Crossing the Widom-line – Supercritical pseudo-boiling

Critical Threshold for Bubble-like Nucleation during Pseudoboiling at Supercritical Pressures

Supercritical pseudoboiling was proposed in the 1950s-1960s. Recently, evaporation-like and boiling-like heat transfer have been directly observed in macroscopic scales, and the contribution of pseudoboiling to the total heat transfer rate has been quantitatively characterized experimentally. Here, we explore the critical threshold to generate a bubble-like nucleus at supercritical pressure at the atomic scale, characterized by the total energy (Te = Ke + Pe, where Ke and Pe are kinetic energy and potential energy, respectively). Molecular dynamics simulations are performed, including an argon fluid box heated by a solid wall having its temperature above the fluid temperature. The fluid pressure is controlled by a movable piston wall opposite the heating wall. The effects of pressure, nonuniform heating, and surface wettability on pseudoboiling are investigated. It is found that the criterion Te > 0 should be satisfied for subcritical boiling, matching that reported previously. The criterion for supercritical pseudoboiling was newly obtained such that Te > 0.012 eV at 8 MPa for argon, but the threshold increases as pressure increases. Nonuniform heating and surface wettability do not affect the critical threshold of Te for bubble-like nucleation but affect the location of the initially generated bubble-like nucleus and the stabilized pseudofilm or pseudonucleate heat transfer modes, where the former is similar to (vapor) film boiling and the latter is similar to nucleate boiling at subcritical pressure. Because pseudoboiling occurs without surface tension at supercritical pressure, we observe that the bubble-like structure may not display a perfectly smooth gas-liquid interface but may display an irregular pattern instead. Our work explains pseudoboiling from the viewpoint of the competition between kinetic energy and potential energy and presents a link regarding boiling in the two domains of subcritical pressure and supercritical pressure.

Widom Line in Supercritical Water in Terms of Changes in Local Structure: Theoretical Perspective

Performing molecular dynamics simulations with the TIP4P/2005 water model along 9 isobars (from 175 to 375 bar) in the temperature range between 300 and 1100 K, we have found that the loci of the extrema in the rate of change of specific structural properties can be used to define purely structure-based Widom lines. We have examined several parameters that describe the local structure of water, such as the tetrahedral arrangement, nearest neighbor distance, local density around the molecules, and the size of the largest dense domain. The last two parameters were determined using the Voronoi polyhedral and density-based spatial clustering of applications with noise methods, respectively. By analyzing the moments of the associated distributions, we show that along a given isobar, the temperature at which we observe a maximum in the fluctuation, the rate of change of the average values, or in the skewness values unambiguously determines the Widom line that is in agreement with the experimentally detected, thermodynamic response function-based ones.

Thermodynamic crossovers in supercritical fluids

Can liquid-like and gas-like states be distinguished beyond the critical point, where the liquid-gas phase transition no longer exists and conventionally only a single supercritical fluid phase is defined? Recent experiments and simulations report strong evidence of dynamical crossovers above the critical temperature and pressure. Despite using different criteria, many existing theoretical explanations consider a single crossover line separating liquid-like and gas-like states in the supercritical fluid phase. We argue that such a single-line scenario is inconsistent with the supercritical behavior of the Ising model, which has two crossover lines due to its symmetry, violating the universality principle of critical phenomena. To reconcile the inconsistency, we define two thermodynamic crossover lines in supercritical fluids as boundaries of liquid-like, indistinguishable, and gas-like states. Near the critical point, the two crossover lines follow critical scalings with exponents of the Ising universality class, supported by calculations of theoretical models and analyses of experimental data from the standard database. The upper line agrees with crossovers independently estimated from the inelastic X-ray scattering data of supercritical argon, and from the small-angle neutron scattering data of supercritical carbon dioxide. The lower line is verified by the equation of states for the compressibility factor. This work provides a fundamental framework for understanding supercritical physics in general phase transitions.

