Diffusion Boundary Conditions Research Articles

Poiseuille and thermal transpiration flows of a dense gas between two parallel plates

The Poiseuille and thermal transpiration flows of a dense gas between two parallel plates are investigated on the basis of the Enskog kinetic equation under the diffuse reflection boundary condition. In contrast to the case of an ideal gas, the density and the gradients of pressure and the normal stress component in the flow direction are not uniform in the direction normal to the plates for a dense gas. The non-uniform normal stress gradient contributes also to the acceleration or deceleration of the thermal transpiration flow for small Knudsen numbers. The profiles of mass and heat flows as well as the net mass flows are obtained for various Knudsen numbers and ratios of the molecular diameter to the distance of plates. In the analysis of the Poiseuille flow, most characteristics of a force-driven flow with a small force are recovered. However, for the case of a dense gas, differences between the force-driven and the present pressure-driven flows are observed even within the linearized regime for small force and pressure gradient, especially at the microscopic level. The behaviour of the velocity distribution functions, in particular, the way in which they approach the ones for the Boltzmann equation as the molecular diameter becomes smaller, is clarified.

From university basic research to firm innovation: diffusion mechanism and boundary conditions under a U-shaped relationship

The paradox between China's dazzling S&T output and the technological dilemma of enterprises challenges the positive effect of basic research on technological innovation, and extant research has not solved this problem. To bridge this theoretical gap, we integrated resource dependence theory and institutional theory, and matched the data of universities and governments at the provincial level and the data of enterprises at the micro level to clarify whether and how university basic research promotes firm innovation. We found that: (1) there is a U-shaped relationship between university basic research and firm innovation. (2) University-enterprise cooperation, S&T services and paper achievements played a mediating role, but invention patent achievements did not. (3) Neither the supporting nor the intervening hand of the government can moderate the U-shaped relationship. (4) Only when the enterprise has no political connection, is located in the eastern region, and is not in the provincial capital city or special economic zone, is the U-shaped relationship established. Furthermore, the functional mechanism and boundary conditions of the U-shaped relationship are further clarified through a robustness test of variable substitution and sample subdivision.

Simulated Trapping of Solar Energetic Protons for the 8–10 March 2012 Geomagnetic Storm: Impact on Inner Zone Protons as Measured by Van Allen Probes

AbstractSolar energetic protons (SEPs) have been shown to contribute significantly to the inner zone trapped proton population for energies <100 MeV and L > 1.3 (Selesnick et al., 2007, https://doi.org/10.1029/2006sw000275). The Relativistic Electron Proton Telescope (REPT) on the Van Allen Probes launched 30 August 2012 observed a double‐peaked (in L) inner zone population throughout the 7‐year lifetime of the mission. It has been proposed that a strong SEP event accompanied by a CME‐shock in early March 2012 provided the SEP source for the higher L trapped proton population, which then diffused radially inward to be observed by REPT at L ∼ 2. Here, we follow trajectories of SEP protons launched isotropically from a sphere at 7 Re in 15 s cadence fields from an Lyon‐Fedder‐Mobarry coupled to Rice Convection Model global magnetohydrodynamic (MHD) simulation driven by measured upstream solar wind parameters. The timescale of the interplanetary shock arrival is captured, launching a magnetosonic impulse propagating azimuthally along the dawn and dusk flanks inside the magnetosphere, shown previously to produce SEP trapping. The MHD‐test particle simulation uses Geostationary Operational Environmental Satellite (GOES) proton energy spectra to weight the initial radial profile required for the radial diffusion calculation over the following 2 years. GOES proton measurements also provide a dynamic outer boundary condition for radial diffusion. A direct comparison with REPT measurements 20 months following the trapping event in March 2012 supports this novel combination of short‐term and long‐term evolution of the newly trapped protons.

