Two-dimensional Transport Research Articles

Convergence Study of 2D Transport Method for Multigroup k-Eigenvalue Problems with High-Order Scattering Source Using Fourier Analysis

The convergence behavior of a two-dimensional (2D) transport method has been derived by Fourier analysis for single-group problems with isotropic sources. However, in real calculation, to pursue precision, a high-order scattering source is a common option, and its influence on convergence performance is worth investigating. No theoretical convergence study of a 2D transport method for multigroup problems with high-order scattering sources was previously performed, but it is important work that would complement existing studies. This study presents a Fourier analysis for solving multigroup problems with high-order scattering. First, the influences of the number of inner iterations for the multigroup isotropic scattering problem are analyzed. It is found that with an increase of the number of inner iterations, the spectral radius decreases and finally reaches an asymptotic value. When the scattering ratio is increased, more inner iterations are required to reach the asymptotic value. Then, the influences of high-order scattering are analyzed. The Fourier analysis results show that for high-order scattering source problems, the influence of the number of inner iterations is different from the isotropic scattering case. The influences of first-order scattering and second-order scattering are not the same. With an increase of first-order scattering, the spectral radius first decreases in the small optical thickness region and then increases in the large optical thickness region, which may lead to the divergence of iterations. If second-order scattering is not too large, an increase of second-order scattering decreases the spectral radius for all optical thickness regions. First-order scattering and second-order scattering that are too large may result in an unpredictable slope of the spectral radius for optical thicknesses between 10−1 and 1.

Heat transfer model analysis of fractional Jeffery-type hybrid nanofluid dripping through a poured microchannel

This study investigates the impact of coupled heat and mass transfer on the peristaltic migration of a magnetohydrodynamic (MHD) stress-strain Jeffery-type hybrid nanofluid flowing through an inclined asymmetric micro-channel with a porous medium. The fundamental two-dimensional momentum and energy transport equations are simplified under the assumptions of long wavelength and low Reynolds number. To solve the momentum and heat transfer problems, two advanced fractional derivative approaches are employed: the fractal integral and the Prabhakar fractional derivative. The pressure difference is determined using numerical integration techniques, such as the Stehfest and Tzou's algorithms. The results are presented through graphs and tables, which illustrate the effects of various parameters on the velocity, heat transfer, and trapping phenomena. As a result, we concluded that, pressure gradients grow with higher Reynolds numbers and channel-inclined angles. The heat transfer rate is observed to decrease as the Darcy number and the orientation of the electromagnetic field increase. When comparing the fractional derivative approaches, the fractal operator exhibits a more significant impact on the momentum profiles compared to the Prabhakar fractional operator. This difference is attributed to the distinct characteristics of the integral kernels associated with each fractional derivative definition. Furthermore, when comparing hybrid nanofluids, water-based (H2O + Ag + TiO2) hybrid fluids have a somewhat more significant effect than (C6H9NaO7 + Ag + TiO2) hybrid nanofluids.

Polyethylene oxide-Based solid electrolytes with fast Li-ion transport channels constructed from 2D montmorillonite for solid-state lithium-metal batteries

Polyethylene oxide (PEO)-based solid-state electrolytes (SSEs) typically struggle with poor ionic conductivity, low lithium (Li)-ion transference number, and narrow electrochemical window. For overcoming these drawbacks, we designed a promising composite SSE (CSSE), i.e., a Li-containing ionic liquid (LiIL) was inserted into the Li-montmorillonite (LiMNT) layered structure to form an active filler (LiIL@LiMNT), involving two-dimensional (2D) fast transport channels of Li-ion inside PEO electrolyte. Benefitting from an enhancement of the 2D Li-ion transport channels, the obtained CSSE exhibited an excellent ion conductivity of 1.38 × 10−4 S cm−1 at 30 °C as well as a satisfactory Li-ion transference number (0.38). A Li symmetric battery with the CSSE exhibited a steady cycle for 3000 h with 0.2 mA cm−2 at 60 °C. Under the rate of 0.5C at 60 °C, the solid-state Li-metal batteries (SSLMBs) assembled with LiFePO4 and LiNi0.33Co0.33Mn0.33O2 cathodes maintained a considerable reversible capacity after 400 and 100 cycles, respectively. The assembled SSLMB also achieved a satisfactory performance at 40 °C. The 2D active filler prepared in this work forms efficient 2D Li-ion transport channels inside the CSSE while maintaining a tight interfacial contact with electrodes, which is crucial to achieve a superior performance for CSSEs. This strategy of constructing 2D ion transport channels in polymer electrolytes also provides another way for the design of other CSSEs.

