Diffusivity Ratio Research Articles

The Combined Effect of Coriolis Force and Double Diffusive for the Convention in a Rectangular Isotropic and Anisotropic Porous Channel

The combined effects of Coriolis force, heat, and mass diffusion for the convection in a horizontal rectangular channel filled with fluid in both isotropic and anisotropic porous channels is studied in the three-dimensional case for which the governing equations with the boundary conditions are derived with the help of the following assumptions: the fluid is incompressible; the flow is axisymmetric about the y-axis; the fluid is steady; thermal diffusion is larger than the viscous diffusion. With the help of the stream function, the resultant equations are made dimensionless, and non-dimension parameters like Rac, Rs along with anisotropic aspect ratio of permeabilities and thermal diffusivities are introduced. Later, the resulting linear partial differential equations are solved by the method of Fourier series analysis. The effect of the non-dimensional numbers plays a vital role in controlling parameters like velocity, temperature, and concentration for both isotropic and anisotropic cases. The expression for critical Rayleigh number has been established for both isotropic and anisotropic cases. Various computations are carried out in order to study the effects of velocity, temperature, concentration, and Critical Rayleigh number for different values of non-dimensional parameters. The obtained results are in good agreement with previous literary works and also have a wide application in the real world which can be seen in different industries.

Effect of Three Types of Gravity Modulation on Rivlin Ericksen Nanofluid Saturated in Porous Medium with Internal Heating

In this paper, authors have studied the Rivlin-Ericksen elastico-viscous nanofluid thermal instability with internal heating under three types of gravity modulation in a horizontal layer of porous medium using both linear and nonlinear ways. Linear stability analysis is done using normal mode approach, whereas nonlinear stability analysis is done using truncated Fourier series method. The results demonstrate that the internal heating, modified diffusivity ratio, and concentration Rayleigh number advance the initiation of convective motion in the system. On the other hand, Darcy number stabilize the system. To understand the behaviour of mass/heat transfer in the system two different approaches viz Mathematica NDSolve and Runge-Kutta-Fehlberg method (RKF-45) are used, and it is found that the rate of heat/mass transfer is exactly the same in both cases. In comparison to other gravity modulation profiles, day-night gravity modulation profile accelerates mass/heat transfer more quickly than the other two types of gravity modulation profiles. Steady state graph has demonstrated, convection occurs earlier when internal heating and amplitude values are increased. Moreover, it is also observed that heat/mass transport is very much affected by the variation of kinematic viscoelasticity parameter.

Anomalous enhancement of energy transfer using two-phase hybrid nanofluid across an elongational sheet with binary chemical species on the sheet surface

The Tiwari-Das nanofluid model has a serious anomaly, while estimating the mass and energy transport rates. Due to the absence of clear correlations and the fact that desirable parameters fluctuate with the characteristics of nanofluids, make it unable for precise predictions. To overcome on this dispute the Tiwari-Das model is coupled with Buongiorno's theory in the current model. The Eyring-Powell fluid with suspended Zinc oxide (ZnO) and iron (Fe2O3) keeping different volume percentage of nanoparticles are used to create a fluid mixture. The flow originates due to stretching sheet. The flow is subjected to upright Lorentz forces, while binary chemical species are consider on the sheet surface and far field. Furthermore, the ratio, reaction diffusion and frictional dissipation are also considered. The dimensionless governing equations are reduced to first order employing shooting mechanism and solved computationally using RK-4 approach. The outcomes for frictional coefficient, energy and mass transfer rate of hybrid nanoparticles and chemical species are reviewed using various statistical charts. From the computational outcomes for drag coefficient, we can adjudged that the frictional coefficient diminished on escalating fluid primary parameter and magnetic number. Increased percentage of nanoparticles, also detract the frictional coefficient. The mechanism of slip for nanoparticles are encouraging for energy transfer. The enhancement of energy and mass is significant with diffusion ratio parameter Nbt. The influence of Lewis number is diminishing function of mass transport rate. The effect of homogenous reaction is encouraging for mass transport, while the heterogeneous and Schmidt number are diminishing.

