Flow Rate Gradient Research Articles

Examining the Mid to Long‐Term Variability in Saturated Hydraulic Conductivity of Sandy Soils and Its Influencing Factors Under Constant Head Test in the Laboratory

AbstractSaturated 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.

Sustainable reuse of oil and gas wells for geothermal energy production: Numerical analysis of deep closed loop solutions in Italy

This study assesses the feasibility of repurposing abandoned oil and gas wells in Italy for geothermal energy production employing a geothermal closed-loop system. A systematic methodology was developed, beginning with raw data collection and progressing to numerical simulations using COMSOL Multiphysics to model a U-shaped deep closed-loop geothermal heat exchanger. The analysis relied on a public database of wells drilled in Italy since the mid-20th century. The Horner plot correction method was applied to measured temperature data to obtain accurate geothermal gradients across Italy, which were then used as input parameters for a numerical sensitivity analysis. The results highlight the critical role of the geothermal gradient and heat carrier fluid flow rate in determining system performance. Regions in Italy with geothermal gradients exceeding 40 °C/km, particularly in the Tyrrhenian area, were identified as having high potential for this technology. A preliminary analysis of a virtual Organic Rankine Cycle (ORC) system estimated power production of 73 kW, with an efficiency of 11.66 % after 25 years of operation under optimal conditions (5 l/s flow rate, 60 °C/km geothermal gradient, and 70 °C evaporation temperature).

Integrating experimental and theoretical investigations of porous graphite materials with scanning electron microscope image processing

Accurate determination of fractal dimension (FD) and permeability of porous graphite materials (PGM) is essential for applications like porous aerostatic bearings (PABs). This study addresses the need for improved measurement methods by employing image processing and computer vision (IPCV) techniques to enhance FD and permeability accuracy. We aimed to refine these measurements by analysing the effects of image size and magnification on accuracy. The research developed theoretical models based on fractal theory, Darcy's law, and a modified Hagen-Poiseuille gas equation to evaluate these effects. A dual-path X-ray imaging detection system was used for experimental validation. The gauge pressure was varied across the surface of the PGM and volume flow rate was measured. MATLAB was utilized for IPCV, enabling precise FD determination and underscoring the importance of image parameters. Results showed that FD values stabilize at specific image sizes and magnifications, improving accuracy. Linear relationships between pressure gradient and volume flow rate were observed, with permeability stabilizing at high pressures. Porosity values varied among materials: Toyo Carbon (15 %), SGL Graphite (17 %), Super Carbon Graphite (27 %), and poplar porous (30 %). FD obtained through theoretical and scanning electron microscope (SEM) methods had a maximum error of 0.08. The study also found a positive correlation between relative density and image grayscale at the macroscopic level. The findings emphasize the importance of optimizing image size and clarity for accurate PGM analysis, providing crucial insights for PAB design and other advanced applications.

Thermal distribution and viscous heating of electromagnetic radiative Eyring–Powell fluid with slippery wall conditions

The research examines the intricate between Eyring-Powell microfluidic heat transfer, electromagnetic radiation and viscous heating in a Riga slippery device as applied in heat exchangers, cooling systems, biomedical devices, energy generation, polymer processing, and others. The viscoelastic property of the fluid is characterized by the Eyring-Powell Cauchy fluid model with shear-thickening and shear-thinning phenomena that are useful in several heat transport processes and thermal management. The developed governing model is taken from the constitutive relations and conservation principles and solved via an adaptive partition weighted residual method. The essential fluid term sensitivities are systematically investigated on the flow and thermal distribution characteristics. An appropriate validation and comparison of results is done and found to agree quantitatively, this confirmed the correctness of the presented outcomes. The results reveal the significant impact of the thermofluidic terms interaction on the viscous flowing fluid and thermal behaviour. As seen, slip conditions momentously increase the flow rate gradients for about 1.7% to 2.4% close to the boundary wall and consequently raise the microfluidic thermal propagation rates with 3.7% non-Newtonian fluid and thickness of the boundary layer. Moreover, the thermal gradient and distribution complexities are modulated within the fluid regime due to radiation and Lorentz force.

