Confinement Gap Research Articles

A mechanistic model to predict saturated pool boiling Critical Heat Flux (CHF) in a confined gap

Boiling enables high rates of heat transfer from a surface made possible at a relatively low thermal resistance motivating the use of two-phase cooling for increasingly compact thermal management solutions. However, extreme geometrical confinement of the liquid above the boiling surfaces is known to have detrimental effects on maximum heat transfer rate by inducing premature onset of film boiling. Moreover, previously developed critical heat flux (CHF) models for confined geometries focused on triggering mechanisms associated with unconfined pool boiling and, thus, are not generalizable. This work proposes a new mechanistic model for predicting CHF during boiling within in narrow gap, specifically developed to account for confinement effects on the triggering mechanism. The model postulates that occurrence of CHF coincides with the irreversible growth of a dry spot on the boiling surface. Three competing forces govern the two-phase interface dynamics, namely vapor momentum, surface tension, and hydrostatic forces. Dryout is triggered when the vapor momentum force due to vaporization at the two-phase interface balances the combined surface tension and hydrostatic forces leading to irreversible growth of the dry spot. The present work offers a predictive confined CHF model that accounts for confined boiling surface shape, size, orientation, confinement gap spacing, and working fluid properties, with a single fluid-specific fitting coefficient that represents the ratio of vapor area to the confinement opening area near CHF conditions. Notably, the developed CHF model is also effective in predicting the threshold gap below which confinement reduces pool boiling CHF. The model is compared to 197 experimentally measured confined CHF data points available from 10 studies in the literature that represent 7 different working fluids and a range of boiling surface inclinations and shapes. The model predicts the confinement-reduced CHF values with a root mean square error of 21%, which is less than half of the error compared to all other available predictive models. This clarification of the triggering mechanism and improved prediction accuracy of CHF, as offered by the current study, will enable broader practical system implementation of compact two-phase cooling technologies.

Stability of destructive quantum interference antiresonances in electron transport through graphene nanostructures

We investigate the stability of destructive quantum interference (DQI) in electron transport through graphene nanostructures connected to source and drain electrodes. The fingerprint of DQI is an antiresonance in the transmission function, and its origin is deeply connected to the topology of the atomic structure, which we discuss in terms of symmetry arguments supported by numerical simulations. A systematic analysis of the transmission function versus system size reveals that the DQI antiresonance persists for large systems in the ballistic regime and establishes the quantum confinement gap as the intrinsic resolution limit to detect QI effects. Furthermore, we consider the influence of disorder, electron–electron and electron–phonon interactions, and provide quantitative criteria for the robustness of DQI in their presence. We find that the conductance is quite sensitive to perturbations, and its value alone may not be sufficient to characterize the quantum interference properties of a junction. Instead, the characteristic behavior of the transmission function is more resilient, and we suggest it retains information on the presence of an antiresonance even if DQI is partially concealed or suppressed. At the same time, DQI results in a non-linear transport regime in the current-bias characteristics that can be possibly detected in transport experiments.

Translational Diffusion of a Fluorescent Tracer Molecule in Nanoconfined Water.

Diffusion of tracer dye molecules in water confined to the nanoscale is an important subject with a direct bearing on many technological applications. It is not yet clear, however, if the dynamics of water in hydrophilic as well as hydrophobic nanochannels remains bulk-like. Here, we present diffusion measurement of a fluorescent dye molecule in water confined to the nanoscale between two hydrophilic surfaces whose separation can be controlled with a precision of less than a nm. We observe that the fluorescence intensities correlate over fast (∼30 μs) and slow (∼1000 μs) time components. The slow time scale is due to adsorption of fluorophores to the confining walls, and it disappears in the presence of 1 M salt. The fast component is attributed to diffusion of dye molecules in the gap. It is found to be bulk-like for sub-10 nm separations and indicates that the viscosity of water under confinement remains unaltered up to a confinement gap as small as ∼5 nm. Our findings contradict some of the recent measurements of diffusion under nanoconfinement; however, they are consistent with many estimates of self-diffusion using molecular dynamics simulations and measurements using neutron scattering experiments.