Wigner transport in linear electromagnetic fields

Applying a Weyl–Stratonovich transform to the evolution equation of the Wigner function in an electromagnetic field yields a multidimensional gauge-invariant equation which is numerically very challenging to solve. In this work, we apply simplifying assumptions for linear electromagnetic fields and the evolution of an electron in a plane (two-dimensional transport), which reduces the complexity and enables to gain first experiences with a gauge-invariant Wigner equation. We present an equation analysis and show that a finite difference approach for solving the high-order derivatives allows for reformulation into a Fredholm integral equation. The resolvent expansion of the latter contains consecutive integrals, which is favorable for Monte Carlo solution approaches. To that end, we present two stochastic (Monte Carlo) algorithms that evaluate averages of generic physical quantities or directly the Wigner function. The algorithms give rise to a quantum particle model, which interprets quantum transport in heuristic terms.

Strong Intervalley Scattering-Induced Renormalization of Electronic and Thermal Transport Properties and Selection Rule Analysis in 2D Tellurium.

The electron-phonon interaction (EPI) and phonon-phonon interactions are ubiquitous in promising two-dimensional (2D) semiconductors, determining both electronic and thermal transport properties. In this work, based on ab initio calculations, the effects of intervalley scattering on EPI and higher-order four-phonon interactions of α-Te and β-Te are investigated. Through the proposed selection rules for scattering channels and calculations of full electron-phonon scattering rates, we demonstrate that multiple nearly degenerate local valleys/peaks produce more scattering channels, resulting in stronger intervalley scattering over intravalley scattering. The lattice thermal conductivities of α-Te and β-Te are decreased by as much as 10.9% and 30.8% by considering EPI under the carrier concentration of 2 × 1013 cm-2 (n-type) at 300 K compared to those limited by three-phonon scattering, respectively. However, when further considering four-phonon scattering, EPI reduces the lattice thermal conductivities by 2.6% and 19.4% for α-Te and β-Te, respectively. Furthermore, it is revealed that the four-phonon interaction is more dominant in phonon transport for α-Te than that for β-Te due to the presence of an acoustic-optical phonon gap in α-Te. Finally, we demonstrate strong intervalley scattering induces significant renormalization effects from EPI on all the constituent parameters of thermoelectric performance. Our results show the contributions of intervalley scattering to the electronic properties as well as thermal transport properties in band-convergent thermoelectric materials are essential and highlight the potential of monolayer tellurium as a promising candidate for advanced thermoelectric applications.

A novel four phase slug single-well push–pull test with regional flux: forward modeling and parameter estimation

The single-well push–pull (SWPP) test has been widely used for several applications, including determination of transport parameters such as regional groundwater flux velocity, effective porosity and dispersivity. A complete SWPP test usually includes four phases of injection, chase, rest, and extraction, while previous models mostly ignore the chase phase for the sake of simplification. Actually, the chase phase is important to minimize the impact of well skins and wellbore storage on the shape of the breakthrough curves (BTCs), thus is necessary and should be included in the model. To this end, two simplified methods are proposed in this study based on two different time tp and ta during a four-phase SWPP test to estimate the parameters related to transport, where tp and ta correspond to the time of the peak concentration during the injection phase and the time when the center of tracer mass returns to the wellbore during the extraction phase, respectively. Specifically, the tp method can be used to estimate the regional groundwater flow velocity and dispersivity (transverse and longitudinal), while the ta method is used to estimate the regional groundwater flow velocity and the effective porosity. Finite-element numerical modeling of the SWPP test based on the coupling of two-dimensional transient groundwater flow and solute transport is employed to test the applicability of the proposed methods. Results indicate that both the tp and ta methods proposed in this study perform satisfactorily in estimation of regional groundwater flow velocity, effective porosity and dispersivity, and these two methods require fewer observations than traditional curve fitting methods and do not require any optimization algorithms. We have also compared the proposed two methods with several previous methods, and conclude that these two new methods generally perform better than those of previous studies in terms of parameter estimation reliability.

