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At least 307 records · Page 17

Robust natural nanocomposites realizing unprecedented ultrafast precise molecular separations

Synthetic polymer membranes can potentially reduce the large energy and carbon footprints that are typically associated with traditional chemical separation technologies. Unfortunately, current production protocols negate the green benefits of membrane separation. To address this bottleneck, here we report the use of natural materials monosaccharide – glucose and polydopamine and Zr-based metal organic frameworks (MOFs) to fabricate ultrathin nanocomposite membranes via interfacial polymerization reaction. The synergistic effect of these three materials on angstrom-scale molecular transport both in organic solvent and aqueous environment was elucidated using a series of complementary techniques. We demonstrate such nature-inspired nanocomposite membranes enable structural stability even in polar aprotic solvents, and unparalleled ultra-fast, low-pressure, precise separations in both nanofiltration modes, which easily surpass state-of-the-art membranes relying on unsustainable materials. Finally, the multi-functionality of saccharide nanocomposites was elegantly harnessed to impact separation applications that contribute towards a better living environment.

36 MATERIALS SCIENCE↗

Electronic and Vibrational Coherence in Heterogeneous Electron Transfer (Final Report)

Interfacial electron transfer reactions constitute key physical phenomena central to a variety of energy related transport and conversion processes such as catalysis, photocatalysis, photovoltaics, energy storage, molecular electronics, etc. Heterogeneous material systems like organic/inorganic interfaces are of particular interest because they provide great potential to tailor properties according to application specific requirements. While electron transfer dynamics has been studied intensively in heterogeneous systems many questions remain unanswered. The significance of electronic-vibrational coupling and coherence is one aspect that has yet to be fully explored. The objective of this project is to develop and implement new ultrafast spectroscopic techniques based on pump four-wave mixing spectroscopy (pump-FWM) for studying the dynamics of vibrational coupling and coherence in heterogeneous electron transfer (HET) at molecule/semiconductor interfaces. The implementation of the spectroscopic setup allows to explore different four-wave mixing techniques and thus to identify a suitable approach to study the significance of vibrational as well as electronic coherence in HET.

14 SOLAR ENERGY↗

Bridging the length scales in ionic separations via data-driving machine learning

We pursued a data science driven machine learning (ML) approach that blended molecular scale attributes informed from molecular dynamics (MD) simulation and materials properties to the selectivity and energy efficiency in targeted ionic separations using electric fields. The model mixtures investigated for ionic separations are pH sensitive and include organic acids, silica and boron, transition metals, such as copper and chromium. There were two major research thrusts of this project. Firstly, we investigated surrogate models and deep learning that relate material chemistries and structures to selective transport of ionic species under applied electric fields. Secondly we investigated how the bipolar junction interfacial design and water dissociation catalyst in bipolar membranes affect reverse bias polarization behavior and pH modulation in deionization platforms as a function of the platform operating parameters (e.g., cell voltage, residence time, and salt feed concentration). As a result of this work, we also were able to start a new direction, namely ML models for molecular design of surfactants.

36 MATERIALS SCIENCE↗

Structure and Dynamics of CO 2 at the Air–Water Interface from Classical and Neural Network Potentials

The accurate description of the structure and dynamics of CO 2 at the instantaneous air–water interface, along with the effects of surface fluctuations on the CO 2 -transport processes, is essential for the development of negative emission technologies aimed at minimizing climate change. In this study, we performed molecular dynamics simulations of CO 2 at the air–water interface using neural network potentials (NNPs) trained on ab initio data generated through density-functional-theory-based molecular dynamics simulations. We compared these results with classical force fields to assess their performance in modeling interfacial CO 2 behavior. Our findings revealed that the asymmetric interactions, coupled with thermal surface fluctuations at the air–water interface, significantly influence CO 2 transport into the aqueous phase. The simulations demonstrate that classical force fields underestimate both the free energy of CO 2 transport and the strength of its interactions at the interface compared with the neural network potentials. In conclusion, the free energy and the interfacial dynamics of CO 2 are primarily influenced by the distribution of water within the instantaneous interfacial water layer, responsible for creating an asymmetric intermolecular interaction environment within the interfacial region.

