of –NH+-brine-muscovite system: Implications for low salinity effect in sandstone reservoirs

Wettability alteration remains the main mechanism of low salinity water flooding (LSWF) which is controlled by several factors including crude oil composition. Although presence of acidic components in crude oil confirmed to be necessary to enhance wettability during LSWF, yet the effect of basic components remain unclear. In this work we used the concept of surface energy to explicate the dependency of wettability on a high base number (BN) oil as a function of water pH, ion type and salinity. We measured Oil/Brine contact angle and interfacial tension, which then were used to compute Oil/Solid (mica) interfacial tension using Neumann's equation of state. In addition, we measured the zeta potential and simulated the concentration of base components (–NH+ groups) in the oil using a surface complexation model to understand the underlying mechanisms of wettability and interfacial tension alterasion. We found that wettebility is also dependant on the basic components of crude oil where pH plays a major role and salinity and ion type play a secondary role. Increasing pH (from pH=3 to pH=11) decreased the contact angle moving the system to a more hydrophilic or water-wet state (contact angle decreased from 162° to 68° for CaCl2 solution and from 163° to 66° for NaCl solution). We also found that Oil/Solid interfacial tension increased with pH, where changes were more pronounced in the presence of divalent cations compared to monovalent. We hypothesise that changes in the contact angle and Oil/Solid interfacial tension are due to the chemo-physical adsorption of –NH+ groups at the oil surface to the muscovite negative sites. The hypothesis is consistent with the changes in the zeta potential and –NH+ surface concentration computed from the surface complexation model. The results of this study underscore the importance of the basic component on system wettability as a function of pH, providing insights into the low salinity EOR in sandstone reservoirs.

Gas Labyrinth Seals: Improved Prediction of Leakage in Gas Labyrinth Seals Using an Updated Kinetic Energy Carry-Over Coefficient

Abstract Though simple and fast, bulk-flow models (BFMs) for gas labyrinth seals (LSs) often predict the mass flow inaccurately. The BFM models rely on classical Neumann's equation model to characterize the flow through a labyrinth tooth. Presently, a computational fluid dynamics (CFD) analysis quantifies the effects of tip clearance (Cr) and operating conditions on the prediction of LS mass flow, and then derives an updated kinetic energy carry-over coefficient (μ1i) to improve the accuracy of Neumann's leakage equation. μ1i is a function of the seal tip clearance (Cr), the tooth pitch, and the total teeth number; but it does not depend on the seal supply or discharge pressures. The analysis selects a 14-teeth on stator LS (length/diameter = L/D = 0.29) with clearance Cr = (1/733)D and operating at nominal supply (Pin) and discharge (Pout) pressures equal to 73 bar and 51 bar, respectively, and at a rotor speed of 12 krpm (surface speed = 138 m/s). The CFD produces flow fields for LSs with a clearance varying from 80% to 200% of the nominal Cr, a gas supply pressure from 60 bar to 100 bar, and with various discharge pressures giving a pressure ratio (PR = Pout/Pin) ranging from 0.40 to 0.85. The numerous predictions deliver the mass flow as well as the bulk-flow velocities and cavity pressures within the seals. The kinetic energy carry-over coefficient (μ1i) increases with respect to the seal radial clearance (Cr). μ1i shows a parabolic correlation with PR; at first, μ1i increases with a rise in PR from a low value; and then, a further increase in PR leads to a decrease in μ1i. The coefficient μ1i is only sensitive to the PR and not to the magnitude of either the supply or discharge pressures. Lastly, for use with Neumann's leakage model, the CFD predictions produce an updated μ1i, a function of the seal geometry and the PR condition. Integration of the new μ1i correlation into a BFM code improves its accuracy to predict LS mass flow rate, a 19% difference against test data reduces to within 6%. A TOS LS tested by Ertas et al. (2012, Rotordynamic Force Coefficients for Three Types of Annular Gas Seals With Inlet Preswirl and High Differential Pressure Ratio,” ASME J. Eng. Gas Turbine Power, 134(4), p. 4250301) serves to further validate the accuracy of the modified leakage model.

