Solid Diffusion Research Articles

Conjugate fluid, heat and species transports inside an enclosure containing miscellaneous solid arrays: General models of electronic cooling and pollutant removals

Double-diffusive natural convection in a vertical enclosure containing various solid block arrays is numerically and analytically investigated in present work, where heat and species source and sink are simultaneously attached on the walls. Rayleigh number, buoyancy force ratio, number of inner solid blocks, solid thermal conductivity and mass diffusion coefficient have been varied to observe inherent flow structures and mechanism of thermal and mass transports, regarding of different levels of solid-to-fluid volume ratios. Correlations have been presented for different flow regimes, namely thermal buoyancy driven flow and solutal buoyancy driven flow. Simulation and correlation results demonstrate that influences of thermal conductivity and mass diffusion coefficient of the solid block arrays on average Nusselt and Sherwood numbers are not evident compared with that of Rayleigh number. Furthermore, there is a positive correlation between average Nusselt number and Sherwood number. In addition, under certain values of Rayleigh number, absolute values of buoyancy force ratio close to unity will cause multiple steady solutions in pure natural convection. This research could benefit the future thermal and species management for electronics and built environment.

Single atom catalysts by atomic diffusion strategy

The depletion of energy and increasing environmental pressure have become one of the main challenges in the world today. Synthetic high-efficiency catalysts bring hope for efficient conversion of energy and effective treatment of pollutants, especially, single-atom catalysts (SACs) are promising candidates. Herein, we comprehensively summarizes the atomic diffusion strategy, which is considered as an effective method to prepare a series of SACs. According to the different diffusion forms of the precursors, we review the synthesis pathways of SACs from three aspects: gas diffusion, solid diffusion and liquid diffusion. The gaseous diffusion method mainly discusses atomic layer deposition (ALD) and chemical vapor deposition (CVD), both of which carry out gas phase mass transfer at high temperatures. The solid-state diffusion method can be divided into nanoparticle transformation into single atoms and solid atom migration. Liquid diffusion mainly describes the electrochemical method and the molten salt method. We hope this review can trigger the rational design of SACs.

Experimental investigation and mass transfer modelling of 3D printed monolithic cation exchangers

3D printing has recently found application in chromatography as a means to create ordered stationary phases with improved separation efficiency. Currently, 3D printed stationary phases are limited by the lack of 3D printing materials suitable for chromatographic applications, and require a strict compromise in terms of desired resolution, model size and the associated print time. Modelling of mass transfer in 3D printed monoliths is also fundamental to understand and further optimise separation performance of 3D printed stationary phases. In this work, a novel 3D printing material was formulated and employed to fabricate monolithic cation exchangers (CEXs) with carboxyl functionalities. CEXs were printed with ligand densities of 0.7, 1.4, 2.1 and 2.8 mmol/g and used in batch adsorption experiments with lysozyme as model protein. All CEXs demonstrated high binding strength towards lysozyme, with maximum binding capacities of up to 108 mg/mL. The experimental results were described using mass transfer models based on lumped pore diffusion and lumped solid diffusion mechanisms adapted to reflect the complex geometry of the 3D printed monoliths. An exact 3D model as well as less computationally demanding 1D and 2D approximations were evaluated in terms of their quality to capture the experimental trend of batch adsorption kinetic data. Overall, the model results indicate that mass transfer in the fabricated CEXs is mostly controlled by pore diffusion at high protein concentrations in the mobile phase, with solid diffusion becoming important at low protein concentrations. Also, the kinetic data were approximated equally well by both the full 3D model as well as the 2D approximation, indicating leaner mathematical models of lower dimensionality can be employed to describe mass transfer in complex three dimensional geometries. We believe this work will help spur the development of 3D printable materials for separations and aid in the development of quantitative platforms to evaluate and optimise the performance of 3D printed monoliths.

