Diffusive Transport Research Articles

Understanding the Effects of Forced and Bubble-Induced Convection in Transport-Limited Organic Electrosynthesis

Organic electrosynthesis offers a sustainable path to decarbonize the chemical industry by integrating renewable energy in chemical manufacturing. However, achieving the selectivity and energy efficiency required for industrial applications is challenging due to the inherent mass transport limitations of most electro-organic reactions. Electrochemical reactions rely on transport of reactants to the electrode surface and become mass transport-limited when the reactant diffusion rate is lower than the reaction rate at the electrode. In organic electrosynthesis with several possible products, mass transport limitations can result in decreased selectivity towards the desired product as the various reaction pathways compete. Convection can mitigate mass transport limitations, but fundamental engineering guidelines for selecting and scaling up convection methods in electrochemical systems do not exist. As a result, the impact of convection on industrial-scale complex organic electrochemical processes remain poorly understood. Here we show that the Sherwood number (Sh)—the ratio of convective mass transport to diffusive mass transport—is a crucial metric to characterize mass transport, determine reactor performance, and enable effective scale-up. We investigate the interplay between mass transport and electrochemical reaction rates under convective flows in the context of the electrosynthesis of adiponitrile, one of the largest organic electrochemical processes in the industry. We use experiments and data-driven predictive models to demonstrate that forced liquid convection and bubble-induced convection produce nearly equivalent mass transport conditions when the corresponding Sherwood numbers are equal. This conclusion shows that the Sherwood number characterizes the mass transport condition independent of the underlying convection mechanism. Additionally, we show that the reactor performance scales with the Sherwood number for a given current density and reactant concentration. This scaling enables accurate prediction of performance irrespective of the convection method, and demonstrates that adiponitrile Faradaic efficiencies of >80% can be achieved for current densities of up to 200 mA/cm2 when Sh > 100. Our results provide guidelines for the design and selection of convection methods, from lab to industrial scale, and contribute to the development of more sustainable chemical manufacturing processes.

Optimal Design and Operation of Electrolytic Hydrogen Production and Storage System for Solar Photovoltaic Power Smoothing

Even though the increasing penetration of solar photovoltaic (PV) energy into the electric grid can reduce the carbon emission of power generation, the intermittency and variability of renewable solar energy lead to frequent and steep ramping operations of conventional fossil fuel power plants. Hydrogen production via water electrolysis using solar power can serve as a controllable load and provide a short/long duration energy storage to mitigate the grid fluctuations (i.e., PV smoothing) and improve the resiliency of power grid. The generated green hydrogen will be further stored under high pressure for subsequent utilizations (e.g., hydrogen fuel cell electric vehicle refueling).Polymer electrolyte membrane (PEM) electrolyzer with high efficiency and quick dynamic response is used to generate hydrogen [1,2]. The capacity factors of PV field and PEM electrolyzer can affect the performance of PV smoothing on the cloudy day. Even though PEM electrolyzers directly producing high pressure hydrogen are more energy efficient than ambient pressure electrolyzers followed by mechanical compression, higher pressure leads to more undesired hydrogen back diffusion to the oxygen side, which causes lower hydrogen production efficiency, cell degradation, and safety risk of hydrogen explosion limit [3,4]. Optimal design and operation of electrolyzer under fluctuating solar power are formulated based on an integrated hydrogen-based energy storage system (renewable solar coupled with green hydrogen production and storage). Different PV smoothing scenarios as well as optimal size and operation conditions of the PEM electrolyzer are investigated.The high-fidelity dynamic model of a PEM electrolyzer cell/stack is established with consideration of two-dimensional (“through-plane” and “in-plane”) mass/heat transfer coupled with electrochemical kinetics. The electrochemical reactions are considered using Butler-Volmer kinetics with varying surface molar concentrations of components. Maxwell-Stefan diffusion equation is adopted to calculate the gas-phase species molar concentration in the backing and catalyst layers. Hydrogen permeation back through membrane is included with consideration of both diffusion and convective transports as a function of operational pressure.To evaluate the transient response of the PEM electrolyzer stack, real-time PV data based on an Orlando Utilities Commission (OUC) solar farm is smoothed using the developed power signal control algorithm. The optimal PV smoothing control algorithm and the electrochemical dynamic stack model show the effectiveness of hydrogen-based energy storage system in smoothing the PV signal to improve the grid stability and flexibility.[1] Kumar, S.S. and Himabindu, V., 2019. Hydrogen production by PEM water electrolysis–A review. Materials Science for Energy Technologies, 2(3), pp.442-454.[2] Götz, M., Lefebvre, J., Mörs, F., Koch, A.M., Graf, F., Bajohr, S., Reimert, R. and Kolb, T., 2016. Renewable Power-to-Gas: A technological and economic review. Renewable energy, 85, pp.1371-1390.[3] Trinke, P., Bensmann, B., Reichstein, S., Hanke-Rauschenbach, R. and Sundmacher, K., 2016. Hydrogen permeation in PEM electrolyzer cells operated at asymmetric pressure conditions. Journal of The Electrochemical Society, 163(11), p.F3164.[4] Scheepers, F., Stähler, M., Stähler, A., Rauls, E., Müller, M., Carmo, M. and Lehnert, W., 2020. Improving the efficiency of PEM electrolyzers through membrane-specific pressure optimization. Energies, 13(3), p.612.

