Nonequilibrium Effects Research Articles

Single-Step Control of Liquid-Liquid Crystalline Phase Separation by Depletion Gradients.

Fine-tuning nucleation and growth of colloidal liquid crystalline (LC) droplets, also known as tactoids, is highly desirable in both fundamental science and technological applications. However, the tactoid structure results from the trade-off between thermodynamics and nonequilibrium kinetics effects, and controlling liquid-liquid crystalline phase separation (LLCPS) in these systems is still a work in progress. Here, a single-step strategy is introduced to obtain a rich palette of morphologies for tactoids formed via nucleation and growth within an initially isotropic phase exposed to a gradient of depletants. The simultaneous appearance is shown of rich LC structures along the depleting potential gradient, where the position of each LC structure is correlated with the magnitude of the depleting potential. Changing the size (nanoparticles) or the nature (polymers) of the depleting agent provides additional, precise control over the resulting LC structures through a size-selective mechanism, where the depletant may be found both within and outside the LC droplets. The use of depletion gradients from depletants of varying sizes and nature offers a powerful toolbox for manipulation, templating, imaging, and understanding heterogeneous colloidal LC structures.

Instantaneous Marcus theory for photoinduced charge transfer dynamics in multistate harmonic model systems

Modeling the dynamics of photoinduced charge transfer (CT) in condensed phases presents challenges due to complicated many-body interactions and the quantum nature of electronic transitions. While traditional Marcus theory is a robust method for calculating CT rate constants between electronic states, it cannot account for the nonequilibrium effects arising from the initial nuclear state preparation. In this study, we employ the instantaneous Marcus theory (IMT) to simulate photoinduced CT dynamics. IMT incorporates nonequilibrium structural relaxation following a vertical photoexcitation from the equilibrated ground state, yielding a time-dependent rate coefficient. The multistate harmonic (MSH) model Hamiltonian characterizes an organic photovoltaic carotenoid-porphyrin-fullerene triad dissolved in explicit tetrahydrofuran solvent, constructed by mapping all-atom inputs from molecular dynamics simulations. Our calculations reveal that the electronic population dynamics of the MSH models obtained with IMT agree with the more accurate quantum-mechanical nonequilibrium Fermi’s golden rule. This alignment suggests that IMT provides a practical approach to understanding nonadiabatic CT dynamics in condensed-phase systems.

Numerical investigations on flow and heat transfer characteristics of a high-enthalpy double-cone in thermal and chemical non-equilibrium for hypersonic propulsion

There are strong interests in hypersonic propulsion communities in predicting the flow and heat transfer characteristics over a hypersonic vehicle. However, this is quite challenging due to the emergence of thermal and chemical out-of-equilibrium effects as prominent in a high-temperature flow. In this work, we conduct 2D numerical investigations on the hypersonic double cone flow in a surrounding of the stagnation enthalpy of 15.23 MJ/kg by solving the laminar Navier–Stokes equation systems with the vibrational non-equilibrium processes and seven species air reactions. We then conduct the sensitivities analyses on the flow and heat transfer features, as different transport models and different thermochemical models are applied. It is shown that the aerodynamic heat is more sensitive to the transport models than the flow, and the transport coefficients computed by the Gupta-Yos model are more suitable for predicting the double cone flow at the high enthalpy. On the other hand, the flow field of the high enthalpy double cone is more sensitive to the thermochemical models than the heat transfer on the wall excluding the peak position. Behind the detached shock, chemical reactions are found to enhance thermal or vibrational out-of-equilibrium effects. However, vibrational non-equilibrium effects are revealed to weaken the degree of molecule dissociation reactions. Two flow separations occur in the flow field computed by using the thermal non-equilibrium gas models, but the flows of thermal equilibrium gas models separate only once. The maximum values of wall parameters without chemical reactions are found to deviate greatly from the experimental measurements. The thermochemical out-of-equilibrium gas model can predict the separation region size closer to the experiment than the two reported numerical results. The wall static pressure and heat flux are also shown to well match the experimental results. The present work should shed lights on better understanding thermochemical non-equilibrium effects of complex flow phenomenon like the shock wave/boundary layer interaction in hypersonic propulsion with high enthalpy surroundings.

