Convection-diffusion Model Research Articles

Understanding the High-energy Hardening in Cosmic Ray Spectra

Abstract Recently, precise measurements on cosmic rays have been provided by various space experiments. A hardening at a few hundred GV has been observed in cosmic ray spectra both for primary and secondary particles. However, the reason for this hardening remains unclear. In this work, we employ the data measured by PAMELA, AMS02, ACE-CRIS and VOYAGER-1 to investigate this question. We study two different scenarios: the diffusion-reacceleration (DR) framework and the diffusion-convection (DC) framework. For each configuration, we investigate both the injection effects and the transport properties which may relate to the hardening. At the low-to-medium energy range, the diffusion slope δL are estimated to be 0.41 to 0.48. It is found that the value of δL estimated in the DR model is lower than that in the DC model. This infers that the reacceleration mechanism can result in steeper shapes in the (Li, Be, B)/C ratios than the convection process. At high energies, a variation in diffusion slope with Δδ ∼ −0.16 is favoured to explain the high-energy hardening structures observed in (Li, Be, B)/C ratios. Recent B/C data measured by DAMPE infers an even stronger high-energy diffusion break with Δδ ∼ −0.19.

A nonlocal convection–diffusion model with Gaussian‐type kernels and meshfree discretization

AbstractNonlocal models have demonstrated their indispensability in numerical simulations across a spectrum of critical domains, ranging from analyzing crack and fracture behavior in structural engineering to modeling anomalous diffusion phenomena in materials science and simulating convection processes in heterogeneous environments. In this study, we present a novel framework for constructing nonlocal convection–diffusion models using Gaussian‐type kernels. Our framework uniquely formulates the diffusion term by correlating the constant diffusion coefficient with the variance of the Gaussian kernel. Simultaneously, the convection term is defined by integrating the variable velocity field into the kernel as the expectation of a multivariate Gaussian distribution, facilitating a comprehensive representation of convective transport phenomena. We rigorously establish the well‐posedness of the proposed nonlocal model and derive a maximum principle to ensure its stability and reliability in numerical simulations. Furthermore, we develop a meshfree discretization scheme tailored for numerically simulating our model, designed to uphold both the discrete maximum principle and asymptotic compatibility. Through extensive numerical experiments, we validate the efficacy and versatility of our framework, demonstrating its superior performance compared to existing approaches.

Development of a Reaction–Diffusion–Convection Model and Its Application to NO Oxidation in Reactors

Development of a Reaction–Diffusion–Convection Model and Its Application to NO Oxidation in Reactors

Deformable baffles coupled with pulsatile flow improve mixing in microfluidic devices

An important objective for many microfluidic mixer devices is to attain a high level of mixing efficiency at low Reynolds numbers. Previous research incorporating rigid obstacles into microchannels has shown enhanced chaotic advection and improved mixing index; however, the increased pressure drop and corresponding shear forces within the fluid domain can create issues in biological applications. In this paper, we show how an innovative micromixer strategy, i.e., incorporating deformable baffles and utilizing pulsatile flow, results in a high level of mixing efficiency at low Reynolds numbers (Re =1.25), where diffusion is the pure mechanism of mixing. The numerical investigation involved solving the continuity, Navier-Stokes, solid mechanics, and fluid-solid interaction equations alongside a convection-diffusion model to analyze species concentration. To find the best conditions of the micromixer, the mixing index as the objective function was optimized, and various parameters, including phase difference, velocity ratio, Strouhal number, baffle distance, and Reynolds number, were investigated. Through optimization of these parameters, we show a notable improvement in the mixing index (increase from 21.7 % to 78.86 %) at a Reynolds number of 1.25 with 2 mixing units, more than 92 % mixing efficiency by using 6 mixing units, and more than 95 % mixing efficiency at a Reynolds number of 0.1. Moreover, the incorporation of deformable baffles and pulsation results in a lower pressure drop. These conditions are optimal for biological applications that require thorough mixing of the sample inputs.