Ab initio molecular dynamics↗

Understanding Thermal Transport in Polymer –Silver Nanowire Composites

Understanding thermal transport across filler-polymer interfaces and filler-filler contacts within polymer composites is of great importance for better thermal design of the composites that are widely used in high-performance heat exchangers, energy storage devices, and flexible electronics. Over the past several decades, considerable progress has been made in improving the thermal conductivity of polymer composites, but several key questions concerning the influence of interfacial thermal resistance, or Kapitza resistance, still remain. Firstly, the thermal properties of these composites are highly dependent on thermal transport through the filler network and its contacts. For metallic nanofillers, the thermal conductivity is often estimated using the Wiedemann-Franz law based on electrical conductivity; however, it remains a question whether the Wiedemann-Franz law still holds at nanoscale contacts. Through investigation of silver nanowires of varying sizes, we were able to demonstrate that the Lorenz number for silver nanowire increases with decreasing nanowire diameter. Examination of the corresponding electrical and thermal conductivities indicate that these changes are due to that the relative contribution of phonons becomes more significant as a result of elastic stiffening. Furthermore, we show that for silver nanowires, the contact thermal resistance is ~8 times lower than that of multi-walled carbon nanotube (MWCNT) of similar diameters. Additionally, through systematic studies of electrospun polymer-silver nanowire composite nanofibers, we investigated the impact of interface morphology on the thermal conductivity enhancement of the composite system and probed the value of the Kapitza resistance for individual polymer-filler interfaces. For polymer nanofibers containing continuous, single silver nanowires, the thermal conductivity increases linearly with increasing volume fraction of silver, which is consistent with the prediction of percolation theory for samples above the percolation limit. By comparing this linear trend to the measured thermal conductivities of composite nanofibers with more complex structures, we were able to determine the resistance associated with any additional polymer-filler boundaries. In doing so we find that the thermal boundary resistance for polyvinylpyrrolidone (PVP)–silver interfaces is significantly lower than that of comparable polymer-MWCNT composite systems.Together our studies provide new insights into thermal transport in polymer nanocomposites and should help facilitate the design of high performance polymeric thermal interface material.

Thermal transport↗

Understanding Thermal Transport in Polymer - Silver Nanowire Composites

Understanding thermal transport across filler-polymer interfaces and filler-filler contacts within polymer composites is of great importance for better thermal design of the composites that are widely used in high-performance heat exchangers, energy storage devices, and flexible electronics. Over the past several decades, considerable progress has been made in improving the thermal conductivity of polymer composites, but several key questions concerning the influence of interfacial thermal resistance, or Kapitza resistance, still remain. Firstly, the thermal properties of these composites are highly dependent on thermal transport through the filler network and its contacts. For metallic nanofillers, the thermal conductivity is often estimated using the Wiedemann-Franz law based on electrical conductivity; however, it remains a question whether the Wiedemann-Franz law still holds at nanoscale contacts. Through investigation of silver nanowires of varying sizes, we were able to demonstrate that the Lorenz number for silver nanowire increases with decreasing nanowire diameter. Examination of the corresponding electrical and thermal conductivities indicate that these changes are due to that the relative contribution of phonons becomes more significant as a result of elastic stiffening. Furthermore, we show that for silver nanowires, the contact thermal resistance is ~8 times lower than that of multi-walled carbon nanotube (MWCNT) of similar diameters. Additionally, through systematic studies of electrospun polymer-silver nanowire composite nanofibers, we investigated the impact of interface morphology on the thermal conductivity enhancement of the composite system and probed the value of the Kapitza resistance for individual polymer-filler interfaces. For polymer nanofibers containing continuous, single silver nanowires, the thermal conductivity increases linearly with increasing volume fraction of silver, which is consistent with the prediction of percolation theory for samples above the percolation limit. By comparing this linear trend to the measured thermal conductivities of composite nanofibers with more complex structures, we were able to determine the resistance associated with any additional polymer-filler boundaries. In doing so we find that the thermal boundary resistance for polyvinylpyrrolidone (PVP)–silver interfaces is significantly lower than that of comparable polymer-MWCNT composite systems. Together our studies provide new insights into thermal transport in polymer nanocomposites and should help facilitate the design of high performance polymeric thermal interface material.