Investigating the Differences between the in-Situ Galvanostatic Test and Ex-Situ Fenton Test on Nafion Membranes for PEM Water Electrolysis

Perfluorinated sulfonic acid (PFSA) ionomer membranes (e.g Nafion) are widely employed as the benchmark materials for the electrolyte membranes in PEM water electrolysis (PEMWE). It is broadly acknowledged that the state of health of PFSA membranes is detrimentally impacted by the chemical degradation occurring during operation of PEMWE. The cross-over gases interacting with the catalytic surface lead to the generation of hydrogen peroxide. This compound can undergo homolytic cleavage or, in the presence of ferrous salts, yield reactive oxygen species such as hydroperoxyl (HOO.) and hydroxyl (HO.) radicals. These radicals attack the ionomer subsequently leading to chain scission, unzipping and loss of functional groups and release of HF in the effluent water. However, the degree of degradation differs when exposed to ex-situ conditions compared to real proton exchange membrane (PEM) water electrolysis conditions.This work depicts a methodical investigation of degradation of catalyst coated Nafion membranes (CCM) using a Fenton's accelerated aging experiment and in-situ test. In the Fenton's approach, the durability of Nafion 117 and catalyst coated Nafion membrane with counter ions such as ferrous ions against H2O2 was explored as a degradation factor of polymer electrolyte water electrolyser. CCMs were submerged to a solution containing ferrous ions and peroxide. Accelerated aging experiments were conducted over a period of 3-7 days. An in-situ ageing test has been performed on a MEA with and without the presence of Ferrous ions by applying galvanostatic pulses for 7 days. Experimental confirmation of degradation mechanisms has been obtained by post-mortem analysis of the MEA using microscopy and chemical analysis and mechanical investigation. To quantify the effect of water activity in Nafion and CCM chemical structure on both water diffusion and interfacial transport, pulse field gradient spin echo nuclear magnetic resonance (PFGSE-NMR) technique has been employed. Morphological characteristics before and after aging tests were also investigated. Comparative estimation of the fluoride release rate in case of both in-situ and ex-situ test was also performed. This work offers a comprehensive dataset comparing the performance of degraded membranes both in situ and ex situ.

(Digital Presentation) Multiscale Modeling of Two-Phase Transport in the Membrane Electrode Assembly of Polymer Electrolyte Membrane Fuel Cells: Effect of Relative Humidity and Temperature

