Search NASA⌕ Search

SEARCH · Search NASA

Results for “liquid solution”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16

Divertorlets concept for low-recycling fusion reactor divertor: experimental, analytical and numerical verification

The 'divertorlets' concept is a potential non-evaporative liquid metal solution for heat removal at low recycling regime. A toroidal divertorlets prototype was built and tested in LMX-U at Princeton Plasma Physics Laboratory to evaluate the performance of this configuration. Here, details of the design, experimental results, comparison with analytical theory and MHD numerical simulations of toroidal divertorlets are covered. Experiments, analytical model and simulations showed agreement and allowed the projection of operation properties at higher magnetic flux densities (reactor-like operation), proving the concept to be a compelling solution for divertor applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Solution growth of crystals in zero gravity

A series of experiments will be performed in which triglycine sulfate (TGS) crystals will be grown by a low-temperature solution growth technique in the microgravity environment of the orbital Spacelab. Triglycine sulfate (TGS) crystals will be grown in the Fluid Experiment System (FES) facility on Spacelab 3 by slowly extracting heat at a controlled rate through a seed crystal of TGS suspended on an insulated sting in a saturated solution of TGS. The FES rack assembly designed for SL-3 is shown in Figure I-1, and a detailed view of the test cell layout is presented in Figure I-2. Variations in the liquid density, solution concentration and temperature around the growing crystal will be studied using a variety of techniques, such as schlieren, shadowgraph, and interferometric measurements. Growth in Earth gravity will also be studied by the same optical techniques, and in both cases the resulting crystalline features will be compared and correlated with the growth conditions.

Lai, R. B.↗

Microstructural Evolution and Mechanical Properties of LP-DED NASA HR-1 – A Hydrogen Resistant AM Superalloy for Space Propulsion Applications

The National Aeronautics and Space Administration (NASA) has actively pursued metal additive manufacturing (AM) technologies for spaceflight applications since the late 2000s. AM offers transformative advantages in cost, schedule, part consolidation, and design flexibility. Among the various AM techniques, laser powder directed energy deposition (LP-DED) is particularly well suited for fabricating complex geometries with fine feature resolution. In propulsion systems that utilize high-pressure gaseous hydrogen—such as liquid hydrogen rocket engines—hydrogen environment embrittlement (HEE) presents a serious threat to material performance 1,2 . Mechanical property degradation under these conditions can compromise component reliability, especially under cyclic loading. To address this challenge, NASA developed NASA HR-1 (Hydrogen Resistant-1) as a solution for liquid rocket engine components operating in hydrogen-rich environments, using the LP-DED technique 3-9 . A key component in a liquid rocket engine is the exhaust nozzle, which is typically regeneratively cooled (regen) due to the high heat flux. NASA HR-1 was specifically developed for regen nozzle applications using hydrogen as a propellant, providing resistance to HEE, a critical issue for many materials. The AM version of NASA HR-1 was also formulated to achieve high ultimate tensile strength, along with high yield strength and ductility in this environment 5,6 . Low-cycle fatigue (LCF) is another important consideration in nozzle design, as components are expected to endure multiple starts and missions. Additionally, the LP-DED version of the alloy exhibits improved thermal conductivity compared to its wrought counterpart, which benefits nozzle cooling. Overall, NASA HR-1 offers an excellent balance of high strength, HEE resistance, LCF performance, thermal conductivity, and ductility to meet the demanding requirements of channel-cooled nozzles and other components used with hydrogen and other propellants. The LP-DED–processed NASA HR-1 requires several post-processing heat treatment steps to achieve the material properties desirable for its intended application 6 . These steps include stress relief, homogenization, solution annealing, and aging for precipitation hardening. The stress relief treatment mitigates residual stresses accumulated during the LP-DED process and minimizes the potential for distortion. Homogenization, a common step for AM materials, reduces elemental segregation and promotes recrystallization to develop a more equiaxed grain structure. The subsequent solution annealing treatment heats the part to a solid solution temperature to dissolve the undesirable η-phase that forms during cooling from homogenization, followed by rapid cooling to retain an η-phase–free microstructure. Finally, aging promotes precipitation of the strengthening γ′ phase in the alloy. The integration of compositional design and optimized thermal processing enables high-quality LP-DED NASA HR-1 components with excellent microstructural and mechanical stability. Improved chemical and microstructure homogeneity enhances ductility and fatigue resistance—both critical for safe and reliable operation in high-pressure hydrogen environments. NASA has successfully fabricated and hot-fire tested multiple subscale and full-scale channel wall nozzles using LP-DED NASA HR-1 5,6, 9-14 . These efforts included process refinements to support thin-wall construction and various channel geometries. Throughout development, several key observations emerged. After homogenization, the as-built columnar grain structure transforms into a fully equiaxed microstructure. However, subsequent treatments—such as solution annealing and aging—result in changes that are more difficult to track. The grain structure remains largely unchanged, and the γ′ precipitates, typically 5–10 nm in diameter, are beyond the resolution of scanning electron microscopy (SEM). While transmission electron microscopy (TEM) can resolve these fine precipitates, TEM sample preparation is time-consuming and difficult for LP-DED material. As an alternative, differential scanning calorimetry (DSC) offers a useful, qualitative approach to monitor precipitate evolution throughout different stages of heat treatment. The overall goal is to improve the understanding of how heat treatment affects the microstructure and mechanical performance of LP-DED NASA HR-1. This paper presents heat treatment design considerations, microstructural characterization, mechanical testing – including tensile and LCF testing in both air and hydrogen environments.