Influence of thermochemical non-equilibrium effects on non-uniform entrance scramjet nozzle

The high Mach number scramjet nozzle flow has prominent non-uniform characteristics and high-temperature non-equilibrium effects. Thus, the thermochemical non-equilibrium gas model was developed for simulating flows in the non-uniform and uniform entrance of a Mach 10 hydrocarbon fuel scramjet nozzle. The results show that the non-uniform entrance has a higher non-uniform degree in the flow-field compared to the uniform entrance. Additionally, the expansion degree inside the nozzle is greater and the thermal non-equilibrium effects downstream of the nozzle exit are stronger. The non-uniform entrance condition has a more intense chemical reaction near the nozzle exit but has less impact on the flow parameters. For the nozzle performance, under the influence of the non-uniform entrance, the greater gas expansion degree inside the nozzle results in a lower pressure acting on the upper wall, and then the nozzle thrust decreases by 1.68%. Hence, the structural design and performance optimization of the high Mach number scramjet nozzle must consider entrance non-uniform characteristics and thermochemical non-equilibrium effects.

An improved continuum model for hypersonic thermal nonequilibrium flow in the near-continuum regime

In this work, the rarefied Couette flow of diatomic gases with thermal nonequilibrium effects is investigated by the direct simulation Monte Carlo (DSMC) method, and a macroscopic computational model is developed to consider the local rarefaction effects for diatomic gases in the near-continuum regime. The nonlinear transport properties of the diatomic gases are studied, indicating that effective viscosity and effective translational thermal conductivity in the shear nonequilibrium state are affected by translational nonequilibrium effects, which obey the same laws for both monatomic and diatomic gases. The transport coefficients of internal energy modes are affected by both translational nonequilibrium and internal energy relaxation, therefore, the effective rotational and vibrational thermal conductivities are related to the effective viscosity through a modified Eucken relation that accounts for internal energy relaxation. Conclusively, effective constitutive relations are newly established as a function of the shear nonequilibrium parameter and the modified Eucken factors for thermal nonequilibrium flows, and these are integrated into the macroscopic two-temperature model. Subsequently, it is assessed in the simulation of hypersonic flows over flat plates and cylinders at various Knudsen numbers. The results show that the surface shear stress and heat flux obtained by the proposed model agree well with the DSMC results, indicating significantly improved performance compared to the conventional Navier–Stokes two-temperature model for hypersonic flows in the near-continuum regime.

A phase-splitting approach to describe macroscopically non-equilibrium transport in porous media

Classical macro-scale dispersion equation cannot correctly represent non-local, non-equilibrium effects, and alternatives had to be proposed to overcome these discrepancies. Two-equation models have been widely used and proved useful to incorporate, to some extent, local non-equilibrium effects. More accurate descriptions may be obtained through the introduction of additional complex terms in the one-equation dispersion equation, e.g. spatial and time convolutions. An alternative more practical route rely on the introduction of a N-equations description. For instance, instead of a two-temperature model, transfers in the solid and/or fluid phase maybe represented by several equations, each one defined by some splitting framework. Splitting of the solid phase has been proposed in the past (multi-rate models). Splitting of the flowing phase has a rustic illustration in the case of the Coats and Smith model, i.e., ”flowing” and ”stagnant” fluid equations. In this paper, we explore further the possibilities offered by N-equations splitting of the flowing phase. The N-equations macro-scale model is developed applying an averaging technique to N-pseudo phases obtained by splitting the flowing phase based on different criteria, e.g. the velocity histogram. Most important model properties are the matrices of dispersion tensors and exchange coefficients, which are provided by a system of specific ”closure” problems. To illustrate this approach, the methodology is applied to Taylor’s dispersion problem, in which non-local effects are produced by pore-scale spatially distributed inlet conditions. The proposed N-equations description was compared to estimates of the N-temperatures obtained from direct numerical simulations. The N-equations model was able to reproduce accurately the dynamic of pore-scale computations, for such reputedly non-homogenizable problems, with a relatively small number of equations.