Water management plays an important role in the performance and durability of polymer electrolyte membrane fuel cells (PEMFCs). Achieving enhanced water removal at high current density without membrane dehydration requires an optimal design of the membrane electrode assembly (MEA) and MEA-channel interaction depending on operating conditions. The analysis of two-phase transport is challenged by the wide range of pore sizes found in porous layer assemblies, varying from 1-100 nm in the catalyst layer (CL), 50-1000 nm in the microporous layer (MPL) and 10 µm in the gas diffusion layer (GDL), up to the millimeter-sized channel. In this work, a hybrid multiscale model is presented to describe two-phase transport and performance of a representative unit cell as a function of relative humidity (RH) and temperature [1-3]. A control volume (CV) decomposition is used to represent the multiscale pore space of the GDL, MPL and CL in terms of local effective transport properties (porosity, effective diffusivity, permeability, thermal/electrical conductivity and entry capillary pressure) [4]. The model incorporates a macroscopic continuum formulation for gas flow and species, energy, liquid-phase pressure, water dissolved in ionomer, and electronic and ionic potentials [5]. Liquid water transport is modeled by means of a multi-cluster invasion-percolation algorithm, which is coupled to the macroscopic continuum formulation by the phase-change source term of water (evaporation/condensation). Water clusters with a net condensation rate grow by invading the adjacent dry CV with the lowest entry capillary pressure, while clusters with a net evaporation rate shrink by drying the wet CV of the cluster with the lowest entry capillary pressure. An all-or-nothing invasion law is adopted for saturation in the GDL (one pore per CV), while a macroscopic description in terms of capillary pressure curve at the representative elementary volume scale (REV) is used for the MPL and the GDL (thousands to millions of pores per CV). An example of the saturation distribution in the cathode MEA is shown in Figure 1. Local saturation remains between 0.1-0.4 in REVs of the CL and the MPL, increasing up to 1 in macropores of the GDL. Water condenses preferentially under the ribs and transport by capillary action to the GDL/channel interface, where the water flow is released to the channel. The channel saturation remains low, around 0.1, due to the large gas flow velocity used in the differential cell.[1] P.A. García-Salaberri, Modeling diffusion and convection in thin porous transport layers using a composite continuum-network model: Application to gas diffusion layers in polymer electrolyte fuel cells, 167 (2021) 120824.[2] D. Zapardiel, P.A. García-Salaberri, Modeling the interplay between water capillary transport and species diffusion in gas diffusion layers of proton exchange fuel cells using a hybrid computational fluid dynamics formulation, J. Power Sources 520 (2022) 230735.[3] P.A. García-Salaberri, Effect of thickness and outlet area fraction of macroporous gas diffusion layers on oxygen transport resistance in water injection simulations, Transp. Porous Media 145 (2022) 413-440.[4] P.A. García-Salaberri, I.V. Zenyuk, A General-Purpose Tool for Modeling Multifunctional Thin Porous Media (POREnet): From Pore Network To Effective Property Tensors, Heliyon (2023), submitted.[5] P.A. García-Salaberri, A. Sánchez-Ramos, A numerical analysis of the effect of layer-scale and microscopic parameters of membrane electrode assembly in proton exchange fuel cells under two-phase conditions, J. Power Sources (2023), accepted. Figure 1. Saturation distribution in the cathode MEA of a PEMFC operated at 70 oC and RH=0.95 at high stoichiometric conditions. The current density is I=0.5 A cm-2.- Figure 1

Effect of Heterojunction Dynamics on Charge Transfer Mechanism in Type-II ZnS/MoS2 Nanocomposite

The development of novel nanocomposites holds immense potential for various applications in optoelectronics, catalysis, energy storage systems and photovoltaic applications. In this manuscript, the synthesis and comprehensive characterization of type-II ZnS/MoS2 nanocomposite synthesized by hydrothermal roue are reported. The synthesized nanocomposite was characterized by numerous analytical techniques to analyse its structural, morphological, optical, and electrochemical properties. XRD analysis revealed the presence of both ZnS and MoS2 phases in the nanocomposite, validating its successful formation. UV-visible spectroscopy (UV) was utilized to study its optical properties which revealed a band gap of 3.2 eV. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) imaging demonstrated the presence of large ZnS sheets with smaller nanoparticles of MoS2 dispersed over the surface, indicating the hierarchical structure of the composites. Cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) were performed to evaluate the electrochemical performance and charge transfer dynamics of the nanocomposite. These techniques facilitated the investigation of their suitability for solar cells. CV analysis displayed prominent reduction peaks, indicating the presence of active electrochemical sites in the nanocomposites. Furthermore, it revealed diffusion-controlled behaviour which indicates the potential of the nanocomposite for efficient solar cells. EIS analysis revealed the presence of Warburg diffusion in the Nyquist plot which indicates the possibility of efficient charge transport and ion diffusion within the nanocomposites. This shows the suitability of nanocomposite material for solar cell applications.

Out-of-Plane Electron Transport in Graphite Intercalation Compounds with Applications in Battery Anodes

Graphite intercalation compounds (GICs) are commonly used as anode materials for alkali metal-ion batteries, such as Li-ion and K-ion batteries. Although typically prepared as a low-stage intercalation compound (with a high concentration of the intercalating metal), over several electrochemical cycles, the distribution of intercalate within the graphite sample is expected to be non-uniform with domains of high-stage regions where the intercalant fraction is low [1]. The mechanism of interlayer electron transport in GICs strongly depends on the intercalation staging and temperature, and is expected to vary over the lifetime of a battery.High-stage GICs and highly oriented pyrolytic graphite (HOPG), which is the upper limit of infinite-stage GIC, have an out-of-plane electrical conductivity that exponentially increases with temperature, whereas low-stage GICs have a conductivity that decreases as a function of temperature [2, 3, 4]. Although out-of-plane electron transport in low-stage GICs can be described by a metallic conduction model, the mechanism of out-of-plane electron transport in HOPG and high-stage GICs is a hitherto unresolved problem [5]. Out-of-plane electrical conductivity for HOPG and high-stage GICs increases exponentially with temperature, which cannot be described by metallic conduction, nor by conventional impurity or defect hopping mechanisms [6].We propose a new mechanism of electron transport that takes place in HOPG and high-stage GICs at temperatures relevant to battery operation. Electrons are transferred between graphite and intercalant layers through tunneling that is enhanced by large amplitude out-of-plane phonon modes in graphite layers. Due to weak interlayer interactions in adjacent graphite layers, GICs can accommodate large amplitude phonon modes in the out-of-plane direction that locally enhance the interlayer electron tunneling probability. The tunneling enhancement is temperature dependent, and exponentially depends on the population of out-of-plane phonon modes excited at a given temperature. The expression for the conductivity 𝜎 for the phonon amplitude-driven tunneling mechanism as a function of temperature T is shown in Eq. 1; the exponential dependence of conductivity with temperature qualitatively agrees with experimental observations in HOPG and high-stage GICs. On a quantitative level, we also observe from Fig.1 that the theory agrees with experimental values for out-of-plane conductivity in HOPG.The phonon amplitude-driven tunneling mechanism of electron transport is relevant in describing the kinetic over-potential in batteries that employ layered materials as anodes in ambient temperature operating conditions, and optimally sizing the anode accounting for both electron transport and ion diffusion rates.

