Negative Diffusion Coefficient Research Articles

The sensitive detection of the early-stage internal short circuit triggered by lithium plating through the simplified electrochemical model at various working conditions

The internal short circuit (ISC) is one of the main causes of thermal runaway in batteries. Facing the current fast charging scenario of batteries, this paper aims to explore the sensitivity of solid-phase diffusion coefficient to ISC during high current charging. The voltage and current data of the real ISC is input into the simplified pseudo-two-dimensions model to identify the intrinsic parameters. The results indicate that the positive solid-phase diffusion coefficient (Ds,p) has higher sensitivity and stability than the negative solid-phase diffusion coefficient (Ds,n). For real ISC, the sensitivity of the solid-state diffusion coefficient increases as the charging current increases. This is consistent with the trends in ISC that we have derived from our low-temperature ISC extension experiment. For #1 ISC battery at 25 °C (SOC = 0.3–0.85), Ds,p changes by 56 % (3C) and 96 % (5C), and Ds,n changes by 6.87 × 10−14m2/s (166 %) (3C), 8.38 × 10−14m2/s (670 %) (5C). Moreover, the sensitivity of the solid-state diffusion coefficient to ISC decreases after battery aging, but it still has sufficient ability to diagnose ISC. High temperature will reduce the sensitivity of the solid phase diffusion coefficient.

Spatiotemporal patterns in a diffusive resource–consumer model with distributed memory and maturation delay

In this paper, we propose a diffusive consumer–resource model in which the consumer is involved with spatiotemporal memory and the resource has maturation delay. Firstly, for the case without maturation delay, the influence of the spatiotemporal distributed memory on the stability of the positive steady state is investigated. It has been shown that memory delay can induce Turing bifurcation for the negative memory-based diffusion coefficient and induce Hopf bifurcation for the positive memory-based diffusion coefficient. Then the joint effect of the memory delay and the maturation delay on the stability of the positive steady state is investigated and it has been shown that the joint effect of the memory delay and the maturation delay can induce more complicated spatiotemporal dynamics via Turing–Hopf bifurcation and double Hopf bifurcation. Finally, we apply our theoretical analysis results to a consumer–resource model with Holling-II type functional response to illustrate the existence of the different spatiotemporal patterns.

The unexpected weirdness of rate-based simulation of some high-pressure column operations

Diffusion is the process by which molecules move. One way to model multicomponent diffusion is with a version of Fick’s law: (J) = - [D] d(c)/dz where [D] is a matrix of multicomponent diffusion coefficients. [D] is the product of two other matrices, one of which involves partial derivatives of the fugacity or activity coefficients. It is usually the case that all of the elements on the main diagonal of [D] have a positive value. Wambui Mutoru and Firoozabadi (2011, 2012) showed that CO2-rich and N2-rich hydrocarbon systems could have main diagonal elements of [D] that are negative. Using rate-based column simulations, we have found that these negative main diffusion coefficients readily occur in some high-pressure distillation operations. We investigate these processes in more detail and explore the consequences for the design and operation of columns in which this phenomenon is predicted to occur.

Steady-state and transient electronic transport properties of β-(Al x Ga1–x )2O3/Ga2O3 heterostructures: An ensemble Monte Carlo simulation

The steady-state and transient electron transport properties of β-(Al x Ga1−x )2O3/Ga2O3 heterostructures were investigated by Monte Carlo simulation with the classic three-valley model. In particular, the electronic band structures were acquired by first-principles calculations, which could provide precise parameters for calculating the transport properties of the two-dimensional electron gas (2DEG), and the quantization effect was considered in the Γ valley with the five lowest subbands. Wave functions and energy eigenvalues were obtained by iteration of the Schrödinger–Poisson equations to calculate the 2DEG scattering rates with five main scattering mechanisms considered. The simulated low-field electron mobilities agree well with the experimental results, thus confirming the effectiveness of our models. The results show that the room temperature electron mobility of the β-(Al0.188Ga0.812)2O3/Ga2O3 heterostructure at 10 kV⋅cm−1 is approximately 153.669 cm2⋅V−1⋅s−1, and polar optical phonon scattering would have a significant impact on the mobility properties at this time. The region of negative differential mobility, overshoot of the transient electron velocity and negative diffusion coefficients are also observed when the electric field increases to the corresponding threshold value or even exceeds it. This work offers significant parameters for the β-(Al x Ga1−x )2O3/Ga2O3 heterostructure that may benefit the design of high-performance β-(Al x Ga1−x )2O3/Ga2O3 heterostructure-based devices.