Numerical calculation of unsteady MHD nanofluid flow across two fluctuating discs with chemical reaction and zero mass flux

AbstractThe fluid flow across spinning discs has several applications in different fields of engineering such as flywheels, gas turbine engines, brakes, and gears. The significance of heat source, Hall current, and magnetic field on the nanofluid flow between two spinning disks is studied in the present analysis. The upper disk spins as well as rotates, which generates the 3D flow. The evaluation and modeling of the mass density, flow motion, and energy transfer are performed using a system of partial differential equations (PDEs). The computational technique parametric continuation method (PCM) is employed to solve the modeled equations. The outcomes are relatively compared to the published literature for validity purposes. It has been noticed that during the downward motion of the upper disc, the effect of the magnetic field declines, while the influence of the hall current improves the velocity field. The temperature field rises with the ascending motion of the upper disk, whereas it shrinks with the downhill oscillation. Moreover, the mass diffusion ratio develops with the impact of hall current, while lessens with the influence of chemical reaction.

Modelling heat-mass transport for MHD Eyring-Powell hybrid nanofluid over an expanding surface laden by autocatalytic chemical reaction and nanoparticles diffusion

Prior hybrid nanofluid research is restricted to single or two-phase models, which were dominated by homogeneous nanofluid models. These models adhere a serious flaw with the heat-mass transfer indices. To handle this problem, we develop an entirely novel hybrid nanofluid models based on the fundamental slip mechanisms of nanofluids induced by Brownian and thermophoretic diffusion as well as the chemical reaction of binary species. The laminar flow of MHD rheological model with suspended nanoparticles is striking at the stagnation region laden over a stretching surface. In order to reach the real world scenario, the expression of radiative heat, non-uniform heat source and frictional heating are all included. The coupled Buongiorno's model and Tiwari-Das mixtures models incorporate the effect of particles diffusion and volumetric friction, respectively. It is hypothesized that first order kinetics can describe homogeneous events in the immediate proximity, while isothermal cubic autocatalysis kinetics frequently describe heterogeneous reactions occur on the sheet surface. The restructured mathematical equations are solved with a proficient Runge Kutta Fehlberg technique together with the shooting procedure. According to the outcomes, the presence of higher magnetic field diminished the flow and velocity gradient. The effect of elastic parameters is diminishing frictional coefficient. The effect of first and second Brownian (Nb1, Nb2) and thermophoretic parameters (Nt1, Nt2) are similar for temperature. The mass-heat transfer rate is significant with higher estimations of diffusivity ratio Nbt. The momentum rate of diffusion outweighs the species diffusion rate as the Schmidt number increases, resulting in a decrease in concentration values. Higher intensities of Lorentz's force results in denser streamlines. The streamlines split into an opposite direction because of stagnation point.

Effect of non-isothermal adsorption model on gas diffusion in coal particle

Gas diffusion is of great importance for coalbed methane (CBM) recovery and CO2 storage in coal seam. Most of the existing models of gas diffusion in coal particles are derived under isothermal conditions, while the coupled effect between gas adsorption/desorption and temperature variation is often neglected. The effect of accurate non-isothermal adsorption model on gas diffusion simulation also needs further study. In this work, isothermal adsorption tests of CO2 in anthracite/bitumite particles at different temperatures are conducted. The fitting results of Langmuir/Freundlich adsorption models are analyzed and the optimal non-isothermal adsorption models for anthracite/bitumite are obtained respectively. Non-isothermal desorption-diffusion tests of CO2 in anthracite/bitumite particles are carried out and corresponding non-isothermal desorption-diffusion model is also proposed, based on which the effect of non-isothermal adsorption model on gas diffusion in coal is numerically analyzed comprehensively. The results show that the non-isothermal Langmuir/Freundlich adsorption models are optimal for anthracite/bitumite respectively. Based on the optimal adsorption models, simulated gas diffusion amounts agree well with the experimental results and consistent diffusion coefficients can be back calculated. For sub-optimal adsorption model with R2 > 0.9, its deviation from adsorption data would significantly affect the accuracy of gas desorption-diffusion simulation. Moreover, if ‘diffusion ratio’ is taken as evaluation index, the inaccurate diffusion amount caused by inaccurate adsorption model in numerical simulation may be ignored, and the diffusion coefficient determined by ‘diffusion ratio’ would deviate from the true value.