RS-AAT for enhancing saturation and chloride resistance in unsaturated concrete: Experimental and numerical assessment

In this paper, the effect of RS-AAT (Reverse-seepage and Saturation based Active Anti-corrosion Technology) on chloride ion erosion and saturation of unsaturated concrete is studied. The design of partially opening of permeable pipes is proposed for partial purpose. The infiltration of chloride ions in cylindrical concrete by RS-AAT is experimentally and numerically analyzed. Based on the water vapor adsorption and adsorption isotherm test and chloride ion erosion test, a convection-diffusion model of chloride ions with varying saturation is established by using simultaneous V-G model and Richards' equation. It can be used for characterizing the effect of pore opening on saturation change and chloride ion erosion. The results show that the use of RS-AAT can accelerate the growth of concrete saturation in the alternating wet and dry zones, and keep the area in a saturated state, under the effect of reverse seepage and saturation, the durability of the structure is increased. Moreover, the opening size and spacing of the permeable pipe are especially investigated. The results recommend 8 mm opening diameter and 2 mm opening spacing, by which the opening spacing is reduced as much as possible, and the ability to resist chloride ion erosion for a long time can be improved s under the combined action of reverse seepage and saturation. The significance of these results is immense for the continued utilization of the novel anti-chloride attack technology in engineering applications.

Gradient-based adaptive neural network technique for two-dimensional local fractional elliptic PDEs

This paper introduces gradient-based adaptive neural networks to solve local fractional elliptic partial differential equations. The impact of physics-informed neural networks helps to approximate elliptic partial differential equations governed by the physical process. The proposed technique employs learning the behaviour of complex systems based on input-output data, and automatic differentiation ensures accurate computation of gradient. The method computes the singularity-embedded local fractional partial derivative model on a Hausdorff metric, which otherwise halts the computation by available approximating numerical methods. This is possible because the new network is capable of updating the weight associated with loss terms depending on the solution domain and requirement of solution behaviour. The semi-positive definite character of the neural tangent kernel achieves the convergence of gradient-based adaptive neural networks. The importance of hyperparameters, namely the number of neurons and the learning rate, is shown by considering a stationary anomalous diffusion-convection model on a rectangular domain. The proposed method showcases the network’s ability to approximate solutions of various local fractional elliptic partial differential equations with varying fractal parameters.

Studying behavior of the asymptotic solutions to P-Laplacian type diffusion-convection model

Studying behavior of the asymptotic solutions to P-Laplacian type diffusion-convection model

An Unconditionally Stable Numerical Method for Space Tempered Fractional Convection-Diffusion Models

An Unconditionally Stable Numerical Method for Space Tempered Fractional Convection-Diffusion Models

Semi-Mechanistic Prediction and Optimization of Residence Time Metrics of a Starve-Fed Extruder via a Hybrid Machine-Learning Convection–Diffusion Model

Semi-Mechanistic Prediction and Optimization of Residence Time Metrics of a Starve-Fed Extruder via a Hybrid Machine-Learning Convection–Diffusion Model

Numerical modeling of fill-level and residence time in starve-fed single-screw extrusion: a dimensionality reduction study from a 3D CFD model to a 2D convection-diffusion model

This research delves into the numerical predictions of fill-level and residence time distribution (RTD) in starve-fed single-screw extrusion systems. Starve-feeding, predominantly used in ceramic extrusion, introduces challenges which this study seeks to address. Based on a physical industrial system, a comprehensive 3D computational fluid dynamics (CFD) model was developed using a porous media representation of the complex multi-hole plate die. Validations performed using real sensor data, accounting for partial wear on auger screw flights, show an ~11% discrepancy without accounting for screw wear and ~6% when considering it. A 2D convection-diffusion model was introduced as a dimensionality reduced order model (ROM) with the intention of bridging the gap between comprehensive CFD simulations and real-time applications. Central to this model’s prediction ability was both the velocity field transfer from the CFD model and calibration of the ROM diffusion coefficient such that a precise agreement of residence time distribution (RTD) curves could be obtained. Some discrepancies between the CFD and the ROM were observed, attributed to the loss of physical information of the system when transitioning from a higher fidelity CFD model to a semi-mechanistic ROM and the inherent complexities of the starved flow in the compression zone of the extruder. This research offers a comprehensive methodology and insights into reduced order modeling of starve-fed extrusion systems, presenting opportunities for real-time optimization and enhanced process understanding.