Nonlinear evolution of Buneman instability in inhomogeneous plasmas using Adomian decomposition method

Nonlinear development of the Buneman instability in current-driven plasmas is investigated using Adomian decomposition method (ADM). Considering the continuity and momentum transfer equations for electrons and ions and using Poisson’s equation, a nonlinear diffusion equation with positive and negative nonlinear diffusion coefficients is obtained. Assuming the inhomogeneity of the collision frequency, the nonlinear equation is solved using ADM. Results show that by increasing the time and electron velocity, the amplitude of the electron density increases. Furthermore, it is shown that the collision frequency can decrease the amplitude of the electron density which leads to stabilizing the plasma system. Finally, it is found that ADM is a convergent method in the Buneman instability with real parameters.

Examining Solvent Motion in Polarized Concentrated Electrolytes

Historically, ion transport in electrolytes has been described in terms of current – potential response. This behavior is often explained using macroscopic transport properties such as ionic conductivity, transference number, and salt diffusivity.1,2 In contrast, recent X-ray3 and magnetic resonance4 techniques capture ion motions at smaller yet continuum scales. Interestingly, some of these measurements observe the directed motion of solvent in polarized electrolytes, while traditionally solvent is assumed to be a stationary species. Driven by this mismatch of two interpretations, we revisit Newman’s concentrated solution theory1,2,5–8 to examine the role of solvent motion in polarized electrolytes (Figure 1(a)). We use LiTFSI in PEO as an exemplar electrolyte since it is one of the few electrolytes with a full set of transport properties measured previously.9 We find that as the electrolyte is polarized, salt concentration gradients can create a thermodynamic drive for the solvent to travel against the salt motion. Time evolution of voltage (a macroscopic quantity), as well as velocity fields for each species (Figure 1(b)), are examined. We study polarizations at various currents and concentrations to identify when and how the solvent motion contributes to electrolyte response. We find that the solvent, even if it is a charge-neutral species, moves in the direction of ionic current. Apart from these new insights into electrolyte transport dynamics, the results help rationalize recent direct measurements of ion fluxes.Figure 1. (a) A schematic showing physical situation of interest. x=0 is the left interface between Li electrode and electrolyte, while x=L is the right interface. As time passes by, the electrolyte fields evolve as well as the interfaces move equally in the opposite direction of current density, iapp. (b) Example distribution of cation, anion, and solvent velocities in the polarized electrolyte. Directions of these velocities are shown when current flows along the positive coordinate. In this scenario, ions pile up close to the left electrode, while they deplete near the right electrode.(1) Newman, J.; Thomas-Alyea, K. E. Electrochemical Systems; John Wiley & Sons, 2012.(2) Newman, J.; Bennion, D.; Tobias, C. W. Mass Transfer in Concentrated Binary Electrolytes. Berichte der Bunsengesellschaft für Phys. Chemie 1965, 69 (7), 608–612. https://doi.org/10.1002/bbpc.19650690712.(3) Steinrück, H. G.; Takacs, C. J.; Kim, H. K.; MacKanic, D. G.; Holladay, B.; Cao, C.; Narayanan, S.; Dufresne, E. M.; Chushkin, Y.; Ruta, B. et al. Concentration and Velocity Profiles in a Polymeric Lithium-Ion Battery Electrolyte. Energy Environ. Sci. 2020, 13 (11), 4312–4321. https://doi.org/10.1039/d0ee02193h.(4) Bazak, J. D.; Allen, J. P.; Krachkovskiy, S. A.; Goward, G. R. Mapping of Lithium-Ion Battery Electrolyte Transport Properties and Limiting Currents with In Situ MRI. J. Electrochem. Soc. 2020, 167 (14), 140518. https://doi.org/10.1149/1945-7111/abc0c9.(5) Liu, J.; Monroe, C. W. Solute-Volume Effects in Electrolyte Transport. Electrochim. Acta 2014, 135, 447–460. https://doi.org/10.1016/j.electacta.2014.05.009.(6) Dees, D.; Gunen, E.; Abraham, D.; Jansen, A.; Prakash, J. Alternating Current Impedance Electrochemical Modeling of Lithium-Ion Positive Electrodes. J. Electrochem. Soc. 2005, 152 (7), A1409. https://doi.org/10.1149/1.1928169.(7) Pollard, R.; Comte, T. Determination of Transport Properties for Solid Electrolytes from the Impedance of Thin Layer Cells. J. Electrochem. Soc. 1989, 136 (12), 3734–3748. https://doi.org/10.1149/1.2096540.(8) Nyman, A.; Behm, M.; Lindbergh, G. Electrochemical Characterisation and Modelling of the Mass Transport Phenomena in LiPF6-EC-EMC Electrolyte. Electrochim. Acta 2008, 53 (22), 6356–6365. https://doi.org/10.1016/j.electacta.2008.04.023.(9) Villaluenga, I.; Pesko, D. M.; Timachova, K.; Feng, Z.; Newman, J.; Srinivasan, V.; Balsara, N. P. Negative Stefan-Maxwell Diffusion Coefficients and Complete Electrochemical Transport Characterization of Homopolymer and Block Copolymer Electrolytes. J. Electrochem. Soc. 2018, 165 (11), A2766–A2773. https://doi.org/10.1149/2.0641811jes. Figure 1