Parametric analysis of reverse electrodialysis process for improved power generation: Influence of spacer thickness, feed solution flow rate, membrane, and concentration

Reverse electrodialysis (RED) technology produces electrical energy from a salinity gradient by transporting ions through ion-exchange membranes (IEM). Although research into this technology has recently seen considerable growth, there is still interest in improving its efficiency. As a result, a mathematical model to study the RED process was developed using Aspen Custom Modeler software, focusing on three membranes (Fumasep (FAD/FKD), Fujifilm Type 10, and Selemion (AMV/CMV)). A parametric analysis was conducted, considering spacer thickness, salinity gradient, and feed-solution flow rates. Evaluation of internal resistance, gross power density, and net power density was also performed. Results showed that using a thicker spacer (270 μm) in the high compartment and a thinner spacer (150 μm) with a high Reynolds number in the low compartment led to higher net power densities of 2.17 W·mcp−2 and 6.74 W·mcp−2 for Fumasep (FAD/FKD) membrane with (brackish/seawater) and (brackish/brine), respectively. Among the membranes tested, Fumasep (FAD/FKD) and Fujifilm Type 10 had similar results, with the former slightly exceeding the latter. However, the Selemion membrane (AMV/CMV) performed poorly in all tests.

Improvement of field falling-head test and determination of hydraulic conductivity using Darcy’s equation

This study presents a novel permeameter design for field falling-head tests to determine vertical hydraulic conductivity (K) using Darcy's equation. The design features an open-ended standpipe with two ports for simultaneous measurement of hydraulic heads at both ends of the sediment column, enabling direct estimation of flow rate (q) and hydraulic gradient (i). Flow rate is calculated by differentiating the best-fit curve for water level change above the sediment, and the hydraulic gradient is derived from the head difference between the ports. Laboratory and field tests consistently demonstrated a strong linear relationship between q and i (R2 > 0.999), validating the applicability of Darcy's equation for this new permeameter design. The K values obtained using the proposed method matched those obtained using the Hvorslev equation method. Furthermore, the design allows for continuous measurement of heads after the falling-head permeameter test, facilitating the collection of time series data for the hydraulic gradient. When combined with a pre-determined K value, this enables calculation of time series for the seepage rate across the surface water/sediment interface. To demonstrate this capability, preliminary tests were conducted using commercially-available pressure transducers to monitor heads and obtain seepage time series. The results of these tests are also presented.

Non‐isothermal flow dynamics during reverse roll coating phenomena of non‐Newtonian polymer

AbstractRoll coating plays a major role in industrial coating, including wallpapers, plastic and photographic films, sticky tapes, magnetic recordings, wrapping magazines and books, and so on. The current study proposes a mathematical model for a non‐isothermal, incompressible Sutterby fluid flowing through a narrow gap between two heated, counterrotating rollers. Lubrication approximation theory is used to simplify nondimensional expressions. The perturbation technique provides exact results for velocity profile, temperature, flow rate, and pressure gradient, whereas the numerical technique (Simpson rule) is used to compute the pressure profile and flow rate, respectively. The effects of the involved parameters on various physical characteristics like pressure, flow rate, temperature, pressure gradient, force, and power input are depicted in graphs and tabular form. A mechanism for controlling the coating thickness, power input, flow rate, separation force, and pressure distribution is provided by the material properties involved. With variations to a Sutterby fluid parameter and the velocity ratio K, both the pressure gradient and pressure decrease. It is significant to note that the temperature distribution is controlled by the velocities ratio and Brinkman number. Moreover, the separation point is shifted towards the nip area and the coating thickness on the web reduces with increasing velocities ratio K.