Microscopic study of submonolayer nucleation characteristics during GaN (0001) homoepitaxial growth

An on-lattice kinetic Monte Carlo model is constructed to investigate microscopic nucleation behavior during the submonolayer epitaxial growth of GaN islands, where the Ga and N atoms are treated as the basic particles. The input kinetic parameters of Ga and N, including their surface diffusion energy barriers, were obtained from previous ab initio calculations. Furthermore, a simple and effective bond counting rule is applied in our kinetic Monte Carlo model, and the statistics of the GaN islands on the surface are realized via the application of the Hoshen–Kopelman algorithm. The growth temperature range covers the typical growth temperatures used in the molecular beam epitaxy of GaN. The results obtained show that triangular GaN flakes are observed and that the shapes of the GaN islands remain triangular when the growth temperature is changed. Additionally, the power law for the maximum density of islands versus the ratio of the effective diffusion to the deposition rate is obtained; the exponent of this law is −0.506 ± 0.006, indicating that these triplets represent the seeds required for further nucleation. Finally, the coexistence of the Ga-edge and N-edge types of triangular GaN islands is observed. The island formation mechanism is attributed to a local monomer density misbalance, and it is also shown that a slight variation in the Ga/N ratio in the deposition flux changes the proportion of the Ga-edge and N-edge type triangles; this represents a further indication that controllable GaN morphologies can be obtained by tuning the chemical potentials of the constituent elements.

Impact of rotation on thermal instability of Darcy–Brinkman porous layer filled with a Jeffrey nanofluid

The novelty of this research lies in its investigation of the initiation of thermal instability within a Darcy–Brinkman porous layer containing a Jeffrey nanofluid under the influence of rotation. While non-Newtonian fluids complex flow patterns and heat transfer enhancements due to thermal gradients are known, this study addresses a specific and previously unexplored aspect, the impact of rotation on Darcy–Brinkman porous layer containing a Jeffrey nanofluid. When a fluid is subjected to rotation, it can induce additional forces and flow patterns within the fluid. The linear stability theory and normal mode analysis method are used to analyze the stability of the system analytically and are computed numerically using the software Mathematica version 11.3. The investigation focuses on understanding the influence of various factors, namely, the Taylor number, the Lewis number, the Jeffrey parameter, the modified diffusivity ratio, nanoparticles Rayleigh number, the Darcy–Brinkman number, and medium porosity on the onset of thermal instability in the physical system. This novel perspective can contribute to a deeper understanding of heat transfer processes in non-Newtonian fluids and has potential applications in improving the efficiency of industrial systems, such as cooling systems, heat exchangers, and microfluidic devices where efficient heat transfer is crucial for performance improvement.

Thermogravitational Convection in a Controlled Rotating Darcy-Brinkman Nanofluids Layer Saturated in an Anisotropic Porous Medium Subjected to Internal Heat Source

Thermogravitational convection in a controlled rotating Darcy-Brinkman nanofluids layer saturated in an anisotropic porous medium heated from below is Thermogravitational convection in a controlled rotating Darcy-Brinkman nanofluids layer saturated in an anisotropic porous medium heated from below is investigated. The presence of a uniformly distributed internal heat source and considers the Brinkman model for different boundary conditions: rigid-rigid, free-free, and lower-rigid and upper-free are considered. The effect of a control strategy involving sensors located at the top plate and actuators positioned at the bottom plate of the nanofluids layer is analysed. Linear stability analysis based on normal mode technique is employed. The resulting eigenvalue problem is solved numerically using the Galerkin method implemented with Maple software. The model used for the nanofluids associates with the mechanisms of Brownian motion and thermophoresis. The influences of the internal heat source strength, mechanical anisotropy parameter, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection. Conversely, the Darcy number, thermal anisotropy parameter, porosity, rotation, and controller effects are observed to slow down the process of convective instability.investigated. The presence of a uniformly distributed internal heat source and considers the Brinkman model for different boundary conditions: rigid-rigid, free-free, and lower-rigid and upper-free are considered. The effect of a control strategy involving sensors located at the top plate and actuators positioned at the bottom plate of the nanofluids layer is analysed. Linear stability analysis based on normal mode technique is employed. The resulting eigenvalue problem is solved numerically using the Galerkin method implemented with Maple software. The model used for the nanofluids associates with the mechanisms of Brownian motion and thermophoresis. The influences of the internal heat source strength, mechanical anisotropy parameter, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection. Conversely, the Darcy number, thermal anisotropy parameter, porosity, rotation, and controller effects are observed to slow down the process of convective instability.