Fast Identification of Micro-Health Parameters for Retired Batteries Based on a Simplified P2D Model by Using Padé Approximation

Better performance consistency of regrouped batteries retired from electric vehicles can guarantee the residual value maximized, which greatly improves the second-use application economy of retired batteries. This paper develops a fast identification approach for micro-health parameters characterizing negative electrode material and electrolyte in LiFePO4 batteries on the basis of a simplified pseudo two-dimensional model by using Padé approximation is developed. First, as the basis for accurately identifying micro-health parameters, the liquid-phase and solid-phase diffusion processes of pseudo two-dimensional model are simplified based on Padé approximation, especially according to enhanced boundary conditions of liquid-phase diffusion. Second, the reduced pseudo two-dimensional model with the lumped parameter is proposed, the target parameters characterizing negative electrode material (εn, Ds,n) and electrolyte (De, Ce) are grouped with other unknown but fixed parameters, which ensures that no matter whether the target parameters can be achieved, the corresponding varying traces is able to be effectively and independently monitored by lumped parameters. Third, the fast identification method for target micro-health parameters is developed based on the sensitivity of target parameters to constant-current charging voltage, which shortens the parameter identification time in comparison to that obtained by other approaches. Finally, the identification accuracy of the lumped micro-health parameters is verified under 1 C constant-current charging condition.

Galvanomagnetic properties of a thin metal film considering dimensional quantization and diffuse surface scattering of electrons

The Expressions for the transverse magnetoresistance coefficient and the Hall coefficient of a film are analytically obtained and analyzed. Quantum dimensional effect is taken into account, but Landau levels are not considered. The film zone structure is spherically symmetric and obeys the parabolic law. Galvanomagnetic coefficients are calculated from the Liouville (von Neumann) equation taking into account diffuse boundary conditions for the distribution function.

On the Rarefied Thermally-Driven Flows in Cavities and Bends

This study examined rarefied thermally-driven flow in a square cavity (Case 1) and rectangular bend (Case 2), with various uniform wall temperatures in two dimensions. We employed the direct simulation Monte Carlo (DSMC) to solve problems with a wide range of Knudsen numbers Kn = 0.01 to 10, and the discrete unified gas kinetic scheme (DUGKS) solver was used at Kn = 0.01. The scenario was that, in case 1, the bottom side and its opposite were set hot, and the other sides were set cold. Diffuse reflector boundary conditions were set for all walls. The imposed temperature differences created four primary vortices. The results of the continuum set of equations of the slow non-isothermal flow (SNIT) solver proved that the primary vortices in the square cavity were caused by nonlinear thermal stress effects, and other smaller vortices appearing at Kn = 0.01, 0.1 were brought about by thermal creep processes. As the Kn increased, vortices generated by thermal creep disappeared, and eddies created by nonlinear thermal stress occupied the cavity. In case 2, i.e., a rectangular bend, two sides were set cold, and the others were hot. Two primary vortices were formed, which were caused by nonlinear thermal stress effects. The direction of streamlines in the two main vortices was opposite, from the warm to the cold zone, as some eddies on the left were counterclockwise, and others were clockwise.

Fractional diffusion limit of a kinetic equation with diffusive boundary conditions in a bounded interval

We investigate the fractional diffusion approximation of a kinetic equation set in a bounded interval with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time asymptotic, we show that the asymptotic density function is the unique solution of a fractional diffusion equation with Neumann boundary condition. This analysis completes a previous work by the same authors in which a limiting fractional diffusion equation was identified on the half-space, but the uniqueness of the solution (which is necessary to prove the convergence of the whole sequence) could not be established.

Contact angle ageing and anomalous capillary flow of a molten metal

Recent capillary flow experiments, conducted on a combined wetting/non-wetting assemble, consistently feature an anomalous flow over the non-wetting substrate: (i) apparent abrupt or gradual recession stages in the motion of the contact line, (ii) non-monotonic abrupt changes in the receding contact angle, and (iii) contact angle overshoot above the nominal equilibrium contact angle. We find that such behavior of a liquid metal alloy cannot be explained by the standard capillary flow models. However, a model that includes the ageing of the equilibrium contact angle predicts all the observed features qualitatively. We use the phase field formulation for capillary flows with a diffusive motion of the triple line to accommodate the novel diffusive boundary condition with the time-evolving quasi-equilibrium contact angle. We discover that the observed anomalies in capillary flow are qualitatively explained by two factors: (1) time evolution (ageing) of the quasi-equilibrium contact angle and (2) high viscosity of the partially molten braze. We also discover that for the given flow geometry, the transition from the initial to the final configuration may follow two distinct topological paths: one is characterized by a coalescence of liquid–solid contact domains, the other by a contact separation. The selection of the two paths in the configurational space is dependent on both contact ageing parameters and viscosity.