Instability in strongly stratified plane Couette flow, with application to supercritical fluids

This paper addresses the stability of plane Couette flow in the presence of strong density and viscosity stratifications. It demonstrates the existence of a generalised inflection point that satisfies the generalised Fjørtoft's criterion of instability when a minimum of kinematic viscosity is present in the base flow. The characteristic scales associated with this minimum are identified as the primary controlling parameters of the associated instability, regardless of the type of stratification. To support this finding, analytical stability models are derived in the long wave approximation using piecewise linear base flows. Numerical stability calculations are carried out to validate these models and to provide further information on the production of disturbance vorticity. All instabilities are interpreted as arising from the interaction between two vorticity waves. Depending on the type of stratification, these two waves are produced by different physical mechanisms. When both strong density and viscosity stratifications are present, we show that they result from the concurrent action of shear and inertial baroclinic effects. The stability models developed for simple fluid models ultimately shed light on a recently observed unstable mode in supercritical fluids (Ren et al., J. Fluid Mech., vol. 871, 2019, pp. 831-864), providing a quantitative prediction of the stability diagram and identifying the dominant mechanisms at play. Furthermore, our study suggests that the minimum of kinematic viscosity reached at the Widom line in these fluids is the leading cause of their instability. The existence of similar instabilities in different fluids and flows (e.g., miscible fluids) is finally discussed.

Holding water in a sieve-stable droplets without surface tension

Our understanding of supercritical fluids has seen exciting advances over the last decades, often in direct contradiction to established textbook knowledge. Rather than being structureless, we now know that distinct supercritical liquid and gaseous states can be distinguished and that a higher order phase transition - pseudo boiling - occurs between supercritical liquid and gaseous states across the Widom line. Observed droplets and sharp interfaces at supercritical pressures are interpreted as evidence of surface tension due to phase equilibria in mixtures, given the lack of a supercritical liquid-vapor phase equilibrium in pure fluids. However, here we introduce an alternative physical mechanism that unexpectedly causes a sharpening of interfacial density gradients in absence of surface tension: thermal gradient induced interfaces (TGIIF). We show from first principles and simulations that, unlike in gases or liquids, stable droplets, bubbles, and planar interfaces can exist without surface tension. These results challenge and generalize our understanding of what droplets and phase interfaces are, and uncover yet another unexpected behavior of supercritical fluids. TGIIF provide a new physical mechanism that could be used to tailor and optimize fuel injection or heat transfer processes in high-pressure power systems.

Non-ideal gas behavior matters in hydrodynamic instability

Hydrodynamic instability, the foundation for flow's laminar-turbulent transition and various predicting models, has been helping to understand the physics and shape the design of aerodynamic devices. While for hypersonic flow it is clear that thermodynamic/-chemical effects need be accounted for due to the high temperatures occurring, this letter unveils that also for low-speed flow at ambient temperatures non-ideal, i.e. real-gas effects can play a strong role-a feature missed by the classic theory for Newtonian fluids. By considering a three-dimensional low-speed boundary-layer flow in different thermodynamic regimes-subcritical, supercritical and transcritical-we show the importance of coupling thermodynamics by sensitivity studies of the perturbation growth rate to various inputs of the full stability equations. High sensitivities are found, and not only the transition-onset location but also the transition mechanism may be concerned.

Phase boundaries and the Widom line from the Ruppeiner geometry of fluids

The Ruppeiner geometry has been shown to provide novel ways for constructing the phase boundaries and the Widom line of certain fluids. This paper examines the applicability of these geometric constructions to more general fluids. We develop a general equation-of-state expansion for fluids near a critical point that mainly assumes analyticity with respect to the number density. Based on this general parametrization of fluids, we prove the equivalence of the Ruppeiner geometric construction and the standard Maxwell construction of phase boundaries near the critical point. In contrast, we find that the usual prescription based on the Ruppeiner geometry for the Widom line does not produce the expected Widom line for arbitrary cases of our general fluid equation of state. This usual prescription relies on the Ruppeiner metric induced on a particular hypersurface of the thermodynamic manifold. We show that by choosing a different hypersurface, which we call the Ruppeiner-N surface, and using its associated induced metric, the Ruppeiner construction generates the entire Widom line of the van der Waals fluid exactly, even away from the critical point. Interestingly, this alternative hypersurface yields another benefit. It improves the classification scheme originally proposed by Diósi et al. for partitioning the van der Waals state space into its different phases using geodesics of a thermodynamic metric. We argue that, whereas the original Diósi boundaries did not correspond to any clear thermodynamic lines, the corresponding boundaries based on the Ruppeiner-N metric become sensitive to the presence of the van der Waals Widom line and provide the correct classification of all van der Waals states. These results suggest that the Ruppeiner-N surface may be the more appropriate hypersurface to use when studying phase diagrams with thermodynamic geometry.