Superalloy↗

Collaborative Research Proposal: Time Resolved Optical Emissions Spectroscopy and Laser Induced Fluorescence Spectroscopy of Nanosecond Pulsed Discharges in a Gas-Liquid Water Film Reactor

Electrical discharge plasma formed in contact with liquid water is of interest for a wide range of applications in chemical, biomedical, agricultural, electrical, and materials science and engineering. Such plasma reactors are of very timely importance since they also have significant disinfection capability by inactivating bacteria, viruses and other pathogens. Many types of plasma sources including those driven by AC, DC, RF, microwave, and pulsed electrical power supplies coupled to a wide range of different electrode configurations and reactor designs have been developed and explored which contact the plasma with liquid water. Recent roadmaps have recommended that further work is needed to develop our understanding of the fundamental chemical and physical process which occur at the interface of non-thermal plasma with liquid water solutions in order to advance this large diversity of applications which ultimately depend upon efficient production of key reactive chemical species. There is a wide range of interacting factors that affect the chemical reactions that occur in the plasma, in the liquid phase, and at the interface. These factors ultimately govern the key reactive chemical species formed and used in the various applications and they include a) the reactor design and input parameters, b) the discharge and transport processes, c) the plasma properties, and d) the resulting chemical reactions. For pulsed discharges, the power supply design and output parameters control the applied voltage, frequency, rise time, and width (duration) of the applied pulses. The reactor design involves specification of the gas-liquid contacting methods, electrode gap distance, reactor volume and shape, and gas and liquid flow rates achievable. The gas and liquid compositions as well as the liquid properties such as pH and conductivity are also of key importance in determination of the resulting chemical reactions. In addition, the important plasma properties include plasma gas temperature, electron density, electron energy (distribution), and size of the plasma channels which are all affected by the discharge and transport properties. Many studies have focused on specific aspects of these various processes. Of particular important and relevance to the proposed work is the utilization of nanosecond pulses to generate plasma in gas-liquid systems, liquid bubbles, underwater, and in gases. Recent advances in nanosecond pulses provide significant advantages in utilization with liquid water. For example, fast rise time and short pulses are less sensitive to water conductivity, such short pulses may provide advantages in fast temporal quenching of the plasma, and fundamental analysis of pulse properties, including pulse shape and width, may be facilitated by investigation of single filamentary fast pulses. Many studies have also dealt with the role of the gas composition on formation of reactive oxygen species (ROS) (i.e., hydroxyl radicals – ·OH, hydrogen peroxide – H 2 O 2 , various atomic oxygen species, ozone-O 3 , hydroperoxyl radicals HO 2 ·) and reactive nitrogen species (RNS) (i.e., nitrogen oxides – NO, NO 2 , N 2 O - collectively termed NO X , nitrite-NO 2 - , nitrate-NO 3 - , peroxynitrite-ONOO - ). The hydroxyl radical is the critical species in many chemical oxidation reactions for chemical degradation of toxic compounds in water and gases and for synthesis of some compounds. The mixture of various nitrogen oxide species is important for many biochemical and biological processes involved in biomedical and agricultural applications including disinfection and fertilizer production. The present proposal focuses on determination of the effects of time resolved electron density and hydroxyl radicals on plasma chemical reactions through collaboration with the Princeton Collaborative Low Temperature Plasma Research Facility (PCRF) at the Princeton Plasma Physics Laboratory (PPPL). In order to further investigate the role of the plasma generated electrons and hydroxyl radicals on the overall formation of the key species including hydrogen peroxide, hydroxyl radicals, and nitrogen oxides, the proposed work, thus seeks to determine high resolution time resolved electron density by optical emissions spectroscopy and time resolved hydroxyl radicals using laser induced fluorescence in the nanosecond discharge reactor. The combination of data on electron density and hydroxyl radical concentration will be utilized in the present work to more fully characterize the chemical reaction processes in this system and to advance the design, development, and operation of such chemical reactors for a wide range of applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Aqueous geochemistry at gigapascal pressures: NMR spectroscopy of fluoroborate solutions