Anomalous Diffusion with an Apparently Negative Diffusion Coefficient in a One-Dimensional Quantum Molecular Chain Model

An interesting anomaly in the diffusion process with an apparently negative diffusion coefficient defined through the mean-square displacement in a one-dimensional quantum molecular chain model is shown. Nevertheless, the system satisfies the H-theorem so that the second law of thermodynamics is satisfied. The reason why the “diffusion constant” becomes negative is due to the effect of the phase mixing process, which is a characteristic result of the one-dimensionality of the system. We illustrate the situation where this negative “diffusion constant” appears.

Bifurcation and turing instability for a predator-prey model with nonlinear reaction cross-diffusion

A nonlinear reaction cross-diffusion predator-prey system under Neumann boundary condition is considered. Negative diffusion coefficients with local accumulation effect of prey are introduced. Firstly, the criteria for local asymptotic stability of the positive homogeneous steady state with or without cross-diffusion are discussed. Moreover, the conditions for diffusion-driven instability are obtained and the Turing regions in the plane of cross-diffusion coefficients is achieved. Secondly, the existence and multiplicity of spatially nonhomogeneous/homogeneous steady-state solutions are studied by virtue of the Lyapunov–Schmidt reduction. Finally, to clarify the theoretical results, some numerical simulations are carried out. One of the most interesting finding is that Turing instability in the model is induced by the negative diffusion coefficients.

Particle transport of electron cyclotron resonant heating plasma in Large Helical Device

The particle diffusion coefficient and convection velocity of electron cyclotron resonant heating plasmas have been evaluated using a density modulation experiment in the Large Helical Device. The diffusion coefficients and convection velocities were estimated by a newly developed analysis method. This method combines conventional quasi-Newton optimization and a genetic algorithm (GA). The GA finds the appropriate initial values. By giving the appropriate initial values for the quasi-Newton method, falling into an inappropriate solution which is not applicable for transport physics such as negative diffusion coefficients or extremely high values can be avoided. The diffusion coefficient obtained with the modulation experiment (Dmod) in the core region increases monotonically with the increase of the effective collisionality (). The experimental results of Dmod and the convection velocity (Vmod) can reconstruct the density profile at , but they do not reconstruct it at . The values of Dmod were from several times to three orders higher than those obtained by neoclassical prediction. On the other hand, Vmod was comparable with the neoclassical estimation. Ion-scale microturbulence was measured and compared with Dmod and Vmod. The comparison suggested possible linkage between the two.

The stationary distribution of Ornstein–Uhlenbeck process with a two-state Markov switching

ABSTRACTIn this article, we consider some characterizations for the stationary distribution of Ornstein–Uhlenbeck process with a two-state Markov switching. We show that if the drift coefficients α(1), α(2) are negative real numbers and diffusion coefficients σ(1), σ(2) are not equal to zero, then the stationary distributions of OU process with a two-state Markov switching have the density functions and the explicit Fourier transform of stationary density functions are obtained under some special cases. Furthermore, under some stronger assumptions for transition rate of the Markov chain, the Fourier transform of the density functions of stationary distribution can be approximated bywhere , πj is the invariant measure of Markov chain. Besides, some explicit expressions for the stationary distribution are presented and a numerical figure is used to illustrate our result.