A quantum annealing approach to ionic diffusion in solids

We have developed a framework for using quantum annealing computation to evaluate a key quantity in ionic diffusion in solids, the correlation factor. Existing methods can only calculate the correlation factor analytically in the case of physically unrealistic models, making it difficult to relate microstructural information about diffusion path networks obtainable by current ab initio techniques to macroscopic quantities such as diffusion coefficients. We have mapped the problem into a quantum spin system described by the Ising Hamiltonian. By applying our framework in combination with ab initio technique, it is possible to understand how diffusion coefficients are controlled by temperatures, pressures, atomic substitutions, and other factors. We have calculated the correlation factor in a simple case with a known exact result by a variety of computational methods, including simulated quantum annealing on the spin models, the classical random walk, the matrix description, and quantum annealing on D-Wave with hybrid solver . This comparison shows that all the evaluations give consistent results with each other, but that many of the conventional approaches require infeasible computational costs. Quantum annealing is also currently infeasible because of the cost and scarcity of qubits, but we argue that when technological advances alter this situation, quantum annealing will easily outperform all existing methods.

Fully Coupled Large Eddy Simulation-Conjugate Heat Transfer Analysis of a Ribbed Cooling Passage Using the Immersed Boundary Method

Abstract The study focuses on evaluating fully coupled conjugate heat transfer (CHT) simulation in a ribbed cooling passage with a fully developed flow assumption using large eddy simulation (LES) with the immersed boundary method (IBM-LES-CHT). The IBM-LES and the IBM-CHT frameworks are validated by simulating purely convective heat transfer in the ribbed duct, and a laminar boundary layer flow over a 2D flat plate with heat conduction, respectively. For the main conjugate simulations, a ribbed duct geometry with a blockage ratio of 0.3 is simulated at a bulk Reynolds number of 10,000 with a conjugate boundary condition applied to the rib surface. The nominal Biot number is kept at 1, which is similar to the comparative experiment. It is shown that the time scale disparity between turbulent fluid flow and heat conduction in solid can be overcome by using an artificially high solid thermal diffusivity. While the diffusivity impacts the instantaneous fluctuations in temperature and heat transfer, it has an insignificant effect on the predicted Nusselt number. Comparison between IBM-LES-CHT and iso-flux heat transfer simulations shows that the iso-flux case predicts higher local Nusselt numbers at the back face of the rib. Furthermore, the local Nusselt number augmentation ratio (EF) predicted by IBM-LES-CHT is compared with experiment and another LES conjugate simulation. The present LES calculations predict higher EFs on the leading face of the rib and show a different trend at the trailing face when CHT is activated.

Improved stability and efficiency of perovskite via a simple solid diffusion method

CsPbBr3 perovskite quantum dots (QDs) have excellent properties such as high emission quantum yield, adjustable spectrum, and wide color range. They have potential prospects in light-emitting diode (LED) displays and solar cells. However, CsPbBr3 QDs suffer from a low stability with a high sensitivity to water, heat, and light. Here, for the first time, we report a simple method to improve their stability using a high-temperature solid state diffusion to synthesize highly stable and high-quality CsPbBr3 QDs in a small pore size LTA zeolite (0.41 nm). First, the mixture of PbBr2, CsBr and LTA zeolite was heated at 650 °C, and the raw materials PbBr2 and CsBr were diffused into the LTA zeolite through a small aperture. Then, the CsBr/PbBr2 in the composite was reassembled into CsPbBr3 QDs (CsPbBr3@LTA) at room temperature. The CsPbBr3@LTA obtained by this synthesis method have a high photoluminescence quantum yield (PLQY ∼66%) and extremely high stability. The PLQY of CsPbBr3@LTA remained above 66% after being kept in the air for 17 months. The PL intensity of CsPbBr3@LTA remained 78% of the initial value after being immersed in water for 554 days and the PL intensity changed insignificantly after laser irradiation for 20 days.

Kinetics of the Boride Layers Obtained on AISI 1018 Steel by Considering the Amount of Matter Involved

Boride layers are typically used to combat the wear and corrosion of metals. For this reason, to improve our knowledge of the boriding process, this research studied the effect of the size of the treated material on the kinetics of the growth of the boride layers obtained during a solid diffusion process. The purpose was to elucidate how the layers’ growth kinetics could be affected by the size of the samples since, as the amount of matter increases, the amount of energy necessary to make the process occur also increases. Furthermore, the level of activation energy seems to change as a function of the sample size, although it is considered an intrinsic parameter of each material. Six cylindrical samples with different diameters were exposed to the boriding process for three different exposure times (1.5, 3, and 5 h). The treatment temperatures used were 900, 950, and 1000 °C for each size and duration of treatment. The results show that the layer thickness increased not only as a function of the treatment conditions but also as a function of the sample diameter. The influence of the sample size on the growth kinetics of the boride layers is clear, because the growth rate increased even though the treatment conditions (time and temperature) remained constant.