A Green Liquid Chromatography Method for Simultaneous Quantification of Caffeine and its Three Major Metabolites in Urine, Drinks, and Herbal Products

ABSTRACTA green reversed‐phase liquid chromatography method was developed to determine caffeine (CF), theobromine (TB), theophylline (TP), and paraxanthine (PX). The stationary phase was a silica‐based C18 monolithic column (100 × 3.0 mm2 i.d.), eluted with a gradient from 6% to 10% (v/v) of ethanol in water, at a flow rate of 0.75 mL/min (35°C) and UV detection at 272 nm. The compounds were separated in less than 6 min, with a total time of 10 min for column reconditioning. The effect of gradient composition, flow rate, injection volume, and column temperature was evaluated in the separation efficiency, especially regarding the critical pair PX/TP, for which the best resolution was 1.37. The linear range was between 0.5 and 100 µg/mL. The LODs were 0.065, 0.057, 0.040, and 0.044 mg/mL for TP, TB, PX, and CF, respectively. The method was applied to green tea and yerba mate infusions, soft drinks, energy drinks, and soluble coffee. Urine samples were analyzed before and after solid‐phase extraction. The accuracy was evaluated by the spiking/recovery strategy standing in the 79.6% to 116.4% range. The separation performance and the mobile phase consumption were compared to those of another method using a gradient of methanol in water.

Instrumental and theoretical advancements in pulsed elution-LC × LC: Investigation of pulse parameters and application to wastewater effluent

Due to the decoupling of the first (1D) and second (2D) dimension in pulsed elution-LC × LC (PE-LC × LC), method development is more flexible and straightforward compared to fast comprehensive LC × LC where the dependencies of key parameters between the two dimensions limits its flexibility. In this study we present a method for pulse generation, which is based on a switching valve alternating between one pump that delivers the gradient and a second pump that delivers low eluotrophic strength for the pause state. Consequently, the dwell volume of the system was circumvented and 7.5, and 3.75 times shorter pulse widths could be generated at flow rates of 0.2, and 0.4 mL/min with satisfactory accuracies between programmed and observed mobile phase composition (relative deviation of 6.0 %). We investigated how key parameters including pulse width and step height, 2D gradient time and flow rate affected the peak capacity in PE-LC × LC. The conditions yielding the highest peak capacity for the PE-LC × LC- high-resolution mass spectrometry (HRMS) system were applied to a wastewater effluent sample. The results were compared to a one dimensional (1D)-LC-HRMS chromatogram. The peak capacity increased with a factor 34 from 112 for the 1D-LC run to 3770 for PE-LC × LC-HRMS after correction for undersampling. The analysis time for PE-LC × LC-HRMS was 12.1 h compared to 67.5 min for the 1D-LC-HRMS run. The purity of the mass spectra improved for PE-LC × LC-HRMS by a factor 2.6 (p-value 3.3 × 10−6) and 2.0 (p-value 2.5 × 10−3) for the low and high collision energy trace compared to the 1D-LC-HRMS analysis. Furthermore, the signal-to-noise ratio (S/N) was 4.2 times higher (range: 0.06–56.7, p-value 3.8 × 10−2) compared to the 1D-LC-HRMS separation based on 42 identified compounds. The improvements in S/N were explained by the lower peak volume obtained in the PE-LC × LC-HRMS.

Research progress on the detection of water-soluble vitamins in food using liquid chromatography

Currently, liquid chromatography is widely used for the analysis and determination of water-soluble vitamins (WSVs) in functional foods. However, due to the diversity of sample characteristics and the requirement for purification accuracy, the chromatographic conditions and specific methods used vary. This paper reviews the chromatographic conditions of liquid chromatography techniques for detecting WSVs in food, as well as the selection of liquid chromatography methods in different application fields. The chromatographic conditions include chromatographic columns, column temperature, mobile phase, flow rate, and elution gradient, and the application scope of different chromatographic conditions is compared. Liquid chromatography methods include high-performance liquid chromatography and liquid chromatography-tandem mass spectrometry, and discussions are made on the applications and prospects of these two methods under different chromatographic conditions. Therefore, this review provides research insights into different chromatographic conditions and methods for food quality inspection and biochemical analysis research.