Aqueous geochemistry could be extended considerably if nuclear-magnetic resonance (NMR) methods could be adapted to study solutions at elevated temperatures and pressures. We therefore designed an NMR probe that can be used to study aqueous solutions at gigapascal pressures. Fluoride solutions were chosen for study because 19 F couples to other nuclei in the solutions ( 31 P and 11 B) in ways that make peak assignments unequivocal. Correspondingly, NMR spectra of 19 F- and 11 B were collected on aqueous HBF 4 -NH 4 PF 6 solutions to pressures up to 2.0 GPa. At pressure, peaks in the 19 F spectra were clear and assignable to the BF 4 – (aq), F – (aq) and BF 3 OH – (aq) ions, and these aqueous complexes varied in signal intensity with pressure and time, for each solution. Peaks in the 11 B spectra at pressure could be assigned to the BF 4 – (aq) and BF 3 OH – (aq) species. Additionally, there is a single peak that is assignable to H 3 BO 3 o (aq) and B(OH) 4 – (aq) in rapid-exchange equilibria. These peaks broaden and move with pressure in ways that suggest reversible interconversion of borate and fluoroborate species. The PF 6 – ion was found to provide a suitable 19 F shift and intensity standard for high-pressure spectra because it was chemically inert. Here, the positions and intensities of the doublet peak also remains constant as a function of pressure and pH. Addition of electrolytes considerably distorts the phase diagram of water such that the stability region of the aqueous solution expands to well beyond the 0.8 GPa freezing pressure of pure water; some fluoroborate solutions remain liquid until almost 2.0 GPa.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Membrane contactor assisted extraction/reaction process employing ionic liquids

The present invention relates to a functionalized membrane contactor extraction/reaction system and method for extracting target species from multi-phase solutions utilizing ionic liquids. One preferred embodiment of the invented method and system relates to an extraction/reaction system wherein the ionic liquid extraction solutions act as both extraction solutions and reaction mediums, and allow simultaneous separation/reactions not possible with prior art technology.

47 OTHER INSTRUMENTATION↗

Multiphysics analysis of liquid metal annular linear induction pumps: A project overview