Single-molecule observation of diffusion and catalysis in nanoporous solids

Nanoporous solids, including microporous, mesoporous and hierarchically structured porous materials, are of scientific and technological interest because of their high surface-to-volume ratio and ability to impose shape- and size-selectivity on molecules diffusing through them. Enormous efforts have been put in the mechanistic understanding of diffusion–reaction relationships of nanoporous solids, with the ultimate goal of developing materials with improved catalytic performance. Single-molecule localization microscopy can be used to explore the pore space via the trajectories of individual molecules. This ensemble-free perspective directly reveals heterogeneities in diffusion and diffusion-related reactivity of individual molecules, which would have been obscured in bulk measurements. In this article, we review developments in the spatial and temporal characterization of nanoporous solids using single-molecule localization microscopy. We illustrate various aspects of this approach, and showcase how it can be used to follow molecular diffusion and reaction behaviors in nanoporous solids.

In-situ transformational mycelium-like metal phosphides-encapsulated carbon nanotubes coating on the stainless steel mesh as robust self-supporting electrocatalyst for water splitting

Herein, In-situ conversional mycelium-like metal phosphides-encapsulated N, P co-doped carbon nanotubes (CNTs) coating on the stainless steel mesh (PSD-SM) as self-supporting electrocatalyst was fabricated via solid-diffusion (SD) and phosphorization process, which was the first time to fabricated the “chainmail for catalysts” use stainless steel mesh worked as self-reaction template and electrode-base materilas. The in-situ transformational mycelium-like CNTs array structure greatly enhanced the specific surface area of steel mesh and the graphitized carbon layer coating with high capacitance increases the electrochemical active sites. And the subsequent phosphorization treatment further improved the intrinsic catalytic activity of the material. PSD-SM exhibits the low overpotential of 231 mV at 10 mA·cm−2 with a Tafel slope of 88 mV·dec−1 for OER and 172 mV at 10 mA·cm−2 with a Tafel slope of 125 mV·dec−1 for HER. Further more, there are only 1.77 V deliver potential for water electrolysis of PSD-SM at 10 mA·cm−2 and the kinetic mechanism of as-fabricated samples for HER and OER was analyzed by Tafel slope and other measurement. This report provides an promising method to prepare efficient and robust electrocatalytic materials based on steel mesh for practical application.

Numerical Investigation of the Centrifugal Compressor Stability Improvement by Half Vaned Low Solidity Diffusers

Centrifugal compressors for the fuel cell vehicles often operate near the surge line compared with the turbocharger compressors. Low solidity and half vaned diffusers are recognized as good ways to improve the stability of the centrifugal compressor. The presented work investigated four diffuser configurations (i.e., the vaneless diffuser (VLD), full-height low solidity vaned diffuser (LSVD), hub-side half vaned diffuser (HVD) and shroud-side half vaned diffuser (SVD)) through steady-state and unsteady numerical simulations. The results show that the best performance is achieved by the LSVD, HVD and SVD at the design, surge and choke conditions. The flow rate at the surge operating point of the HVD has decreased by 15.53% compared with the LSVD, and 9.21% compared with the VLD. At near surge operating point, a longitudinal suction side passage vortex is formed on the hub of the LSVD and rotates as circumferential stall cells. A hairpin vortex is formed along the leading edge and is dragged by the main flow along the suction side as a local vortex shedding. The mechanism of the stability improvement by half vaned diffusers is that the tip leakage vortex migrates from the clearance side to the vane mounting side and replenishes the low-momentum zone on the mounting side. The best position where the half vaned diffuser should be mounted is based on the impeller outlet flow conditions, namely, the location of the wake region, where the meridional velocity and relative stagnation pressure is low.