Excitable FitzHugh-Nagumo model with cross-diffusion: long-range activation instabilities

AbstractIn this paper, we shall study a spatially extended version of the FitzHugh-Nagumo model, where one describes the motion of the species through cross-diffusion. The motivation comes from modeling biological species where reciprocal interaction influences spatial movement. We shall focus our analysis on the excitable regime of the system. In this case, we shall see how cross-diffusion terms can destabilize uniform equilibrium, allowing for the formation of close-to-equilibrium patterns; the species are out-of-phase spatially distributed, namely high concentration areas of one species correspond to a low density of the other (cross-Turing patterns). Moreover, depending on the magnitude of the inhibitor’s cross-diffusion, the pattern’s development can proceed in either case of the inhibitor/activator diffusivity ratio being higher or smaller than unity. This allows for spatial segregation of the species in both cases of short-range activation/long-range inhibition or long-range activation/short-range inhibition.

Effect of variable gravity on thermal convection in Jeffrey nanofluid: Darcy-Brinkman model

The subject under consideration in this research has various geophysical and astrophysical applications. Specifically, we investigate the impact of variable gravity on the onset of thermal instability within a layer of Jeffrey nanofluid confined in a Darcy-Brinkman porous medium. The solution of the fluid layer, which is positioned between two free-free boundaries, is determined using a linear stability analysis employing the normal mode technique. The Rayleigh number on the onset of convection is derived by using the Galerkin method. For stationary convection, the effects of different variable gravity parameters on the Jeffrey parameter, Darcy-Brinkman number, Lewis number, moderated diffusivity ratio, porosity of porous media and nanoparticle Rayleigh number are analyzed and presented graphically. The choices of using Jeffrey nanofluid as the base fluid for the study add novelty. Non-Newtonian fluids encompass a diverse range of substances, such as engine oils, oil extraction, wallpaper paste, and various biological liquids like blood etc.

Detection of Propionic Acids Trapped in Thin Zeolite Layer Using Thermal Desorption Analysis.

Volatile organic compounds (VOCs) have recently received considerable attention for the analysis and monitoring of different biochemical processes in biological systems such as humans, plants, and microorganisms. The advantage of using VOCs to gather information about a specific process is that they can be extracted using different types of samples, even at low concentrations. Therefore, VOC levels represent the fingerprints of specific biochemical processes. The aim of this work was to develop a sensor based on a photoionization detector (PID) and a zeolite layer, used as an alternative analytic separation technique for the analysis of VOCs. The identification of VOCs occurred through the evaluation of the emissive profile during the thermal desorption phase, using a stainless-steel chamber for analysis. Emission profiles were evaluated using a double exponential mathematical model, which fit well if compared with the physical system, describing both the evaporation and diffusion processes. The results showed that the zeolite layer was selective for propionic acid molecules if compared to succinic acid molecules, showing linear behavior even at low concentrations. The process to define the optimal adsorption time between the propionic acid molecules was performed in the range of 5 to 60 min, followed by a thermal desorption process at 100 °C. An investigation of the relationship between the evaporation and diffusion rates showed that the maximum concentration of detected propionic acid molecules occurred in 15 min. Other analyses were performed to study how the concentration of VOCs depended on the desorption temperature and the volume of the analysis chamber. For this purpose, tests were performed using three analysis chambers with volumes of 25 × 10-6, 50 × 10-6, and 150 × 10-6 m3 at three different desorption temperatures of 20 °C, 50 °C, and 100 °C, respectively. The results demonstrated that the evaporation rate of the VOCs increased rapidly with an increasing temperature, while the diffusion rate remained almost constant and was characterized by a slow decay time. The diffusion ratio increased when using a chamber with a larger volume. These results highlight the capabilities of this alternative technique for VOC analysis, even for samples with low concentrations. The coupling of a zeolite layer and a PID improves the detection selectivity in portable devices, demonstrating the feasibility of extending its use to a wide range of new applications.