Effects of high-temperature and entropy layer of Mach 12 oblique shock wave

In the current study, we numerically investigate the high-temperature inviscid flows over the 15-degree wedges with the sharp and blunt leading-edges. Firstly, the vibrational non-equilibrium effects in sharp wedge flow with different deflection angles are analyzed. Then, the influence of the vibrational non-equilibrium effects on the flow parameters behind the oblique shock wave is provided. Lastly, we discuss the high-temperature non-equilibrium flow over the 15-degree wedge with the entropy layer.

Effect of near-wall distance on velocity slip and temperature jump conditions in hypersonic rarefied gas flows

In nonequilibrium slip and jump conditions, normal gas velocity and temperature gradients are used to calculate the gas slip velocity and temperature at the surface, respectively. Gökçen et al. (Computational fluid dynamics near the continuum limit, AIAA Paper No. 87-1115, 1987, and Gökçen and MacCormack, Nonequilibrium effects for hypersonic transitional flows using continuum approach, AIAA Paper No. 89-0461, 1989) stated that the tangential velocity and temperature of the gas molecules before a collision with the surface could be interpreted as the macroscopic tangential velocity and temperature of the gas molecules at the so-called near-wall distances auλ and aTλT away from the surface, respectively. The coefficients au and aT are the order of unity. In the present work, new forms of the slip and jump conditions are proposed by modifying the Gökçen slip and jump conditions to include the coefficients (au, aT). Numerical investigations are comprehensively conducted to determine the numerically proper values (au, aT) for the hypersonic rarefied gas flows. Cases such as the circular cylinder in cross-flow and sharp and blunted leading edge wedge are considered in the present work, with nitrogen as the working gas. The simulation results show the significant effects of the coefficients (au, aT) on the accuracy of the slip velocity and surface gas temperature predictions, and the values of au = 1.2 and aT = 1.1 show good agreement with the direct simulation Monte Carlo data.

Synthetic Gaia DR3 Surveys from the FIRE Cosmological Simulations of Milky Way-mass Galaxies

The third data release (DR3) of Gaia has provided a fivefold increase in the number of radial velocity measurements of stars, as well as a stark improvement in parallax and proper motion measurements. To help with studies that seek to test models and interpret Gaia DR3, we present nine Gaia synthetic surveys, based on three solar positions in three Milky Way-mass galaxies of the Latte suite of the Fire-2 cosmological simulations. These synthetic surveys match the selection function, radial velocity measurements, and photometry of Gaia DR3, adapting the code base Ananke, previously used to match the Gaia DR2 release by Sanderson et al. The synthetic surveys are publicly available and can be found at http://ananke.hub.yt/. Similarly to the previous release of Ananke, these surveys are based on cosmological simulations and thus are able to model nonequilibrium dynamical effects, making them a useful tool in testing and interpreting Gaia DR3.

All-Atom Photoinduced Charge Transfer Dynamics in Condensed Phase via Multistate Nonlinear-Response Instantaneous Marcus Theory.

Photoinduced charge transfer (CT) in the condensed phase is an essential component in solar energy conversion, but it is challenging to simulate such a process on the all-atom level. The traditional Marcus theory has been utilized for obtaining CT rate constants between pairs of electronic states but cannot account for the nonequilibrium effects due to the initial nuclear preparation. The recently proposed instantaneous Marcus theory (IMT) and its nonlinear-response formulation allow for incorporating the nonequilibrium nuclear relaxation to electronic transition between two states after the photoexcitation from the equilibrium ground state and provide the time-dependent rate coefficient. In this work, we extend the nonlinear-response IMT method for treating photoinduced CT among general multiple electronic states and demonstrate it in the organic photovoltaic carotenoid-porphyrin-fullerene triad dissolved in explicit tetrahydrofuran solvent. All-atom molecular dynamics simulations were employed to obtain the time correlation functions of energy gaps, which were used to generate the IMT-required time-dependent averages and variances of the relevant energy gaps. Our calculations show that the multistate IMT could capture the significant nonequilibrium effects due to the initial nuclear state preparation, and this is corroborated by the substantial differences between the population dynamics predicted by the multistate IMT and the Marcus theory, where the Marcus theory underestimates the population transfer. The population dynamics by multistate IMT is also shown to have a better agreement with the all-atom nonadiabatic mapping dynamics than the Marcus theory does. Because the multistate nonlinear-response IMT is straightforward and cost-effective in implementation and accounts for the nonequilibrium nuclear effects, we believe this method offers a practical strategy for studying charge transfer dynamics in complex condensed-phase systems.