Magnetophoresis of paramagnetic metal ions in porous media.

We report a numerical investigation of the magnetophoresis of solutions containing paramagnetic metal ions. Using a simulated magnetic field of a superconducting magnet and the convection-diffusion model, we study the transport of transition metal salts through a porous medium domain. In particular, through a detailed comparison of the numerical results of magnetophoretic velocity and ion concentration profiles with prior published experiments, we validate the model. Subsequent to model validation, we perform a systematic analysis of the model parameters on the magnetophoresis of metal ions. Magnetophoresis is quantified with a magnetic Péclet number Pem. Under a non-uniform magnetic field, Pem initially rises, exhibiting a local maximum, and subsequently declines towards a quasi-steady value. Our results show that both the initial and maximum Pem values increase with increasing magnetic susceptibility, initial concentration of metal solutes, and ion cluster size. Conversely, Pem decreases as the porosity of the medium increases. Finally, the adsorption of metal salts onto the porous media surface is modeled through a dimensionless Damkohler number Daad. Our results suggest that the adsorption significantly slows the magnetophoresis and self-diffusion of the paramagnetic metal salts, with a net magnetophoresis velocity dependent on the kinetics and equilibrium adsorption properties of the metal salts. The latter result underscores the crucial role of adsorption in future magnetophoresis research.

Mathematical Modeling of Absorption-adsorption Processes for Waste Free Decontamination of Gases from SO2 in a Bubble Tray Column

Mathematical Modeling of Absorption-adsorption Processes for Waste Free Decontamination of Gases from SO₂ in a Bubble Tray Column

Simulation study on transport characteristics of leakage gas from the condenser of power plant

Exploring the transport characteristics of leakage gas in the condenser can facilitate quicker identification of leak points when using Helium tracer gas method for detection. We construct a 3-D physical model of the condenser to simulate the Helium gas leakage process within the tube bundle. On the steam side, we adopt RNG k-?, porous media, steam condensation, and convective diffusion models to describe steam and leakage gas-flow. On the waterside, we use the tube bundle thermal resistance model to describe the steam-water heat transfer. The research concludes with three key points. When the centripetal pressure gradient is insufficient, there will be leakage gas enrichment, resulting in flowing out in the form of diffusion. When there is no centripetal pressure gradient in the tube bundle region, it will extract only a small amount of upstream leakage gas along with steam through the flow. When reaching a stable level for leakage gas, the leakage intensity is proportional to the outlets? flow rate but is independent of the transport form. The deviation of the mass-flow rate decreases with the mesh quantity increasing, which is less than 2% when the mesh quantity is over 638228. The deviation between simulated and actual values of the two parameters is less than 5%, which reveals the good agreement between numerical calculation and actual work conditions. These conclusions can assist employees and researchers in evaluating data on leak points and enhancing detection techniques.

Electroosmotic flow modulation and dispersion of uncharged solutes in soft nanochannel.