Maternal Thyroid Function During Pregnancy and Offspring White Matter Microstructure in Early Adulthood: A Prospective Birth Cohort Study.

Background: The fetus is fully dependent on maternal thyroid hormones until mid-gestation and suboptimal maternal thyroid function has been associated with alterations in the neurodevelopment of the offspring. We used maternal free thyroxine (fT4) and thyrotropin (TSH) levels in early gestation to study the association of maternal thyroid function during early pregnancy and offspring brain white matter (WM) integrity in early adulthood. Methods: Our study population consisted of a total of 292 mother-child pairs. Maternal fT4 and TSH were used as predictors and offspring multimodal imaging measures of fractional anisotropy, mean diffusivity, and magnetization transfer ratio (FA, MD, and MTR) as dependent variables. First, as Global analysis, all analyzed 14 WM tracts were studied simultaneously using linear-mixed effect models. Second, if a global effect was detected, a post hoc Tract-wise analysis was carried out using linear models individually in each WM tract. Study population was stratified by sex. Results: We found a positive association between maternal fT4 and offspring Global FA in males when adjusted for all maternal and offspring covariates (n = 114; β = 0.154; confidence interval = 0.045-0.263; p = 0.006). The finding was observed to be driven by multiple WM tracts, of which three projection fiber tracts and the forceps minor survived correcting for multiple comparisons in Tract-wise analysis. Conclusions: Maternal thyroid function in early pregnancy was observed to be associated with WM microstructure in male offspring in early adulthood. Our results suggest that maternal fT4 levels in early pregnancy may modulate axonal characteristics, with a long-term effect on offspring WM development.

Linear stability of longitudinal convective rolls in a non-Darcy porous layer filled with nanofluid due to viscous dissipation effect: A realistic approach

The onset of longitudinal convective rolls of nanofluid flow inside a horizontal porous material using Brinkman theory due to the viscous dissipation effect has been addressed numerically. An infinitely long horizontal porous region has been considered which is confined between two rigid boundaries. The boundaries of the channel are considered adiabatic (lower) and isothermal (upper). Brownian motion and thermophoresis properties are taken into consideration for nanofluid. In the linear stability analysis, oblique roll disturbances with arbitrary orientation are taken into account, where the preferred mode of instability i.e., longitudinal rolls (when P=0 or ϑ=π/2) are shown. Finally, the resulting eigenvalue problem is solved in MATLAB using the bvp4c technique. The impact of improving the modified diffusivity ratio (NA<10), Lewis number (Le<,=,>1), concentration Rayleigh number (Rn) and modified particle density increment (NB≈10−2−10−5) is to accelerate the instability boundaries, while the switching parameter (ξ) has a dual character on it. Further, the pattern of the streamlines are slightly compressed in the channel’s center for large values of ξ, whereas no markable changes are noticed for higher values of NA. The isotherms lines are closer near the adiabatic boundary when ξ takes small values.

Glymphatic function assessment in Parkinson's disease using diffusion tensor image analysis along the perivascular space