Matthew L. Fitzgerald↗

Ultrathin epitaxial MgB 2 on SiC: Substrate surface-polarity-dependent properties

High-quality, ultrathin superconducting films are required for advanced devices such as hot-electron bolometers, superconducting nanowire single-photon detectors, and quantum applications. Using hybrid physical-chemical vapor deposition, we show that MgB 2 films as thin as 4 nm can be fabricated on the carbon-terminated 6⁢H-SiC (0001) surface with a superconducting transition temperature above 33 K and a rms roughness of 0.7 nm. Remarkably, the film quality is a function of the SiC surface termination, with the C-terminated surface preferred to the Si-terminated surface. To understand the MgB 2 thin film/SiC substrate interactions giving rise to this difference, we characterized the interfacial structures using Rutherford backscattering spectroscopy/channeling, electron-energy-loss spectroscopy, and x-ray photoemission spectroscopy. The MgB 2 /SiC interface structure is complex and different for the two terminations. Both terminations incorporate substantial unintentional oxide layers influencing MgB 2 growth and morphology, but with a different extent, intermixing, and interface chemistry. In this paper, we report measurements of transport, resistivity, and the critical superconducting temperature of MgB 2 /SiC that are different for the two terminations, and they link interfacial structure variations to observed differences. The result shows that the C face of SiC is a preferred substrate for the deposition of ultrathin superconducting MgB 2 films.

36 MATERIALS SCIENCE↗

Tungsten and Barium Transport in the Internal Plasma of Hollow Cathodes

The effect of tungsten erosion, transport and redeposition on the operation of dispenser hollow cathodes was investigated in detailed examinations of the discharge cathode inserts from an 8200 hour and a 30,352 hour ion engine wear test. Erosion and subsequent re-deposition of tungsten in the electron emission zone at the downstream end of the insert reduces the porosity of the tungsten matrix, preventing the flow of barium from the interior. This inhibits the interfacial reactions of the barium-calcium-aluminate impregnant with the tungsten in the pores. A numerical model of barium transport in the internal xenon discharge plasma shows that the barium required to reduce the work function in the emission zone can be supplied from upstream through the gas phase. Barium that flows out of the pores of the tungsten insert is rapidly ionized in the xenon discharge and pushedback to the emitter surface by the electric field and drag from the xenon ion flow. Thisbarium ion flux is sufficient to maintain a barium surface coverage at the downstream endgreater than 0.6, even if local barium production at that point is inhibited by tungsten deposits. The model also shows that the neutral barium pressure exceeds the equilibrium vapor pressure of the impregnant decomposition reaction over much of the insert length,so the reactions are suppressed. Only a small region upstream of the zone blocked by tungsten deposits is active and supplies the required barium. These results indicate that hollowcathode failure models based on barium depletion rates in vacuum dispenser cathodes are very conservative.

Hollow cathodes↗

Barium Depletion in Hollow Cathode Emitters

The effect of tungsten erosion, transport and redeposition on the operation of dispenser hollow cathodes was investigated in detailed examinations of the discharge cathode inserts from an 8200 hour and a 30,352 hour ion engine wear test. Erosion and subsequent re-deposition of tungsten in the electron emission zone at the downstream end of the insert reduces the porosity of the tungsten matrix, preventing the ow of barium from the interior. This inhibits the interfacial reactions of the barium-calcium-aluminate impregnant with the tungsten in the pores. A numerical model of barium transport in the internal xenon discharge plasma shows that the barium required to reduce the work function in the emission zone can be supplied from upstream through the gas phase. Barium that flows out of the pores of the tungsten insert is rapidly ionized in the xenon discharge and pushed back to the emitter surface by the electric field and drag from the xenon ion flow. This barium ion flux is sufficient to maintain a barium surface coverage at the downstream end greater than 0.6, even if local barium production at that point is inhibited by tungsten deposits. The model also shows that the neutral barium pressure exceeds the equilibrium vapor pressure of the impregnant decomposition reaction over much of the insert length, so the reactions are suppressed. Only a small region upstream of the zone blocked by tungsten deposits is active and supplies the required barium. These results indicate that hollow cathode failure models based on barium depletion rates in vacuum dispenser cathodes are very conservative.

plasma discharges↗

Time-Resolved Spectroscopy of Insulator-Metal Transitions: Exploring Low-Energy Dynamics in Strongly Correlated Systems. Final Report