Fingerprints of the Crossing of the Frenkel and Melting Line on the Properties of High-Pressure Supercritical Water

Using molecular dynamics simulations in combination with the two-phase thermodynamic model, we reveal novel characteristic fingerprints of the crossing of the Frenkel and melting line on the properties of high-pressure water at a near-critical temperature (1.03T_c). The crossing of the Frenkel line at about 1.17 GPa is characterized by a crossover in the rotational and translational entropy ratio S^rot/S^trans, indicating a change in the coupling between translational and rotational motions which is also reflected in the shape of the rotational density of states. The observed isosbestic points in the translational and rotational density of states are also blue-shifted at density and pressure conditions higher than the ones corresponding to the Frenkel line. The first-order phase transition from a rigid liquid to a face-centered cubic plastic crystal phase at about 8.5 GPa is reflected in the discontinuous changes in the translational and rotational entropy, particularly in the significant increase of the ratio S^rot/S^trans. A noticeable discontinuous increase of the dielectric constant has also been revealed when crossing this melting line, which is attributed to the different arrangement of the water molecules in the plastic crystal phase. The reorientational dynamics in the plastic crystal phase is faster in comparison with the "rigid" liquid-like phase, but it remains unchanged upon a further pressure increase in the range of 8.5-11 GPa.

Numerical Investigation of Heat Transfer Characteristics of scCO2 Flowing in a Vertically-Upward Tube with High Mass Flux

In this work, the heat transfer characteristics of supercritical pressure CO₂ in vertical heating tube with 10 mm inner diameter under high mass flux were investigated by using an SST k-ω turbulent model. The influences of inlet temperature, heat flux, mass flux, buoyancy and flow acceleration on the heat transfer of supercritical pressure CO₂ were discussed. Our results show that the buoyancy and flow acceleration effect based on single phase fluid assumption fail to explain the current simulation results. Here, supercritical pseudo-boiling theory is introduced to deal with heat transfer of scCO₂. scCO₂ is treated to have a heterogeneous structure consisting of vapor-like fluid and liquid-like fluid. A physical model of scCO₂ heat transfer in vertical heating tube was established containing a gas-like layer near the wall and a liquid-like fluid layer. Detailed distribution of thermophysical properties and turbulence in radial direction show that scCO₂ heat transfer is greatly affected by the thickness of gas-like film, thermal properties of gas-like film and turbulent kinetic energy in the near-wall region. Buoyancy parameters Bu < 10⁻⁵, Bu* < 5.6 × 10⁻⁷ and flow acceleration parameter K_v < 3 × 10⁻⁶ in this paper, which indicate that buoyancy effect and flow acceleration effect has no influence on heat transfer of scCO₂ under high mass fluxes. This work successfully explains the heat transfer mechanism of supercritical fluid under high mass flux.

Structure and Properties of Supercritical Water: Experimental and Theoretical Characterizations

Water in the supercritical region of the phase diagram exhibits a markedly different structure and properties from that at ambient conditions, which is useful in controlling chemical reactions. Nonetheless, the experimental, as well as theoretical, characterization of the substance is not easy because the region is next to the critical point. This article reviews the experimental as well as theoretical studies on water in the supercritical region and its properties as a solvent for chemical reactions, as carried out by the authors and based on small-angle X-ray scattering and the statistical mechanics theory of molecular liquids, also known as reference interaction-site model (RISM) theory.

The Anomalous Behavior of Thermodynamic Parameters in the Three Widom Deltas of Carbon Dioxide-Ethanol Mixture

Using molecular dynamics, we demonstrated that in the mixture of carbon dioxide and ethanol (25% molar fraction) there are three pronounced regions on the p-T diagram characterized by not only high-density fluctuations but also anomalous behavior of thermodynamic parameters. The regions are interpreted as Widom deltas. The regions were identified as a result of analyzing the dependences of density, density fluctuations, isobaric thermal conductivity, and clustering of a mixture of carbon dioxide and ethanol in a wide range of pressures and temperatures. Two of the regions correspond to the Widom delta for pure supercritical carbon dioxide and ethanol, while the third region is in the immediate vicinity of the critical point of the binary mixture. The origin of these Widom deltas is a result of the large mixed linear clusters formation.