IntroductionGlymphatic dysfunction can contribute to α-synucleinopathies. We examined glymphatic function in idiopathic Parkinson's disease (PD) utilizing Diffusion Tensor Image Analysis aLong the Perivascular Space (DTI-ALPS). MethodsThis study enrolled consecutive patients diagnosed with de novo PD between June 2017 and March 2019 who underwent brain DTI with concurrent 123I-2β-carbomethoxy-3β-(4-iodophenyl)-N-(3-fluoropropyl)-nortropane (123I-FP-CIT) SPECT, and age- and sex-matched controls. From DTI-ALPS, the ALPS-index was calculated as a ratio of diffusivities along the x-axis in the region of neural fibers passing vertically to the diffusivities perpendicular to them, which reflected perivascular water motion at the lateral ventricular body level. The ALPS-index of the PD and control groups was compared using Student's t-test; its correlations with clinical scores for motor and cognition (UPDRS-III, MMSE, and MoCA) and striatal dopamine transporter uptake measured by 123I-FP-CIT specific binding ratios (SBRs) were examined using a correlation coefficient. ResultsIn all, 54 patients in the de novo PD group (31 women, 23 men; mean age, 68.9 ± 9.4 years) and 54 in the control group (mean age, 69.0 ± 10.5 years) were included. The ALPS-index was lower in the PD group than in the controls (1.51 ± 0.22 versus 1.66 ± 0.20; P < 0.001). In the PD group, the ALPS-index negatively correlated with the UPDRS-III score (r = −0.526), and positively correlated with the MMSE (r = 0.377) and MoCA scores (r = 0.382) (all, P < 0.05). No correlation was observed between the ALPS-index and striatal 123I-FP-CIT SBRs (P > 0.05). ConclusionsDTI-ALPS can reveal glymphatic dysfunction in patients with PD, whose severity correlated with motor and cognitive dysfunction, but not striatal dopamine transporter uptake.

Permeability coupling model of multiple migration mechanisms in rough micro-fractures of shales

To study the gas transmission characteristics in organic pores of rough shale reservoirs, firstly, considering the effect of roughness, adsorption layer, and stress sensitivity on fracture width variation, the effective fracture width model was established. On this basis, the real gas transport models of the adsorbed gas and bulk gas in rough reservoirs have been studied respectively, and the apparent permeability coupling model of rough microfracture of shale are proposed according to the difference of actual flow area. The validity of the proposed models was verified by comparing them with the simulation data, and the contribution of each migration mechanism to the total flow under different roughness and fracture width variation factors was analyzed. It is found that the formation pressure is proportional to the influence of roughness on permeability. When the initial crack width increases, the corresponding pore pressure decreases when the roughness has a greater influence on the proportion of slip flow. The influence of roughness on the Knudsen diffusion ratio and surface diffusion ratio will be greater when the initial crack width is smaller. In addition, if the initial crack width and pore pressure are constant, the greater the relative roughness, the greater the Knudsen diffusion ratio and surface diffusion ratio, and the smaller the slippage flow proportion.

Combined effect of helical force and rotation on the double convection of a binary viscoelastic fluid in a porous medium: Linear and weakly nonlinear analysis

AbstractWe used linear stability theory based on the normal mode decomposition technique and nonlinear stability theory based on the minimum representation of double Fourier series to study the criterion of appearance of the stationary convection and the oscillatory convection; and the rate of heat and mass transfer in a binary viscoelastic fluid mixture in a rotating porous medium under the effect of helical force. We have determined the analytical expression of the Rayleigh number of the system as a function of the dimensionless parameters. Expressions for heat and mass transfer rates are determined as a function of Nusselt and Sherwood number, respectively. The transient behaviors of the Nusselt number and the Sherwood number are studied by solving the finite amplitude equations using the Runge‐Kutta method. Then, the effect of each dimensionless parameter on the system is studied pointed out interesting results. According to the analysis of the different results obtained, it appears that in a porous medium saturated by a binary mixture of viscoelastic fluid in rotation, the Taylor‐Darcy number , the delay time parameter λ2 and the mass Rayleigh‐Darcy number delay the onset of stationary and oscillatory convection. On the other hand, the helical force , the relaxation time parameter λ1, the ratio of diffusivities τ and the number of Vadasz accelerate the onset of stationary and oscillatory convection. In the case of the nonlinear stability study, at steady state, the helical force accelerates the rate of heat and mass transfer. On the other hand, the Taylor‐Darcy number , the diffusivity ratio τ and the mass Rayleigh‐Darcy number retard the rate of heat and mass transfer. In the unsteady state, the helical force , the relaxation time parameter λ1 and the mass Rayleigh‐Darcy number accelerate the rate of heat and mass transfer. This is not the case for the Taylor‐Darcy number and the delay time parameter λ2.

Precipitation governing vegetation patterns in an arid or semi-arid environment.