All-in-one chitosan-based aerogel with a semi-clad structure for solar-driven interfacial evaporation

Solar-driven interfacial water evaporation is a promising technique for recovering clean fresh water and alleviating water scarcity. In this work, an all-in-one chitosan-based composite aerogel with a highly porous semi-clad structure was fabricated. In the process of interfacial water evaporation, the hydrophilic outer layer of the aerogel efficiently transported water to the upper surface through two-dimensional transport channels. Simultaneously, it rapidly converted absorbed sunlight into heat, demonstrating excellent photothermal conversion capabilities for efficient water evaporation. The hydrophobic inner core enabled the aerogel to float stably on the water surface, and had a low thermal conductivity to reduce heat dissipation into the water body. Under 1 sun illumination (1 kW m−2), the composite aerogel showed an evaporation rate of up to 1.547 kg m−2 h−1, corresponding to an evaporation efficiency of 91.47 %. Notably, the composite aerogel demonstrated high stability and recyclability in desalination and heavy metal wastewater treatment, which had great potential in recovering both clean water and heavy metal salts. The evaporator with a semi-clad structure had practical applications in solar desalination and sewage treatment due to its stable and efficient evaporation performance and simple preparation method.

Investigation of the effect of O doping on the Li-ion mobility of Li3PS4 solid-state electrolytes: an ab initio molecular dynamics study

The new channel brought by O doping can transform two-dimensional transport into a three-dimensional transport network for a Li3PS4 solid-state electrolyte.

A Novel Cellular Automata Framework for Modeling Depth-Averaged Solute Transport during Pluvial and Fluvial Floods

Currently, for modeling two-dimensional (2D) solute transport during pluvial and fluvial floods, the finite volume (FV) models are widely used because of their strong ability to handle steep concentration and velocity gradients from the flow advection term. However, heavy computational requirements are subsequently introduced which limit the numerical efficiency. To further increase numerical efficiency but keep the required accuracy, this study proposes a novel Solute Transport Modeling based on Cellular Automata framework (STMCA) to simulate solute transport due to the flow advection, turbulent diffusion, and material decay mechanisms in several sets of explicit algebraic equations. Four studied cases involving steep gradients of solute concentration and velocities in steady/unsteady violent flow conditions are used to compare the accuracy of the STMCA approach with a Godunov-type FV solute transport approach with a total variation diminishing (TVD) scheme. Then, the performances of the two approaches on water quality modeling are assessed through the E. Coli transport modeling during pluvial/fluvial floods on a real-scale terrain. The proposed STMCA approach is found to achieve almost the same accuracy as the FV approach. As to the numerical efficiency, the STMCA approach is faster than the FV approach by 289.6–328.6%. Hence, the proposed STMCA approach is proven to be an effective tool for simulating solute transport.