Surface properties and bacterial behavior of micro conical dimple textured Ti6Al4V surface through micro-milling

Although several techniques have been utilized to alter micro/nanotopographies of implant surfaces to improve the osseointegration rate, it has been challenging to fabricate micro/nano directional textures of desired shape size and accuracy. In the present study, mechanical micro-milling is utilized to create orderly conical dimple textures on the Ti6Al4V surface. The surface characterization, 3D surface topography, form measurement, and surface roughness were performed using FESEM and 3D surface analyzer. The wetting behavior of surfaces assisted by measuring advancing, receding contact angle, and contact angle hysteresis with ultrapure water and diiodomethane. Further, the Surface free energy of implants using the Chibowski approach, Neumann's equation, and Owen &Wendt method were calculated. The surface properties were studied with the roughness factor. The bacterial cell behavior of textured surfaces was studied in detail. Bacterial response studies on various surfaces are highly essential to gain insightful information about the usage of implants. Results indicate that the formed textures are uniform, dimensionally accurate with no defects, and as per the design of the experiment. The area surface roughness, hydrophilicity rate, and surface free energy increased in all cases, and all the surface properties alter with a change in textures density. Further, the results show that bacteria respond to surface modifications through changes in cell surface membrane, cellular roughness, morphological changes, the appearance of cellular appendages, and EPS production. The present study provides insight details about the surface properties of the Ti6Al4V implant and will be helpful to facilitate cell attachment, adhesion, proliferation, and protein adsorption.

Estimation of the Surface Free Energy of Hydrophobic Monolithic Silica Aerogels

AbstractAerogels are prepared by quantifying the sol–gel process of the organo‐metallic precursors. The objective of the present article is to synthesize ultralow density, low index of refraction, and monolithic silica aerogels. The quantification of hydrophobicity of the silica aerogels using water drop contact angle is not only crucial but also the estimation of the surface free energy is an important parameter to understand the interfacial behavior of the aerogel surface and liquid. To provide insight on this behavior, calculation of the surface free energy is done by using Neumann's equation of state. These synthesized aerogels emerged with ultralow density 24 kg m−3 and low thermal conductivity ∼0.091 W m−1 K−1.

Adhesion of an elastic sphere on a tensioned membrane

Inspirited by the fact that classical models of adhesion contact (such as the Johnson–Kendall–Roberts model, Young’s equation or the Neumann equation) cannot be directly applied to adhesion of an elastic sphere on a membrane, the present work aims to develop an explicit general model for axisymmetric adhesion mechanics of an elastic sphere on a tensioned circular membrane. An explicit expression for the potential energy of the sphere–membrane system is derived, and explicit equations are given to determine the adhesion equilibrium state. The validity and accuracy of the proposed model are verified by good agreement between the predicted results and known results on both adhesion of a rigid sphere on a membrane and the critical condition for full wrapping of a rigid sphere by a membrane of non-zero bending rigidity.

Highly Efficient, Flexible Wireless‐Powered Circuit Printed on a Moist, Soft Contact Lens

AbstractContact lens with built‐in electronics is a next‐generation wearable product with potential applications such as biomedical sensing and wearable displays. However, fabricating a wireless‐powered circuit on a moist, soft contact lens, via common dry lithography, makes producing smart contact lenses challenging. Here, electrochemically (EC) printing a wireless‐powered circuit onto a moist, soft contact lens is demonstrated. EC printing involves adding a conductive polymer at the interface between a metal contact and a hydrogel‐based contact lens, resulting in strong adhesion of the circuit to the lens without losing high power transfer efficiency (50%) from an eyeglass transmitter to the printed receiver lens. The energy transfer characteristics during eye movement are modeled using the Neumann equation and Kirchhoff's voltage law for wireless power transfer. The energy transfer efficiency between the eyeglass transmitter and the printed receiver lens is derived, and illumination of a wireless‐powered single light‐emitting diode display as a function of eye rotation angle is demonstrated. This work opens the door to integrating more complex circuits at soft contact lens interface to produce smart contact lens with increased functionality.

Solid-Liquid-Liquid Wettability of Surfactant-Oil-Water Systems and Its Prediction around the Phase Inversion Point.