We perform a systematic study on the modulation of electroosmotic flow (EOF), tuning the selectivity using electrolyte ions and hydrodynamic dispersion of the solute band across the soft nanochannel. The supporting walls of the channel are considered to be hydrophobic and bear non-zero surface charge. For such a channel, the inner side of the supporting rigid walls of the channel are coated with a soft polyelectrolyte layer (PEL). The inhomogeneous distribution of monomers and accompanying volume charge within the PEL is modelled via soft-step function. The dielectric permittivity of the PEL and electrolyte solution are in general different, which in turn leads to the ion partitioning effect. The impact of ion steric effects due to finite sized ions is further accounted through the modified ion activity coefficient. To model the EOF modulation considering the combined impact of the ion steric and ion partitioning effects as well as inhomogeneous distribution of monomers across the PEL, we adopt the modified Poisson-Boltzmann equation as the governing equation for electrostatic potential. The Debye-Bueche model is adopted to study the flow field across the PEL and the Stokes equation governs the EOF outside the PEL. In order to study the impact of the modulated EOF field on the dispersion of uncharged solution, we adopt three different models, i.e., a general 2D convective-diffusion model as well as cross-sectional averaged dispersion models due to Gill and late-time Taylor and Aris. Going beyond the widely employed Debye-Hückel approximation and uniform distribution of the monomer as well as accompanying volume charge, we find the results for the electric double layer (EDL) potential, EOF field and averaged throughput, by tuning the ion selectivity, etc., which is sufficient to analyze the transport of ionized liquid across the channel. The numerical results are supplemented with analytical results for the EDL potential as well as the EOF field under various limiting situations. Besides, we have further shown the impact of the modulated EOF field on the solute dispersion process. We have presented results that highlight the impact of parameters related to EOF field modulation, on solute dispersion governed by a convective-diffusive process, as well as obtaining the results for an effective dispersion coefficient. The dispersion models under the modulated EOF field adopted in the present study can thus be applied to study the dispersion process in engineered microdevices.

Lattice Boltzmann convection-diffusion model with non-constant advection velocity

Lattice Boltzmann convection-diffusion model with non-constant advection velocity

Effect of Mass Fraction on Leaching Kinetics of Hydrophobic Ultraviolet Stabilizers in Low-Density Polyethylene.

The leaching kinetics of five hydrophobic ultraviolet (UV) stabilizers from low-density polyethylene (LDPE) (micro)fibers into water was evaluated in this study, with variation of the mass fraction (ω = 0.1-2.0 wt %) of the stabilizers. A one-dimensional convection-diffusion model for a cylindrical geometry, requiring partitioning between the LDPE fibers and water (KLDPEw) and the internal diffusion coefficients (DLDPE), was used to evaluate the leaching process and the leaching half-life of the target UV stabilizers at ω < 0.5 wt % (Case I). Diffusion through the aqueous boundary layer is the rate-determining step, and the leaching half-life is predicted to be very long (a few months to years) under unaffected conditions. When the UV stabilizers are supersaturated within LDPE fibers (i.e., ω > 0.5 wt %, Case II), the possible formation of a surficial crystal layer of the additives on the LDPE fiber extends the time scale for leaching compared to that in Case I due to the requirement of overcoming the crystallization energy. This study provides a fundamental understanding of the leaching profiles of plastic additives for assessing their potential chemical risks in aquatic environments; further studies under the relevant environmental conditions are required.

Numerical evaluation of heat-triggered drug release via thermo-sensitive liposomes: A comparison between image-based vascularized tumor and volume-averaged porous media models

In this study, two numerical models for controlled drug delivery through thermo-sensitive liposomes under mild microwave hyperthermia are compared. The first model simulates blood flow directly in a realistic tumor vascular network. The second one, at the volume-averaged macro scale, employs the porous media model. Using the vascular-scale approach is helpful for these kind of applications since the porous media assumption does not allow to account for local vascular blood flow, which is a crucial variable to quantify outputs like local drug accumulations. In the present study, the vascularized tumor model is obtained from a photo-acoustic scan and used as computational domain. The vascular-scale model considers heat and drug transfer in vascular and intracellular spaces, employing energy equations for heat transfer and a three-compartment convection-diffusion model for drug diffusion. Blood flow is simulated using the momentum equation for non-Newtonian fluids. The volume-averaged model shows good agreement with the vascular-scale model even if provides less precise information about temperature field distribution and drug localization within the tumor tissue. Also, the volume-averaged model underestimates Fraction of Killed Cells by 3 % post-treatment, presenting a more uniform temperature field and drug distribution compared to the vascular-scale one. Despite these small limitations, the porous media model is reliable for obtaining average results, while the vascular-scale model is suitable when more accurate results are needed. This study's findings aid those who aim to predict hyperthermia-driven drug delivery, suggesting the vascular-scale approach for precision and accuracy and the volume-averaged approach for average outcomes.