Vertical non-linear Darcy seepage characteristics of coarse upper and fine lower saturated sand

The investigation of seepage characteristics in double-layer sand contributes to a deeper comprehension of the seepage mechanism in porous media, as well as enhancing the accuracy of porous media seepage calculations. By employing a configuration consisting of six variations of upper coarse and lower fine double-layer sand, alterations in flow rate and hydraulic gradient were achieved by manipulating liquid level heights. This analysis examines the correlation between hydraulic gradient, flow velocity and hydraulic conductivity. The research reveals that the double-layer sand exhibits Darcy non-linear flow, despite having a very low Reynolds number (Re), and emphasises the influence of particle size in the lower sand layer on hydraulic gradient and hydraulic conductivity. Moreover, the enhanced Ergun formula was utilised to evaluate viscous resistance and local resistance during the flow process, while also presenting an empirical formula for interface resistance derived from experimental data.

Numerical simulation on converting abandoned wells into double-well open-loop geothermal system

Converting abandoned oil wells into geothermal systems holds immense potential and has garnered international attention. However, research on converting abandoned oil wells into Open-Loop Geothermal Systems (OLGS) remains insufficient and requires further exploration. To address this gap, this study utilizes COMSOL software employing the Finite Element Method (FEM) to establish a numerical model of a double-well OLGS with 3D multi-physics field coupling, investigating geothermal extraction through numerical simulation. The findings indicate that in double-well OLGS, utilizing high flow rates in the early production stage and lower flow rates in the later stages enhances system thermal power. Additionally, employing lower inlet temperatures in the early production stage and higher inlet temperatures in the later stages favors geothermal extraction. Higher geothermal gradients and larger well spacings further benefit geothermal extraction. Increasing the length of the production well's insulating layer in the early production stage helps minimize heat loss. The outlet temperature exhibits high sensitivity to flow rate and geothermal gradient throughout the production phase, while sensitivity shifts towards inlet temperature and well spacing in the later stages. In the five-spot OLGS, outlet temperature and thermal power increase with a reduction in the number of production wells; moreover, assuming identical outlet temperatures (100 ℃) after 50 years of production, the thermal power of the five-spot OLGS exceeds that of the double-well OLGS by an average of 20937.88 kW per year.

Analysis of unsaturated alginate oligosaccharides using high-performance anion exchange chromatography coupled with mass spectrometry.

Alginate is a commercially important polysaccharide composed of mannuronic acid and its C5 differential isomer guluronic acid. Comprehensive research on alginate and alginate lyases requires efficient and precise analytical methods for alginate oligosaccharides. In this research, high-performance anion exchange chromatography (HPAEC) in parallel with pulsed amperometric detection (PAD) and mass spectrometry (MS) was applied to the analysis of oligosaccharides obtained by alginate lyase. By optimizing the chromatographic conditions including mobile phase concentration, flow rate, and elution gradient, the analysis of a single sample could be completed in 30 min. Seven unsaturated alginate oligosaccharides were separated and identified through their analysis time observed with PAD, including all structurally different unsaturated disaccharides and trisaccharides. The quantitative analysis of seven oligosaccharides was performed based on the quantitative capability of PAD. The method exhibited adequate linearity and precision parameters. All the calibration curves showed good linearity at least in the concentration range of 0.002 to 0.1 mg/mL. The HPAEC-PAD/MS method provides a general and efficient online method to analyze alginate oligosaccharides.