Semi-analytical models for two-dimensional multispecies transport of sequentially degradation products influenced by rate-limited sorption subject to arbitrary time-dependent inlet boundary conditions

Most of the semi-analytical and analytical models employed to depict multidimensional, multispecies transport of sequentially degrading reaction products are built upon solving a set of coupled advection-dispersion equations (ADEs). Within these equations, sorption is considered as being equilibrium-controlled. However, it has been demonstrated that more realistic predictions of the transport of contaminants in the groundwater could be obtained by the use of a rate-limited sorption process instead of an equilibrium sorption assumption. This study is thus designed to devise semi-analytical models for the two-dimensional multispecies transport of a chemical mixture comprised of a parent compound and its degradation-daughter products which is influenced by rate-limited sorption subject to arbitrary time-dependent inlet boundary conditions. Three integral transforms are applied to generate a set of linear algebraic equations (AEs) resulting from the reductions of the ADEs. The contaminant concentration of each species is calculated by solving these AEs and then retransforming the solutions back to the original time-space domain. The simulation results obtained with our newly developed semi-analytical model are nearly identical to those generated using a numerical model based on the Laplace transform finite difference (LTFD) method. This confirms the validity of the new semi-analytical model. An investigation of the effect of rate-limited sorption on the migration of the contaminant plume is carried out using various time-dependent inlet boundary conditions. The sorption rate values vary from low to high, specifically, 0.05, 0.5, 5, and 50 years−1. The results show that the predicted concentrations of all contaminants within in the decay chain decrease as the sorption rate constant increases, for both constant and exponentially time-dependent boundary sources. However, under pulse loading boundary conditions, the concentrations of the later degradation products tend to increase with the sorption rate constant. The semi-analytical models created in this study, allow for different inlet boundary conditions, so can be utilized to simulate the transport of sequentially degrading reaction products. This greater accuracy makes them useful for many applications.

A Two-Dimensional Transport Model of Bipolar Membrane Electrodialysis for the Electro-Regeneration of Carbon Capture Solvents

Bipolar membrane electrodialysis (BPMED) is a promising technology that uses an electric field to split water into H+ and OH- ions. A repeating stack of cation selective, anion selective, and bipolar membranes are placed between two electrodes, creating a repeating pattern of acid, base, and diluting flow chambers. A major application of BPMED is the electrochemical solvent regeneration of capture solutions used in CO2 point source (PS) or direct air capture (DAC). Protons generated using BPMED can be used to shift the acid-base equilibria back to CO2, providing a more sustainable alternative to traditional thermal regeneration methods when integrated with renewable electricity sources. This method combines electrosynthesis and separation, producing a pure stream of CO2 for sequestration and a concentrated base stream.Despite its potential, current limitations to BPMED implementation for this application stem from a large power consumption and high membrane costs. In addition, gas bubbles in solution can cause high electrical resistances, and experimental studies of this phenomenon are challenging due to the small scale on which it occurs. To address these challenges, we present a two-dimensional model of BPMED for CO2 capture solvent recovery. This model depicts a single repeating cell triplet and was constructed using COMSOL Multiphysics version 6.1. The Navier-Stokes equations were implemented to compute a convection field, and the ionic species concentration was found by solving the Nernst-Planck equation. A source term in the concentration partial differential equations was implemented to account for ionic speciation and water splitting reactions, captured through kinetic rate expressions.Experimental validation was conducted on a PC Cell BED 1-4 recirculating batch system with a stack of seven cell pairs of PC acid 60 (anion selective), PC SK (cation selective), and PC Bip (bipolar) membranes. Good agreement between the model and experimental results across a range of conditions and variables demonstrates accuracy and robustness. The calculated pH and concentration profiles revealed that the majority of the speciation reaction takes place inside, or directly adjacent to, the bipolar membrane, including bubble nucleation. Bubbles form inside membrane pores and displace the electrolyte, greatly increasing the electrical resistance of the membrane, particularly when membrane porosity is low. However, the reaction plane location where bubbles are generated can be manipulated by increasing the channel width or reducing the applied voltage.Future research will focus on expanding to multiphase CFD simulations to investigate the effect on flow. Our two-dimensional model provides valuable insights into the complex and multifaceted nature of BPMED, offering a powerful tool for investigating small-scale processes and advancing the use of BPMED for CO2 capture solvent recovery. Figure 1

Scaling laws of two-dimensional incompressible turbulent transport

The diffusive transport in two-dimensional incompressible turbulent fields is investigated with the aid of high-quality direct numerical simulations. Three classes of turbulence spectra that are able to capture both short and long-range time-space correlations and oscillating features are employed. We report novel scaling laws that depart from the γ = 7/10 paradigm of percolative exponents and are dependent on the features of turbulence. A simple relation between diffusion in the percolative and frozen regimes is found. The importance of discerning between differential and integral characteristic scales is emphasized.