Conversation game: talking bacteria.

The story of autonomous unicellular organisms, bacteria with unimaginable computational and evolutionary capabilities along with collective behavior has been running since the first six decades of the twentieth Century. However, do not consider them to be small and simple, because they possess the generic term quorum sensing adopted to describe the cell communication process which co-ordinate gene expression, when the population has reached a high cell density. Bacteria release diffusible signal molecules known as autoinducers or quorum sensing molecules. In recent research, the direction for activating or deactivating nature of a wave of gene expression is predicted experimentally which control bacterial populations subject to a diffusing autoinducer signal. On the other hand, it has been observed that the accumulation of the quorum sensing molecules leads to a negative diffusion coefficient in the solution of governing differential equation.

Double-Diffusive Interleaving: Properties of the Steady-State Solution

AbstractDouble-diffusive interleaving is examined as it progresses from a linear instability toward finite amplitude. When the basic stratification is in the “finger” sense, the initial series of finger interfaces is unstable and one grows in strength at the expense of the others. At an intermediate stage of its development, the interleaving motions pass through a stage when every second interface in the vertical is stable to double diffusion. At a later time this interface turns into a “diffusive” double-diffusive interface. This study takes the fluxes of heat and salt across both the finger and diffusive interfaces to be given by the laboratory flux laws, and the authors ask whether a steady state is possible. It is found that the fluxes across the diffusive interfaces must be many times stronger relative to the corresponding fluxes across the finger interfaces than is indicated from existing flux expressions derived from laboratory experiments. The total effect of the interleaving motion on the vertical fluxes of heat and of salt are calculated for the steady-state solutions. It is found that both the fluxes of heat and salt are upgradient, corresponding to a negative vertical diffusion coefficient for all heat, salt, and density. For moderate to large Prandtl numbers, these negative effective diapycnal diffusivities of heat and salt are approximately equal so that the interleaving process acts to counteract some of the usual turbulent diapycnal diffusivity due to breaking internal waves.

Self-organization of ascending-bubble ensembles

Self-organization of hydrogen bubbles generated by laser-treated areas of an aluminum plate etched in a basic aqueous solution of ammonia is studied experimentally and theoretically. The dynamics of the establishment of a stationary pattern of gas bubbles is experimentally is shown. In the theoretical model, the velocity field of liquid flows around an ensemble of several bubbles is obtained. Modeling of the process of self-organization of gas bubbles is performed on the basis of a continuum model of a bubble jet. Under certain assumptions, the pressure of a diluted system of bubbles is described by an equation similar to that for nonideal gas, which follows the van der Waals equation of state. The model predicts an alignment of gas bubbles along bisectors of the laser-treated area limited by a square, which is in good agreement with experimental observations. Further development of the model leads to an equation with a negative diffusion coefficient that may be responsible for symmetry breakdown and pattern formation.

Water uptake and salt transport through Nafion cation-exchange membranes with different thicknesses

The water uptake of different aqueous salt solutions in different Nafion membranes, and the salt transport through those membranes under the driving force of a concentration gradient, have been studied. These experiments have been performed by using the following salts: lithium chloride, sodium chloride, potassium chloride and cesium chloride. Different homogeneous Nafion membranes, NF111, NF112, NF115 and NF117, have been used in this work, with the aim of studying the membrane thickness influence. It has been observed that the membrane water uptake increases with the membrane thickness and decreases with the size of the cation. The integral permeability coefficient has been determined from the time evolution of the salt concentration in the dilute solution. The results show that the integral permeability coefficient decreases with the membrane thickness. In general, the influence of the type of electrolyte on the integral permeability coefficient is not significant for the membranes with larger thickness (that is, NF115 and NF117). Average apparent cation transport number has been determined for the same salt solutions, and from that membrane apparent permselectivity has been estimated. In general, in membranes with large thickness, the average apparent cation transport number increases with the cation size. Finally, from fluxes and membrane potentials membrane negative ionic permeabilities have been determined finding also that they decrease with membrane thickness. Salt diffusion coefficient has been also determined from membrane negative ionic diffusion coefficient.