Vapor stem bubbles dominate heat transfer enhancement in extremely confined boiling

Boiling has long been sought as the heat dissipation mechanism for a wide variety of compact thermal management applications owing to low-resistance heat transport, high heat flux limits, and surface isothermalization. This work aims to elucidate the thermofluidic transport mechanisms of boiling in extremely confined gaps through experimental measure of the temporal evolution of heat fluxes and surface temperatures during deionized water boiling, as well as high-speed visualization of bubble formation. The flow visualizations reveal small residual pockets of vapor, termed ‘stem bubbles’ herein, that remain on the boiling surface through a pinch-off process where vapor escapes through the edges of the confined heated region. These stem bubbles act as seeds for vapor growth in the next phase of the boiling process. These bubbles dictate the boiling performance for extremely confined boiling as defined based on a dimensionless ratio of the gap spacing to capillary length (Bo≤ 0.35 - 0.5). This conclusion is supported by the enhanced thermal response of the surface compared to nucleate boiling. Because activation of nucleation sites is not required for stem bubble boiling, phase change occurs at a reduced surface superheat at a given heat flux compared to nucleate boiling. Criteria for the dimensionless confinement gap spacing are identified to harness this improved heat transfer rate of the stem bubble boiling regime. This new understanding of boiling in extremely confined gaps offers a new direction to design compact two-phase thermal management solutions through using the unique enhancements provided by the vapor stem bubble boiling regime.

Topological defects and confinement with machine learning: The case of monopoles in compact electrodynamics

We investigate the advantages of machine learning techniques to recognize the dynamics of topological objects in quantum field theories. We consider the compact U(1) gauge theory in three spacetime dimensions as the simplest example of a theory that exhibits confinement and mass gap phenomena generated by monopoles. We train a neural network with a generated set of monopole configurations to distinguish between confinement and deconfinement phases, from which it is possible to determine the deconfinement transition point and to predict several observables. The model uses a supervised learning approach and treats the monopole configurations as three-dimensional images (holograms). We show that the model can determine the transition temperature with accuracy, which depends on the criteria implemented in the algorithm. More importantly, we train the neural network with configurations from a single lattice size before making predictions for configurations from other lattice sizes, from which a reliable estimation of the critical temperatures are obtained.

On the role of confinement plate wettability on pool boiling heat transfer

Remarkably high heat transfer coefficient observed during boiling makes it one of the most sought-after thermal management solutions. However, the heat dissipation potential deteriorates in practical scenarios of confined spaces typically encountered in electronic packages and compact heat exchangers, among others. Contrary to unconfined pool boiling, confinement hinders buoyancy aided vapor removal from the heater surface. Accordingly, vapor crowding inhibits the continuous supply of fresh liquid to the heater surface, eventually resulting in premature dryout/critical heat flux (CHF) in comparison to the baseline case of unconfined boiling on the same surface. While studies in literature report the effect of various parameters such as gap dimensions, heater surface to confinement plate area ratio, and surface inclination on confined pool boiling, the role of confinement plate wettability on bubble behavior and heat transfer has yet not been reported. Here we perform controlled experiments to show that superhydrophobic (SHPo) surfaces attract vapor/air bubbles and can be used to enhance heat transfer during confined boiling. In comparison to the typical case of boiling with hydrophilic (HPi) confinement plate, nucleating bubbles underneath a SHPo confinement plate detach easily from the heater surface to provide a continuous pathway for liquid re-supply and heater surface rewetting. Using this strategy, we shown a significant increase of up to 82% in heat dissipation capacity using SHPo confinement plate in comparison to the baseline case of the HPi confinement plate. Detailed parametric investigation of the effect of confinement gap and heater surface to confinement plate area ratio on heat transfer performance is also reported. We believe that the ability to improve confined boiling heat transfer performance by merely tuning the wettability of the confinement plate will find wide applications in two-phase heat sinks for high heat flux applications.