Effect of bottom stirring on bath mixing and transfer behavior during scrap melting in BOF steelmaking: A review

Abstract Basic oxygen furnace (BOF) steelmaking is a widely used method for steelmaking production, and the bath stirring has a significant influence on dynamics of bath flow and mixing. Therefore, the effect of bottom gas flowrate, nozzle number and configuration, and bottom gas distribution mode on bath stirring are summarized in this study. Reasonable matching of bottom gas flowrate, nozzle number and configuration, as well as intensive study on the coupling effect of gas flowrate gradient and exchange frequency on non-uniform stirring would receive more and more attention in the coming years. With wide concern on the low-carbon and high-efficient production for BOF steelmaking, as a kind of recyclable iron-containing resource, the rapid melting and reasonable utilization of scrap in converter bath were emphasized in recent works, which could be promoted with high-efficient bottom stirring. The effect of bottom stirring on heat and mass transfer during scrap melting process was reviewed in this work, and the influence mechanism of bottom stirring on coupled heat and mass transfer should be further investigated. In addition, an overview of recently published physical and numerical simulation describing the bottom stirring and its effect on scrap melting would provide an outlook for future work.

Conformal and approximate analysis of the effect of cutoff wall thickness on finite depth seepage characteristics

ABSTRACT An analytical solution to the problem of two-dimensional steady-state seepage flow beneath a water-retaining structure is presented using conformal mapping and complex variables. This paper addresses the question of to what extent the cut-off thickness affects the values of seepage characteristics. The closed-form analytical equations are calculated numerically. The analytical results have been validated by comparing them with the available exact solutions for finite-depth seepage. The resulting implicit equations, involving elliptic integrals, are used to create design diagrams. Increasing the thickness can cause a reduction in hydraulic gradient, seepage discharge, and uplift pressure at the left tip of the cut-off. A customized fragment type considering the cut-off’s thickness is developed using the analytical results to estimate seepage quantities and exit gradients. The form factor for this fragment is obtained in the form of dimensionless charts, which predict the flow rate and exit gradient more precisely than the existing solutions.

Interpreting pore-scale fluctuations: Predicting transport coefficients in multiphase flow through porous media using the Green–Kubo formulation—An experimental investigation

Flow fluctuations that are commonly associated with multiphase flow in porous media are studied using concepts from non-equilibrium thermodynamic and statistical mechanics. We investigate how the Green–Kubo formulation of the fluctuation dissipation theorem can be used to predict the transport coefficient from the two-phase extension of Darcy's law. Flow rate-time series data are recorded at the millisecond timescale using a novel experimental setup that allows for the determination of flow fluctuation statistics. By using Green–Kubo relations, a transport coefficient is predicted based on the integrated autocorrelation function. Notably, this coefficient aligned closely with the total effective phase mobility computed using Darcy's equation for multiphase flow, particularly in scenarios where a linear relationship between flow rate and pressure gradient was observed. Our results open a new field of coefficient explorations where microscale fluctuations during multiphase flow are directly linked to macroscale parameters.

The seepage driving mechanism and effect of CO2 displacing CH4 in coal seam under different pressures

The technology of CO2-ECBM holds the potential to enhance the efficiency of coalbed CH4 extraction by boosting the driving force of CH4 seepage and the desorption of adsorbed CH4 in coal. To investigate the seepage characteristics and displacement effects of gas during CO2-ECBM, the experiment of CO2 displacing CH4 in coal was conducted using a triaxial experimental system within a displacement pressure range of 1.5–4.0 MPa. The results showed that increased displacement pressure led to large coal swelling. This swelling caused a reduction in permeability, leading to high resistance to gas flow and the generation of elevated pore pressure. The distribution of the pore pressure in coal displayed a nonlinear feature, predominantly influenced by coal swelling during CO2 adsorption process. With the injection of CO2, the pressure field in the coal transitioned from an unstable to a stable state. The coal strain induced by CO2/CH4 adsorption-desorption varied, leading to the variation in pore pressure gradient and seepage flow rate, which ultimately impacted the displacement efficiency. The evolution of pressure field during CO2-ECBM provides valuable guidance for displacement effects. It contributes to a parametric optimization for CO2-ECBM application in CH4 extraction.