Traveling Wavefronts in an Antidiffusion Lattice Nagumo Model

We consider a system of lattice Nagumo equations with cubic nonlinearity, but with a negative discrete diffusion coefficient. We are interested in the existence, uniqueness, stability, and nonexistence of the traveling wavefront solutions of this system, and we shall call this problem the antidiffusion lattice Nagumo problem. By rewriting this system as a spatially periodic system with inhomogeneous but positive periodic diffusion coefficients and periodic nonlinearities, we uncover a rich solution behavior that includes many possible connecting orbits in the antidiffusion case. Second, we observe the presence of bistable and monostable dynamics. In the bistable region, we study the phenomenon of propagation of failure while in the monostable region, we compute the minimum wave speed.

Quantitative Visualization of Buoyant Rise Process in a Swarm of Microbubble Plumes

The evolution of a plume formed by ascending micro-bubbles is investigated by using quantitative visualization to understand the elementary processes that contribute to the inverse energy cascade as small scale flow grows to a large convective flow process. To make the visualization manageable, the plume is confined between two close parallel plates so that the plume-driven convection is restricted to two-dimensions. The results indicate that the bubble plume self-organizes, with a negative diffusion coefficient of buoyancy distribution. A mechanism for the enlargement of the plume is given in terms of two-dimensional flow interaction with the liquid phase. It is confirmed that the kinetic energy is concentrated in the low wavenumber flow from the energy spectra of the liquid phase.

Evolution of non-resonant Buneman instability with a negative diffusion equation

A new method for investigating the spatiotemporal behavior of electron density under the condition of non-resonant Buneman instability is presented. We consider a weakly ionized plasma under the action of a constant electric field. It is shown that electron density satisfies a nonlinear diffusion-like equation with a negative diffusion coefficient. By solving this equation by the Adomian decomposition method, it is concluded that small perturbations of electron density are amplified and the density profile is steepened due to the development of Buneman instability.

Negative diffusion coefficient in a two-dimensional lattice-gas system with attractive nearest-neighbor interactions

Collective diffusion in a two-dimensional lattice-gas system undergoing first-order phase transition is studied both theoretically and by means of Monte Carlo (MC) simulations. The nearest-neighbor attractive interactions result in the formation of a two-phase mixture in which the characteristic size of the dense phase grows with time as ${t}^{1/3}$. It is shown analytically that the evolution of large-scale coverage inhomogeneities is governed by the diffusion equation with a negative diffusion coefficient. Similar to the phenomenon of Ostwald ripening, the Gibbs-Thompson effect is responsible for this abnormal diffusion. MC simulations of random jumps of individual particles also show the presence of negative diffusion caused by the macroscopically inhomogeneous distribution of particle density. The collective diffusion coefficients obtained both theoretically and by means of MC simulations are in satisfactory agreement.

Investigation of spatiotemporal behavior of the plasma density during the development of the thermocurrent instability

Considering a weakly ionized, collisional, quasineutral plasma placed in an electric field under the condition of nonresonant Cerenkov radiation and using the hydrodynamic model, a nonlinear diffusionlike equation with negative diffusion coefficient is obtained, which describes the dynamics of plasma density during the development of the thermocurrent instability. This equation is solved by the Adomian decomposition method. According to this solution, the spatiotemporal behavior of the plasma density during the growth of the thermocurrent instability is investigated. It is shown that the development of the thermocurrent instability causes the initial perturbations in the plasma density to grow. Also, it is shown that the increment in these perturbations continues until the growth of the thermocurrent instability ceases due to the breakdown of the quasineutrality condition. In this case, it is seen that the profile of the plasma density does not change any more and gets to a constant limit.

On the existence of transiently negative diffusion coefficients for electrons in gases in E × B fields

A recent study (Raspopović Z et al 2000 J. Phys. D: Appl. Phys. 33 1298) reported the existence of negative diagonal diffusion tensor elements for electrons in a neutral gas under the influence of crossed radiofrequency electric and magnetic fields. In this paper we demonstrate, using a time-dependent multi-term solution of the Boltzmann equation and time-resolved Monte Carlo simulation, that this phenomenon is a transient relaxation effect obtainable under dc crossed field conditions.