Enhanced Specific Heat Capacity of Liquid Entrapped between Two Solid Walls Separated by a Nanogap

Size and thermal effect on molar heat capacity of liquid at constant volume (Cv) on a nanometer scale have been investigated by controlling the temperature and density of the liquid domain using equilibrium molecular dynamics (EMD) simulations. Lennard-Jones (LJ) type molecular model with confinement gap thickness (h) 0.585 nm to 27.8 nm has been used with the temperature (T) ranging from 100 K to 140 K. The simulation results revealed that the heat capacity of the nanoconfined liquid surpasses that of the bulk liquid within a defined interval of gap thickness; that the temperature at which maximum heat capacity occurs for a nanoconfined liquid vary with gap thickness following a power law, TCv,max = 193.4 × (h/a)−0.3431, ‘a’ being the lattice constant of Argon (solid) at 300 K; and that for a specified gap thickness and temperature, the confined liquid can exhibit a heat capacity that can be more than twice the heat capacity of the bulk liquid. The increase in heat capacity is underpinned by an increase in non-configurational (phonon and anharmonic modes of vibration) and configurational (non-uniform density distribution, enhanced thermal resistance, guided molecular mobility, etc.) contributions.

Nanostructured graphene for nanoscale electron paramagnetic resonance spectroscopy

The opening of a quantum confinement gap in nanostructured graphene yields extremely sensitive photodetectors, with electrical noise equivalent power lower than 10−15 W Hz−0.5 at temperatures below 3 K, for detection of radiation in a very broad frequency range, including ultraviolet, visible and terahertz. Here we demonstrate the operation of these detectors in the presence of magnetic field as high as 7 T, paving the way to in situ spectroscopy of molecular nanomagnets.

A new method for measurement and quantification of tracer diffusion in nanoconfined liquids.

We report development of a novel instrument to measure tracer diffusion in water under nanoscale confinement. A direct optical access to the confinement region, where water is confined between a tapered fiber and a flat substrate, is made possible by coating the probe with metal and opening a small aperture (0.1 μm-1 μm) at its end. A well-controlled cut using an ion beam ensures desired lateral confinement area as well as adequate illumination of the confinement gap. The probe is mounted on a tuning-fork based force sensor to control the separation between the probe and the substrate with nanometer precision. Fluctuations in fluorescence intensity due to diffusion of a dye molecule in water confined between the probe and the sample are recorded using a confocal arrangement with a single photon precision. A Monte Carlo method is developed to determine the diffusion coefficient from the measured autocorrelation of intensity fluctuations which accommodates the specific geometry of confinement and the illumination profile. The instrument allows for measurement of diffusion laws under confinement. We found that the diffusion of a tracer molecule is slowed down by more than 10 times for the probe-substrate separations of 5 nm and below.

Structure and Dynamics of Confined Liquids: Challenges and Perspectives for the X-ray Surface Forces Apparatus.

The molecular-scale structure and dynamics of confined liquids has increasingly gained relevance for applications in nanotechnology. Thus, a detailed knowledge of the structure of confined liquids on molecular length scales is of great interest for fundamental and applied sciences. To study confined structures under dynamic conditions, we constructed an in situ X-ray surface forces apparatus (X-SFA). This novel device can create a precisely controlled slit-pore confinement down to dimensions on the 10 nm scale by using a cylinder-on-flat geometry for the first time. Complementary structural information can be obtained by simultaneous force measurements and X-ray scattering experiments. The in-plane structure of liquids parallel to the slit pore and density profiles perpendicular to the confining interfaces are studied by X-ray scattering and reflectivity. The normal load between the opposing interfaces can be modulated to study the structural dynamics of confined liquids. The confinement gap distance is tracked simultaneously with nanometer precision by analyzing optical interference fringes of equal chromatic order. Relaxation processes can be studied by driving the system out of equilibrium by shear stress or compression/decompression cycles of the slit pore. The capability of the new device is demonstrated on the liquid crystal 4′-octyl-4-cyano-biphenyl (8CB) in its smectic A (SmA) mesophase. Its molecular-scale structure and orientation confined in 100 nm to 1.7 μm slit pores was studied under static and dynamic nonequilibrium conditions.