Monitoring the Dynamics of the Galvanic Replacement Reaction to Develop Free-Standing Electrocatalysts

Hydrogen (H2) is well-known for its potential to become the future fuel and bring a more sustainable energy system [1]. The selective electrooxidation of organic compounds from biomass appears to be a possible substitute for the kinetically slow oxygen evolution reaction (OER) at the anode, which increases the electrical energy input for a conventional water electrolysis in alkaline media [2]. However, this approach is currently impeded by limited fundamental knowledge of the different active sites of electrocatalysts. The latter can be used to control selectivity at low potential and high current density to co-generate value-added products at the anode instead of CO2 by complete oxidation. Nanostructured gold-based multi-metal electrocatalysts can meet such objectives. Particularly in the electro-valorization of cellulosic biomass at electrode potentials unfavorable to C-C bond breaking and high overall cell voltage.To develop such electrocatalysts, we have initiated a multivariate methodology to study the dynamics of galvanic replacement between silver and gold. This procedure allows us to control nanoporosity and nanoalloying in the resulting gas diffusion electrode (GDE): GDE-Ag1-xAux. GDE-Ag represents the electrode upon which Ag particles were electrochemically grown prior to reaction with Au(III). Thermodynamically, silver with E°(Ag+/Ag) = 0.8 V vs SHE (standard hydrogen electrode) can be replaced by gold with E°(AuCl4 –/Au) = 1.0 V vs SHE according to: 3Ag + xKAuCl4(aq) → 3xAgCl + xKCl + Ag3-3xAux.[2,3] From a kinetic point of view, the challenge is to capture in real time the formation of metal cages of Ag-Au alloys after a '3by1' atomic exchange that introduces nanoporosity and electronic strain as silver and gold have a similar atomic radius. To interrogate the driving force behind this redox process, we have also established an electrochemical methodology to extract quantitative data, allowing detailed capture of the mixed electrochemical and mass transport (diffusion) kinetics. As the precipitation product AgCl leads to pore fouling, we have developed an efficient methodology to trigger its instant dissolution as soon as it is formed, thus promoting the production of a high-quality alloy. As shown in Figure 1, upon injection of a KAuCl4 solution into a degassed solution in contact with the GDE-Ag electrode, the open circuit potential (OCP) begins to change. This evolution is due to the modification of the electrochemical interface as silver atoms are progressively replaced by gold atoms. Thereby, leading to a regulated potential defined either by the Ag(I)/Ag redox couple, or by the Au(III)/Au pair. Interestingly, we found that the OCP variation logically depends on initial conditions such as Ag loading on the GDE, KAuCl4 concentration, Ag particle size, etc. This fundamental knowledge has led to the synthesis of efficient electrocatalysts for the oxidation of cellulose subunits in alkaline media with an onset electrode potential much lower than OER (E < 1 V vs RHE (reversible hydrogen electrode)). Indeed, the formation of an alloy phase, the creation of nanoporosity within it and the free-standing nature amplify, through synergistic and electronic effects, the electrocatalytic efficiency. Acknowledgments This work was funded by French National Research Agency (ANR-22-CE43-0004).