Heat Transfer Problem for the Boltzmann Equation in a Channel with Diffusive Boundary Condition

In this paper, the authors study the 1D steady Boltzmann flow in a channel. The walls of the channel are assumed to have vanishing velocity and given temperatures θ0 and θ1. This problem was studied by Esposito-Lebowitz-Marra (1994, 1995) where they showed that the solution tends to a local Maxwellian with parameters satisfying the compressible Navier-Stokes equation with no-slip boundary condition. However, a lot of numerical experiments reveal that the fluid layer does not entirely stick to the boundary. In the regime where the Knudsen number is reasonably small, the slip phenomenon is significant near the boundary. Thus, they revisit this problem by taking into account the slip boundary conditions. Following the lines of [Coron, F., Derivation of slip boundary conditions for the Navier-Stokes system from the Boltzmann equation, J. Stat. Phys., 54(3–4), 1989, 829–857], the authors will first give a formal asymptotic analysis to see that the flow governed by the Boltzmann equation is accurately approximated by a superposition of a steady CNS equation with a temperature jump condition and two Knudsen layers located at end points. Then they will establish a uniform L∞ estimate on the remainder and derive the slip boundary condition for compressible Navier-Stokes equations rigorously.

Damping of Kinetic Transport Equation with Diffuse Boundary Condition

We prove that exponential moments of a fluctuation of the pure transport equation decay pointwisely almost as fast as $t^{-3}$ when the domain is any general strictly convex subset of $\mathbb{R}^3$ with the smooth boundary of the diffuse boundary condition. We prove the theorem by establishing a novel $L^1$-$L^\infty$ framework via stochastic cycles.

A thin-layer diffusion model-based intelligent cyclic voltammetry analysis method to capture electrochemical parameters in flow batteries

Contrary to the conventional approach that utilizes the planar electrode model to achieve the electrochemical parameters of the electrode in flow batteries, this work proposes an intelligent cyclic voltammetry (CV) analysis method to accurately capture the electrochemical parameters of the carbon-based porous electrode: (i) the transient diffusion process is elaborated by the Fick's second law; (ii) the thin-layer diffusion boundary condition is determined based on the structural characteristics of porous electrodes; (iii) CV response on the porous electrode is obtained by the Bulter-Volmer equation in assocition with the Fick's first law; and (iv) the electrochemical parameters of the porous electrode are automatically extracted from the experimental data via the genetic algorithm. The feasibility of the intelligent CV analysis method is proven by studying the electrochemical parameters including the diffusion coefficient D and the standard rate constant k0 of [Fe(CN)6]4−/[Fe(CN)6]3−. Additionally, this analysis method is applied to investigate the vanadium redox flow battery by providing accurate electrochemical parameters for the 3D multi-physics model to predict the charge/discharge performance at different current densities. The simulation results demonstrate a maximum relative error of 2% in comparison to the experimental data, suggesting the good reliability in developing the advanced model. The proposed intelligent CV analysis method provides a potential application in accurately capturing the electrochemical parameters in other electrochemical energy conversion and storage devices.

Mathematical Study of a Resource-Based Diffusion Model with Gilpin-Ayala Growth and Harvesting.

This paper focuses on a Gilpin-Ayala growth model with spatial diffusion and Neumann boundary condition to study single species population distribution. In our heterogeneous model, we assume that the diffusive spread of population is proportional to the gradient of population per unit resource, rather than the population density itself. We investigate global well-posedness of the mathematical model, determine conditions on harvesting rate for which non-trivial equilibrium states exist and examine their global stability. We also determine conditions on harvesting that leads to species extinction through global stability of the trivial solution. Additionally, for time periodic growth, resource, capacity and harvesting functions, we prove existence of time-periodic states with the same period. We also present numerical results on the nature of nonzero equilibrium states and their dependence on resource and capacity functions as well as on Gilpin-Ayala parameter [Formula: see text]. We conclude enhanced effects of diffusion for small [Formula: see text] which in particular disallows existence of nontrivial states even in some cases when intrinsic growth rate exceeds harvesting at some locations in space for which a logistic model allows for a nonzero equilibrium density.