Liquid metal-cooled fission reactors are both moderated and cooled by a liquid metal solution. These reactors are typically very compact and they can be used in regular electric power production, for naval and space propulsion systems or in fission surface power systems for planetary exploration. The coupling between the electromagnetics and thermo-fluid mechanical phenomena observed in liquid metal thermo-magnetic systems for nuclear and space applications gives rise to complex engineering magnetohydrodynamics and numerical problems. It is known that electromagnetic pumps have a number of advantages over rotating mechanisms: absence of moving parts, low noise and vibration level, simplicity of flow rate regulation, easy maintenance and so on. However, while developing annular linear induction pumps, we are faced with a significant problem of magnetohydrodynamic instability arising in the device. The complex flow behavior in this type of devices includes a time-varying Lorentz force and pressure pulsation due to the time-varying electromagnetic fields and the induced convective currents that originates from the liquid metal flow, leading to instability problems along the device geometry. The determinations of the geometry and electrical configuration of liquid metal thermo-magnetic devices give rise to a complex inverse magnetohydrodynamic field problem were techniques for global optimization should be used, magnetohydrodynamics instabilities understood –or quantified- and multiphysics models developed and analyzed. Lastly, we present a project overview as well as a few computational models developed to study liquid metal annular linear induction pumps using first principles and the a few results of our multi-physics analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Dynamics of polymer film formation during spin coating

Standard models explaining the spin coating of polymer solutions generally fail to describe the early stages of film formation, when hydrodynamic forces control the solution behavior. Using in situ light scattering alongside theoretical and semi-empirical models, it is shown that inertial forces (which initially cause a vertical gradient in the radial solvent velocity within the film) play a significant role in the rate of thinning of the solution. The development of thickness as a function of time of a solute-free liquid (toluene) and a blend of polystyrene and poly(methyl methacrylate) cast from toluene were fitted to different models as a function of toluene partial pressure. In the case of the formation of the polymer blend film, a concentration-dependent (Huggins) viscosity formula was used to account for changes in viscosity during spin coating. A semi-empirical model is introduced, which permits calculation of the solvent evaporation rate and the temporal evolution of the solute volume fraction and solution viscosity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

In Liquid Infrared Scattering Scanning Near-Field Optical Microscopy for Chemical and Biological Nanoimaging

Imaging biological systems with simultaneous intrinsic chemical specificity and nanometer spatial resolution in their typical native liquid environment has remained a long-standing challenge. In this paper we demonstrate a general approach of chemical nanoimaging in liquid based on infrared scattering scanning near-field optical microscopy (IR $s$-SNOM). It is enabled by combining AFM operation in a fluid cell with evanescent IR illumination via total internal reflection, which provides spatially confined excitation for minimized IR water absorption, reduced far-field background, and enhanced directional signal emission and sensitivity. We demonstrate in-liquid IR $s$-SNOM vibrational nanoimaging and conformational identification of catalase nano-crystals and spatio-spectral analysis of biomimetic peptoid sheets with monolayer sensitivity and chemical specificity at the few zeptomole level. This work establishes the principles of in-liquid and in-situ IR $s$-SNOM spectroscopic chemical nano-imaging and its general applicability to biomolecular, cellular, catalytic, electrochemical, or other interfaces and nano-systems in liquids or solutions.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Isopentane Disproportionation in Lewis Acidic Chloroaluminate Ionic Liquid

Lewis acidic chloroaluminate ionic liquid diluted in dichloromethane catalyzes the disproportionation of alkanes, such as isopentane, via carbenium ions in a reaction readily initiated by carbenium ion precursors such as tert-butyl chloride (TBC). The carbenium ion-AlCl 4 – ion-pairs stabilized by the ionic liquid-dichloromethane solution are the key intermediates in two distinctive kinetic regimes, i.e., a transient regime (0–5 min) and a steady-state regime (after 5 min). The transient regime constitutes the majority of isopentane conversion and is governed by the initial carbenium ion concentration. In the steady-state regime, disproportionation occurs at a considerably lower rate, affected by the carbenium ion concentration, the concentration of the ionic liquid, and the reaction temperature. The formation of alkenes observed in the 1 H NMR spectra of the reacting substrates, along with the DFT calculations, suggests that deprotonation of carbenium ion-pairs reduces their concentration, decreasing, in turn, the reaction rate. Kinetic modeling indicates that the transient regime is significantly controlled by the hydride transfer (k HT ) and the deprotonation rate constants (k DP ), while the steady-state regime is additionally influenced by the alkene protonation rate constant (k –DP ). The overall activation energy of the reaction at the steady state, expressed as E a,steady-state regime = E a,HT – E a,DP + E a,–DP , was 54 kJ/mol. The reaction mechanism and the kinetics highlight the potential of Lewis acid-catalyzed conversions of hydrocarbons under remarkably mild conditions.