Visualizing near-wall two-phase flow morphology during confined and submerged jet impingement boiling to the point of critical heat flux

Confined and submerged two-phase jet impingement is a compact, low-pressure-drop solution for high heat flux dissipation from electronic components. Nucleate boiling can be sustained up to significantly higher heat fluxes during two-phase jet impingement as compared to pool boiling. The increases in critical heat flux are explained via hydrodynamic mechanisms that have been debated in the literature. In this study, the two-phase flow morphology of a single subcooled jet of water that impinges on a circular heat source is visualized at high speed with synchronized top and side views of the confinement gap. The impinging jet issues from a 3.75-mm-diameter orifice that is held at a height of 2 orifice diameters above a 25.4-mm-diameter heat source. The experiments are conducted at a jet Reynolds number of 15,000 and a jet inlet subcooling of 10 °C across a range of heat fluxes up to the critical heat flux. When boiling occurs under subcooled exit flow conditions and at moderate heat fluxes, a regular cycle is observed of formation and collapse of vapor structures that bridge the heated surface and the orifice plate, which causes significant oscillations in the pressure drop. Under saturated exit flow conditions, the vapor agglomerates in the confinement gap into a bowl-like vapor structure that recurrently shrinks, due to vapor break-off at the edge of the orifice plate, and is again replenished due to vapor generation at the heater surface. The optical visualizations from the top of the confinement gap provide a unique perspective and indicate that the liquid jet flows downwards through the vapor structure, impinges on the heated surface, and then flows underneath the vapor structure as a fluid wall jet that wets the heated surface upon which discrete bubbles are generated due to boiling. At high heat fluxes, intense vapor generation causes the fluid wall jet to transition from a bubbly to a churn-like regime, shearing off some liquid droplets into the vapor structure. The origin of critical heat flux appears to result from a significant portion of the liquid in the wall jet being deflected off the surface, and the remaining liquid film on the surface drying out before reaching the edge of the heater.

Quantitative Assessment of Thermodynamic Theory in Elucidating the Behavior of Water under Hydrophobic Confinement.

A macroscopic thermodynamics-based theory that can quantitatively describe the behavior of water confined between hydrophobic solutes has so far remained elusive. In this work, we progress toward this goal by comparing the predictions of macroscopic theory with the results from computer simulations. We have determined free energy profiles of water confined between two nanometer-sized surfaces of varying hydrophobicity using molecular simulations and have estimated thermodynamic properties such as contact angle, line tension, and size of the critical vapor tube from independent simulations. We show that the scaling of free energy barrier to evaporation is fairly well captured by the factor ( D/2 + λ/ϒLV)2, where D is the confinement gap and λ/ ϒLV is the ratio of line-tension and liquid-vapor surface tension. The radius of the critical vapor tube necessary for nucleating evaporation scales by the factor ( D/2 + λ/ϒLV). Exclusion of the line-tension term from thermodynamic theory leads to a qualitative disagreement between theoretical predictions and results from molecular simulations. We also demonstrate that macroscopic theory that includes the line-tension term is able to quantitatively match the entire free energy profile associated with the formation of a vapor-tube inside the confined region for conditions when the vapor state is the most stable state. The match is however only qualitatively correct for the conditions when the liquid state is more stable. Overall, the conclusion is that the inclusion of line-tension in macroscopic theory is necessary to describe the behavior of water under nanoscale confinement between two hydrophobic solutes.

Identification of nucleate boiling as the dominant heat transfer mechanism during confined two-phase jet impingement

Thermal management of high-power electronics requires cooling strategies capable of dissipating high heat fluxes while maintaining the device at low operating temperatures. Two-phase jet impingement offers a compact cooling technology capable of meeting these requirements at a low pressure drop. Generally, confined impingement geometries are used in electronics cooling applications, where the flow is constrained between the hot surface and orifice plate. Understanding the primary heat transfer mechanisms occurring as boiling takes place on the surface during jet impingement is important, specifically under such confined conditions. In this study, heat transfer from a copper surface is experimentally characterized in both confined jet impingement and pool boiling configurations. The dielectric liquid HFE-7100 is used as the working fluid. For the jet impingement configuration, the jet issues through a single 2 mm-diameter orifice, at jet exit velocities of 1, 3, 6, and 9 m/s, into a confinement gap with a spacing of 3 jet diameters between the orifice and heat source. Additional orifice-to-target spacings of 0.5, 1, and 10 jet diameters are tested at the lowest (Vj = 1 m/s) and highest (Vj = 9 m/s) jet velocities. By incrementing the heat flux applied to the surface and observing the steady-state response at each flux, the single-phase and two-phase heat transfer performance is characterized; all experiments were carried through to critical heat flux conditions. The jet impingement data in the fully boiling regime either directly overlap the pool boiling data, or coincide with an extension of the trend in pool boiling data beyond the pool boiling critical heat flux limit. This result confirms that nucleate boiling is the dominant heat transfer mechanism in the fully boiling regime in confined jet impingement; the convective effects of the jet play a negligible role over the wide range of parameters considered here. While the presence of the jet does not enhance the boiling heat transfer coefficient, the jet does greatly increase single-phase heat transfer performance and extends the critical heat flux limit. Critical heat flux displays a linear dependence on jet velocity while remaining insensitive to changes in the orifice-to-target spacing.