Limiting Current Density in Water Vapor-Fed Polymer Electrolyte Membrane Electrolyzers

Polymer electrolyte membrane water electrolyzers (PEMWE) are a critical technology in development for addressing the need for efficient hydrogen production. In order to make hydrogen a cost-effective fuel or industrial feedstock, the overpotentials across the cell needs to be decreased and platinum-group metal loading reduced. Devising novel electrode structures that enable ultra-high current densities at low oxygen evolution reaction (OER) catalyst (e.g. Iridium oxide) loadings is one approach to achieving efficiency and cost targets. One of the overpotentials that needs to be addressed is due to mass transport limitations within the porous transport layer (PTL) and anode catalyst layer, which could be a limiting factor at ultra-high current densities. When operating at ultra-high current densities, the rate of the OER may reach a point at which oxygen gas bubbles fill the pores of the anode catalyst layer PTL, blocking access of liquid water to the anode catalyst layer. Because of this, there is a possibility that the cell will rely on water vapor diffusion through the evolving oxygen gas to deliver the water reactant to the OER catalyst. To assess the limitation of a PEMWE while relying on water vapor diffusion, a commercially manufactured membrane electrode assembly (MEA) was tested by flowing water vapor into the anode as the reactant. With the aim of identifying a limiting current density (LCD) of the electrolyzer under these conditions, potentiostatic polarization curves were obtained for a range of relative humidities (RH) and back pressures. The RH was varied to assess the impact of reactant concentration on the LCD, while the back pressure was varied to identify the impact of the molecular gas diffusion coefficient on the LCD. In this presentation, we will present our analysis of the significance of the water vapor diffusion transport resistance through the pressure-dependent resistance evaluation. Furthermore, we will discuss application of this approach to evaluating the impact of vapor operation on membrane water transport and OER reaction kinetics.

High-Capacity and Ultra-Long-Life Mg-Metal Batteries Enabled by Intercalation-Conversion Hybrid Cathode Materials.

The advancement of rechargeable Mg-metal batteries (RMBs) is severely impeded by the lack of suitable cathode materials. Despite the good cyclic stability of intercalation-type compounds, their specific capacity is relatively low. Conversely, the conversion-type cathodes can deliver a higher capacity but often suffer from poor cycling reversibility and stability. Herein, a WSe2/Se intercalation-conversion hybrid material with elemental Se uniformly distributed into WSe2 nanosheets is fabricated via a simple solvothermal method for high-performance RMBs. The uniformly introduced Se confined in WSe2 nanosheets can not only efficiently improve the conductivity of the hybrid cathodes, facilitating the fast electron transport and ion diffusion, but also provide additional specific capacity. Besides, the WSe2 can effectively inhibit the detrimental Se dissolution and polyselenide shuttle, thereby activating the activity of Se and improving its utilization. Consequently, the synergy of intercalation and conversion mechanisms endows WSe2/Se hybrids with superior reversible capacity of 252mAhg-1at 0.1Ag-1 and ultra-long cyclability of up to 5000 cycles at 2.0Ag-1 with capacity retention of 78.1%. This work demonstrates the feasibility of the strategy by integrating intercalation and conversion mechanisms for developing high-performance cathode materials for RMBs.

Integrating CoP/Co heterojunction into nitrogen-doped carbon polyhedrons as electrocatalysts to promote polysulfides conversion in lithium-sulfur batteries

Lithium-sulfur (Li-S) batteries have garnered extensive research interest as one of the most promising energy storage devices due to their ultra-high theoretical energy density. However, the sluggish reaction kinetics, abominable shuttling effect and inferior cycling stability severely restrict its practical application. Herein, a multifunctional CoP/Co@NC/CNT heterostructure host material was elaborately designed and synthesized by integrating CoP/Co heterojunction, N-doped carbon hollow polyhedrons (NC) and carbon nanotubes (CNTs). Specifically, the CoP/Co heterojunction can reconfigure the local electronic structure, resulting in a synergistic effect that enhances adsorption capacity and catalytic activity compared to CoP and Co alone. Furthermore, the CNTs-grafted NC not only provides multi-dimensional pathways for rapid electron transport and ion diffusion, but also physically restricts the diffusion of polysulfides during charge-discharge processes. Owing to these advantages, the battery assembled with the CoP/Co@NC/CNT/S cathode yields an impressive discharge specific capacity of 1479.9 mAh g−1 at 0.1C, and excellent capacity retention of 793.7 mAh g−1 over 500 cycles at 2C (∼85.5 % of initial capacity). The rational integration of multifunctional heterostructures could provide an effective strategy for designing high-efficiency nanocomposite electrocatalysts to promote sulfur redox kinetics in Li-S batteries.