Deprotonation↗

Vibrations of Elastic Shells of Revolution Partially Filled with Ideal Liquid

We propose an algorithm for the numerical analyses of vibrations of elastic shells of revolution partially filled with ideal incompressible liquids. In the solution of this problem, the wave motions of liquid on its free surface are taken into account. The solution of the problem of hydroelasticity is based on the application of the method of decomposition of the domain of integration of equations of the theory of shells with the use of the variational statement of the problem and on the approximate construction of the operator inverse to the operator of the hydrodynamic part of the problem. We construct a generalized functional of displacements of the shell for which the role of conditions of matching for the solutions in different subdomains is played by the natural boundary conditions. The obtained numerical results are compared with the existing exact solutions of the analyzed problem for a shell in the form of a straight circular cylinder.

42 ENGINEERING↗

Sodium Sulfate Separation from Aqueous Alkaline Solutions via Crystalline Urea-Functionalized Capsules: Thermodynamics and Kinetics of Crystallization

We measured the thermodynamics and kinetics of crystallization of sodium sulfate with a tripodal tris-urea receptor (L1) from aqueous alkaline solutions in the 15 55 C temperature range, with the goal of identifying the optimal conditions for efficient and quick sulfate removal from nuclear wastes. The use of radiolabeled Na 2 35 SO 4 provided a practical way to monitor the sulfate concentration in solution by liquid scintillation counting. Our results are consistent with a two-step crystallization mechanism, involving relatively quick dissolution of crystalline L1 followed by the rate-limiting crystallization of the Na 2 SO 4 (L1) 2 (H 2 O) 4 capsules. We found that temperature exerted relatively little influence over the equilibrium sulfate concentration, which ranged between 0.004 and 0.011 M. Moreover, this corresponds to 77 91% removal of sulfate from a solution containing 0.0475 M initial sulfate concentration, as found in a typical Hanford waste tank. The apparent pseudo-first-order rate constant for sulfate removal increased 20-fold from 15 to 55 C, corresponding to an activation energy of 14.1 kcal/mol. At the highest measured temperature of 55 C, 63% and 75% of sulfate was removed from solution within 8 h and 24 h, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Algorithms and file structures to extend and enhance liquid chromatography and ion mobility mass spectrometry workflows (CRADA Final Report)

The purpose of this project was to continue supporting customizations of algorithms and raw data file structures to enhance software workflows for liquid chromatography (LC), mass spectrometry (MS) and ion mobility mass spectrometry (IM-MS)-based protein and metabolite characterization. PNNL worked with Agilent to design, implement, evaluate, and demonstrate new algorithms and integrated them as functionalities into the PNNL-PreProcessor software. The project augmented PNNL’s capabilities to analyze complex proteomics and metabolomics samples. These capabilities are directly beneficial to DOE and PNNL efforts to characterize and analyze these compounds in microbial and plant communities. The project assisted Agilent in further developing improved instrument-software solutions combining liquid chromatography and ion mobility with mass spectrometry for widespread applications in life sciences and other fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Upper critical solution temperature polymer assemblies via variable temperature liquid phase transmission electron microscopy and liquid resonant soft X-ray scattering

Abstract Here, we study the upper critical solution temperature triggered phase transition of thermally responsive poly(ethylene glycol)- block -poly(ethylene glycol) methyl ether acrylate- co -poly(ethylene glycol) phenyl ether acrylate- block -polystyrene nanoassemblies in isopropanol. To gain mechanistic insight into the organic solution-phase dynamics of the upper critical solution temperature polymer, we leverage variable temperature liquid-cell transmission electron microscopy correlated with variable temperature liquid resonant soft X-ray scattering. Heating above the upper critical solution temperature triggers a reduction in particle size and a morphological transition from a spherical core shell particle with a complex, multiphase core to a micelle with a uniform core and Gaussian polymer chains attached to the surface. These correlated solution phase methods, coupled with mass spectral validation and modeling, provide unique insight into these thermoresponsive materials. Moreover, we detail a generalizable workflow for studying complex, solution-phase nanomaterials via correlative methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Non-Equilibrium Plasma Interactions with Biomaterials, Biological Solutions and Tissues