Navier-Stokes characteristic boundary conditions for high-enthalpy compressible flows in thermochemical non-equilibrium

This fundamental study presents Navier-Stokes characteristic boundary conditions (NSCBCs) for high-enthalpy hypersonic flows in thermochemical non-equilibrium. In particular, the relevant locally one-dimensional inviscid (LODI) relations are derived within a two-temperature framework for high-enthalpy hypersonic flows undergoing finite-rate thermochemical processes, including air dissociation and vibrational relaxation. Using these LODI relations, a set of NSCBCs are proposed and later demonstrated in canonical test cases, including the interaction of homogeneous isotropic turbulence with a shock wave subject to high-enthalpy thermochemical non-equilibrium effects.

A modified local thermal non-equilibrium model of transient phase-change transpiration cooling for hypersonic thermal protection

Aiming to efficiently simulate the transient process of transpiration cooling with phase change and reveal the convection mechanism between fluid and porous media particles in a continuum scale, a new two-phase mixture model is developed by incorporating the local thermal non-equilibrium effect. Considering the low-pressure and high overload working conditions of hypersonic flying, the heat and mass transfer induced by capillary and inertial body forces are analyzed for sub-cooled, saturated and super-heated states of water coolant under varying saturation pressures. After the validation of the model, transient simulations for different external factors, including spatially-varied heat flux, coolant mass flux, time-dependent external pressure and aircraft acceleration are conducted. The results show that the vapor blockage patterns at the outlet are highly dependent on the injection mass flux value and the external pressure, and the reduced saturation temperature at low external pressure leads to early boiling off and vapor blockage. The motion of flying has a large influence on the cooling effect, as the inertial force could change the flow pattern of the fluid inside significantly. The comparison of the results from 2-D and 3-D simulations suggests that 3-D simulation shall be conducted for practical application of transpiration cooling, as the thermal protection efficiency may be overestimated by the 2-D results due to the assumption of an infinite width length of the porous plate.

Three-dimensional characteristics of aerodynamic shockwave and condensation shockwave in steam ejectors

Characteristics of aerodynamic and condensation shockwaves are not clear in steam ejectors as the three-dimensional and non-equilibrium condensation effects in many simulation research are ignored. In the article, a non-equilibrium condensation model was developed to study the three-dimensional shockwave characteristics of steam ejectors. The formation, physical form, occurrence condition, location, quantity, intensity, and asymmetry of aerodynamic and condensation shockwave in different regions of three-dimensional steam ejectors were illustrated from mechanism. The coupling effect and interaction mechanism of aerodynamic and condensation shockwave were investigated. The influences of aerodynamic and condensation shockwaves on the flow field were analyzed. The similarities and differences between aerodynamic and condensation shockwaves were clarified. Results show that non-equilibrium condensation induces the condensation shockwave, but the condensation shockwave inhibits the non-equilibrium condensation. There is mutual inhibition between condensation shock and aerodynamic shock. A condensation shockwave appears downstream of the steam ejector's nozzle throat and another condensation shockwave may appear in the mixing chamber. The condition of the condensation shockwave in the mixing chamber is that the supercooling degree and the supersaturation ratio after the expansion wave exceed their critical values. In the critical condition, the supercooling degree is 19.6 K when the condensation shockwave appears in the mixing chamber.