Dispersivity calculation in digital twins of multiscale porous materials using the micro-continuum approach

The micro-continuum method is a novel approach to simulate flow and transport in multiscale porous materials. For such materials, the domain can be divided into three sub-domains depending on the local porosity ε: fully resolved solid phase, for which ε = 0, fully resolved pores, for which ε = 1.0, and unresolved pores, for which 0 < ε < 1.0. For such domains, the flow can be solved using the Darcy-Brinkman-Stokes (DBS) equation, which offers a seamless transition between unresolved pores, where flow is described by Darcy’s law, and resolved pores, where flow is described by the Stokes equations. Species transport can then be modelled using a volume-averaged equation. In this work, we present a derivation of the closure problem for the micro-continuum approach. Effective dispersivity tensors can then be calculated through a multi-stage process. First, high resolution images are chosen for characterizing the structure of the unresolved pores. Porosity, permeability and effective dispersivity for the unresolved parts are calculated by solving a closure problem based on Direct Numerical Simulation (DNS) in the high-resolution images. The effective dispersivity is then expressed as a function of the Péclet number, which describes the ratio of advective to diffusive transport. This relationship, along with porosity and permeability, is then integrated into the multiscale domain and the effective dispersivity tensor for the full image is calculated. Our novel method is validated by comparison with the numerical solution obtained for a fully-resolved simulation in a multiscale 2D micromodel. It is then applied to obtain an effective dispersivity model in digital twins for two multiscale materials: hierarchical ceramic foams and microporous carbonate rocks.

Online Hemodiafiltration: A New Perspective for Patients With End-Stage Renal Disease.

Introduction Online hemodiafiltration (OL-HDF) is the most effective renal replacement therapy (RRT), which allows the enhanced removal of small and large uremic toxins by combining diffusion and convective transport of solutes. Although the goal of OL-HDF is to provide greater clearance of solutes with a preference for intermediate molecules responsible for many of the complications of chronic kidney disease (CKD), the studies reported to date and their meta-analyses are conflicting in nature and do not show a significant advantage of convective therapies on patient prognosis. Materials and methods At the Clinic of Nephrology and Dialysis, University Hospital "St. Marina", Varna, Bulgaria, 41 patients were monitored in a retrospective study for a two-year period, randomized into two groups, conducting OL-HDF after dilution and hemodialysis (HD) with the aim of studying the effect of convective therapies on the clinical outcome, the achieved quality of life, and the prognosis of the patient. Results The study found a significantly higher quality of life in patients undergoing OL-HDF with significantly higher values ​​of indicators of dialysis adequacy and nutritional status, better control of the anemic syndrome with the reduction of erythropoietin doses, significantly lower frequency of episodes of intradialytic hypotension with improved recovery, and 3.6-fold lower risk of death compared with conventional dialysis. Discussion Three major randomized controlled trials have compared survival outcomes in patients receiving HD or post-dilution OL-HDF, reporting conflicting results. Meta-analyses of the published studies have also been unable to provide a clear and definitive answer regarding the potential benefits of choosing one treatment over the other. Overall mortality, anemia, phosphate control, and small molecule clearance appear to be insufficiently influenced by the treatment method. On the other hand, cardiovascular mortality, hemodynamic stability, and clearance of middle and protein-bound molecules seem to be better in patients treated with OL-HDF. Conclusions Despite the conflicting data reported so far, OL-HDF is associated with better clinical outcome and prognosis for end-stage renal disease (ESRD) patient and undoubtedly warrants extensive future study with a view to improved quality of life in the growing dialysis population.

Peridynamics modeling of coupled gas convection transport and thermal diffusion in heterogeneous porous media

Peridynamics modeling of coupled gas convection transport and thermal diffusion in heterogeneous porous media

Optimal control of variably distributed‐order time‐fractional diffusion equation: Analysis and computation

AbstractFractional diffusion equations exhibit competitive capabilities in modeling many challenging phenomena such as the anomalously diffusive transport and memory effects. We prove the well‐posedness and regularity of an optimal control of a variably distributed‐order fractional diffusion equation with pointwise constraints, where the distributed‐order operator accounts for, for example, the effect of uncertainties. We accordingly develop and analyze a fully‐discretized finite element approximation to the optimal control without any artificial regularity assumption of the true solution. Numerical experiments are also performed to substantiate the theoretical findings.

A dimensionless heat transfer coefficient for free convection that is more appropriate than Nusselt number

Heat transfer in flows created by buoyancy, or natural convection, is a widely studied topic across various disciplines spanning natural flows as well as those with engineering applications. The convective heat transfer rate on a surface is commonly represented by the Nusselt number (Nu), a ratio of convective to diffusive transport, expressed often as RanPrm, where Ra is the Rayleigh number, the buoyancy forcing parameter, and Pr the Prandtl number. Motivated by the observation that n∼1/3 for turbulent convection, which implies the heat flux is independent of the length scale (L, characteristic length related to the geometry), we propose an alternate and physically more meaningful non-dimensional heat transfer parameter, denoted by Cq. Cq is derived using only the near wall variables and does not contain L. For n=1/3, Cq is constant. Even for laminar convection, where n∼1/4, Cq∼Ra−1/12, a weak function of Ra. We show that for natural convection over several geometries and a wide range of Ra, the Cq values within a narrow range while the corresponding Nu values span several orders of magnitude. We also show that Cq is akin to the non-dimensional representation of wall shear stress, skin friction coefficient Cf. We believe that just like Cf, Cq will be an equally useful non-dimensional measure of heat transfer in natural convection flows.