In an arid or semi-arid environment, precipitation plays a vital role in vegetation growth. Recent researches reveal that the response of vegetation growth to precipitation has a lag effect. To explore the mechanism behind the lag phenomenon, we propose and investigate a water-vegetation model with spatiotemporal nonlocal effects. It is shown that the temporal kernel function does not affect Turing bifurcation. For better understanding the influences of lag effect and nonlocal competition on the vegetation pattern formation, we choose some special kernel functions and obtain some insightful results: (i) Time delay does not trigger the vegetation pattern formation, but can postpone the evolution of vegetation. In addition, in the absence of diffusion, time delay can induce the occurrence of stability switches, while in the presence of diffusion, spatially nonhomogeneous time-periodic solutions may emerge, but there are no stability switches; (ii) The spatial nonlocal interaction may trigger the pattern onset for small diffusion ratio of water and vegetation, and can change the number and size of isolated vegetation patches for large diffusion ratio. (iii) The interaction between time delay and spatial nonlocal competition may induce the emergence of traveling wave patterns, so that the vegetation remains periodic in space, but is oscillating in time. These results demonstrate that precipitation can significantly affect the growth and spatial distribution of vegetation.

Modeling Segregation of Fe–C Alloy in Solidification by Phase-Field Method Coupled with Thermodynamics

The primary carbide in high carbon chromium bearing steels, which arises from solute segregation during non-equilibrium solidification, is one of the key factors affecting the mechanical properties and performance of the related components. In this work, the effects of carbide forming element diffusion, primary austenite grain size, and the cooling rate on solute segregation and carbide precipitation during the solidification of an Fe–C binary alloy were studied by the phase-field method coupled with a thermodynamic database. It was clarified that increasing the ratio of solute diffusivity in solid and liquid, refining the grain size of primary austenite to lower than a critical value, and increasing the cooling rate can reduce the solute segregation and precipitation of primary carbide at late solidification. Two characteristic parameters were introduced to quantitatively evaluate the solute segregation during solidification including the phase fraction threshold of primary austenite when the solute concentration in liquid reaches the eutectic composition, and the maximum segregation ratio. Both parameters can be well-correlated to the ratio of solute diffusivity in solid and liquid, the grain size of primary austenite, and the cooling rate, which provides potential ways to control the solute segregation and precipitation of primary carbide in bearing steels.

Revised Enskog theory for Mie fluids: Prediction of diffusion coefficients, thermal diffusion coefficients, viscosities, and thermal conductivities.

Since the 1920s, the Enskog solutions to the Boltzmann equation have provided a route to predicting the transport properties of dilute gas mixtures. At higher densities, predictions have been limited to gases of hard spheres. In this work, we present a revised Enskog theory for multicomponent mixtures of Mie fluids, where the Barker-Henderson perturbation theory is used to calculate the radial distribution function at contact. With parameters of the Mie-potentials regressed to equilibrium properties, the theory is fully predictive for transport properties. The presented framework offers a link between the Mie potential and transport properties at elevated densities, giving accurate predictions for real fluids. For mixtures of noble gases, diffusion coefficients from experiments are reproduced within ±4%. For hydrogen, the predicted self-diffusion coefficient is within 10% of experimental data up to 200 MPa and at temperatures above 171K. Binary diffusion coefficients of the CO2/CH4 mixture from simulations are reproduced within 20% at pressures up to 14.7 MPa. Except for xenon in the vicinity of the critical point, the thermal conductivity of noble gases and their mixtures is reproduced within 10% of the experimental data. For other molecules than noble gases, the temperature dependence of the thermal conductivity is under-predicted, while the density dependence appears to be correctly predicted. Predictions of the viscosity are within ±10% of the experimental data for methane, nitrogen, and argon up to 300bar, for temperatures ranging from 233 to 523K. At pressures up to 500bar and temperatures from 200 to 800K, the predictions are within ±15% of the most accurate correlation for the viscosity of air. Comparing the theory to an extensive set of measurements of thermal diffusion ratios, we find that 49% of the model predictions are within ±20% of the reported measurements. The predicted thermal diffusion factor differs by less than 15% from the simulation results of Lennard-Jones mixtures, even at densities well exceeding the critical density.