Action for the infrared regime of gauge theories and the problem of color transformations

It has been known for a while that there is spontaneous breaking of Lorentz symmetry in the nonzero charged sectors of quantum electrodynamics due to the infrared problem of soft photons. More recently, it has also been suggested that similar results hold for color transformations in a nonabelian gauge theory. Here we show that an action where a diffeomorphism has been carried out for the part describing hard gauge particles and matter fields can be used to analyze these issues. In addition to rederiving old results in this formalism, we also show that color transformations cannot be unitarily implemented on perturbative gluon states if gluon fields of arbitrarily low energy are allowed. Implications for confinement and mass gap are briefly commented upon.

Suggested design of gold-nanoobjects-based terahertz radiation source for biomedical research

Gold nanoparticles (GNPs) may serve as devices to emit electromagnetic radiation in the terahertz (THz) range, whereby the energy is delivered by radio frequency or microwave photons which will not by themselves induce transitions between sparse confinement-shaped electron levels of a GNP, but may borrow the energy from longitudinal acoustic (LA) phonons to overcome the confinement gap. Upon excitation, the Fermi electron cannot relax otherwise than via emitting a THz photon, the other relaxation channels being blocked by force of shape and size considerations. Within this general scope that has already been outlined earlier, the present work specifically discusses two-phonon processes, namely (i) a combined absorption–emission of two phonons from the top of the LA branch, and (ii) an absorption of two such phonons with nearly identical wavevectors. The case (i) may serve as a source of soft THz radiation (at ≃0.54 THz), the case (ii) the hard THz radiation at 8.7 THz. Numerical estimates are done for crystalline particles in the shape of rhombicuboctahedra, of 5–7 nm size. A technical realisation of this idea is briefly discussed, assuming the deposition of GNPs onto/within the substrate of Teflon®, the material sustaining high temperatures and transparent in the THz range.

Ultra-broadband photodetectors based on epitaxial graphene quantum dots

AbstractGraphene is an ideal material for hot-electron bolometers due to its low heat capacity and weak electron-phonon coupling. Nanostructuring graphene with quantum-dot constrictions yields detectors of electromagnetic radiation with extraordinarily high intrinsic responsivity, higher than 1×109 V W−1 at 3 K. The sensing mechanism is bolometric in nature: the quantum confinement gap causes a strong dependence of the electrical resistance on the electron temperature. Here, we show that this quantum confinement gap does not impose a limitation on the photon energy for light detection and these quantum-dot bolometers work in a very broad spectral range, from terahertz through telecom to ultraviolet radiation, with responsivity independent of wavelength. We also measure the power dependence of the response. Although the responsivity decreases with increasing power, it stays higher than 1×108 V W−1 in a wide range of absorbed power, from 1 pW to 0.4 nW.