Directionality of gravitational and thermal diffusive transport in geologic fluid storage.

Diffusive transport has implications for the long-term status of underground storage of hydrogen (H_{2}) fuel and carbon dioxide (CO_{2}), technologies which are being pursued to mitigate climate change and advance the energy transition. Once injected underground, CO_{2} and H_{2} will exist in multiphase fluid-water-rock systems. The partially soluble injected fluids can flow through the porous rock in a connected plume, become disconnected and trapped as ganglia surrounded by groundwater within the storage rock pore space, and also dissolve and migrate through the aqueous phase once dissolved. Recent analyses have focused on the concentration gradients induced by differing capillary pressure between fluid ganglia which can drive diffusive transport ("Ostwald ripening"). However, studies have neglected or excessively simplified important factors, namely the nonideality of gases under geologic conditions, the opposing equilibrium state of dissolved CO_{2} and H_{2} driven by the partial molar density of dissolved solutes, and entropic and thermodiffusive effects resulting from geothermal gradients. We conduct an analysis from thermodynamic first principles and use this to provide numerical estimates for CO_{2} and H_{2} at conditions relevant to underground storage reservoirs. We show that while diffusive transport in isothermal systems is upwards for both gases, as indicated by previous analysis, entropic contributions to the free energy are so significant as to cause a reversal in the direction of diffusive transport in systems with geothermal gradients. For CO_{2}, even geothermal gradients less than 10^{∘}C/km (far less than typical gradients of 25^{∘}C/km) are sufficient to induce downwards diffusion at depths relevant to storage. Diffusive transport of H_{2} is less affected but still reverses direction under typical gradients, e.g., 30^{∘}C/km, at a depth of 1000m. This reversal occurs independent of the solute's thermophobicity or thermophilicity in aqueous solutions. The entropic contribution also modifies the magnitude of flux where geothermal gradients are present, with the largest diffusive fluxes estimated for CO_{2} with a 30^{∘}C/km gradient, despite the higher diffusion coefficient of H_{2}. We find a maximum flux on the order of 10^{-13} mol/(cm^{2}s) for CO_{2} in the 30^{∘}C/km scenario; significantly lower than literature estimates for maximum convective fluxes in moderate to high permeability formations. Contrary to previous studies, we find that in diffusion and convection will likely work in concert-both driving CO_{2} downwards, and both driving H_{2} upwards-for conditions representative of their respective storage reservoirs.

Evaluation of the coupling of EMACv2.55 to the land surface and vegetation model JSBACHv4

Abstract. We present the coupling of the Jena Scheme for Biosphere–Atmosphere Coupling in Hamburg version 4 (JSBACHv4) to the ECHAM/MESSy Atmospheric Chemistry (EMAC) model. With JSBACH, the soil water bucket model in EMAC is replaced by a diffusive hydrological transport model for soil water that includes water storage and infiltration in five soil layers, preventing soil from drying too rapidly and reducing biases in soil temperature and moisture. A three-layer soil scheme is implemented, and phase changes in water in the soil are considered. The leaf area index (LAI) climatology in EMAC has been substituted with a phenology module calculating the LAI. Multiple land cover types are included to provide a state-dependent surface albedo, which accounts for the absorption of solar radiation by vegetation. Plant net primary productivity, leaf area index and surface roughness are calculated according to the plant functional types. This paper provides a detailed evaluation of the new coupled model based on observations and reanalysis data, including ERA5/ERA5-Land datasets, Global Precipitation Climatology Project (GPCP) data and Moderate Resolution Imaging Spectroradiometer (MODIS) satellite data. Land surface temperature (LST), terrestrial water storage (TWS), surface albedo (α), net top-of-atmosphere radiation flux (RadTOA), precipitation (precip), leaf area index (LAI), fraction of absorbed photosynthetic active radiation (FAPAR) and gross primary productivity (GPP) are evaluated in particular. The strongest correlation (r) between reanalysis data and the newly coupled model is found for LST (r=0.985, with an average global bias of −1.546 K), α (r=0.947, with an average global bias of −0.015) and RadTOA (r=0.907, with an average global bias of 3.56 W m−2). Precipitation exhibits a correlation with the GPCP dataset of 0.523 and an average global bias of 0.042 mm d−1. The LAI optimisation yields a correlation of 0.637 with observations and a global mean deviation of −0.212. FAPAR and GPP exemplify two of the many additional variables made available through JSBACH in EMAC. FAPAR and observations show a correlation of 0.663, with an average global difference of −0.223, while the correlation for GPP and observations is 0.564 and the average global difference is −0.001 kg carbon km−1. Benefiting from the numerous added features within the simulated land system, the representation of soil moisture is improved, which is critical for vegetation modelling. This improvement can be attributed to a general increase in soil moisture and water storage in deeper soil layers and a closer alignment of simulated TWS with observations, mitigating the previously widespread problem of soil drought. We show that the numerous newly added components strongly improve the land surface, e.g. soil moisture, TWS and LAI, while surface parameters, such as LST, surface albedo or RadTOA, which were mostly prescribed according to climatologies, remain similar. The coupling of JSBACH brings EMAC a step closer towards a holistic comprehensive Earth system model and extends its versatility.