Surfactant-oil-water (SOW) systems are important for numerous applications, including hard surface cleaning, detergency, and enhanced oil-recovery applications. There is limited literature on the wettability of solid-liquid-liquid (SLL) systems around the surfactant phase inversion point (PIP), and the few references that exist point to wettability inversion accompanying the microemulsion (μE) phase inversion. Despite the significance of this phenomenon and the extreme changes in contact angles, there are no models to predict SLL wettability as a function of proximity to the PIP. Recent works on SLL wettability in surfactant-free systems suggest that SLL contact angles can be predicted with an extension of Neumann's equation of state (e-EQS) if the interfacial tension (IFT or γo-w) is known and if there is a good estimate for the interfacial energy between the wetting phase and the surface (γS-wettingliquid). In this work, IFT predictions for SOW systems around the PIP were obtained via the combined hydrophilic-lipophilic difference (HLD) and net-average-curvature (NAC) framework. To test the hypothesis that the combined HLD-NAC + e-EQS can predict wettability inversion around the PIP, with a given γS-μE, the contact angles (measured through the light oil phase, θO) for the μE of sodium dihexyl sulfosuccinate-toluene-saline water system were measured on high surface free energy (SFE) materials (glass, stainless steel, and mica) and on polytetrafluoroethylene (low SFE) around the PIP. Considering that at the PIP, most systems have a contact angle of 90°, an estimated γS-μE = 1/4γo-w@PIP was found to be suitable for the systems considered in this work and for systems presented in the literature. The largest deviations between the predictions and the experimental values were found in the positive HLD range (surfactant in the light oil phase). Although there is room for improvement, this framework can estimate the wetting behavior of SOW systems starting solely from formulation parameters.

A rapid method for interfacial tension calculation between rock plug and crude oil based on contact angles, application for EOR

ABSTRACTInterfacial tension and contact angle are two specific important parameters to take decisions for enhanced oil recovery, for instance, proper chemicals to use for surface tension reduction, expected wettability of solids, interaction between crude oil and rock. For this purpose, the article presents a method for easy calculation of the solid-liquid interfacial tension based on contact angle measurements applying Neumann's correlation and Young's equation. The main idea stands on the calculation of the rock parameters, like wettability, with known substances and extend these results to crude oils. It was possible, based on the results obtained, to establish a relationship between solid-liquid interfacial tension and contact angle for the crude oil – rock system, which can definitively be used for the calculation of interfacial tension of any other fluid spread out on the same kind of rock. A linear regression was obtained with an accuracy as good as R2 = 0.9989. Viscosity as a function of contact angle could also be obtained for the studied crude oils in the same kind of rock.

Impact of Solid Surface Energy on Wettability of CO2-brine-Mineral Systems as a Function of Pressure, Temperature and Salinity

CO2 storage refers to the methods employed to inject CO2 in depleted oil and gas reservoirs and deep saline aquifers for long term storage of CO2 with the objective to reduce the anthropogenic CO2 emissions. Wettability and interfacial tension are two important multiphase parameters which are used to characterize the flow behavior of CO2 in reservoirs. Numerous studies have reported wettability data of CO2-brine systems on various rock forming minerals as function of pressure, temperature and salinity. However, the associated trends have not been physically well-understood and require considerable attention which is objective of our present work.In this work, we apply Neumann's equation of state method to our measured contact angle data for CO2-brine-mica systems and contact angle data of CO2-brine-quartz from Sarmadivaleh et al., 2015.Our results indicate that for mica, solid-CO2 interfacial tension decrease with pressure and salinity and increase with temperature. Moreover, solid-liquid interfacial tension decrease with temperature and decrease with salinity. For quartz, although the solid-CO2 interfacial tension decrease with pressure and increase with temperature, yet solid-liquid interfacial tension increase with temperature which explains the increase in contact angle with temperature for quartz. Overall, we find that results are in accordance with wettability data as function of pressure, temperature and salinity. We thus conclude that hotter reservoirs with lower injection pressure and lower brine salinities exhibit relatively better water wetting state and hence better seal capacity leading to higher CO2 storage potential. We also conclude that solid surface energy approach adequately explains the dependency of wettability on pressure, temperature and salinity.