Transition metal oxides (TMOs) have attracted much attention in recent years. The strong coupling between charge, spin, and orbital degrees of freedom creates novel functional properties. The research at the interplay between ferromagnetism, ferroelectricity and conductivity provides a promising way to the development of future spintronic devices. The interface characterization of multifunctional oxide heterostructures is crucial to understand deeply the magnetic response, spin injection and spin transport. In year one, we characterized optically the magnetic property with the method of magnetization-induced second-harmonic generation (MSHG), which is a sensitive technique to selectively probe the interface where the spatial inversion symmetry is broken. The interface of n-type BaTiO 3 (BTO)/La 0.67 Sr 0.33 MnO 3 (LSMO) forms a Schottky barrier and displays a good diode effect. By applying an external electric field across the sample, we observe the magnetoelectric (ME) coupling effect to modulate the interface magnetization. The voltage dependent magnetic contrast sharply vanishes at positive voltage (applied to LSMO contact) and reveals a ferromagnetic (FM)-to- antiferromagnetic (AFM) transition occurring at the interface, while the magneto-optic Kerr effect (MOKE) indicates that the bulk property is not affected. The strain mediated mechanism and ferroelectric (FE) polarization induced charge medicated mechanism are both discussed, but they do not play an important role in the observed magnetization transition. A new mechanism is proposed - the injected minority spins through strong Hund's interaction with the local magnetic moments at positive voltage weaken the double-exchange interaction of nearby Mn e g electrons, thereby reducing the ferromagnetic (FM) ordering. The dominant superexchange interaction of localized t 2g electrons finally leads to the AFM configuration. By reducing the electron carrier concentration of BTO, a positive voltage shift of the transition is observed. The oxygen richer sample with lower carrier concentration requires a higher voltage to increase the hole doping level of LSMO to induce the interfacial AFM phase. By inserting a thin (1nm) La 0.5 Ca 0.5 MnO 3 layer between BTO and LSMO, the interface magnetic response from LSMO is enhanced. In year two, a non-multiferroic heterostructure SrTiO 3 (STO)/ La 0.5 Ca 0.5 MnO 3 (LCMO)/La 0.67 Sr 0.33 MnO 3 (LSMO) was studied. In this system, the interface FM-AFM transition is observed at negative voltage. The STO layer may act as a hole-donating layer, which induces the hole transfer to LSMO making it overdoped, while the LCMO interlayer at the 0.5 hole doping level displays complicated CE type AFM phase. Thus the AFM phase is dominant at the interface and electron accumulation is required to induce the FM phase by applying a negative voltage. For oxygen rich sample, the magnetic MSHG loop reappears at high positive voltage (around +2.5 V). At high doping level (x > 0.5), LSMO exhibits A-type AFM order, consisting of AFM superexchange coupling between adjacent layers and intralayer FM double-exchange coupling. The less tensile strain of STO and LSMO due to a smaller lattice mismatch as compared to BTO would result in a weaker interlayer coupling . Thus, interfacial A-type AFM order can occur in STO/LCMO/LSMO heterostructure at high hole doping concentration. The study of ME coupling of multifunctional oxide heterostructures is definitely important to the development and performance of future spintronic devices. The results presented here regarding the interfacial magnetic transition controlled by an external electric field offer some new perspective to study the spin transport of magnetic tunnel junctions.

36 MATERIALS SCIENCE↗

Chemical transformations and transport phenomena at interfaces

Abstract Interfaces, the boundary that separates two or more chemical compositions and/or phases of matter, alters basic chemical and physical properties including the thermodynamics of selectivity, transition states, and pathways of chemical reactions, nucleation events and phase growth, and kinetic barriers and mechanisms for mass transport and heat transport. While progress has been made in advancing more interface‐sensitive experimental approaches, their interpretation requires new theoretical methods and models that in turn can further elaborate on the microscopic physics that make interfacial chemistry so unique compared to the bulk phase. In this review, we describe some of the most recent theoretical efforts in modeling interfaces, and what has been learned about the transport and chemical transformations that occur at the air–liquid and solid–liquid interfaces. This article is categorized under: Structure and Mechanism > Reaction Mechanisms and Catalysis Structure and Mechanism > Computational Materials Science Software > Quantum Chemistry Software > Simulation Methods

Hao, Hongxia↗

Dual–Interface–Reinforced Flexible Perovskite Solar Cells for Enhanced Performance and Mechanical Reliability