Two-Dimensional Heavy Metal Migration in Soil with Adsorption and Instantaneous Injection

This paper studies a two-dimensional transport model to investigate the behavior of heavy metal migration in porous media, specifically considering their transport in soil. The model takes into consideration the combination of adsorption term as well as instantaneous injection at the boundary. Also, the model accounts for both longitudinal and transverse movements, providing a comprehensive understanding of heavy metal transport phenomena. In order to obtain the analytical solution Laplace transform has been implemented. It is found that the peak concentration of heavy metals is found to be greatly affected by the changes in the instantaneous injection value. Additionally, a correlation is observed between retardation factors and heavy metal concentrations, with a decrease in retardation factors resulting in an increase in heavy metal concentration.

Palygorskite-Derived Ternary Fluoride with 2D Ion Transport Channels for Ampere Hour-Scale Li-S Pouch Cell with High Energy Density.

Although various excellent electrocatalysts/adsorbents have made notable progress as sulfur cathode hosts on the lithium-sulfur (Li-S) coin-cell level, high energy density (WG ) of the practical Li-S pouch cells is still limited by inefficient Li-ion transport in the thick sulfur cathode under low electrolyte/sulfur (E/S) and negative/positive (N/P) ratios, which aggravates the shuttle effect and sluggish redox kinetics. Here a new ternary fluoride MgAlF5 ·2H2 O with ultrafast ion conduction-strong polysulfides capture integration is developed. MgAlF5 ·2H2 O has an inverse Weberite-type crystal framework, in which the corner-sharing [AlF6 ]-[MgF4 (H2 O)2 ] octahedra units extend to form two-dimensional Li-ion transport channels along the [100] and [010] directions, respectively. Applied as the cathode sulfur host, the MgAlF5 ·2H2 O lithiated by LiTFSI (lithium salt in Li-S electrolyte) acts as a fast ionic conductor to ensure efficient Li-ion transport to accelerate the redox kinetics under high S loadings and low E/S and N/P. Meanwhile, the strong polar MgAlF5 ·2H2 O captures polysulfides by chemisorption to suppress the shuttle effect. Therefore, a 1.97Ah-level Li-S pouch cell achieves a high WG of 386Whkg-1 . This work develops a new-type ionic conductor, and provides unique insights and new hosts for designing practical Li-S pouch cells.

Surface-confined two-dimensional mass transport and crystal growth on monolayer materials

Surface-confined two-dimensional mass transport and crystal growth on monolayer materials

Rationally Tunable Phase Change Material Thermal Properties Enabled by Three-Dimensionally Printed Structural Materials and Carbon-Based Functional Additives

Passive cooling using phase change materials (PCMs) is a promising solution to address thermal challenges for modern electronics, electric vehicles, and energy storage systems. The high latent heat of PCMs can significantly decrease overheating or thermal shock; however, their low thermal conductivity and unstable shape limit their practical application. Herein, we report a multiscale rational design strategy for tuning the thermal properties of PCM (octadecane), enabled by 3D-printed structural materials and multiwalled carbon nanotubes (MWCNTs)/graphene nanoplatelets (GNPs), serving as PCM reservoirs and thermally functional additives. Octadecane, used as the PCM, was thermally reinforced with MWCNT/GNP functional additives using one- and two-dimensional thermal transport at the micro-/nanoscale, and the developed nanocomposite PCM was incorporated into the 3D-printed grid structures serving two purposes: thermal transport at the macroscale and mechanical support during the liquid–solid phase change. Thus, the fabricated 3D-printed structures with incorporated thermal energy management composites (3DS-TEMCs), with different infill density/MWCNT/GNP parameters, exhibited tunable latent heat/thermophysical properties and outstanding thermal conductivity (~0.45–0.79 W/(m K)) higher than that of pure octadecane (~0.15 W/(m K)). In passive cooling tests implemented in a local heating configuration, the 3DS-TEMCs inhibited overheating and thermal shock under transient thermal loads in the operating temperature ranges of electronic devices and batteries. The proposed 3DS-TEMC offers a tunable and scalable strategy to impart PCMs with advanced thermophysical characteristics compared to conventional PCMs.