Mathematical analysis of spin transport in topological insulators to optimize memory devices performance using numerical simulations

Understanding spin transport in topological insulators (TIs) is crucial for the development of spin-based technologies, such as magnetic memory, sensors, and quantum bits. To optimize memory device performance, we developed a comprehensive mathematical model that describes the evolution of spin density, as a function of space and time, taking into account spin-momentum locking, spin-orbit coupling, spin dynamics, and diffusive transport processes (including phonon and impurity scattering). Using numerical simulations (finite element method and Backward Euler Method) implemented in Python, we analyzed the spin transport in TIs. Our study demonstrated a critical dependence of spin transport efficiency on device length, with a maximum efficiency of 75% at a length of 8 micrometers. Beyond a critical length of 10 micrometers, efficiency recovered, reaching 80% at 14 micrometers. We observed oscillatory behavior in spin polarization, with amplitude modulation indicating constructive and destructive interference patterns. The inclusion of spin-orbit coupling and Dirac terms in our model revealed a non-uniform spin polarization distribution, with a 30% increase in polarization near the center. Defects and boundaries significantly impacted spin transport, reducing polarization by 40% near the defect region. Through optimization, we achieved a 25% increase in spin transport efficiency and a 20% enhancement in memory device performance. Our results demonstrate the crucial role of optimizing device length, material quality, and interface engineering in achieving efficient spin transport and improved memory device performance, paving the way for the development of high-performance spin-based technologies.

Solution-plasma treatment for synthesizing Ketjenblack-supported Pt (1 1 1) nanocatalysts with ultra-low overpotential for Li-O2 batteries

Reducing the loading of noble metals to achieve high catalytic activity is key to enhancing the performance and reducing the cost of lithium-oxygen (Li-O2) batteries. In this study, a highly dispersed platinum (111) catalyst supported on Ketjenblack (p-Pt/KBs) is synthesized using a novel approach that involves the interaction between solution and nonthermal plasma (SNP). The influence of different glow discharge voltages on morphology and performance of catalytic materials is investigated. The results show that the electrocatalyst prepared at 400 V has uniform Pt (111) nanocrystals embedded on Ketjenblack, achieved through plasma-induced decomposition of H2PtCl6 followed by nucleation and growth. The designed catalyst, when used as the cathode catalyst in Li-O2 batteries, demonstrates lower polarization losses with an overall overpotential of only 0.24 V compared to commercial platinum on carbon (Pt/C). The plasma effect results in significantly increased defects and grafted oxygen-containing functional groups on the support surface, providing abundant active sites conducive to anchoring of Pt nanoparticles (NPs) onto the scaffold and promoting their electronic coupling. Moreover, dominant mesopores offer ample triple-phase active zones that facilitates lithium-ion transport and rapid oxygen diffusion, further lowering energy barrier for Li2O2 decomposition and reducing the charge overpotential.

Inference of Constitutive Relation of Phase‐Separated Polymers by Integrating Physics‐Informed Neural Networks and Symbolic Regression

AbstractHarnessing data to discover the underlying constitutive relation of phase‐separated polymers can significantly advance the fabrication of high‐performance materials. This work introduces a novel data‐driven method to learn the constitutive equation of diffusional transport of polymers from spatiotemporal density field. In particular, the data‐driven method seamlessly integrated physics‐informed neural networks for inference of approximate solution of diffusivity, and symbolic regression that form explicit expressions of diffusivity. The efficacy and robustness of this method are demonstrated by learning the distinct forms of diffusivity for the phase separation of homopolymer blends with various compositions. In addition, the data‐driven method is generalized to extract the constitutive relation of homogenous chemical potential in the phase separation of homopolymer blends. The data‐driven framework shows the potential for model discovery of nonlinear dynamic system from the spatiotemporal state variables.