Two key interfaces in flexible perovskite solar cells (f-PSCs) are mechanically reinforced simultaneously: one between the electron-transport layer (ETL) and the 3D metal-halide perovskite (MHP) thin film using self-assembled monolayer (SAM), and the other between the 3D-MHP thin film and the hole-transport layer (HTL) using an in situ grown low-dimensional (LD) MHP capping layer. The interfacial mechanical properties are measured and modeled. This rational interface engineering results in the enhancement of not only the mechanical properties of both interfaces but also their optoelectronic properties holistically. As a result, the new class of dual-interface-reinforced f-PSCs has an unprecedented combination of the following three important performance parameters: high power-conversion efficiency (PCE) of 21.03% (with reduced hysteresis), improved operational stability of 1000 h T90 (duration at 90% initial PCE retained), and enhanced mechanical reliability of 10 000 cycles n88 (number of bending cycles at 88% initial PCE retained). Furthermore, the scientific underpinnings of these synergistic enhancements are elucidated.

14 SOLAR ENERGY↗

Improved Mechanical Adhesion Enabled by Bilayer Hole Transport Layers in Perovskite Solar Cells

We investigate buried-interface mechanical integrity in metal-halide perovskite half-cells using carbazole-based self-assembled monolayers (SAMs) and bilayer hole transport layers composed of metal oxide underlayers and SAMs. Combining macroscopic and microscopic characterization, we quantify interfacial fracture energy (Gc) and identify delamination pathways. SAM deposition on NiOx increases Gc by approximately 10-fold compared with ITO, highlighting the importance of oxide underlayer selection. To isolate the effect of removing noncovalently bonded SAM molecules, we use vapor-deposited perovskite as a solvent-free model system, decoupling the rinse step inherent to solution processing. Removing loosely bound SAM molecules increases Gc from 0.94 +- 0.08 J.m-2 to 4.82 +- 0.79 J.m-2. These results show that oxide selection and SAM binding quality are both critical for strengthening buried interfaces and designing mechanically robust perovskite solar cells.

14 SOLAR ENERGY↗

Tunable Topological Phonon for Next-generation Quantum Transduction

This project aims to understand the critical factors that determine transduction performance of topological phonons across an oxide perovskite/tungsten diselenide heterojunction. We will investigate mechanisms of their propagation and interfacial coupling using modeling and machine learning approaches. Methods include density functional theory, molecular dynamics, numerical transport simulations, and active learning for building up a training dataset for force field development.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Transport Modeling of Kinetically Limited Microscale Extraction Systems: Droplet and Supported Liquid Membrane Separations

Microfluidic droplet extraction devices can be used to efficiently measure solute phase transfer kinetics in liquid–liquid extraction systems. In this work, a droplet extraction apparatus was constructed using off-the-shelf and custom 3D printed parts for less than 110 USD. The interfacial kinetics of the transfer of Pu(IV) between an aqueous nitric acid phase and a 5 v/v% tridodecylamine (TDA) in toluene phase were characterized by determining the extent of Pu(IV) transfer between phases at different flow rates. Forward interfacial rate constants calculated from this data using an analytical model are 5.6 × 10 –3 mm s –1 under extraction (aqueous-to-organic solute transfer) conditions and 3.3 × 10 –3 mm s –1 under stripping (organic-to-aqueous solute transfer) conditions. The analytical model is valid when the rate of solute transfer across the interface between the two liquid phases has pseudo-first-order reversible reaction kinetics and is slow relative to the rate of solute transport to the interface. The change in the outlet concentration with residence time determined using the analytical model was compared with the results of a numerical model accounting for advection/diffusion to the interface in addition to kinetically limited interfacial solute transfer. These calculations revealed that for systems with forward interfacial rate constants greater than approximately 10 –2 mm s –1 , the analytical model must be supplemented with a numerical transport model accounting for an additional advection/diffusion mass transfer resistance. This threshold corresponds to a Damköhler number of one. The measured interfacial kinetic rate constants for Pu(IV)/TDA were used in a supported liquid membrane (SLM) numerical model, which showed that the Pu(IV) phase transfer kinetics are fast enough for use in a practical separation.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Prediction of Bi 2 Te 3 -Sb 2 Te 3 Interfacial Conductance and Superlattice Thermal Conductivity Using Molecular Dynamics Simulations