Solution of Two-Dimensional Solute Transport Model for Heterogeneous Porous Medium Using Fractional Reduced Differential Transform Method

This study contains a two-dimensional mathematical model of solute transport in a river with temporally and spatially dependent flow, explicitly focusing on pulse-type input point sources with a fractional approach. This model is analyzed by assuming an initial concentration function as a declining exponential function in both the longitudinal and transverse directions. The governing equation is a time-fractional two-dimensional advection–dispersion equation with a variable form of dispersion coefficients, velocities, decay constant of the first order, production rate coefficient for the solute at the zero-order level, and retardation factor. The solution of the present problem is obtained by the fractional reduced differential transform method (FRDTM). The analysis of the initial retardation factor has been carried out via plots. Also, the influence of initial longitudinal and transverse dispersion coefficients and velocities has been examined by graphical analysis. The impact of fractional parameters on pollution levels is also analyzed numerically and graphically. The study of convergence for the FRDTM technique has been conducted to assess its efficacy and accuracy.

Diamond Electronics and Related Wideband Gap Semiconductors for High Temperature Applications

This presentation is focused on understanding the basic science of two-dimensional carrier systems in diamond-based semiconductor electronics. Over the course of the presentation, we will present the following: • Process technology for diamond power field effect transistors (FETs) based on two-dimensional (2D) carrier transport in subsurface boron delta-doped structures • The theory of carrier transport in diamond FETs with 2D conducting channels • The results from materials and defect characterization techniques to locate, characterize, and monitor radiation-induced defects in these structures over various timescales • New research directions in applying 2D conduction channels to ultra-wide bandgap semiconductor transistors based on diamond materials as well as related wide band gap semiconductors, • Understand the dominant failure mechanisms operative in diamond-based FETs exposed to ionizing and non-ionizing radiation.

Reactive Transport Modelling of Elevated Dissolved Sulphide Concentrations in Sedimentary Basin Rocks

Groundwater with total dissolved sulphide concentrations in excess of 1.0 × 10 − 4 mol L − 1 3 mg L − 1 is relatively common at intermediate depths in sedimentary basins. However, the mechanisms responsible for the formation and spatial distribution of these sulphidic waters in sedimentary basins, which have been affected by periods of glaciation and deglaciation, are not fully understood. Sulphate reduction rates depend on many factors including redox conditions, salinity, temperature, and the presence and abundance of sulphate, organic matter, and sulphate-reducing bacteria. Two-dimensional reactive transport modelling was undertaken to provide potential explanations for the presence and distribution of sulphidic waters in sedimentary basins, partially constrained by field data from the Michigan Basin underlying Southern Ontario, Canada. Simulations were able to generally reproduce the observed depth-dependent distribution of sulphide. Sulphate reduction was most significant at intermediate depths due to anoxic conditions and elevated sulphate concentrations in the presence of organic matter in waters with relatively low salinity. The simulations indicate that glaciation-deglaciation periods increase mixing of waters at this interfacial zone, thereby enhancing rates of sulphate reduction and the formation of sulphide. In addition, the simulations indicate that glaciation-deglaciation cycles do not significantly affect sulphide concentrations in low permeability units, even at shallow depths (e.g., 25 m), while concentrations in permeable units remain stable below depths of 500 m.

Two-Dimensional Transport Dispersive Model for Separating Glycolic Acid and NaCl with Ligand Exchange Chromatography

Two-Dimensional Transport Dispersive Model for Separating Glycolic Acid and NaCl with Ligand Exchange Chromatography