Phases of circle-compactified QCD with adjoint fermions at finite density

We study chemical-potential dependence of confinement and mass gap in QCD with adjoint fermions in spacetime with one spatial compact direction. By calculating the one-loop effective potential for the Wilson line in the presence of chemical potential, we show that a center-symmetric phase and a center-broken phase alternate when the chemical potential in unit of the compactification scale is increased. In the center-symmetric phase we use semiclassical methods to show that photons in the magnetic bion plasma acquire a mass gap that grows with the chemical potential as a result of anisotropic interactions between monopole-instantons. For the neutral fermionic sector which remains gapless perturbatively, there are two possibilities at non-perturbative level. Either to remain gapless (unbroken global symmetry), or to undergo a novel superfluid transition through a four-fermion interaction (broken global symmetry). If the latter is the case, this leads to an energy gap of quarks proportional to a new nonperturbative scale $L^{-1}\exp[-1/(g^4 \mu L)]$, where $L$ denotes the circumference of $S^1$, the low-energy is described as a Nambu-Goldstone mode associated with the baryon number, and there exists a new type of BEC-BCS crossover of the diquark pairing as a function of the compactification scale at small chemical potential.

Quantum transport in Weyl semimetal thin films in the presence of spin-orbit coupled impurities

Topological semimetals have been at the forefront of experimental and theoretical attention in condensed matter physics. Among these, recently discovered Weyl semimetals have a dispersion described by a three-dimensional Dirac cone, which is at the root of exotic physics such as the chiral anomaly in magnetotransport. In a time reversal symmetric (TRS) Weyl semimetal film, the confinement gap gives the quasiparticles a mass, while TRS is preserved by having an even number of valleys with opposite masses. The film can be tuned through a topological phase transition by a gate electric field. In this work, we present a theoretical study of the quantum corrections to the conductivity of a topological semimetal thin film, which is governed by the complex interplay of the chiral band structure, mass term, and scalar and spin-orbit scattering. We study scalar and spin-orbit scattering mechanisms on the same footing, demonstrating that they have a strong qualitative and quantitative impact on the conductivity correction. We show that, due to the spin structure of the matrix Green's functions, terms linear in the extrinsic spin-orbit scattering are present in the Bloch and momentum relaxation times, whereas previous works had identified corrections starting from the second order. In the limit of small quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to a potentially observable density dependence in the weak antilocalization correction. Moreover, when the mass term is around 30 percent of the linear Dirac terms, the system is in the unitary symmetry class with zero quantum correction and switching the extrinsic spin-orbit scattering drives the system to the weak antilocalization. We discuss the crossover between the weak localization and weak antilocalization regimes in terms of the singlet and triplet Cooperon channels, tuning the spin-orbit scattering strength.

Axisymmetric wall jet development in confined jet impingement

The flow field surrounding an axisymmetric, confined, impinging jet was investigated with a focus on the early development of the triple-layered wall jet structure. Experiments were conducted using stereo particle image velocimetry at three different confinement gap heights (2, 4, and 8 jet diameters) across Reynolds numbers ranging from 1000 to 9000. The rotating flow structures within the confinement region and their interaction with the surrounding flow were dependent on the confinement gap height and Reynolds number. The recirculation core shifted downstream as the Reynolds number increased. For the smallest confinement gap height investigated, the strong recirculation caused a disruption of the wall jet development. The radial position of the recirculation core observed at this small gap height was found to coincide with the location where the maximum wall jet velocity had decayed to 15% of the impinging jet exit velocity. After this point, the self-similarity hypothesis failed to predict the evolution of the wall jet further downstream. A reduction in confinement gap height increased the growth rates of the wall jet thickness but did not affect the decay rate of the wall jet maximum velocity. For jet Reynolds numbers above 2500, the decay rate of the maximum velocity in the developing region of the wall jet was approximately −1.1, which is close to previous results reported for the fully developed region of radial wall jets. A much higher decay rate of −1.5 was found for the wall jet formed by a laminar impinging jet at Re = 1000.

Molecular dynamics investigation of a model ionic liquid lubricant for automotive applications

In the current work we present a new modelling approach for simulating meso–scopic phenomena related to lubrication of the piston ring–cylinder liner contact. Our geometry allows a variable confinement gap and a varying amount of lubricant in the gap, while avoiding the squeeze-out of the lubricant into vacuum. We have implemented a coarse grain molecular dynamics description of an ionic liquid as a lubricant which can expand into lateral reservoirs. The results have revealed two regimes of lubrication, an elasto-hydrodynamic one under low loads and one with low, velocity-independent specific friction, under high loads. The observed steep rise of normal forces at small plate-to-plate distances is an interesting behaviour that could potentially be exploited for preventing solid–solid contact and wear.