Towards Understanding the Structure of Subcritical and Transcritical Liquid–Gas Interfaces Using a Tabulated Real Fluid Modeling Approach

A fundamental understanding and simulation of fuel atomization, phase transition, and mixing are among the topics researchers have struggled with for decades. One of the reasons for this is that the accurate, robust, and efficient simulation of fuel jets remains a challenge. In this paper, a tabulated multi-component real-fluid model (RFM) is proposed to overcome most of the limitations and to make real-fluid simulations affordable. Essentially, a fully compressible two-phase flow and a diffuse interface approach are used for the RFM model, which were implemented in the CONVERGE solver. PISO and SIMPLE numerical schemes were modified to account for a highly coupled real-fluid tabulation approach. These new RFM model and numerical schemes were applied to the simulation of different fundamental 1-D, 2-D, and 3-D test cases to better understand the structure of subcritical and transcritical liquid–gas interfaces and to reveal the hydro-thermodynamic characteristics of multicomponent jet mixing. The simulation of a classical cryogenic injection of liquid nitrogen coaxially with a hot hydrogen jet is performed using thermodynamic tables generated by two different equations of state: Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK). The numerical results are finally compared with available experimental data and published numerical studies with satisfactory agreement.

Phase distribution including a bubblelike region in supercritical fluid

Pseudoboiling in supercritical fluid (SF) has been paid great attention in recent years. Available works mainly focus on thermodynamics analysis. Fewer studies were reported on the spatial time phase distribution. Here, SF is investigated in a multiphase fluid framework using molecular dynamics (MD) simulations. A simulation box contains 10 976 argon atoms, with periodic boundary conditions applied on all the box surfaces. Pressure and temperature are well controlled. Based on MD simulation results, an onset pseudoboiling temperature T^{-} and a termination pseudoboiling temperature T^{+} are defined using the neighboring molecules method, the radial distribution function method, and the two-body excess entropy method. The two transition temperatures divide the whole phase diagram into three regimes of liquidlike, two-phase-like (TPL), and gaslike, and the MD determined T^{-} and T^{+} well matched the thermodynamics-determined values. In the TPL regime, nanovoids are observed to have two distinct characteristics: (1) Particles are sparsely distributed to have gas density inside the void, but are densely populated to have liquid density outside the void. (2) Voids have a curved interface. These characteristics are very similar to bubble characteristics in subcritical pressure. Hence, voids in the supercritical state are called "bubblelike" in this paper. Nonlinear dynamics demonstrates chaotic behavior in the TPL regime, similar to the two-phase regime in the subcritical domain. The above findings give strong evidence that SF in the TPL regime consists of a mixture of bubblelike voids and surrounding liquids. Our work highlights the multiphase feature of a SF, hence, the well-established multiphase theory in subcritical pressures can be introduced to handle the complex SF.

Quasi-equilibrium phase coexistence in single component supercritical fluids

In their supercritical state simple fluids are generally thought to assume a homogeneous phase throughout all combinations of pressures and temperatures, although various response functions or transport properties may exhibit anomalous behavior, characterizing a state point as either more gas-like or liquid-like, respectively. While a large body of results has been compiled in the last two decades regarding the details of the supercritical phase in thermodynamic equilibrium, far less studies have been dedicated to out-of-equilibrium situations that nevertheless occur along with the handling of substances such as carbon dioxide or Argon. Here we consider successive compression-expansion cycles of equal amounts of Argon injected into a high-pressure chamber, traversing the critical pressure at two times the critical temperature. Due to expansion cooling, the fluid temporarily becomes sub-critical, and light scattering experiments show the formation of sub-micron-sized droplets and nanometer-scale clusters, both of which are distinct from spontaneous density fluctuations of the supercritical background and persist for a surprisingly long time. A kinetic rate model of the exchange of liquid droplets with the smaller clusters can explain this behavior. Our results indicate non-equilibrium aspects of supercritical fluids that may prove important for their processing in industrial applications.

In their supercritical state simple fluids are generally thought to assume a homogeneous phase throughout. Lee et al. find that liquid droplets temporarily formed in a supercritical background after sub-critical injection can survive for a surprisingly long time.