Surface properties of Ti-6Al-4V alloy part I: Surface roughness and apparent surface free energy

Titanium (Ti) and its alloys are the most often used implants material in dental treatment and orthopedics. Topography and wettability of its surface play important role in film formation, protein adhesion, following osseointegration and even duration of inserted implant. In this paper, we prepared Ti-6Al-4V alloy samples using different smoothing and polishing materials as well the air plasma treatment, on which contact angles of water, formamide and diiodomethane were measured. Then the apparent surface free energy was calculated using four different approaches (CAH, LWAB, O-W and Neumann's Equation of State). From LWAB approach the components of surface free energy were obtained, which shed more light on the wetting properties of samples surface. The surface roughness of the prepared samples was investigated with the help of optical profilometer and AFM. It was interesting whether the surface roughness affects the apparent surface free energy. It was found that both polar interactions the electron donor parameter of the energy and the work of water adhesion increased with decreasing roughness of the surfaces. Moreover, short time plasma treatment (1min) caused decrease in the surface hydrophilic character, while longer time (10min) treatment caused significant increase in the polar interactions and the work of water adhesion. Although Ti-6Al-4V alloy has been investigated many times, to our knowledge, so far no paper has been published in which surface roughness and changes in the surface free energy of the alloy were compared in the quantitative way in such large extent. This novel approach deliver better knowledge about the surface properties of differently smoothed and polished samples which may be helpful to facilitate cell adhesion, proliferation and mineralization. Therefore the results obtained present also potentially practical meaning.

Assessment of earthing system location for wind turbines using finite element method

A new proposal for the assessment of earthing system location used for wind turbines is presented. This proposal depends on the simulation of the electric field as well as the calculation of current density at the ground surface above the earthing system and distribution inside the soil when the wind turbine is exposed to high voltage. The electrical potential simulation around the earthing system of wind turbine using ring earth electrode with and without auxiliary vertical rods was also studied. Accurate calculations and simulation of the electric field are prerequisite for the simulation of current density. The electric field distribution is obtained by calculating the electric potential in three-dimensional domain surrounding the earthing system using Finite Element Method. The boundary conditions satisfy both Dirichlet's and Neumann's equations. The simulated electrodes are energized with one per unit voltage to be available for different types of applied potential. The resistance of the earthing system is calculated. This simulation model shows reasonably close agreement which gives confidence in predicting the assessment of the earthing grid location which is around 66.6% out of the total depth length of the affected domain. Different types of soils were checked to satisfy this ratio of the location assessment. The results showed that the vertical component of electrical field intensity and current density were improved at the assessment location of the earthing grid.

Improved Stefan Equation Correction Factors to Accommodate Sensible Heat Storage during Soil Freezing or Thawing

AbstractIn permafrost regions, the thaw depth strongly controls shallow subsurface hydrologic processes that in turn dominate catchment runoff. In seasonally freezing soils, the maximum expected frost depth is an important geotechnical engineering design parameter. Thus, accurately calculating the depth of soil freezing or thawing is an important challenge in cold regions engineering and hydrology.The Stefan equation is a common approach for predicting the frost or thaw depth, but this equation assumes negligible soil heat capacity and thus exaggerates the rate of freezing or thawing. The Neumann equation, which accommodates sensible heat, is an alternative implicit equation for calculating freeze‐thaw penetration. This study details the development of correction factors to improve the Stefan equation by accounting for the influence of the soil heat capacity and non‐zero initial temperatures. The correction factors are first derived analytically via comparison to the Neumann solution, but the resultant equations are complex and implicit. Explicit equations are obtained by fitting polynomial functions to the analytical results. These simple correction factors are shown to significantly improve the performance of the Stefan equation for several hypothetical soil freezing and thawing scenarios. Copyright © 2015 John Wiley & Sons, Ltd.

A method for estimating interfacial tension of liquid crystal embedded in polymer matrix forming PDLC

ABSTRACTA simple and convenient method based on sessile drop technique for measuring surface tensions of polymer and nematic liquid crystal (LC) is described. Contact angles formed by drops of probe liquids and a nematic LC on a photocurable polymer were measured. The surface energies were evaluated using the Fowkes method, Neumann's equation, and new equations developed based on Neumann's approach. The values of surface tensions were used to evaluate the interfacial interaction in term of work of adhesion between the LC and polymer. Further, the effect of dichroic dye on the extent of interaction and work of adhesion was examined by measuring contact angle in consequence of dye addition. A difference in work of adhesion between the lower and higher dye‐doped LC droplets gave an indication of affinity relationship between polymer and LC molecules. A change in work of adhesion resulted in variability of nematic director configurations inside phase separated LC droplets embedded in polymer matrix; when viewed under polarizing optical microscope. Thus, our approach of estimating surface energy of polymer and LC has found to be useful in determining interaction at polymer–LC interface. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 41137.