Discontinuous dewetting dynamics of highly viscous droplets on chemically heterogeneous substrates

HypothesisDroplet spreading on heterogeneous (chemical/structural) surfaces has revealed local disturbances that affect the advancing contact line. With droplet dewetting being less studied, we hypothesize that a receding droplet can be perturbed by localized heterogeneity which leads to irregular and discontinuous dewetting of the substrate. ExperimentsThe sessile drop method was used to study droplet dewetting at a wettability boundary. One-half of a hydrophilic surface was hydrophobically modified with either i) methyloctyldichlorosilane or ii) clustered macromolecules. A Lattice Boltzmann method (LBM) simulation was also developed to determine the effect of contact angle hysteresis and boundary conditions on the droplet dynamics. FindingsThe two surface treatments were optimized to produce comparable water wetting characteristics. With a negative Gibbs free energy on the hydrophilic-half, the oil droplet receded to the hydrophobic-half. On the silanized surface, the droplet was pinned and the resultant droplet shape was a distorted spherical cap, having receded uniformly on the unmodified surface. Modifying the surface with clustered macromolecules, the droplet receded slightly to form a spherical cap. However, droplet recession was non-uniform and daughter droplets formed near the wettability boundary. The LBM simulation revealed that daughter droplets formed when θR > 164°, with the final droplet shape accurately described by imposing a diffuse wettability boundary condition.

Transition Gas Flow Between Two Parallel Plates with a Slit-Type Obstacle of Various Geometry by Event Driven Molecular Dynamics Simulation

In this study, pressure-driven flow through a slit-type obstacle with various length (L) and height (H) placed in between two parallel plates was investigated by Event Driven Molecular Dynamics (EDMD) simulation. Mach number, temperature and pressure distributions were obtained along the channel in the transition regime. The change in these macroscopic properties and flow rate were examined for different cases created by changing Knudsen number (Kn) of the gas, the geometry of the slit and the outlet/inlet pressure ratio of the flow. Collision of gas molecules with plates and the obstacle were modeled with diffuse reflection boundary condition. The flow rate showed a sudden change in the transition regime and significant differences in the molecular regime depending on the pressure ratio. Except for the Kn, H and L dimensions were found to be effective in Mach disc formation. Pressure drops at the exit of the slit were shaped differently in normalized pressure profiles depending on Kn, H and L dimensions. In addition, the structure of the vortices formed at the entrance and exit of the slit varies depending on Kn. Some of the results obtained were confirmed to be consistent with the similar studies in the literature.

Novel Modeling of Heat and Moisture Diffusion in Adhesive Joints

Abstract A novel two-dimensional shear stress-heat and moisture diffusion model is proposed for adhesive single-lap joints. Spatial and time-dependent material properties are derived from coupled partial differential equations governing moisture diffusion and heat transfer through the exposed adhesive edges. Constituting differential equations are numerically solved for the shear stress distribution in the bonded area. Several diffusion scenarios and boundary conditions are analyzed. Significant improvements are achieved in the prediction of the shear stress distribution in the adhesive layer when compared to the one-dimensional models in the literature. Scenarios of moisture diffusion generate stress gradients through the bondline, while the relatively fast internal thermal conductivity reduces temperature differentials within the joint. Moisture diffusion in the adhesive layer is significantly accelerated at high temperatures. The results of the proposed model show reasonable agreement with a three-dimensional finite element analysis.

IMPEDANCE BOUNDARY CONDITION OF NON-UNIFORM ELECTROMAGNETIC FIELD PENETRATION INTO CONDUCTING HALF-SPACE

The influence of the non-uniformity of the external field to its distribution on the surface of the conducting half-space is investigated on the basis of exact analytical and approximate asymptotic calculation methods of an arbitrary three-dimensional electromagnetic field. The function that generalizes the impedance boundary condition for diffusion of non-uniform field into conducting body is proposed. On the basis of calculations results comparison by exact and approximate methods for concrete model of electromagnetic system the admissible value of the upper limit of the introduced small parameter is established. References 10, figures 5.

Boundary Layer Solution of the Boltzmann Equation for Diffusive Reflection Boundary Conditions in Half-Space

We study steady Boltzmann equation in half-space, which arises in the Knudsen boundary layer problem, with diffusive reflection boundary conditions. Under certain admissible conditions and the source term decaying exponentially, we establish the existence of boundary layer solution for both linear and nonlinear Boltzmann equation in half-space with diffusive reflection boundary condition in $L^\infty_{x,v}$ when the far-field Mach number of the Maxwellian is zero. The continuity and the spacial decay of the solution are obtained. The uniqueness is established under some constraint conditions.