Supercritical Water Choking Flow Experiments Through a Convergent-Divergent Test Section

The heat transport system of Gen-IV supercritical water-cooled reactors (SCWRs) will operate at pressures close to 25 MPa and outlet temperatures of up to 625 °C. The design and safety analyses of this type of reactors still necessitate among others, experimental information and validation of critical (choked) flows models of water above the thermodynamic critical state. Up to now, choked flow data were collected at atmospheric discharge pressure conditions, without changing the discharge pressure to verify the occurrence of choking flow; in most of the cases, using fluids different from water. This paper presents experimental supercritical water choking flow data collected by using a convergent-divergent test section by changing the discharge pressure to verify the occurrence of choked flow. The critical mass flux is presented as a function of the temperature difference between a pseudo-critical temperature and the bulk fluid temperature. This representation allows us to assess similar experiments performed by using different test sections. Hence, a comparison of actual data with those previously obtained using 1.0 mm and 1.4 mm diameter sharp-edged orifices, shows peculiar differences. The actual experiments were limited by very low values of choking mass flow rates. Furthermore, in some cases, it was observed the presence of an increase in the discharge pressure that seems to indicate the existence of shock-wave structures. We are also able to estimate a pseudo-critical temperature difference below which choking flow systematically occurs.

Thermodynamics and Dynamics of Supercritical Water Pseudo-Boiling

Supercritical fluid pseudo-boiling (PB), recently brought to the attention of the scientific community, is the phenomenon occurring when fluid changes its structure from liquid-like (LL) to gas-like (GL) states across the Widom line. This work provides the first quantitative analysis on the thermodynamics and the dynamics of water's PB, since the understanding of this phase transition is mandatory for the successful implementation of technologies using supercritical water (scH2O) for environmental, energy, and nanomaterial applications. The study combines computational techniques with in situ neutron imaging measurements. The results demonstrate that, during isobaric heating close to the critical point, while water density drops by a factor of three in the PB transitional region, the system needs >16 times less energy to increase its temperature by 1 K than to change its structure from LL to GL phase. Above the PB-Widom line, the structure of LL water consists mainly of tetramers and trimers, while below the line mostly dimers and monomers form in the GL phase. At atomic level, the PB dynamics are similar to those of the subcritical water vaporization. This fundamental knowledge has great impact on water science, as it helps to establish the structure-properties relationship of scH2O.

Two-Component Dynamics and the Liquidlike to Gaslike Crossover in Supercritical Water

Molecular-scale dynamics in sub- to supercritical water is studied with inelastic x-ray scattering and molecular dynamics simulations. The obtained longitudinal current correlation spectra can be decomposed into two main components: a low-frequency (LF), gaslike component and a high-frequency (HF) component arising from the O-O stretching mode between hydrogen-bonded molecules, reminiscent of the longitudinal acoustic mode in ambient water. With increasing temperature, the hydrogen-bond network diminishes and the spectral weight shifts from HF to LF, leading to a transition from liquid- to gaslike dynamics with rapid changes around the Widom line.

Numerical Modeling of Transcritical and Supercritical Fuel Injections Using a Multi-Component Two-Phase Flow Model

In the present numerical study, implicit large eddy simulations (LES) of non-reacting multi-components mixing processes of cryogenic nitrogen and n-dodecane fuel injections under transcritical and supercritical conditions are carried out, using a modified reacting flow solver, originally available in the open source software OpenFOAM®. To this end, the Peng-Robinson (PR) cubic equation of state (EOS) is considered and the solver is modified to account for the real-fluid thermodynamics. At high pressure conditions, the variable transport properties such as dynamic viscosity and thermal conductivity are accurately computed using the Chung transport model. To deal with the multicomponent species mixing, molar averaged homogeneous classical mixing rules are used. For the velocity-pressure coupling, a PIMPLE based compressible algorithm is employed. For both cryogenic and non-cryogenic fuel injections, qualitative and quantitative analyses are performed, and the results show significant effects of the chamber pressure on the mixing processes and entrainment rates. The capability of the proposed numerical model to handle multicomponent species mixing with real-fluid thermophysical properties is demonstrated, in both supercritical and transcritical regimes.