Leaching Kinetics of Rare Earth Elements in Phosphoric Acid from Phosphate Rock

Phosphate rock has been considered as one of the most significant secondary rare-earth resource, and the utilization of rare earth elements (REEs) in phosphate rock has attracted increasing attention. In this study, the leaching kinetics of REEs from a phosphate ore from China was studied with the variation of temperature and phosphoric acid concentration under the conditions: ratio of liquid to solid of 12 mL/g, stirring speed of 120 r/min, and phosphate particle size of −0.074 mm amounts 61.1%. The results suggest that there were two distinct stages in leaching process and kinetics of both stages followed shrinking core model. At fast reaction stage, the semi-empirical equation describing the kinetics was 1 − 3(1 − α)2/3 + 2(1 − α) = 1.885CH3PO40.89exp(−11220/8.31T)t. The semi-empirical equation for slow reaction stage was 1 − 3(1 − α)2/3 + 2(1 − α) = 0.299CH3PO42.50exp(−18720/8.31T)t. Using shrinking core model and time-to-a-given-fraction method, we found that leaching rate of fast reaction stage was controlled by solid product layer diffusion, and both solid product layer diffusion and chemical reaction determined slow reaction stage.

Cu Plating with Sn and Subsequent Bronze Formation under Mild Conditions

In a well-known bronze plating experiment, a Cu coupon is subjected to Sn plating and heating with a Bunsen burner. Currently, aqueous NaOH or HCl is typically used as the plating solution; however, the use of a strong acid or base provides operational risks, particularly in educational settings (e.g., schools). Herein, we introduce a modified method that uses aqueous NaHSO4 as the plating solution. This method reduces the operational risks and allows for the smooth deposition of silver-white Sn onto the Cu coupon in a higher yield than that obtained by the HCl method, which uses 30 times the concentration of the solute. When the Sn-plated Cu coupon is heated, it changes to bronze plating. This experiment is ideal for high school students, as it allows them to observe metal plating and solid diffusion.

Dependence of Heat Transport in Solids on Length-Scale, Pressure, and Temperature: Implications for Mechanisms and Thermodynamics.

Accurate laser-flash measurements of thermal diffusivity (D) of diverse bulk solids at moderate temperature (T), with thickness L of ~0.03 to 10 mm, reveal that D(T) = D∞(T)[1 − exp(−bL)]. When L is several mm, D∞(T) = FT−G + HT, where F is constant, G is ~1 or 0, and H (for insulators) is ~0.001. The attenuation parameter b = 6.19D∞−0.477 at 298 K for electrical insulators, elements, and alloys. Dimensional analysis confirms that D → 0 as L → 0, which is consistent with heat diffusion, requiring a medium. Thermal conductivity (κ) behaves similarly, being proportional to D. Attenuation describing heat conduction signifies that light is the diffusing entity in solids. A radiative transfer model with 1 free parameter that represents a simplified absorption coefficient describes the complex form for κ(T) of solids, including its strong peak at cryogenic temperatures. Three parameters describe κ with a secondary peak and/or a high-T increase. The strong length dependence and experimental difficulties in diamond anvil studies have yielded problematic transport properties. Reliable low-pressure data on diverse thick samples reveal a new thermodynamic formula for specific heat (∂ln(cP)/∂P = −linear compressibility), which leads to ∂ln(κ)/∂P = linear compressibility + ∂lnα/∂P, where α is thermal expansivity. These formulae support that heat conduction in solids equals diffusion of light down the thermal gradient, since changing P alters the space occupied by matter, but not by light.

Mechanically robust and self-healable perovskite solar cells

Skin-like self-healing electronics have been pursued for decades with limited success. The trade off between excellent electronic properties and suitable rheological properties do not allow high-performance inorganic semiconductor materials to be self-healable. Here, we report a mechanically self-healable hybrid halide perovskite semiconductor. A molecularly tailored self-healing polymer is incorporated into a polycrystalline perovskite thin film to form a composite with a bi-continuous interpenetrating network. This composite heals using synergistic grain growth and solid diffusion processes at slightly elevated temperatures. Mechanically robust and self-healable perovskite solar cells are fabricated with power conversion efficiencies over 10% and excellent stability. The healable composite is presented in flexible devices retaining 94% of their power conversion efficiency after 3,000 bending cycles and 80% performance recovery after extreme bending. These results foreshadow the use of polymer-perovskite hybrid materials for ultra-flexible and wearable energy-harvesting devices and demonstrate the effectiveness of marrying dissimilar materials to achieve unique functionalities.