Pathological detonation in H[formula omitted]-Cl[formula omitted] mixtures: Uncertainty quantification and thermal non-equilibrium effects

Pathological detonations are detonations with a propagation velocity higher than the classical Chapman–Jouguet velocity and which depends on the wave structure. Such a behavior has been experimentally observed in low-pressure hydrogen-chlorine mixtures and important discrepancies were reported between the experimental and the theoretical velocities. Using the steady planar detonation model, along with a state-of-the-art chemical mechanism this work aims at investigating two aspects potentially responsible for these discrepancies: (i) the impacts of uncertainties in chemical kinetics mechanisms, and (ii) thermal non-equilibrium effects. The uncertainties in the rate constants of reactions R2: 2Cl+M=Cl2+M and R3: Cl2+H=HCl+Cl are found to be the dominant sources of uncertainty for the steady propagation velocity and the induction length of the pathological detonations. The multi-temperature, thermal non-equilibrium model is found to provide generally higher detonation velocity than the experimental value and the eigenvalue solutions obtained under thermal equilibrium. Nevertheless, for specific values of the initial vibrational temperature of HCl, the results can be closer to the experimental values. This latter aspect provides the motivation for future work that relies on more comprehensive thermal non-equilibrium modeling.

Non-equilibrium thermal transport study in steady state GaN MISHEMT channel layer based on electron Monte Carlo and phonon BTE

An electro-thermal coupling simulator for GaN devices based on electron Monte Carlo (e-MC) simulations is established. Taking GaN Metal Insulator Semiconductor High Electron Mobility Transistor (MISHEMT) as example, the non-equilibrium thermal transport processes of self-heating effect in the channel layer are studied. This simulator is mainly coupled by e-MC and the phonon Boltzmann transport equation (pBTE), physical property parameters and electric field parameters are provided by first-principles and Technology Computer Aided Design (TCAD), respectively. We first verify the e-MC program by calculating the electron transport properties of GaN materials, verify the feasibility of the established GaN MISHEMT model by using TCAD and obtained its operating characteristics. Further, the simulator is used to evaluate the non-equilibrium processes inside the channel layer in detail, the results show that there is significant consistency in the peak positions of electric field strength, heat generation and diffusion temperature, the diffusion temperature peak occurs at the secondary peak of heat generation. The frequency distribution of phonon emission under different drain-source bias voltages is revealed by phonon emission spectrum analysis. The strength of the non-equilibrium effect is measured by effective temperature. Increasing the drain-source bias voltage will significantly increase the peak temperature of hotspot and further enhance the non-equilibrium effect. Our study reports an efficient scheme for electro-thermal simulations of GaN MISHEMT, which provides insights for thermal management of GaN-based transistor devices.

Hypersonic boundary layer over a flat plate with slip and shear nonequilibrium effects

Near-space hypersonic vehicles could encounter significant rarefied nonequilibrium effects during the flight through atmosphere, which largely influence the gas-surface momentum and heat transfer. In this paper, hypersonic boundary layer over a flat plate with velocity slip, temperature jump, and shear nonequilibrium effects is theoretically considered. The slip boundary conditions and nonlinear transport relations are embedded into the boundary-layer equations to describe the flow. Local similar solutions are derived, and key parameters for characterizing slip and shear nonequilibrium effects are determined. The velocity-slip and temperature-jump effects are determined by [(2−σu)/σu]Mae/Rex and [(2−σT)/σT]Mae/Rex respectively, and the shear nonequilibrium effect is characterized by Mae2/Rex. The obtained boundary-layer solutions are compared with the Navier–Stokes solutions for a Mach 4.5 slip flow, and the results of Direct Simulation Monte Carlo for a Mach 10 rarefied flow, good agreements are achieved. The separate and combined effects of velocity slip, temperature jump, and shear nonequilibrium on boundary-layer solutions and momentum/heat transfer are clarified. The results show that both the slip and shear nonequilibrium effects cause the boundary layer to become thinner and decrease the skin friction and Fourier heat conduction. However, with including sliding friction, the total heat flux might even increase as the slip degree increases. These results provide valuable insight into the boundary-layer characteristics of hypersonic near-continuum flows.