Wearable microfluidic sweat collection platform with a calorimetric flow rate sensor for realtime and long-term sweat rate measurements

This work presents the design and fabrication of a wearable microfluidic patch-based system for sweat collection with a calorimetric flow rate sensor based on heat convection for measuring sweat rate (SR). The effects were predicted using a 3D multi-physics simulator and were verified on a fabricated patch made of polyimide layers. The sensor can detect surface temperature gradients of 302–312 K caused by fluid flowing thru the microfluidic channels at a rate of 0.5–23 µg s−1 that fall within the physiological range of SR. Meanwhile, the relation between flow rate and temperature gradient is highly linear (Pearson r2 = 0.999) and repeatable. This work also demonstrates a low-cost method for patterning microfluidic channels on flexible substrates which can be used for mass production of wearable patches.

Bidimensional Dynamic Magnetic Levitation: Sequential Separation of Microplastics by Density and Size.

There is a current gap in sample preparation techniques integrating the separation of microplastics according to their different material types and particle sizes. We describe herein the Bidimensional Dynamic Magnetic Levitation (2D-MagLev) technique, enabling the resolution of mixtures of microplastics sorting them by plastic type and particle size. Separations are carried out in a bespoke flow cell sandwiched between two ring magnets and connected to programmable pumps for flow control. The first separation dimension is based on sequential increases in the concentration of a paramagnetic salt (MnCl2), enabling magnetic levitation of microplastics with determined densities. The second dimension is based on increasing flow rate gradients and maintaining constant MnCl2 concentrations. This fractionates the magnetically levitating microplastics according to their different particle sizes. Microplastics are therefore collected by their increasing density, and the particles corresponding to each density are fractionated from smaller to larger size. Using polyethylene microspheres with defined density (1.03-1.13 g cm-3) and size (98-390 μm) as microplastic mimicking materials, we investigated their optimum threshold velocities for their size fractionation, potential effects of medium viscosity and sample loading, and types of flow rate gradients (linear, step). Performing a separation using a combination of step gradients in both MnCl2 concentration and flow rate, mixtures comprising microplastics of two different densities and three different particle sizes were separated. 2D-MagLev is simple, fast, versatile, and robust, opening new avenues to facilitate the study of the environmental presence and impact of microplastics.

A novel and sensitive method for simultaneous determination of 6 low-calorie bulk sweeteners by HPLC-ELSD

A novel and sensitive method for the simultaneous analysis of six low-calorie bulk sweeteners (D-allulose, D-tagatose, D-mannitol, mycose, palatinose, and erythritol) without derivatisation was developed using high-performance liquid chromatography-evaporative light scattering detector (HPLC-ELSD). Chromatographic separations were carried out on a Zorbax Original NH2 (5 μm particle size, 250 mm×4.60 mm id, 70 Å) column with flow rate gradient elution with acetonitrile: water (80:20, v/v). Drift tube temperature was set at 50 ℃, the nebuliser carrier gas flow rate was 1.0 mL·min-1, and nitrogen pressure was regulated to 276 kPa with gain:3. The regression equation showed good linearity (R2 = 0.9985-0.9998) for all six low-calorie bulk sweeteners in the tested range (0.060-0.60 mg·mL-1). The limits of detection (LOD) for the six low-calorie bulk sweeteners ranged from 0.02 to 0.06 mg·mL-1. The proposed HPLC-ELSD method was validated for the quantification of the low-calorie bulk sweeteners in 14 types of foods, and the results were satisfactory. In addition, the results showed that the number of sweeteners in each food product varied. The presence of multiple low-calorie bulk sweeteners in certain foods is interesting. This method is successful in monitoring low-calorie bulk sweeteners in food.