Investigation of Bonding Strength of Al Solid Phase Diffusion Bonded Joint with Surface Treatment Using Electrolyzed Water

In this study, the effect of surface treatment of Al with alkaline (pH 10.5 and pH 12.4) and acidic (pH 3.7) electrolyzed water was investigated on bonding strength of solid phase diffusion bonded Al. Aluminum hydroxide and hydroxyl groups were appeared on the surface of Al which was treated with alkaline electrolyzed water of pH 12.4 at 323 K for 2700 s. It was found that such treatment is similar to the one with NaOH aqueous solution at 323 K for 30 s. For bonding strength, shear strength of the bonded Al specimens treated with electrolyzed water of pH 12.4 at 293 K for 3 s and 30 s were higher than that of the untreated specimen.

Rotating cylinder and magnetic field on solid particles diffusion inside a porous cavity filled with a nanofluid

This study deals with the roles of a magnetic field and circular rotation of a circular cylinder on the dissemination of solid phase within a nanofluid-filled square cavity. Two wavy layers of the non-Darcy porous media are situated on the vertical sides of a cavity. An incompressible smoothed particle hydrodynamics (ISPH) method was endorsed to carry out the blending process concerning solid phase into nanofluid and porous media layers. Initially, the solid phase is stationed in a circular cylinder containing two open gates. Implications of a buoyancy ratio ( N = −2: 2), Hartmann number ( Ha = 0: 100), rotational frequency [Formula: see text], Darcy parameter [Formula: see text], Rayleigh number [Formula: see text], nanoparticles parameter [Formula: see text], and amplitude of wavy porous layers [Formula: see text] on the lineaments of heat/mass transport have been carried out. The results revealed that the diffusion of the solid phase is permanently moving toward upward except at opposing flow mode [Formula: see text] toward downward. The lower Rayleigh number reduces the solid-phase diffusions. A reduction in a Darcy parameter lessens the nanofluid speed and solid-phase diffusions in the porous layers. A reduction in [Formula: see text] from [Formula: see text] to [Formula: see text] diminishes the maximum of streamlines [Formula: see text] by 13.19% at [Formula: see text], by 46.75% at [Formula: see text], and by 74.75% at [Formula: see text].

Finite element implementation of coupled hydro-mechanical modeling of transversely isotropic porous media in DEAL.II

In geotechnical engineering, modeling geo-structures is challenging, particularly in cases where the interaction between the structures and soil or rock is complex. Most well-known commercial modeling software is based on homogenous and isotropic materials. However, soil and rock are often modeled in heterogeneous and anisotropic media because of the inherent anisotropy of sedimentary rock masses and their stratified structure. In recent decades, coupled hydro-mechanical (HM) interactions in isotropic porous media have been studied; however, the behavior of transversely isotropic porous media is rarely considered. In addition, it is difficult for commercial software such as Plaxis and Flac3D to express complex rock formation where the anisotropy of the material and the associated cracks and fractures could be assembled into a single model. In this study, a finite element implementation using Differential Equation Analysis Library (DEAL.II), an open-source library of finite element codes, was developed to model the fully coupled HM behavior of transversely isotropic porous media. The proposed implementation can be applied to both isotropic and transversely isotropic porous media based on Biot’s theory. The developed code can be used to model poroelastic media with (1) equations of linear elasticity for the solid matrix and (2) diffusion equations for fluid flow based on mass and linear-momentum conservation laws. We verified the performance and accuracy of the code through two examples, i.e., Mandel’s problem with a compared analytical solution and a tunnel excavation process with the Flac3D software. On the basis of these numerical applications, we present the code to model the behavior of various geo-structures such as tunnels and pile–soil interactions with anisotropic materials.