Regular reflection of shock waves in steady flows: viscous and non-equilibrium effects

Numerical analysis of a steady monatomic gas flow about the point of the regular reflection of a strong oblique shock wave from the symmetry plane is conducted with the Navier–Stokes–Fourier (NSF) equations, the regularized Grad 13-moment (R13) equations and the direct simulation Monte Carlo (DSMC) method. In contrast to the inviscid solution to this problem completely defined by the Rankine–Hugoniot (RH) relations, all three models predict a complicated flow structure with strong thermal non-equilibrium and a long wake with flow parameters not predicted by the RH relations. The temperature $T_y$ related to thermal motion of molecules in the direction normal to the symmetry plane has a maximum inside the reflection zone while in a planar shock wave the maximum is observed for the $T_x$ temperature. The R13 equations predict these features much better than the NSF equations and are in good agreement with the benchmark DSMC results. An analysis of the flow with the conservation equations was conducted in order to evaluate the effects of various processes on a fluid element moving along the symmetry plane. In contrast to the shock wave where effects of viscosity and heat conduction are one-dimensional with zeroth net contribution to the fluid-element energy across the shock, the flow across the zone of the shock reflection is dominated by two-dimensional effects with positive net contribution of viscosity and negative contribution of heat conduction to the fluid-element energy. These effects are believed to be the main source of the wake with parameters deviating from the RH values.

Bubble wall velocities with an extended fluid Ansatz

We compute the terminal bubble wall velocity during a cosmological phase transition by modelling non-equilibrium effects in the plasma with the so-called “extended fluid Ansatz”. A ϕ 6 operator is included in the Standard Model effective potential to mimic effects of new physics. Hydrodynamical heating of the plasma ahead of the bubble is taken into account. We find that the inclusion of higher order terms in the fluid Ansatz is typically relevant, and may even turn detonation solutions into deflagrations. Our results also corroborate recent findings in the literature that, for a Standard Model particle content in the plasma, only deflagration solutions are viable. However, we also show that this outcome may be altered in a theory with a different particle content.

Data-driven nonlinear turbulent flow scaling with Buckingham Pi variables

Nonlinear machine learning for turbulent flows can exhibit robust performance even outside the range of training data. This is achieved when machine-learning models can accommodate scale-invariant characteristics of turbulent flow structures. This study presents a data-driven approach to reveal scale-invariant vortical structures across Reynolds numbers that provide insights for supporting nonlinear machine-learning-based studies of turbulent flows. To uncover conditions for which nonlinear models are likely to perform well, we use a Buckingham-Pi-based sparse nonlinear scaling to find the influence of the Pi groups on the turbulent flow data. We consider nonlinear scalings of the invariants of the velocity gradient tensor for an example of three-dimensional decaying isotropic turbulence. The present scaling not only enables the identification of vortical structures that are interpolatory and extrapolatory for the given flow field data but also captures non-equilibrium effects of the energy cascade. As a demonstration, the present findings are applied to machine-learning-based super-resolution analysis of three-dimensional isotropic turbulence. We show that machine-learning models reconstruct vortical structures well in the interpolatory space with reduced performance in the extrapolatory space revealed by the nonlinearly scaled invariants. The present approach enables us to depart from labelling turbulent flow data with a single parameter of Reynolds number and comprehensively examine the flow field to support training and testing of nonlinear machine-learning techniques.

An anisotropic lattice Boltzmann - phase field model for dendrite growth and movement in rapid solidification of binary alloys

A model coupling the lattice Boltzmann and the phase field methods with anisotropic effects is proposed, which is used to numerically describe the growth and movement of dendrites in rapid solidification of alloys. The model is quantitatively validated by the simulation of the continuous growth and the drafting-kissing-tumbling phenomenon of two falling particles, and then applied to investigate the effects of dendrite movement and interfacial non-equilibrium on evolution of dendritic patterns for Si-9.0at%As and the CET for Al-3.0wt%Cu alloys. Both the growth and remelt processes of isolated dendrites are studied, and the result reveals the remelting influences on dendrite growth and solute micro-segregation in the condition of directional solidification. This work demonstrates that the proposed model has a wide range of applicability and great potential to simulate the microstructure evolution with various solidification conditions.