Cold atmospheric pressure plasma discharges offer an abundant source of reactive oxygen and nitrogen species (RONS) at room temperature enabling unique interactions with biomaterials, biological solutions and tissues. These interactions particularly with living matter are presently an important intellectual frontier in plasma science with promising potential applications ranging from human health care to advanced biomaterial processing. Exciting case studies have been reported that illustrate the huge potential of cold atmospheric plasma technology in wound healing and cancer treatment. The interaction of plasma with conducting and dielectric biomaterials such as tissue strongly influences the plasma properties. In turn this changes the impact of the plasma on the biomaterial. Particularly in the case of living matter, liquid based solutions are ubiquitous which complicates interfacial processes. The lack of insight into the underlying mechanisms of the interaction of plasma with wounds and tumors is currently a bottleneck for the further development of the technology and gives rise to many interesting scientific questions. This project was focused on plasma properties and kinetics during plasma-biomaterial interactions. Both DC pulsed and RF driven atmospheric pressure plasma jets, extensively used by the plasma community were studied. The bio-interfaces included hydrogel as a tissue model, (saline) solutions, bacteria and virus. Plasma diagnostics used include Thomson scattering, Rayleigh scattering, Raman scattering, (two-photon absorption) laser induced fluorescence, optical emission spectroscopy, absorption spectroscopy, molecular beam mass spectrometry and fast imaging allowing to determine electron densities and temperatures, ionic species, reactive species including radicals, gas temperatures, gas composition, electric fields and solution components transferred to the gas phase.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Radiative Importance of Aerosol-Cloud Interaction

Aerosol particles are input into the troposphere by biomass burning, among other sources. These aerosol palls cover large expanses of the earth's surface. Aerosols may directly scatter solar radiation back to space, thus increasing the earth's albedo and act to cool the earth's surface and atmosphere. Aerosols also contribute to the earth's energy balance indirectly. Hygroscopic aerosol act as cloud condensation nuclei (CCN) and thus affects cloud properties. In 1977, Twomey theorized that additional available CCN would create smaller but more numerous cloud droplets in a cloud with a given amount of liquid water. This in turn would increase the cloud albedo which would scatter additional radiation back to space and create a similar cooling pattern as the direct aerosol effect. Estimates of the magnitude of the aerosol indirect effect on a global scale range from 0.0 to -4.8 W/sq m. Thus the indirect effect can be of comparable magnitude and opposite in sign to the estimates of global greenhouse gas forcing Aerosol-cloud interaction is not a one-way process. Just as aerosols have an influence on clouds through the cloud microphysics, clouds have an influence on aerosols. Cloud droplets are solutions of liquid water and CCN, now dissolved. When the cloud droplet evaporates it leaves behind an aerosol particle. This new particle does not have to have the same properties as the original CCN. In fact, studies show that aerosol particles that result from cloud processing are larger in size than the original CCN. Optical properties of aerosol particles are dependent on the size of the particles. Larger particles have a smaller backscattering fraction, and thus less incoming solar radiation will be backscattered to space if the aerosol particles are larger. Therefore, we see that aerosols and clouds modify each other to influence the radiative balance of the earth. Understanding and quantifying the spatial and seasonal patterns of the aerosol indirect forcing may have even greater consequences. Presently we know that through the use of fossil fuel and land-use changes we have increased the concentration of greenhouse gases in the atmosphere. In parallel, we have seen a modest increase of global temperature in the last century. These two observations have been linked as cause and effect by climate models, but this connection is still experimentally not verified. The spatial and seasonal distribution of aerosol forcing is different from that of greenhouse gases, thus generating a different spatial fingerprint of climate change. This fingerprint was suggested as a method to identify the response of the climate system to anthropogenic forcing of greenhouse gases and aerosol. The aerosol fingerprint may be the only way to firmly establish the presence (or absence) of human impact on climate. Aerosol-cloud interaction through the indirect effect will be an important component of establishing this fingerprint.

Tsay, Si-Chee↗