Selective enrichment and separation of Ag(I) from electronic waste leachate by chemically modified persimmon tannin

A 2,5-dimercapto-1,3,4-thiadiazole (DMTD)-immobilized and persimmon tannin (PT)-based biosorbent, DMTD-PT, was synthesized via a one-pot method and used for selective enrichment of Ag(I) from electronic waste (e-waste) leachate. Batch adsorption revealed that both PT and DMTD-PT had a weaker affinity for co-existing metal cations. However, DMTD-PT and PT adsorbed 98.7% and 20.7% of Ag(I), respectively, with a dose of 5.0 g L−1 each at pH 3.0 from e-waste leachate that contained 117.3 mg L−1 of Ag(I) at room temperature. These observations indicate that the selectivity of DMTD-PT is superior to that of PT. The column adsorption further proved that DMTD-PT can be used to separate Ag(I) from e-waste leachate. The adsorption of Ag(I) on DMTD-PT fit the Langmuir isotherm well with a maximum adsorptive capacity of 50.7 mg g−1. A thermodynamics study further indicated that the adsorption was spontaneous and was dominated by chemisorption. The two mass transfer models of homogeneous solid diffusion model (HSDM) and a Linear Driving Force (LDF) model were used to study the kinetics and generally well fitted the experimental data. Analyses of Fourier transform infrared spectroscopy (FTIR) and X-ray photoelectron spectroscopy (XPS) of fresh and Ag(I)-adsorbed DMTD-PT further revealed that the plausible adsorption mechanism was principally attributable to the complexation of N and S on the diazole ring. Also, DMTD-PT exhibited better reusability and qualified durability without a distinct decrease in Ag(I) adsorption even after 5 repeated cycles.

Pore/skeleton structure and compressive strength of porous Mo3Si-Mo5Si3-Mo5SiB2 intermetallic compounds prepared by spark plasma sintering and homogenization treatment

Next to aluminum-based porous alloys, porous Mo-Si-B intermetallic compounds are the most promising filtration and separation material to handle harsh service conditions of ultra-high-temperature corrosive environment. Porous Mo3Si-Mo5Si3-Mo5SiB2 intermetallics were fabricated by a two-step method of spark plasma sintering (SPS) and homogenization treatment (HT) using Mo, Si, and B as the starting powders. In addition, the evolution of the pore/skeleton structure and compressive behavior of porous Mo3Si-Mo5Si3-Mo5SiB2 intermetallic compounds by the two-step method was investigated. In SPS, the phase transformation included a solid–liquid reaction and solid–solid diffusion, and the pore structure changed significantly with the increase of sintering temperature. By HT, smooth skeletons and size centralized pores were obtained. With the increase in the HT time, the precise control of pore/skeleton structure parameters was achieved while simultaneously maintaining stable porosity. Combined SPS+HT led to a wide range of porosities, and pore/skeleton parameters were controlled by the sintering temperature and SPS pressure. Compression test results indicate that the porous Mo3Si-Mo5Si3-Mo5SiB2 intermetallics do not exhibit a plastic deformation ability at room temperature and that the transgranular cleavage fracture dominates the crack propagation in the skeletons. The quantitative relationship between porosity and compressive strength was established by σc = σc0 × (1 – ρ)1/J. The effect of HT on the pore structure factor J was revealed: at constant porosity, the strength can be increased by the increase in the J value via HT.

A review to the specific problems of nano thermal physics

The paper is devoted to three current problems that related to thermal transfer in the solid-state nanostructures. The first task is the analysis of interaction of phonons with rough solid boundaries, the presence of which leads to a significant increase in the resistance to heat transfer in nanostructures. This fundamental problem is discussed in a connection to the theoretical formulation of rough interface between solids. The second task is exploring methods to calculate diffusion and heat transfer in solids within the framework of detailed consideration of phonon interaction processes. The development of the computational model that adequately represents the physics of interaction processes and allows to calculate thermal properties that are in a good agreement with experimental data remains open. The third task is to calculate the thermal bound-ary conductance. The problem is solved by considering the processes of scattering and refraction of elastic waves at the interface. For the first time, the dispersion properties of elastic waves are taken into account in the problems of this kind. The result is the applicability of the new model in a much wider temperature range than in the existing models.