Valorization of pure poultry manure for biomass applications: Drying and energy potential characteristics

Poultry manure has gained attention as an alternative biomass. This study evaluated pure poultry manure (without adsorbent materials) by immediate analysis, scanning electron microscopy (SEM), thermal degradation (TG), and solid-state nuclear magnetic resonance spectroscopy (NMR). The drying characteristics were analyzed by operating conditions effects, and energy quality by measuring calorific value. In nature pure poultry manure has a pasty aspect and high humidity (>75 % w w−1) and dry manure, interesting energetic physicochemical characteristics, such as 65 % w w−1 volatile matter, 5 % w w−1 fixed carbon content, and a 11 MJ kg−1 calorific value. Furthermore, pure poultry manure showed characteristics also resemble those of lignocellulosic biomass materials. Samples were dried in a convective dryer with varying temperatures (60, 70, and 80 °C) and air velocity values (1.0, 1.2, and 1.8 m s−1). The drying experimental data by a convection–diffusion model to obtain the effective diffusivity and activation energy of the manure. Greater temperatures reduced resistance to moisture diffusion and influence of drying air velocity was observed from model data. Dry poultry manure enables easy transportation and shows adequate energy characteristics for use as a thermal energy source to heat poultry farms and supply some of producers’ electrical consumption.

Computational analysis of an electrostatic separator design for removal of volatile organic compounds from indoor air

ABSTRACT Concentrations of volatile organic compounds (VOCs) in air can be reduced in electrostatic separators where VOCs are ionized using ion-molecule reactions, extracted using electric fields, and eliminated in a waste flow. Embodiments for such separator technology have been explored in only a few studies, despite the possible advantage of purification without adsorbent filters. In one design, based on ionization of VOCs in positive polarity with hydrated protons as reactant ions, efficiencies for removal were measured as 30–40% . The results were fitted to a one-dimensional convective diffusion model requiring an unexpectedly high production rate of reactant ions to match both the model and data. A realistic rate of reactant ion production was used in finite element method simulations (COMSOL) and demonstrated that low removal efficiency could be attributed to non-uniform patterns of sample flow and to incomplete mixing of VOCs with reactant ions. In analysis of complex systems, such as this model, even limited computational modeling can outperform a pure analytical approach and bring insights into limiting factors or system bottlenecks. Implications: In this work, we applied modern computational methods to understand the performance of an air purifier based on electrostatics and ionized volatile organic compounds (VOCs). These were described in the publication early 2000s. The model presented was one-dimensional and did not account for the effects of flow. In our multiphysics finite element models, the efficiency and operation of the filter is better explained by the patterns of flow and flow influences on ion distributions in electric fields. In general, this work helps using and applying computational modelling to understand and improve the performance bottlenecks in air purification system designs.

Modeling of bidirectional chloride convection-diffusion for corrosion initiation life prediction of RC square piles under drying-wetting cycle

Modeling chloride penetration mechanism in unsaturated concrete is essential for corrosion initiation life prediction of marine reinforced concrete (RC) structures. This paper presents a bidirectional chloride convection-diffusion model for the chloride concentration distribution of RC square piles in the tidal and splash zone. The finite difference numerical method is used to solve the convection-diffusion governing equations with the drying-wetting cycle. The numerical model is validated by two experimental results and the analytical solution with constant surface chloride conditions. The peak value and convection depth in the chloride distribution curve of RC square piles are investigated. The results show that the periodic drying-wetting chloride environment is the dominant factor of the convection effect formed in the surface layer of the square piles. Moreover, a coupling effect is observed in the diagonal areas of square piles. The corrosion initiation life under a periodic drying-wetting chloride environment is shorter than that with constant surface chloride concentration. Furthermore, the sensitivity analysis results show that the diffusion coefficient, the concrete cover depth, and the variable rate of drying-wetting cycles are the critical parameters for predicting the corrosion initiation life of RC square piles under the drying-wetting cycle.