Understanding Sub and Supercritical Cryogenic Fluid Dynamics in Conditions Relevant to Novel Ultra Low Emission Engines

In this paper we provide insight into the thermophysical properties and the dynamics of cryogenic jets. The motivation of the work is to optimise the use of cryogenic fluids in novel ultra low emission engines. For demonstration, we use conditions relevant to an internal combustion engine currently being developed by Dolphin N2 and the University of Brighton, the CryoPower recuperated split cycle engine (RSCE). The principle of this engine is a split-cycle combustion concept which can use cryogenic injection in the compression cylinder to achieve isothermal compression and thus help maximise the efficiency of the engine. Combined experimental and numerical findings are presented and the effects of atomisation dynamics of the LN 2 are explored at both sub- and supercritical conditions in order to cover different pressure and temperature conditions representative of the engine compression cycle. For subcritical regimes, we observe that the appearance of the jet coincides with the predicted atomisation regimes based on the Weber, Ohnesorge and Reynolds numbers for other common fluids. For the modelling of supercritical jets, a new methodology within OpenFoam which accounts for Real Fluid Thermodynamics has been developed and the jet behaviour under various pressure and temperature conditions has been investigated. To our knowledge this is the first study where a cryogenic spray process evolution is examined for conditions relevant to the ones prevailing in a compression chamber accounting for both sub and supercritical conditions.

Turbulence Modeling Insights into Supercritical Nitrogen Mixing Layers

In Liquid Rocket Engines, higher combustion efficiencies come at the cost of the propellants exceeding their critical point conditions and entering the supercritical domain. The term fluid is used because, under these conditions, there is no longer a clear distinction between a liquid and a gas phase. The non-conventional behavior of thermophysical properties makes the modeling of supercritical fluid flows a most challenging task. In the present work, a Reynolds Averaged Navier Stokes (RANS) computational method following an incompressible but variable density approach is devised on which the performance of several turbulence models is compared in conjunction with a high accuracy multi-parameter equation of state. In addition, a suitable methodology to describe transport properties accounting for dense fluid corrections is applied. The results are validated against experimental data, making it clear that there is no trend between turbulence model complexity and the quality of the produced results. For several instances, one- and two-equation turbulence models produce similar results. Finally, considerations about the applicability of the tested turbulence models in supercritical simulations are given based on the results and the structural nature of each model.

The use of process simulation in supercritical fluids applications

Modelling and simulation from micro- to macro-scale are needed to attain a broader commercialization of supercritical technologies.

Visualization of supercritical water pseudo-boiling at Widom line crossover

Supercritical water is a green solvent used in many technological applications including materials synthesis, nuclear engineering, bioenergy, or waste treatment and it occurs in nature. Despite its relevance in natural systems and technical applications, the supercritical state of water is still not well understood. Recent theories predict that liquid-like (LL) and gas-like (GL) supercritical water are metastable phases, and that the so-called Widom line zone is marking the crossover between LL and GL behavior of water. With neutron imaging techniques, we succeed to monitor density fluctuations of supercritical water while the system evolves rapidly from LL to GL as the Widom line is crossed during isobaric heating. Our observations show that the Widom line of water can be identified experimentally and they are in agreement with the current theory of supercritical fluid pseudo-boiling. This fundamental understanding allows optimizing and developing new technologies using supercritical water as a solvent.

Supercritical water exists in gas- and liquid-like forms, but these have not been distinguished yet at the macroscale. Here the authors investigate supercritical water interacting with microporous carbon by neutron imaging, and observe the coexistence of gas- and liquid-like states upon crossing the Widom line.

Experimental and theoretical evidence of a supercritical-like transition in an organic semiconductor presenting colossal uniaxial negative thermal expansion

Thermal expansion coefficients of most materials are usually small, typically up to 50 parts per million per kelvin, and positive, i.e. materials expand when heated. Some materials show an atypical shrinking behavior in one or more crystallographic directions when heated. Here we show that a high mobility thiophene-based organic semiconductor, BHH-BTBT, has an exceptionally large negative expansion between 95 and 295 K (-216 < α2 = αb < -333 MK-1), being compensated by an even larger positive expansion in the perpendicular direction (287 < α1 < 634 MK-1). It is shown that these anomalous expansivities are completely absent in C8-BTBT, a much studied organic semiconductor with a closely related molecular formula and 3D crystallographic structure. Complete theoretical characterization of BHH-BTBT using ab initio molecular dynamics shows that below ∼200 K two different α and β domains exist of which one is dominant but which dynamically exchange around and above 210 K. A supercritical-like transition from an α dominated phase to a β dominated phase is observed using DSC measurements, UV-VIS spectroscopy, and X-ray diffraction. The origin of the extreme negative and positive thermal expansion is related to steric hindrance between adjacent tilted thiophene units and strongly enhanced by attractive S···S and S···C interactions within the highly anharmonic mixed-domain phase. This material could trigger the tailoring of optoelectronic devices highly sensitive to strain and temperature.