Super-suppression of long phonon mean-free-paths in nano-engineered Si due to heat current anticorrelations

The ability to minimize the thermal conductivity of dielectrics with minimal structural intervention that could affect electrical properties is an important capability for engineering thermoelectric efficiency in low-cost materials such as Si. We recently reported the discovery of special arrangements for nanoscale pores in Si that produce a particularly large reduction in thermal conductivity accompanied by strongly anticorrelated heat current fluctuations [1] – a phenomenon that is missed by the diffuse adiabatic boundary conditions conventionally used in Boltzmann transport models. This manuscript presents the results of molecular dynamics simulations and a Monte Carlo ray tracing model that teases apart this phenomenon to reveal that special pore layouts elastically backscatter long-wavelength heat-carrying phonons. This means that heat carriage by a phonon before scattering is undone by the scattered phonon, resulting in an effective mean-free-path that is significantly shorter than the geometric line-of-sight due to the pores. This effect is particularly noticeable for the long-wavelength, long mean-free-path phonons whose transport is impeded drastically more than is expected purely from the usual considerations of scattering defined by the distance between defects. This “super-suppression” of the mean-free-path below the characteristic length scale of the nanostructuring offers a route for minimizing thermal conductivity with minimal structural impact, while the stronger impact on long wavelengths offers possibilities for the design of band-pass phonon filtering. Moreover, the ray tracing model developed in this paper shows that different forms of correlated scattering imprint a unique signature in the heat current autocorrelation function that could be used as a diagnostic in other nanostructured systems.

Multiscale modeling of gas flow behaviors in nanoporous shale matrix considering multiple transport mechanisms.

This study proposes a multiscale model combining molecular simulation and the lattice Boltzmann method (LBM) to explore gas flow behaviors with multiple transport mechanisms in nanoporous media of shale matrix. The gas adsorption characteristics in shale nanopores are first investigated by molecular simulations, which are then integrated and upscaled into the LBM model through a local adsorption density parameter. In order to adapt to high Knudsen number and nanoporous shale matrix, a multiple-relaxation-time pore-scale LBM model with a regularization procedure is developed. The combination of bounce-back and full diffusive boundary condition is adopted to take account of gas slippage and surface diffusion induced by gas adsorption. Molecular simulation results at the atomic scale show that gas adsorption behaviors are greatly affected by the pressure and pore size of the shale organic nanopore. At the pore scale, the gas transport behaviors with multiple transport mechanisms in nanoporous shale matrix are explored by the developed multiscale model. Simulation results indicate that pressure exhibits more significant influences on the transport behaviors of shale gas than temperature does. Compared with porosity, the average pore size of nanoporous shale matrix plays a more significant role in determining the apparent permeability of gas transport. The roles of the gas adsorption layer and surface diffusion in shale gas transport are discussed. It is observed that under low pressure, the gas adsorption layer has a positive influence on gas transport in shale matrix due to the strong surface diffusion effect. The nanoporous structure with the anisotropy characteristic parallel to the flow direction can enhance gas transport in shale matrix. The obtained results may provide underlying and comprehensive understanding of gas flow behaviors considering multiple transport mechanisms in shale matrix. Also, the proposed multiscale model can be considered as a powerful tool to invesigate the multiscale and multiphysical flow behaviors in porous media.

Heat transfer in a dense gas between two parallel plates

Time-dependent heat transfer in a dense gas between two parallel plates, which is initiated by an abrupt change in temperature of one plate, is numerically investigated on the basis of the Enskog equation under the diffuse reflection boundary condition. Numerical computation is carried out by a finite-difference scheme combined with the Fourier spectral method for the efficient computation of the collision term of the Enskog equation. As a result, macroscopic quantities of the gas, such as heat flux and temperature, are obtained for various Knudsen numbers and ratios of the molecular diameter to the distance between plates. Compared to the case of an ideal gas, the heat flux in the stationary state is enhanced due to an effect of the finite size of molecules for not only small but also intermediate Knudsen numbers. The results imply that the finite-size effect also affects the propagation of disturbances in the initial stage, particularly for small Knudsen numbers.