Bismuth telluride (Bi 2 Te 3 ) and its alloys with antimony telluride (Sb 2 Te 3 ) have long been considered to be the best room-temperature bulk thermoelectric (TE) materials. In recent decades, proof-of-concept demonstrations on Bi 2 Te 3 -Sb 2 Te 3 nanostructures have shown high TE performance due to reduction in lattice thermal conductivities. Particularly, ultra-low thermal conductivities have been observed in Bi 2 Te 3 -Sb 2 Te 3 1D superlattices, leading to thermoelectric figures of merit (ZT) as high as 2.4. In contrast, very few computational studies have been performed to provide insight into the phonon transport across these nanostructures. In this work, we use non-equilibrium molecular dynamics simulations with previously developed force fields to simulate thermal transport across Bi 2 Te 3 -Sb 2 Te 3 interfaces and superlattices. We first calculate the thermal conductance associated with a Bi 2 Te 3 -Sb 2 Te 3 interface across a temperature range of 200–400 K. Furthermore, the values are also compared with thermal conductances calculated by a modified Landauer transport formalism using phonon transmission coefficients obtained from the diffuse mismatch model. Our results show that inelastic scattering processes contribute to an increase in interfacial thermal conductance at higher temperatures. Finally, we calculate the thermal conductivities of Bi 2 Te 3 -Sb 2 Te 3 superlattices with varying period lengths from 2 to 18 nm. A minimum thermal conductivity of 0.27 W/mK is observed at a period length of 4 nm, which is attributed to the competition between incoherent and coherent phonon transport regimes. In comparison with previous experimental measurements in the literature, our results show good agreement with respect to the range of thermal conductivity values and the period length corresponding to the minimum superlattice thermal conductivity.

42 ENGINEERING↗

Molecular conducting magnetic heterostructures

Building molecular conducting magnets has been of considerable interest due to their metallic transport and magnetic properties. Conjugated aniline anions and transition-metal cations are recognized to synthesize such π–d interaction frameworks. Here, an interfacial assembly of quasi-two-dimensional aniline heterojunction frameworks is developed, which consists of a proton-aniline conducting layer (conductivity of 9.2 × 10 2 S cm -1 ) and a transition metal–aniline magnetic layer. The two-dimensional aniline coordination framework with pronounced π–d interactions is indispensable for obtaining ordered spin states and metallic transport conductivity. We apply optical and Raman spectroscopy to study the interactions between the metal cations and nitrogen atoms in the aniline chains. The bilayer heterostructure maintains a high conductivity of 3.5 × 10 2 S cm -1 and increased magnetization, while the coupling of metallic conducting and magnetic layers leads to an enhanced magnetoconductance of 0.4% under a magnetic field of 70 kOe.

36 MATERIALS SCIENCE↗

CVB: the Constrained Vapor Bubble Capillary Experiment on the International Space Station MARANGONI FLOW REGION

The Constrained Vapor Bubble (CVB) is a wickless, grooved heat pipe and we report on a full- scale fluids experiment flown on the International Space Station (ISS). The CVB system consists of a relatively simple setup a quartz cuvette with sharp corners partially filled with either pentane or an ideal mixture of pentane and isohexane as the working fluids. Along with temperature and pressure measurements, the two-dimensional thickness profile of the menisci formed at the corners of the quartz cuvette was determined using the Light Microscopy Module (LMM). Even with the large, millimeter dimensions of the CVB, interfacial forces dominate in these exceedingly small Bond Number systems. The experiments were carried out at various power inputs. Although conceptually simple, the transport processes were found to be very complex with many different regions. At the heated end of the CVB, due to a high temperature gradient, we observed Marangoni flow at some power inputs. This region from the heated end to the central drop region is defined as a Marangoni dominated region. We present a simple analysis based on interfacial phenomena using only measurements from the ISS experiments that lead to a predictive equation for the thickness of the film near the heated end of the CVB. The average pressure gradient for flow in the film is assumed due to the measured capillary pressure at the two ends of the liquid film and that the pressure stress gradient due to cohesion self adjusts to a constant value over a distance L. The boundary conditions are the no slip condition at the wall interface and an interfacial shear stress at the liquid- vapor interface due to the Marangoni stress, which is due to the high temperature gradient. Although the heated end is extremely complex, since it includes three- dimensional variations in radiation, conduction, evaporation, condensation, fluid flow and interfacial forces, we find that using the above simplifying assumptions, a simple successful model can be developed.

heat pipes↗