Widom Delta of Supercritical Gas-Liquid Coexistence

Density fluctuations and the Widom line are of great importance in understanding the critical phenomena and the behaviors of supercritical fluids (SCFs). We report on the direct classification of liquid-like and gas-like molecules coexisting in the SCF, identified by machine learning analysis on simulation data. The deltoid coexistence region encloses the Widom line and may therefore be termed the Widom delta. Number fractions of gas-like and liquid-like particles are found to undergo continuous transition across the delta, following a simplified two-state model. These fractions are closely related to the magnitude of supercritical anomaly, which originates from the fluctuation between the two types. This suggests a microscopic view of the SCF as a mixture of liquid-like and gas-like structures, providing an integrative explanation to the anomalous behaviors near the critical point and the Widom line.

Cooling beyond the boundary value in supercritical fluids under vibration

Supercritical fluids when subjected to simultaneous quench and vibration have been known to cause various intriguing flow phenomena and instabilities depending on the relative direction of temperature gradient and vibration. Here we describe a surprising and interesting phenomenon wherein temperature in the fluid falls below the imposed boundary value when the walls are quenched and the direction of vibration is normal to the temperature gradient. We define these regions in the fluid as sink zones, because they act like sink for heat within the fluid domain. The formation of these zones is first explained using a one-dimensional (1D) analysis with acceleration in constant direction. Subsequently, the effect of various boundary conditions and the relative direction of the temperature gradient to acceleration are analyzed, highlighting the necessary conditions for the formation of sink zones. It is found that the effect of high compressibility and the action of self-weight (due to high acceleration) causes the temperature to change in the bulk besides the usual action of piston effect. This subsequently affects the overall temperature profile thereby leading to the formation of sink zones. Though the examined 1D cases differ from the current two-dimensional (2D) cases, owing to the direction of acceleration being normal as compared to parallel in case of former, the explanations pertaining to 1D cases are judiciously utilized to elucidate the formation of sink zones in 2D supercritical fluids subjected to thermal quench and vibrational acceleration. The appearance of sink zones is found to be dependent on several factors such as proximity to the critical point and acceleration. A surface three-dimensional plot illustrating the effect of these parameters on onset time of sink zones is presented to further substantiate these arguments.

Widom line, dynamical crossover, and percolation transition of supercritical oxygen via molecular dynamics simulations

Supercritical oxygen, a cryogenic fluid, is widely used as an oxidizer in jet propulsion systems and is therefore of paramount importance in gaining physical insights into processes such as transcritical and supercritical vaporization. It is well established in the scientific literature that the supercritical state is not homogeneous but, in fact, can be demarcated into regions with liquid-like and vapor-like properties, separated by the "Widom line." In this study, we identified the Widom line for oxygen, constituted by the loci of the extrema of thermodynamic response functions (heat capacity, volumetric thermal expansion coefficient, and isothermal compressibility) in the supercritical region, via atomistic molecular dynamics simulations. We found that the Widom lines derived from these response functions all coincide near the critical point until about 25 bars and 15-20 K, beyond which the isothermal compressibility line begins to deviate. We also obtained the crossover from liquid-like to vapor-like behavior of the translational diffusion coefficient, shear viscosity, and rotational relaxation time of supercritical oxygen. While the crossover of the translational diffusion coefficient and shear viscosity coincided with the Widom lines, the rotational relaxation time showed a crossover that was largely independent of the Widom line. Further, we characterized the clustering behavior and percolation transition of supercritical oxygen molecules, identified the percolation threshold based on the fractal dimension of the largest cluster and the probability of finding a cluster that spans the system in all three dimensions, and found that the locus of the percolation threshold also coincided with the isothermal compressibility Widom line. It is therefore clear that supercritical oxygen is far more complex than originally perceived and that the Widom line, dynamical crossovers, and percolation transitions serve as useful routes to better our understanding of the supercritical state.